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CLASSROOM ENVIRONMENT INFLUENCE ON STUDENT SELFEFFICACY IN MATHEMATICS A Dissertation by HILLARY P. CROISSANT Submitted to the Office of Graduate Studies of Texas A&M UniversityCommerce in partial fulfillment of the requirements for the degree of DOCTOR OF EDUCATION May 2014 CLASSROOM ENVIRONMENT INFLUENCE ON STUDENT SELFEFFICACY IN MATHEMATICS A Dissertation by HILLARY P. CROISSANT Approved by: Advisor: Gilbert Naizer Committee: Tami Morton Katy Denson Head of Department: Martha Foote Dean of the College: Gail Johnson Dean of Graduate Studies: Arlene Horne iii Copyright © 2014 Hillary P. Croissant iv ABSTRACT CLASSROOM ENVIRONMENT INFLUENCE ON STUDENT SELFEFFICACY IN MATHEMATICS Hillary P. Croissant, EdD Texas A&M UniversityCommerce, 2014 Advisor: Gilbert Naizer, PhD This study aimed to find the characteristics of public school math classrooms and how they influence selfefficacy of students. Data were collected on math students in grades 4 through 12 in a North Texas school district. Two surveys were administered to students in the district. Within 10 days, the students completed a classroom environment survey, followed by a selfefficacy survey. Both surveys were electronic and administered during the school day. Student data were analyzed by conducting a simple linear regression in order to determine if a relationship existed between classroom environment and student selfefficacy. A multiple regression was used in order to determine which dimensions under classroom environment could predict a high or low selfefficacy. Data analysis was unable to generalize low selfefficacy in mathematics and classroom environment correlation due to a small effect size. High selfefficacy in mathematics was found to increase as cohesion and satisfaction would increase and high selfefficacy in mathematics would increase as friction and difficulty would decrease. v ACKNOWLEDGEMENTS “Teaching is a work of the heart” is a sign I have up in my classroom that reminds me that not only as a teacher can I make a difference, but I am impacted by all kinds of teachers throughout my life. I want to thank the many mentors and supporters from whom I have had the opportunity to be influenced by and taught. You have encouraged me, supported me, and given me the strength to complete this journey. I would like to thank my closest friends for supporting me throughout this journey. First, to my friend Wendy Ulrich for encouraging me to continue on this path while being my work spouse by ensuring me that I could be a teacher and student at the same time. Also, to Laura Ahrens for reminding me how fortunate I am to be on this adventure and keeping me passionate about the knowledge that I was gaining. My inspiration comes from my teachers from the past. This great idea started with my professors from Austin College—Jane White, Julia Shahid, and Barbara Sylvester—and my goal to be like them someday. I appreciate my mentors and support from administration and fellow teachers in my school district for their extended support. A special thanks goes out to my advisor Dr. Gilbert Naizer who has read and reread through my work, emailed and conferenced, and helped me make sure that I am the best that I could be. Also thank you to Katy Denson and Tami Morton for being a part of my dissertation committee and supporting my statistical and literary efforts. Jane Braddock and Kelli Knight for bringing snacks to class and being the perfect support system for this doctoral stage of life. Lastly I would like to thank my family for their continued support. My mom and dad for always being my number one fan as well as my parentsinlaw who support any crazy idea I come up with and ensure I have everything I need to be successful. Most of all I want to thank vi my husband Eric for putting up with the late nights, study sessions, and tears that come with the crazy life of being a doctoral student. You are my greatest supporter and sounding board, and I could not have done it without your continued love and motivation. Weston better be ready for a wild ride as a part of this family. This dissertation is dedicated to students who strongly dislike math in the hope that one day they will be positively impacted by a classroom or a teacher who instills the love of math in them so that it becomes a subject to be passionate about rather than despised. vii TABLE OF CONTENTS LIST OF TABLES ...........................................................................................................................x LIST OF FIGURES ....................................................................................................................... xi CHAPTER 1. INTRODUCTION .........................................................................................................1 Statement of the Problem .........................................................................................1 Purpose of the Study ................................................................................................3 Research Questions ..................................................................................................3 Research Hypotheses ...............................................................................................4 Theoretical Framework ............................................................................................4 Significance of the Problem ...................................................................................10 Method of Procedure..............................................................................................11 Definitions of Terms ..............................................................................................13 Limitations .............................................................................................................14 Delimitations ..........................................................................................................15 Assumptions ...........................................................................................................15 Organization of the Study ......................................................................................16 2. REVIEW OF THE LITERATURE .............................................................................17 Math Anxiety .........................................................................................................17 Classroom Environment.........................................................................................20 SelfEfficacy and Classroom Environment ..........................................................25 SelfEfficacy and Math ..........................................................................................30 SelfEfficacy and Achievement .............................................................................32 viii Student Attitudes and Achievement.......................................................................38 Anxiety and Achievement......................................................................................39 Teacher Attitudes ...................................................................................................42 Conclusions ............................................................................................................46 3. METHOD OF PROCEDURE......................................................................................48 Research Design.....................................................................................................49 Population and Sample ..........................................................................................50 Instrumentation ......................................................................................................51 Procedures ..............................................................................................................55 Data Gathering .......................................................................................................57 Treatment of Data ..................................................................................................58 Summary ................................................................................................................58 4. ANALYSIS OF DATA................................................................................................60 Results ....................................................................................................................60 Summary ................................................................................................................65 5. SUMMARY OF THE STUDY AND THE FINDINGS, CONCLUSIONS, IMPLICATIONS, AND RECOMMENDATIONS FOR FUTURE RESEARCH ......66 Summary of the Study ...........................................................................................66 Summary of the Findings .......................................................................................66 Conclusions ............................................................................................................67 Implications............................................................................................................71 Recommendations for Further Research ................................................................74 Summary ................................................................................................................75 ix REFERENCES ..............................................................................................................................76 APPENDICES .............................................................................................................................107 Appendix A. My Classroom Inventory .....................................................................................108 B. Patterns of Adaptive Learning Survey .................................................................111 C. Parent Permission Form .......................................................................................115 D. Child/Minor Agreement to Be in a Research Study ............................................119 E. District Agreement ...............................................................................................122 F. Parent and Student Recruitment Letters ..............................................................125 G. Demographic Survey ...........................................................................................127 H. Video Script .........................................................................................................129 I. Spanish Translation of Parent Letter....................................................................132 J. Spanish Translation of Parent Permission Form ..................................................134 K. Signed Site Letter .................................................................................................138 L. Tables 14.............................................................................................................141 VITA ...........................................................................................................................................144 x LIST OF TABLES TABLE 1. Means, Standard Deviations and Intercorrelations for High SelfEfficacy, Cohesiveness, Friction, Satisfaction, Difficulty, and Competitiveness .....................................................62 2. Multiple Regression Analysis Summary for Variables Predicting High Math SelfEfficacy ..............................................................................................................................63 3. Means, Standard Deviations and Intercorrelations for Low SelfEfficacy, Cohesiveness, Friction, Satisfaction, Difficulty, and Competitiveness .....................................................64 4. Multiple Regression Analysis Summary for Variables Predicting Low Math SelfEfficacy...........................................................................................................................................65 xi LIST OF FIGURES FIGURE 1. Theoretical Framework ........................................................................................................5 1 Chapter 1 INTRODUCTION Starting at a young age, people are very impressionable through interactions in their environment including at home, at school, and with peers. These impressions can be reinforced or changed throughout the student’s life. An impression that has been an epidemic in our society is the negative attitude toward mathematics. Having a negative attitude in mathematics can lead to lower achievement in mathematics and lack of interest in continuing to develop a knowledge base of this topic. This study aimed to examine existing research and add to the body of knowledge in order to create an environment for students that leads to an increase in mathematics selfefficacy and ultimately improves attitudes and achievement in mathematics. Statement of the Problem A 2005 Associated Press poll found that nearly 40% of adults strongly disliked mathematics in school, twice the percentage of adults who disliked other subjects (Philipp, 2007). The way individuals see mathematics can negatively or positively impact their attitude toward the subject. While students learn mathematics, they acquire skills, understand math’s value, how it is learned, who should learn it, and what is needed for engagement in mathematics understanding. Heller stated, “Be careful how you interpret the world; it is like that” (McFague, 2001, p. 39). This implies that the way that an individual makes sense of the world, not only defines the person for the world, but also the world for that person. The importance and need for math are emphasized in many areas of the world around us and in our life and workplace. Math is a significant part of the scientific and technical community our society has become, as well as our cultural heritage (National Council of Teachers of Mathematics [NCTM], 2000). The increase in the complexity of our everyday life 2 has raised the importance and significance of mathematics and the role it has in our society. Unfortunately, the level of difficulty and abstractness of math are a large reason why people have developed a negative view, attitude, or affect toward mathematics (Adeyemi, 2012). This negative view of educators can trickle down to students and lead to unsatisfactory achievement and participation in mathematics (Malmivuori, 2008). Lack of intrinsic motivation can lead to resistance toward mathematics and the learners’ selfperception will decline and difficulties in mathematics will increase (Royer & Walles, 2007). Students who have difficulties in math often have lower confidence in math and lower achievement in mathematics. Selfefficacy is defined by Bandura (1986) as “people’s judgments of their capabilities to organize and execute courses of action required to attain designated types of performances” (p. 391) and can be easily confused with attitudes. Attitudes toward math have been defined as “a liking or disliking of mathematics, a tendency to engage in or avoid mathematics activities, a belief that one is good or bad at mathematics, and a belief that mathematics is useful or useless” (Neale, 1969, p. 623). While both strongly reflect an individual’s feelings toward an area of focus, in this case mathematics, they are different through the fact that selfefficacy has a greater emphasis on the performance that is associated with the attitude rather than just the feeling. It is crucial that educators create learning environments that build students into adults that approach challenging math and science tasks with full force. Times where students shy away from these tasks should be limited. Educators need to be sure that they present environments where students are getting a positive feeling about how they do mathematics and want to do more. When students feel successful in a school setting, they are more likely to want to explore it further into their adult life. Classroom environment is a topic that needs to be explored so we can not only prevent students from avoiding math, but also encourage them to take it further. 3 Purpose of the Study The purpose of the study was to examine how a classroom and the environment created by the teacher and classmates can impact how students feel about their ability to do and be successful in mathematics. It focused on how students perceived their classroom environment and measured student attitudes toward mathematics in order to determine relationships between the two. The relationship between how the students perceived their classroom environment and their attitudes toward math was analyzed. The quantitative data collected gave insight into the classroom environment characteristics that foster negative and/or positive students’ selfefficacy in mathematics classrooms. This study determined how different characteristics of a classroom correlates to student selfefficacy in mathematics. The researcher sought to find what characteristics in a classroom environment are predictors of negative and/or positive attitudes toward mathematics. Emphasis was placed on examining how students feel about the environment created in a mathematics classroom and how their feelings toward mathematics were affected. Another emphasis of this research was to examine which classroom environment dimensions impact negative and positive student selfefficacy in mathematics. Research Questions This study addressed the following questions: 1. Which dimensions of classroom environment (cohesiveness, friction, satisfaction, difficulty, or competitiveness) are the best predictors of high selfefficacy for students in mathematics? 4 2. Which dimensions of classroom environment (cohesiveness, friction, satisfaction, difficulty, or competitiveness) are the best predictors of low selfefficacy for students in mathematics? Research Hypotheses The following null hypotheses reflect the research questions: 1. No relationship exists among the dimensions of classroom environment (cohesiveness, friction, satisfaction, difficulty, or competitiveness) and students’ high selfefficacy in mathematics. 2. No relationship exists among the dimensions of classroom environment (cohesiveness, friction, satisfaction, difficulty, or competitiveness) and students’ low selfefficacy in mathematics. Theoretical Framework Individuals’ behaviors and attitudes are caused by multiple variables including their environment, peer interactions, feedback from authority figures, and their personal experiences (Battistich, Solomon, Kim, Watson, & Schaps, 1995). In a classroom, all of these variables impact students and their behavior as well as selfefficacy toward the subject being taught. The following historical and current theories support these findings. These theories include the social cognitive theory, attribution theory, selfefficacy theory, person environment fit theory, and the expectancyvalue theory. Each theory supports different variables in this study. Figure 1 shows a visual representation of how each theory is directly connected to the current study. Selfefficacy is connected to the social cognitive theory, attribution theory, and expectancyvalue theory. Classroom environment is supported by the personenvironment fit theory. The social cognitive 5 theory is thinking about and reflecting over your behavior. Selfefficacy is impacted by the social cognitive theory because thinking leads to judgments created about oneself which impact individual future performance. The attribution theory causes individuals to think about why they succeed or fail and these ideas can lead to future behaviors and performance. Expectancyvalue theory involves individual motivation in an area based on its value according to that individual. This can impact future performance from that individual, as well as selfefficacy. Personenvironment fit theory is based on how the environment impacts behavior. This directly connects to how a classroom is conducted, and the culture created within it can impact the students in it. Social Cognitive Theory Social cognitive learning theorists view human functioning as reciprocal interactions among behaviors of individuals, environmental variables, cognition, and personal factors (Bandura, 1986). When individuals perform a task, the perceived importance of the task is a large part of the result of the outcome expectation the individual has for the task. Bandura (1986) stated that beliefs determine expectations; therefore people generally value what they feel 6 capable of accomplishing and do not value the activities in which they have little confidence. Through selfreflection, individuals evaluate their own experiences and thought processes, which powerfully influences how they will behave in future tasks (Pajares, 1996). Bandura’s (1997) social cognitive theory proposed that selfefficacy is strongly affected by previous performance and influenced by observing others, verbal persuasion, and interpretation of physiological states, with possibilities that student perceptions of their learning environment also affect their efficacy. People are selforganizing, proactive, selfreflecting, selfregulating, nonreactive beings easily influenced by their environmental or inner impulses. People interpret their own behavior, which impacts their environment and personal impulses and can therefore alter their subsequent behavior. Pajares (2002) supported the idea that teachers can work to improve their students’ perception of school and students’ emotional state in order to selfcorrect false selfbeliefs and develop habits to improve their academic skill and selfregulatory practices. Additionally, society constructs values and standards that impact the ways students view themselves, depending on their approach and success with given tasks in the education system (Hickey & Granade, 2004). The social cognitive theory is based on the idea that people purposefully engage in their own development and can make things happen through their actions. Attribution Theory The attribution theory emphasizes the thought that for individuals who believe success is due to high ability and failure is due to lack of effort, motivation will remain constant. However, students who believe success is luck and failure is expected are less likely to be motivated (Diener & Dweck, 1978). Students or others who have always failed in the past in a specific task, attribute that failure to themselves, especially if they see others succeeding (Weiner, 2004). 7 The attribution theory is based on causal attributions that people make about the success or failure of their actions that will influence how they feel and how they expect to perform on future tasks or activities of the same nature (Weiner, 1986). The effect of children’s own perceptions of their ability to achieve success has a direct impact on their personal attitude toward math. Attributions influence motivation and performance through the meditational role of selfefficacy (Bandura, 1995; Schunk, 1991). SelfEfficacy Individuals’ selfefficacy influences how people feel, think, motivate themselves, and behave. Bandura (1997) described four major processes that are impacted by selfefficacy including cognitive, motivational, affective, and selection processes. Major focuses of cognition included the impact of comparing, feedback, and amount of control over a situation. Additionally, individuals that believe they will perform well will tend to perform well, while those that feel inferior will perform poorly. Students with high selfefficacy seem to participate more readily, work harder, persist longer, and achieve higher results. Bandura (1986) defined selfefficacy as “people’s judgments of their capabilities to organize and execute courses of action required to attain designated types of performances” (p. 391). Selfefficacy impacts almost every aspect of people’s lives and is the core of human motivation, wellbeing, and personal accomplishment. It influences individual choices, goals, emotional reactions, efforts, coping, and persistence (Gist, Mitchell, & Mitchell, 1992). When individuals are faced with adversity, selfefficacy determines their behavior (Pajares, 2002). Selfefficacy impacts motivation, affect, and actions based on the interaction of what the individual believes rather than what is actually true (Bandura, 1997). 8 Selfefficacy influences the choices that people make and how much effort they put into the tasks, their thought patterns, and their emotional reactions (Pajares, 2002). There are four different sources through which selfefficacy can be developed including mastery experience, vicarious experience, social persuasions, and somatic and emotional states. Mastery experience is the most influential source and is the act of individuals engaging in the actual task or activity and then interpreting the results of their actions. These interpretations are then used to develop a personal belief about their capability to perform the task or activity and then act in line with the beliefs they have created (Pajares, 2002). Researchers have shown that selfefficacy is related to the career path and choices made by individuals along with other decisional behaviors (Betz & Hackett, 1981, 1983; Lent, Brown, & Larkin, 1987). Also, selfefficacy can predict success and persistence in certain academic majors and is strongly related to achievement status (Multon, Brown, & Lent, 1991). Person Environment Fit Theory The personenvironment fit theory (Lewin, 1935; Murray, 1938, 1951) emphasizes the idea that behavior is a function of the person and the environment. There is a mutual relationship between the environment and person such that the environment influences behavior. Hunt (1975) emphasized the need for a match between the person and the environment in the course of learning. Early adolescents have an increase in a need for higher quality interactions with adults, sense of autonomy, and a sense of belonging (Eccles, et al., 1993; Kuperminc, Leadbeater, & Blatt, 2001; Midgley, Feldlaufer, & Eccles, 1989; Osterman, 2000). There is dual emphasis on the person and the environment and behavior, attitudes, and wellbeing are determined by both the person and the environment. Within the research under personenvironment fit theory, the feeling gained by the individual arises not from the person or environment but rather by his or 9 her fit or congruence with one another (Edwards, Caplan, & Harrison, 1998). Classroom environments have a culture of their own created by the people within and surrounding it. The environment created has an impact on the individuals that are a part of it, which include the students. This theory supports the concept that the environment created has an impact on the behavior of those that are a part of the environment, in this case, with emphasis on the students. Expectancyvalue Theory The expectancy value theory emphasizes how motivation is a primary result of an individual’s belief about the outcome of a specific activity and the importance placed on that outcome (Atkinson, 1957; McClelland, 1985; Rotter, 1982). Individuals will be motivated to participate in tasks if they find value in the outcome of that particular task and will not be motivated to take part in a task if they do not find value in the outcome. Researchers have agreed that competence in completing a task plays a crucial role if the task will be valued by the individual (Eccles, 1983; Wigfield & Eccles, 1992). Bandura (1986) emphasized that outcome expectation will have a stronger influence on the motivation and predicting behavior of the task performed. Bandura stated that personal judgments of the individual’s competence are different than the individual’s judgment of the likely outcome from the task. Those who expect success will behave in such a way in order to achieve that goal. The opposite is also true; if individuals expect failure, they will be more likely to fulfill that belief (Pajares, 1996). According to Eccles (2009), achievement related behaviors like course selection and occupational aspiration are most directly influenced by the individual’s expectation for success. Research has indicated that students who are most likely to take math courses and to aspire to math focused careers place higher value and have greater confidence in their math abilities than those who do not (Eccles, 2007). 10 The expectancyvalue theory also shows that the feedback students receive on their academic performance influences their motivational beliefs and academic choices (Eccles, 2009). Wang (2012) concurred; he found that students who earned higher grades in math also reported higher math expectancies and subjective task values, and were more likely to continue with course work in math and have mathrelated jobs in the future. Significance of the Problem Students in our colleges are straying away from majoring in mathematics intensive fields because of the lack of selfefficacy in this area (Committee on Science, Engineering, and Public Policy, 2007). This shortage of math majors and graduates has put the United States behind in mathematics, science, and technology development. The Industrial Revolution spawned a multitude of engineering endeavors that spring boarded the economy in the United States (Committee on Science, Engineering, and Public Policy, 2007). Many areas of our life including transportation, communication, agriculture, education, health, defense, and employment opportunities are available due to the investment in scientific research and engineering (Popper & Wagner, 2002). The United States has been considered a leader in science and engineering activities since the early 1900s with 30% of the world’s scientists and engineers as well as 17 of the world’s top 20 universities (Freeman, 2005). With the reputation so high in the US, other countries have stepped up and increased their competitiveness with the US over the past 20 years. This changing global market requires the US to produce not only more engineers, but higher quality engineers that are needed to be worldwide leaders in this hightech production market. High school graduates pursuing engineering degrees are declining (Noeth, Cruce, & Harmston, 2003), and less than half the freshmen who begin college with engineering as their major finishing with an engineering degree (BesterfieldSacre, Atman, & Shuman, 1997). One 11 attempt to solve this problem is to increase the number of students choosing to study engineering (Fantz, Siller, & Demiranda, 2011). Mathematics is a crucial piece of many fields, including the engineering field. Without mathematics, problem solving, process formation, and application would find disconnect within this field of study. This research study helps to determine what characteristics of classrooms can lead to a low or high selfefficacy in mathematics. Using this information, educators will be able to determine what they can do in their classroom to encourage high mathematics selfefficacy in their students and eliminate characteristics that tend to form a lower selfefficacy. This will lead to improved math interest and achievement as well as an increase in students in mathematic career fields. This boost in mathematics in America could jump start the society with improvement in areas like Science, Technology, Engineering, and Mathematics (STEM) fields. Method of Procedure This research study sought to determine what characteristics of the mathematic classroom environment could predict high or low student selfefficacy in mathematics. Two surveys were administered to participants in order to collect data. The data were then analyzed using multiple regression. Selection of Sample Participants for this study included students in fourth through 12th grade in a small North Texas school district. Only participants with parent permission and student assent were included in the data analysis. The school district superintendent gave prior permission for the researcher to collect the student data. Approximately 400 students participated in this study. 12 Instrumentation The Patterns of Adaptive Learning Scale (PALS) (Midgley et al., 2000) instrument as a whole is a tool used to measure a variety of learning aspects of the student. This study focused solely on high and low selfefficacy, therefore, only parts of the PALS instrument were used in data analysis to emphasize selfefficacy rather than the other student scales. The PALS instrument was chosen because of its validity and reliability and there was no other appropriate mathematics selfefficacy instrument. Selfhandicapping is associated with maladaptive behavior which leads to low selfefficacy (Patrick, Kaplan, & Ryan, 2011), therefore low selfefficacy was measured using the statements under “academic selfhandicapping strategies” (p. 368). Selfefficacy also has been found to be positively related to mastery goal structure, personal mastery goal orientation, effort, not cheating, satisfaction with learning, schoolrelated effort, and achievement (Ames & Archer, 1988; Anderman, 1999; Kaplan & Midgley, 1999; Murdock, Hale, & Weber, 2001). Therefore, high selfefficacy was measured by analyzing the statements that fall under “mastery goal orientation” and “academic efficacy”. Students also took the My Classroom Inventory (MCI) (Fraser, Anderson, & Walberg, 1982) which measured students’ perception of the classroom environment in their mathematics classroom. The MCI measures five dimensions of social climate, including cohesiveness, friction, satisfaction, difficulty, and competitiveness. Collection of Data Students took the two separate surveys, in an electronic version, during the regular school day in their computer lab, the MCI. My Classroom Inventory (MCI) and the selected items from the Patterns of Adaptive Learning Survey (PALS) (Midgley et al., 2000) were used to collect and 13 analyze data from the students. Students entered some demographic information on both surveys, including their ID number in order for their surveys to be matched by a district employee for analysis. The ID number is a school district issued number that students are familiar with and use on a daily basis. Student ID numbers were removed before data were given to the researcher. Treatment of the Data The data were collected and analyzed using Statistical Program for Social Sciences (SPSS) through conducting two multiple regressions to determine which dimensions of classroom environment can predict a high or low math selfefficacy. Student demographics were reported. Definitions of Terms The following terms are used in the present study: Classroom environment. Classroom environment involves interpersonal relationships with peers, relationships between students and their teacher, the relationship between students, the subject studied and teaching methods, in addition to student perceptions of structural characteristics of the class (Fraser et al., 1982). In this study, classroom environment was measured by My Classroom Inventory (MCI) (Fraser et al., 1982). The five subscales under classroom environment are listed below: Cohesiveness extent to which students, know, help and are friendly toward each other; Friction amount of tension and quarrelling among students; Satisfaction extent of enjoyment of class work; Difficulty the extent to which students find difficulty with the work of the class; and Competitiveness emphasis is placed on students competing with each other. 14 High selfefficacy. High selfefficacy is defined as mastery goal orientation and academic efficacy. High selfefficacy was measured by Patterns of Adaptive Learning Survey (PALS) (Midgley et al., 2000) using the “mastery goal orientation” and “academic efficacy” scales. Low selfefficacy. Low selfefficacy is defined as looking at student attribution through “academic selfhandicapping strategies”. Low selfefficacy was measured by Patterns of Adaptive Learning Survey (PALS) (Midgley et al., 2000) using the academic selfhandicapping scale. Mathematics selfefficacy. Selfefficacy of students specifically in the mathematics classroom and academic area of math (Bagaka, 2011). Mathematics classroom. Mathematics classrooms ranged from a selfcontained elementary classroom to a dual credit calculus classroom. Selfefficacy. Selfefficacy was defined by Albert Bandura (1994) as “the belief in one’s capabilities to organize and execute the courses of action required to manage prospective situations” (p. 72). It measures how people think, feel, and behave in certain situations and their personal opinion of how they can succeed in that environment. Students. Students are defined as children from fourth through 12th grades who were approximately age 9 to 19. Limitations The limitations of this study were as follows: 1. The district selected has a small population and limited subgroups (ethnicity, socioeconomic status, languages spoken). 2. The sampled participants were not an exact representation of the population of the 15 school district due to the requirements needed for students to participate. 3. Students completed the surveys on a computerbased survey system that could cause students to make mistakes by incorrectly clicking an answer they do not want. 4. Previous experiences and events that occur prior to students taking the surveys were not controlled by the researcher and could impact the results of the survey. Delimitations The delimitations of this study were as follows: 1. The data were collected from one school district. 2. The data were collected with limited student subgroups. 3. Only the student section of the PALS survey was used to measure students’ perception of classroom environment in mathematics classrooms. No data were collected using the teacher portion of the instrument. 4. The data were collected within a 10day time period which could cause some difference in data collection and change in attitudes of the participants. 5. Only grades four through 12 were analyzed. 6. The researcher chose the order in which the students completed the surveys. Assumptions This study is based on the following assumptions: 1. Students responded accurately and honestly. 2. Teachers administrating the surveys did not impact student responses. 3. Math teachers did not alter their teaching in order to gain specific results from the data collected. 16 4. Both instruments are valid and reliable and the two surveys did not influence each other. Organization of the Study This dissertation is organized into five chapters. Chapter 1 includes a statement of the problem, purpose of the study, research questions, research hypotheses, theoretical framework, significance of the study, definitions of terms, limitations, delimitations, and assumptions. Chapter 2 includes related professional literature regarding selfefficacy and classroom environment in mathematics. In Chapter 3 is a discussion of the research methodology. Chapter 4 includes the analysis of the data; Chapter 5 includes a discussion of the findings and applications to education. 17 Chapter 2 LITERATURE REVIEW This study aimed to determine what dimensions of classroom environment predict high selfefficacy and low selfefficacy in mathematics. Students in a North Texas school district participated in taking two surveys. One survey measured their perception of the classroom environment of their math class while the other measured the high and low selfefficacy in mathematics. Data were analyzed using a multiple regression in order to determine what characteristics of the math class could predict high and low selfefficacy in mathematics. Selfefficacy plays a major role in individuals’ everyday lives. Many different variables can impact each individual’s selfefficacy, especially in the area of mathematics (Hackett & Betz, 1989). Students’ attitudes are influenced by many different things including parents, peers, school, teacher, and classroom environment (Klassen & Usher, 2010). This literature review examines the importance of a positive selfefficacy in students at all ages in the area of mathematics and explains why classroom environment, in regard to selfefficacy, needs to be studied further. Math Anxiety Mathematic anxiety is a worldwide concern. The root of the problem is in schools, where students are developing negative attitudes toward mathematics at a very early age (Ashcraft, 2002). Math anxiety can be described as “a feeling of tension that interferes with the manipulations of numbers and the solving of mathematical problems in academic and ordinary life situations” (Sousa, 2008, p. 171). Math anxiety has been defined as the feeling of tension, helplessness, mental disorganization and dread when one is required to work and manipulate math problems (Ashcraft & Faust, 1994). Math anxiety can conjure up feelings of apprehension, 18 dislike, fear and dread (McLeod, 1994). It can prevent students from interacting with situations that are math intensive and these students avoid upper level math courses (Akin & Kurbanoglu, 2011). Lazarus (1974) believed that mathematic anxiety developed in elementary and secondary grades. Researchers have shown that negative math experiences can start around third or fourth grade (Ashcraft & Ridley, 2005; Beilock, Gunderson, Ramirez, & Levine, 2010). Math anxiety occurs in people from all different race, gender, and age group and can be a product of the home, school, or society. Burns (1998) estimated that 60% of adults have a fear of mathematics. Students develop a fear of mathematics (math anxiety) through negative experiences in math classes or having a lack of selfconfidence with numbers (Sousa, 2008). These experiences and lack of confidence usually lead to fear of calculation, failure, and difficulty in mathematics. The fear causes their minds to go blank and then causes frustration, which leads to additional amnesia. Fear and anxiety is increased when time limits are added to the mathematics activity. Students who have developed math anxiety need help to replace the memory of failure with the possibility for success (Ashcraft, 2002). The most obvious consequence of math anxiety is poor achievement and poor grades in mathematics (Sousa, 2008). Poor performance can be caused by a chemical change happening in the brain through the biology of the body. Any kind of anxiety causes the body to release cortisol into the bloodstream. Cortisol is a hormone that refocuses the brain on the anxiety to determine what action to take to relieve the stress. While this is happening, the frontal lobe is no longer interested in learning or processing the mathematical operation while the brain is dealing with a threat to the individual’s safety. Therefore, the student cannot focus and has to cope with the frustration of inattention. As well as their inability to manipulate and retain numbers and expressions due to a disruption in the working memory (Ashcraft & Kirk, 2001). 19 Beilock, Gunderson, Ramirez, and Levine (2010) focused on how math anxiety can impact students, specifically girls. This study looked at how female elementary teacher’s math anxiety influences the female student’s achievement and how that compared to the male students. Students were first and second grade students who were given math assessments throughout the school year. Students were told two gender neutral stories about students who were good at math and the other was good at reading and then the students drew a picture of what each looked like. The pictures were coded and correlated with the math assessment finding that girls who had confirmed gender ability roles (boys are good at math, and girls are good at reading) performed worse on the math assessment than girls who did not. These girls also performed worse than the boys with these differences related to the anxiety that the teacher had about math. Harper and Daane (1998) studied the causes of math anxiety in preservice elementary teachers and found that the cause usually stemmed from elementary school and included fear of making mistakes, having the right answer, amount of time given for a task, word problems, and problem solving. Philippous and Christou (2003) studied preservice teachers in Greece and found that teachers with negative attitudes toward mathematics were slightly positively impacted when they understood the usefulness of the skill while the deeply rooted anxieties about mathematics did not seem to change. Ma (1999) found that there is a significant relationship between math anxiety and math achievement. Bretscher, Dwindell, Hey, and Higbee (1989) posited that students who learned math because they wanted to, had higher math achievement, therefore the motivation toward performing math increased the student achievement. Norwood (1994) found that the elements of math anxiety included a mixture of truancy, poor selfimage, poor coping skills, teacher attitude, and the emphasis on learning math through drill practice rather than understanding. Zakaria and 20 Nordin (2008) found that students who had a high math anxiety also had a low math achievement as well as the students with low math anxiety had high math achievement. Classroom Environment The term classroom environment refers to the social and psychological surroundings of the classroom (Fraser, 1991). The teacher is a part of and contributes to the classroom environment which influences choices and norms of the classroom (Shuell, 1996). Research has shown that the quality of classroom environment is a significant determinant of student learning (Fraser, 1994, 1998b). Early seminal work by Lewin (1935, 1936) and Murray (1938) recognized that both the environment and its interaction with personal characteristics of the individual are determinants of the human behavior. Students learn better when they perceive the classroom environment positively (Dorman, 2003). Research on classroom environment has been diverse and varied, but began with the work of Walberg (1979) and Moos (1974), who spawned additional research programs all over the world. While questionnaires were used greatly in the beginning of the classroom environment research, both quantitative and qualitative methods are the more typical route of researchers. The majority of classroom environment research has been done in science classrooms and very few have involved mathematics classrooms (Spinner & Fraser, 2005). Classroom environment has been shown to be the most significant factor in students’ learning and attitudes in math and science (Fraser & Kahle, 2007). The classroom environment is a critical context for promoting the development of students’ educational and career interests (Simpkins, DavisKean, & Eccles, 2006). There is evidence to suggest that classroom environment influences how well students achieve a range of desirable outcomes (Fraser, 2007). Research has supported the fact that the social environment of classrooms can significantly 21 impact students’ motivated behavior, specifically the level of friendship students feel for each other measured by students getting to know each other, helping each other, and working together (Fraser & Fisher, 1983; Trickett & Moos, 1974). Students have been found to achieve better in the types of classroom environments that they prefer (Fraser & Fisher, 1983). Teacher techniques that include the focus on memorization rather than understanding the concept are among the main sources of math anxiety. Math anxiety also stems from a classroom culture that searches for one right answer with no recognition or appreciation for the thinking the student goes through or their cognitive process. Flewelling and Higginson (2001) found that students who have rewarding and successful learning experiences with math were able to overcome their math anxiety. Math classrooms and teachers who focus on making sense of that mathematical process and not memorizing or being correct cultivate students who avoid math anxiety. Having a positive classroom environment is a valuable goal of education (Fraser, 2001). Describing the class through the actual participants, students are in a good position to make judgments about classrooms because they have experienced many different learning environments and have spent enough time in the class to form accurate opinions. While teachers can be inconsistent in daily behavior, there is usually a consistent picture of the traditions and features of the classroom environment. While observation is a strategy used to collect data on classroom environments, it does not tell the whole story about the students’ perspective. Classroom environment includes the relationships between students, teachers, and subject material (Fraser et al., 1982). Five components of classroom environment will be emphasized in this research including cohesiveness, friction, satisfaction, difficulty, and competitiveness. 22 Sinclair and Fraser (2002) conducted research that looked into three areas of classroom environment. They worked on developing an instrument (Middle School Inventory of Classroom Environments or ICE), collecting quantitative and qualitative data on typical classroom environments, and used the information so teachers could positively impact their classroom and students. Data were collected from about 745 students on their perceived and preferred classroom environments, along with data collected from ten teachers on their perceived and preferred classroom environments. Sinclair and Fraser also took part in classroom observations of the participating teachers. Analysis of the data collected compared the teacher and student preferred and perceptions of the classroom environment. A oneway analysis of variance (ANOVA) was used in order to analyze the data for each scale within the instrument. After initial scores were collected on the teachers and students, the researchers met with the teachers to share the information and determine what areas that the teacher wanted to improve upon in order to increase student perceived classroom environment. One teacher aimed to improve her students’ perceptions of involvement and teacher empathy in her class. The teacher worked on including students in the science lab preparation as well as assistance with class pet maintenance. Research done on classroom social climates has shown that classrooms characterized by cohesiveness, satisfaction, and goal directions are preferred by students and are associated with positive outcomes for students (Fraser, 1991). Students’ sense of autonomy and participation in decision making has also been shown to have positive effects for children (Lewin, Lippitt, & White, 1939). Having a caring environment conveys a set of values such as mutual respect, valuing individual members’ contributions, and obligation of each member to meet the needs of the community (Battistich, Solomon, Kim, Watson, & Schaps, 1995). Fraser (1998a), with 23 support from Goh, Young, and Fraser (1995) found associations between students’ perception of the classroom environment in mathematical classes and established that students with greater cohesiveness were linked to higher achievement for math and teacher support: task orientation and equity were linked with more positive attitudes and selfesteem. Cooperative classroom strategies are associated with improved peer relations and supporting mutual respect (Anderson, 2004). Johnson and Johnson (1991) found that cooperative learning environments lead to productive classrooms where students exert high effort to achieve positive and supportive relationships and psychologically healthy and socially competent students. In a teachercentered mathematics classroom that is controlled by rules, routines, and individual drilling, there is little room for student autonomy or social belonging within the mathematic learning. Studentcentered classrooms with teamwork and emphasis on meaning making give students many opportunities to have students’ needs met through a variety of approaches (Hannula, 2006). The degree to which a classroom is challenging can also influence academic selfefficacy. Challenging is defined as an environment where students are given progressively difficult tasks as their proficiency increases. Some researchers have suggested that challenging students can lead to a stronger belief in the student’s personal academic abilities (Battistich et al., 1995; Pajares, 1996). One of the essential ways to improve middle grade education is to establish a safe and healthy school environment (Jackson & Davis, 2000). Students can be placed at academic risk of failure because of the quality of their school and classroom learning environment (Montgomery & Rossi, 1994). Ineffective and dysfunctional classrooms and instructional learning environments have been uncovered in multiple middle schools (Midgley, Eccles, & 24 Feldlaufer, 1991; MacIver & Epstein, 1993; Waxman, Huang, & Padron, 1995). Middle schools are usually structured, formal, and less personal than elementary schools and students frequently become bored and alienated with an increase in teacher talk and lack of student involvement (Waxman et al., 1995). Middle school classes tend to be more teachercentered and discipline focused where teacher student relations and student decision making are not a focus (Feldlaufer, Midgley, & Eccles, 1988). Additionally, middle schools often do not encourage personal relationships even though caring and supportive environments are critical for students (Baker, 1998; Roeser, Midgley, & Urdan, 1996). Classroom environment needs to be a focus in the middle grades in order to increase student cognitive and affective outcomes (Fraser, 1998; Haertel, Walberg, & Haertel, 1981). Researchers have shown that cohesiveness, student satisfaction, and teacher support are positively related to student increase in academic achievement (Waxman, Read, & Garcia, 2008). Research has been devoted to comparing the perception students have of their classroom as one which is performance based or encourages mastery (Patrick, Kaplan, & Ryan, 2011). Classrooms structured around mastery goals focus on effort put into a task as well as the intrinsic value of learning. This is compared to the performancebased classroom that focuses on competition and natural ability. Previous research has found that classrooms based around the mastery goal model have higher academic selfefficacy (Friedel, Cortina, Turner, & Midgley, 2007). The degree to which students perceive their classroom as a caring environment also has an influence on selfefficacy. Teachers in these classrooms express personal interest in the students, provide emotional support, and create a comfortable atmosphere. Murdock and Miller (2003) suggested that students who perceive their teachers as caring are more likely to view themselves as more academically capable, set higher goals for themselves, and have significantly 25 higher selfefficacy. The effect of emotional support on math achievement was larger than on quantity of math instruction. Roeser et al. (1996) found that a greater sense of school belonging, along with an emphasis on effort, understanding, and beliefs that all students can learn, were associated with academic selfefficacy. Cowen, Work, Hightower, Wyman, Parker, & Lotyczewski (1991) found those students who perceive high levels of classroom competition, friction, and difficulty, felt less efficacy when approached with an academic challenge. McMahon, Wernsman, and Rose (2009) examined 149 fourth and fifth graders from diverse backgrounds in California that completed two selfreports on their perceived classroom environment. The MCI (My Classroom Inventory) was used to collect data from the students on their perceived classroom environment, school belongingness was measured using the Psychological Sense of School Membership Scale, and selfefficacy in language arts and math was also measured using a The Academic SelfEfficacy Scale. They found that satisfaction, cohesion, and school belonging were significantly and positively correlated along with difficulty, competitiveness and friction. Additionally, classroom environment and school belonging predict selfefficacy and lower difficulty predicted higher math and science selfefficacy. School belonging and satisfaction and cohesion did not significantly predict math and science selfefficacy. SelfEfficacy and Classroom Environment Consistent and convincing research gives evidence that the quality of the classroom environment is a significant determinant of student learning (Fraser, 1994). A positive learning environment can influence student academic achievement and attitudes (Fisher, Henderson, & 26 Fraser, 1995). Fraser (1994) indicated that student perceptions of learning environments are an important factor in explaining their cognitive and affective outcomes. In terms of selfefficacy and classroom climate, these factors play important roles in the learning environment (Pitkaniemi & Vanninen, 2012). Students are more likely to have greater expectancy values in math which can lead to students taking more math courses and pursuing a career in mathematics. These students can then encourage, cooperate, interact, and help their classmates and view the curriculum and teaching as meaningful and relevant to their lives when they perceive their teacher as understanding and supportive while having high expectations for their learning achievement (Wang, 2012). Teacher and school practices that promote students’ mathematical selfefficacy may not only promote mathematic achievements, but also could narrow the achievement gaps in mathematics as found by gender, socioeconomic status, and minority status (Bagaka, 2011). Selfefficacy predicts students’ math achievement, and there are reasons to suspect that the relationship between teachers’ classroom behavior and students’ academic performance are also positively correlated (Weinstein & McKown, 1998). Students carefully observe teacher’s verbal and nonverbal behaviors while developing selfbeliefs and academic behaviors based on these observations (Weinstein & McKown, 1998). When educators demonstrate a direct interest in student care and concern, as well as respect for their thoughts, opinions, and ideas, the outcome supports a decrease in student depressive symptoms and an increase in selfesteem (Reddy, Rhones, & Mulhall, 2003). Further et al. (1998) determined that affective teacher behavior including listening, respect, recognition, and fair treatment significantly influenced young adolescent motivation. Muller, Katz, and Dance (1999) established that students 818 years of age desire a personal connection with their teacher and yearn for the instructor to 27 maintain high academic expectations. Fairness is an additional characteristic that students retain from their educator in the classroom. Students identify with different ways teachers treat students associated with success and ability (Weinstein & McKown, 1998). The powerful relationship that grows between the teacher and student in the classroom plays a crucial role in developing the emotional, motivational, and academic behaviors of the student. Teacher support correlates directly with youth adjustment, achievement, social, and motivational development. While educators have a specialized focus of specific academic content, there needs to be an equal focus on student affect and socialemotional needs (Osterman, 2000). Through selfrecorded data, students show a decline in teacher support throughout school years (Reddy et al., 2003) as well as a decline in a sense of belonging over time (Anderman, 2003). The data from the mathematics selfreports suggest that students feel less valuable and see a lower persistence in middle school years. A supportive teaching style has been positively linked to student achievement. It has been found that if teachers’ academic support (the teacher cares about their learning, tries to help them learn, and wants them to do their best), academic press (the teacher checks for understanding and engagement), and mastery goal (the teacher emphasizes learning and understanding, focuses on student development) are all implemented in the classroom, student achievement improves (Goodenow, 1993; Kaplan & Midgley, 1999; Wentzel, 1994, 1997). Students who perceive that their math teachers take into account student relatedness and competence, and enforce positive demands on students’ academic work show more positive motivational beliefs and achieve higher grades. Students who perceive their teacher as responsive, helpful and recognizant of good work tend to perform better than their peers whose teachers are perceived as less supportive (Ambrose, 2004). These results support Slovene’s 28 findings of early adolescents’ perceptions of their teachers and motivational beliefs (selfefficacy and intrinsic motivation) (Puklek, 2001; Puklek, 2004). Selfefficacy beliefs are created through the individual’s interpretation of information from different internal and external sources (Bandura, 1997; Pajares, 2002). An external source of selfefficacy beliefs is verbal judgments that others provide about their capabilities. Teachers are a crucial element of the classroom environment. Students’ perception of affective teacher support can influence their enjoyment in mathematics. Math and science selfefficacy were significantly negatively correlated with difficulty, and positively correlated with language arts selfefficacy (Pajares, 2002). Predictors of selfefficacy include satisfaction and cohesiveness; difficulty, competitiveness, and friction, and school belonging. In terms of math and science selfefficacy, difficulty was the sole predictor when a selfefficacy test was given for the second time. Other variables that can impact selfefficacy are parental influence, teacherstudent and studentstudent interaction, teacher instructional techniques, and appropriate teacher support. Kaplan, Gheen, and Midgley (2002) suggested that students are more likely to have positive selfefficacy from mastering a subject rather than from performing a standard. This could explain the finding that perceived difficulty predicted math and science selfefficacy. When students have a perceived high academic selfefficacy, they exhibit a positive behavioral adjustment and social competence, greater selfconcept, and stronger relationships with peers and parents (Kuperminc, Blatt, & Leadbeater, 1997). Student academic selfefficacy is a strong predictor of academic engagement, persistence, academic effort and performance (Linenbrink & Pintrich, 1997). School environment significantly influences a student’s selfefficacy. 29 The relationship between academic effort and academic achievement in middle school is important because it has been found to predict math achievement in high school, which will directly impact the student in college (Wang & Goldschmidt, 2003). Previous theory and research suggested a positive relation between academic selfefficacy beliefs and academic outcomes of students (Bandura, 1997; Pajares & Graham, 1999). Lorsbach and Jinks (1999) suggested that student perceptions of their learning environment are influenced by student academic selfefficacy and can lead to an appreciation of what is happening in classrooms. As expected, students who reported a greater sense of belonging in their mathematics classroom were likely to report higher academic enjoyment (Wang, 2012). Researchers did not find any statistical significance between academic enjoyment and academic hopelessness, or between academic enjoyment and academic selfefficacy. Academic enjoyment proved to be a powerful connection with academic effort. Students who reported higher teacher affective support were likely to report lower academic hopelessness, which was associated with greater academic selfefficacy (Pekrun, Goetz, Frenzel, Barchfeld, & Perry, 2011). Academic hopelessness did negatively predict academic effort through its detrimental effect on academic selfefficacy. Students who reported high academic hopelessness were likely to report low academic selfefficacy belief and related to lower academic effort. Students who report higher academic selfefficacy tended to report greater academic success in mathematics. There was a positive correlation between teacher academic press and student motivational beliefs; students’ selfefficacy and mastery goal orientation in math were positively related to their math grade. Results also showed that level of parental involvement would predict student math grades, while the math teaching measures were the most powerful predictors of student selfefficacy in math (Battistich et al., 1995). The students’ ratings of math teachers’ 30 academic support contributed to student mastery goal orientation and math achievement. The perceptions of teacher academic press predicted student selfefficacy and mastery goal orientation in math and their math grade (Anderson, Hamilton, & Hattie, 2004). Overall, it was found that classroom environment does have an impact on student academic selfefficacy and the many different variables that can impact these relate to students and their experiences (Weinstein & McKown, 1998). SelfEfficacy and Math Selfefficacy in mathematics has been studied, but not in great detail. Math selfefficacy is a strong predictor of math performance (Pajares & Miller 1994, 1995). The selfefficacy theory states that perceived selfefficacy influences and is influenced by thought patterns, affective arousal, and choice behavior as well as task performance (Bandura, 1977, 1986). According to the social learning theory, selfefficacy expectations are an important factor in influencing math attitudes and math anxiety (Bandura, 1977; Hackett & Betz, 1981). Bandura (1986), Pajares (1996), and Schunk (1991) found that selfefficacy beliefs predict student performance in mathematics. Selfefficacy can also influence math performance as strongly as general mathematics ability (Pajares & Kranzler, 1995). Across ability levels, students who have high selfefficacy are more accurate in their mathematical computation and are more persistent when faced with a challenge when compared to students with low selfefficacy (Collins, 1985). Lloyd, Walsh, and Yailagh (2005) analyzed fourth and seventh graders in order to compare their math grades, math foundation skills, performance attributions, and selfefficacy looking specifically at gender differences. They found that boys and girls equally attributed their success to effort and fourth graders were more likely to attribute their success to effort when compared to seventh graders. Ability was the attribution that the majority of students believed 31 lead to success. Fourth graders were also more likely than seventh graders to attribute their success to help from their teachers than seventh graders. Fourth graders were more efficacious than seventh graders and girls tended to be underconfident while boys were overconfident; however, girls’ achievement met or exceeded boys’ achievement. Akin and Kurbanoglu (2011) examined the relationship between math anxiety and selfefficacy. Participants included 372 university students in Turkey who took the assessment RMARS (Revised Mathematics Anxiety Rating Scale) to measure anxiety, Mathematics Attitudes Scale to measure mathematic attitudes, and Motivated Strategies for Learning Questionnaire (MSLQ) to measure selfefficacy. They found that selfefficacy is a proximal determinant of math attitudes and selfefficacy and that math anxiety was predicted by negative selfefficacy. Overall, the stronger the selfefficacy, the more active are the individual’s efforts and the longer they will persist. Additionally, selfefficacy predicted negative attitudes and positive attitudes. Pajares and Miller (1996) found that math selfefficacy has stronger direct effects on mathematics problem solving than selfconcept, perceived usefulness, or prior experience. Judgments of individuals’ ability to solve math problems should be more strongly able to predict their ability to solve those problems than their confidence in their ability on math related tasks. Similarly, judgments of their ability to succeed in math related courses should predict their choice to enroll in math courses than should their confidence in their ability to solve specific problems or perform math tasks (Pajares, 1996). Schunk (1981) showed that teacher modeling increased persistence and accuracy on division problems by arising student selfefficacy, which had a direct effect on skill. Additionally, he found that student effort was attributed to feedback of prior performance. This behavior raised student selfefficacy expectations in elementary 32 students. Later, he also discovered that ability feedback had a stronger effect on selfefficacy and performance (Schunk & Gunn, 1986). SelfEfficacy and Achievement Selfefficacy contributes to personal goals individuals set for themselves, how much effort they will exert in order to perform a task, how long an individual will persevere when facing a challenge, and how resilient the individual is toward failures. Bandura (1982) found that selfefficacy is more strongly related to future and actual task performance than past performance. Selfefficacy is not concerned with specific skills an individual has but the judgments and selfbelief of what one can do with the skills they possess (Bandura, 1982). Several studies have established the strong positive connection between student selfefficacy and their academic performance (Pajares, 1996; Pajares & Graham, 1999). Selfefficacy has been shown to predict achievement outcomes in a variety of content areas including mathematics, science, and writing (Klassen & Usher, 2010; Pajares, 1996; Pajares & Urdan, 2006). Selfefficacy is also a powerful predictor of student achievement (AlHarthy, Was, & Isaacson, 2010; Andrew, 1998; Bandura, 1993; Barkly, 2006; Paulsen & Gentry, 1995; Schunk, 1989; Zimmerman, 2000). Bandura (1977, 1997) and Pajares (1996) found that higher selfefficacy scores leads to better performance and persistence in engineering courses. Selfefficacy is a taskspecific capability (Gist, Mitchell, & Mitchell, 1992) and a dynamic construct. The selfefficacy judgment from the individual changes over time as new information and experiences are gained (Bandura, 1989). Personal efficacy beliefs help individuals determine how much effort people will spend on an activity, for how long they will persevere when faced with a challenge, and how resilient they are when the odds are not in their favor (Pajares, 1996). Selfefficacy also 33 influences the thought patterns and emotional reactions of individuals. Selfefficacy beliefs are powerful predictors of the choices that individuals make on a daily basis, the level of effort that they put on the task, and their persistence toward facing challenges (Multon, Brown, & Lent, 1991). Individuals with low selfefficacy may view a challenge and think that it is more difficult than it really is, impacting their stress level, depression, and ability to best solve the problem. In contrast, high selfefficacy helps individuals create a feeling of confidence when approaching difficult tasks and activities (Pajares, 1996). Pekrun et al. (2011) found that focusing on academic enjoyment in a college classroom positively impacted selfefficacy, intrinsic and extrinsic motivation, academic effort, selfregulation, and academic performance. There are four factors that influence selfefficacy: mastery experience, vicarious experience, social persuasions, and somatic emotional state. Mastery experience, interpreting one’s own performance, is the most potent source of selfefficacy (Bandura, 1986, 1997). Prior experience will affect students’ initial belief in their personal capabilities. Those who perform well on the activity believe they are capable of furthering their abilities in that area. Individuals who experience challenge and difficulties may doubt their capabilities (Schunk, 1989). Actions perceived by the individual as successful typically raise selfefficacy and perceived failure lowers it. Positive feedback can enhance selfefficacy but can be short lived if efforts following the feedback are poor as students are generally not motivated to behave in ways that they believe will result in negative outcomes (Schunk, 1989). Research shows that mastery goal orientation is linked to positive, adaptive pattern of attributions, whereas a performance goal orientation was linked to a maladaptive, helpless pattern of attributions (Ames, 1992b; Dweck & Leggett, 1988). Under mastery goal orientation, students are more likely to see a strong link between effort and outcomes and make more effort attributions for success and failure (Schunk, Meece, & Pintrich, 34 2014). Students with performance goal orientation see effort and ability as inversely related, as opposed to the positive relation under mastery goal (Schunk et al., 2014). Selfefficacy has been found to be related to goal orientation and found that people with mastery goals have higher selfefficacy and better task performance than people with performance goals (Locke, Frederick, Lee, & Bobko, 1984; Locke & Latham, 1990; Wood, Bandura, & Bailey, 1990). Researchers have found links between mastery goals and judgments of selfefficacy are generally positive (Sakiz, 2011). As mastery goals were formed, Dweck and Leggett (1988) performed laboratory research that showed that students oriented toward mastery and learning maintained positive and adaptive selfefficacy beliefs and perceptions of competence in the face of difficult tasks. Mastery goals related positively to selfefficacy in college students enrolled in statistics courses (Bandalos, Finney, & Geske, 2003). Bong (2009), Kaplan and Midgley (1997), Middleton and Midgley (1997), Sakiz (2011), and Thorkildsen and Nicholls (1998) have also shown the same general pattern. Vicarious experience, observing the actions of others, is also another way that individuals obtain information about what they can do (Bandura, 1997; Schunk, 1987). Students who observe similar peers perform a task may believe that they are capable as well. This source of selfefficacy is not as strong as mastery experience, but when individuals are uncertain of their abilities or have little prior experience, they become more sensitive to it (Pajares, 2002). Selfefficacy can also be created through the result of social persuasions received from others in their environment. Efficacy will increase when individuals are being told they are capable by a trustworthy source. This can include verbal judgments from peers or adults and play an important role in the development of an individual’s selfbeliefs. Individuals compare themselves to others in their environment around them and evaluate themselves with those who 35 are similar in ability (Festinger, 1954). Lastly, anxiety, stress, arousal, and mood states fall under that category of somatic and emotional states and can influence selfefficacy. Strong emotional reactions to a task can foreshadow the anticipated success or failure of the outcome (Pajares, 2002). Bandura (1997) found that people live in psychic environments that are of their own making, so therefore, individuals have the capability to alter their own thinking and feeling to enhance their selfefficacy beliefs. Selfefficacy can change as a result of learning, experience, and feedback (Gist et al., 1992). Selfefficacy can affect individuals’ psychological wellbeing and performance while exerting some influence over their lives through the environments they select and environments they create. Personal efficacy affects each individual’s choices of activities to take part in. Those who believe they are not capable of a task will avoid it, but the same individual will be willing to take on an alternate activity they feel they are capable of completing or accomplishing (Wood & Bandura, 1989). Perceived selfefficacy also has an impact on the choice of the individual’s career path with stronger selfefficacy connecting to more career options they consider to be possible (Betz & Hackett, 1986; Lent & Hackett, 1987). Selfefficacy also enhances students’ memory performance by enhancing persistence (Berry, 1987). Academic selfefficacy can be seen as a part of student motivation and is defined as students’ beliefs about their ability to learn or perform specific tasks (Bandura, 1986, 1997). Students with high selfefficacy attempt difficult tasks and activities regularly and tend to achieve higher than students with low selfefficacy (Pajares, 1996; Schunk, 1991). Students with low selfefficacy generally give up on a learning activity when the results of success are not as they preferred, which can lead to lower success, and a further reduced sense of academic selfefficacy. High selfefficacy has been linked to higher grade point averages, standardized test 36 scores, persistence on a challenging task, and enrollment in upperlevel math courses (Pajares, 1996; Pintrich & Schunk, 2002). Students with high selfefficacy have a variety of characteristics that help them increase their achievement and success in the classroom (Schunk, 1981). These students try harder, and persevere longer than their lower selfefficacy counterparts (Bandura, 1982; Bandura, 1986; Pajares, 2003; Pajares & Schunk, 2001) while having a strong sense of responsibility. They are more concerned with the subject, deeply involved in the classroom activities, and try different strategies when they meet difficulties, which lead to greater effort and success (Morgan & Jinks, 1999). Students with high selfefficacy set high expectations for themselves and produce behaviors to perform well (Maxwell, 1998) along with being comfortable and confidently approaching tasks (Schunk, 1991; Bandura, 1993). When these students are faced with a challenge, they put forth greater effort to overcome obstacles (Bandura, 1986, 1997) and spend more energy when encountering difficulties (Schunk, 1990) while being more relaxed and efficient when faced with a challenge (Bandura, 1993; Schunk, 1991). Students with higher math selfefficacy persist longer on difficult tasks and are more accurate in computations compared to students with lower math selfefficacy (Collins, 1985; Hoffman & Schraw, 2009). The students with low selfefficacy in writing were easily distracted from activities, wandered around the room, avoided writing tasks, gave up easily, and took a lot of time to write (Kim & Lorsbach, 2005). Other characteristics of low selfefficacy include a lack of strong achievement (Schunk, 1981), giving up easily and that leads to lower success (Morgan & Jinks, 1999). These students also may avoid specific choices (Bandura, 1982) and experience stress and ineffectiveness when faced with a challenge (Bandura, 1986, 1997). 37 Efficacy cues include performance outcomes where success in a task raises the selfefficacy and failure will lower it. Individuals can perceive their success or failure using attribution cues such as ability, effort, task difficulty, or luck (Frieze, 1980; Weiner, 1985). Bodily symptoms like sweating and trembling can symbolize physiological cues for determining efficacy. Selfefficacy can also be assumed to be a motivating factor and is correlated with characteristics of the learning environment such as goal orientation, high cohesion, satisfaction, and a low level of disorder and conflict (Anderson et al., 2004). Bandura (1997), Nichols (1996), and Pajares (1997) argued that student perceptions of selfefficacy have a positive impact on student motivation and achievement. Selfefficacy determines individual’s level of motivation which is reflected in how much effort they will exert and how long they will persevere. The stronger their selfefficacy, the more persistence, effort, and accomplishment they have (Bandura & Cervone, 1983, 1986; Weinberg, Gould, & Jackson, 1979). Selfefficacy can lead to selfaiding or selfhindering thought patterns, as well as personal goal setting. The higher their selfefficacy, the higher goals are set and the firmer the commitments to those goals (Locke et al., 1984; Taylor, Locke, Lee, & Gist, 1984). Student perceived selfefficacy affects their academic interest and motivation as well as management of stress (Bassi, Steca, Fave, & Caprara, 2007) while mediating the effect of skill, previous experience, mental ability, or other selfbeliefs on subsequent achievement (Pajares & Schunk, 2001). Additionally, Eccles, Midgley, Wigfield, Buchanan, Reuman, Flanagan, and MacIver (1993) suggested that achievement related activities selected by individuals are influenced by social contexts of the individual, like the classroom and family. 38 Student Attitudes and Achievement Student achievement in mathematics is impacted by environmental factors including the emotional response to math (Sousa, 2008). Math and reading have been the standard in the United States to determine the academic abilities of students. Over time, society has accepted the stigma that particular individuals are not able to achieve in the area of mathematics. This stigma stems from the interactions between parent, peer, and teacher (Sousa, 2008). Latterell (2005) surveyed students and found that most feel it is much more embarrassing to make nonmathematical mistakes than mathematical mistakes, therefore lessening the value of mathematic achievement and success among students. Despite the push to encourage females in the mathematical field, they still rate themselves less confident than their male peers (Morge, 2005). Researchers have shown that attitudes predict performance and students with positive attitudes about what they are learning achieve more than students with poor attitudes (Singh, Granville, & Dika, 2002). Ma and Kishor (1997) conducted a metaanalysis to investigate the relationship between student attitudes toward mathematics and student achievement in mathematics. They concluded that the results were statistically significant, but not enough for educational practice. Attitudes toward math and achievement were not strong in the elementary level, while the junior high level tended to be the most important period during which students shape their attitudes toward mathematics and then stabilize in high school (Ma & Kishor, 1997). Achievement can be predicted by socioeconomic status, aptitude, and prior achievement (Ma & Wilkins, 2007). Researchers have shown that there is a strong relationship between mathematics coursework and mathematics achievement (Campbell, Hombo, & Mazzeo, 2000; Meyer, 1998; Schmidt et al., 2001; U.S. Department of Education, 1997). Pajares (1996) stated 39 that students underestimating their mathematic capabilities, not their lack of skill, can lead to student avoidances of mathematic courses and careers. Students claim that their academic performance can be caused by certain factors within themselves (ability, effort, traits and disposition) or factors outside themselves (luck, ease, difficulty of the task, and help from the teacher) (Pajares, 1996). It is better for students to attribute their success to ability rather than effort because ability is more strongly related to motivation, selfefficacy, and skill development (Schunk & Gunn, 1986). Achievement affects interest; students who feel more competent may become more interested in the subject taught (Koller, Baumert, & Schnabel, 2001). Interest in mathematics clearly decreases from grade 7 to grade 12 (Baumert & Koller, 1998; Gottfried, Fleming, & Gottfried, 2001). Students who have mathematical accomplishments frequently also have higher levels of mathematics selfefficacy than students with fewer accomplishments. Researchers who have examined the correlation between teacher support and its effect on students have found that when teachers are perceived as supportive, students have greater academic achievement, higher student engagement, less problem behaviors, and more positive peer relations (Birch & Ladd, 1997; Hamre & Pianta, 2001: Skinner, Furrer, Marchand, & Kindermann, 2008). Perceived support from teachers positively contributes to students’ classroom functioning, motivation, and attitudes toward school (Ryan, Stiller, & Lynch, 1994; Wentzel, 1997, 1998). A study conducted by Malecki and Demaray (2006) focusing on 7th and 8th grade students found that perceived teacher support was strongly related to grade point average for students who were lower socioeconomic status (SES) then higher SES students. Anxiety and Achievement Math anxiety negatively affects students’ success (Thomas & Higbee, 1999) and learning processes (Aiken, 1970, 1976; McLeod, 1988; Sloan, Daane, & Geisen, 2002; Vinson, 2001). 40 Math anxiety is a frequent problem faced by educators (Bursal & Paznokas, 2006; Singh et al., 2002; Zettle & Raines, 2002). Smith (1997) defined math anxiety as students’ restlessness during mathematical operations and their fear or fright of failing exams and experience of physical stress that leads to negative math attitudes or dislike for mathematics (Akin & Kurbanoglu, 2011). Richardson and Suinn (1972) described math anxiety as “the feeling of tension that hampers the use of numbers and solving mathematical operations in individual’s daily life and in their academic ambits” (p. 551). Researchers have shown that math anxiety can seriously harm the performance of an individual of all ages and is negatively related to mathematical performance (Betz, 1978; Chiu & Henry, 1990; Frary & Link, 1983; Lee, 1992; Meece, Wigfield, & Eccles, 1990; Quilter & Harper, 1988). The symptoms of anxiety can make the individual seem as if he or she lacks the skills to perform well (Schunk, 1989) and have been found to be closely related to mathematic attitudes and selfefficacy (Akin & Kurbanoglu, 2011). Math anxiety is predicted negatively by selfefficacy (Hackett, 1985; Pajares & Graham, 1999) and can be considered a result of low selfefficacy, according to the social learning theory. A student who feels anxious about math can almost feel incapable of doing mathematics and vice versa. The stronger the selfefficacy, the more active the individual becomes in putting effort toward the task and the longer they will persist. Therefore, math anxiety can be a predictor of selfefficacy by the fact that higher anxiety in math has been related to lower levels of selfefficacy (Akin & Kurbanoglu, 2011). Students with math anxiety tend to have poor attitudes about math and avoid math courses, therefore the result is lower achievement scores (Beilcok, Gunderson, Ramirez, & Levine, 2010). The influence toward math anxiety is the relationship between the math work, the student, and the math class. When student math work is being assessed, math anxiety is 41 aroused. On the other hand, low achievement scores in math may not be connected to math anxiety, but a deeper connection with test anxiety indicating it was not the material giving them anxiety, it was the testing. Ashcraft and Faust (1994) compared achievement and anxiety as the math problems increased in rigor. As problems became more challenging, student anxiety increased. Anxiety also increased when students were performing the math assessment in an online, timed lab format. Furthermore, advanced math concepts result in increased math anxiety and more negative math attitudes (Betz, 1978). Galla and Wood (2012) researched how anxiety can impair student academic achievement. They included 139 children between the ages of 65 and 144 months old who were interviewed and surveyed about their emotional selfefficacy and anxiety using the Multidimensional Anxiety Scale of Children and SelfEfficacy Scale. Math performance was measured using the Stanford Achievement Test. They found that anxiety is negatively associated with performance on math assessments while revealing that students with a highperceived ability to cope with negative emotions were protected from anxiety related math impairments. High levels of anxiety negatively predicted the performance on the standardized math test. Additionally, this research indicated that high anxiety students who reported high levels of selfefficacy did not have evidence of anxiety during the math test; when students reporting a good emotional selfefficacy, buffered against anxiety related performance on the math exam. Shields (2005) suggested that five areas contribute to students’ math anxiety: teachers’ attitudes, curriculum, instructional strategies, the classroom culture, and assessment. Teacher attitudes greatly influence math anxiety and are the most dominating factor in molding student attitudes about mathematics (Harper & Daane, 1998; Ruffell, Mason, & Allen, 1998). By fourth grade, math anxiety surfaces because of the concrete to abstract curriculum shift (Sousa, 2008). 42 Ashcraft (2002) indicated that student performance in mathematics improves when anxiety is alleviated. Teacher Attitudes Teaching is cultural (Stevenson & Stigler, 1992) and it takes major impacts to make a meaningful change within our education society. Even with a major reform initiative for curriculum change, lasting changes would not occur without sustained professional development designed to change teachers’ beliefs and attitudes (Philipp, 2007). Teachers’ beliefs can be changed by examining students’ mathematical thinking, technology, curriculum, and gender (Philipp, 2007). Elementary teachers tend to have high levels of math anxiety (Brady & Bowd, 2005) and their attitudes toward math have shown to influence their instructional techniques and student attitudes toward math (Fennema, Peterson, Carpenter, & Lubinski 1990; Nespor, 1987). Techniques teachers use to bring math anxiety to the forefront include lecturing, using textbooks, lack of time to teach math, and lack of motivation to change their mathematic techniques (Relich, 1996). Elementary teachers care about children, but not necessarily about mathematics (DarlingHammond & Sclan, 1996). Professional development that aims to help teachers learn about children’s mathematical thinking can help teachers create rich instructional environments. These environments promote mathematical inquiry and understanding which can help decrease student negative attitudes toward math (Philipp, 2007). Ambrose (2004) studied the beliefs of preservice elementary school teachers who were a part of a field experience linked to a mathematics course. Ambrose examined two primary sources for beliefs  emotion packed experiences and cultural transmission. Emotion packed 43 experience includes a negative experience with a mathematical situation while a cultural transmission includes hidden curriculum within the culture of the classroom and society. Ambrose (2004) had preservice teachers interview kindergarten students and analyze their problem solving skills. The preservice teachers were very impressed with the problem solving skills of the kindergarten students and how much they had been taught in the first 2 weeks of school, while in reality, these students had been developing these skills their whole life. All children come to school with previous knowledge that educators build upon. This study indicated that teachers are likely to misinterpret student abilities from the onset. Teacher beliefs also have a great impact on student attitudes toward the content area. What teachers do in their classroom is a direct reflection of their personal beliefs (Cooney, 2001). Teachers’ personal interest in and enjoyment of mathematics will magnify the relationship between student achievement and student competence in mathematics (Harper & Daane, 1998). Teachers with greater enjoyment and interest of mathematics have a greater impact on student achievement and tend to reveal mathematical deficiencies of weaker students, which will reduce their perceived level of competence in mathematics (Bagaka, 2011). Identifying teachers with these characteristics could be one way to improve students’ selfefficacy and therefore, increase their performance in mathematics (Bagaka, 2011). Gunderson, Ramirez, Levine, and Beilock (2011) conducted research under the understanding that gender impacts math performance, math course selection, and math career paths. They believe that girls have a more negative math attitude that has been formed by their parents and teachers. Adult attitudes are likely to influence children and can cause intergenerational transmission of math attitudes. They also found that first grade teachers tend to perceive their best male students as more logical, more competitive, more independent, and 44 liking math more that their best female students. Elementary teachers attribute math success in boys to ability and effort, attribute girls’ failure to lack of ability, and attribute boys’ failure to lack of effort. In addition, they report teacher feedback delivered to students can lead students to formulate their abilities according to the teacher beliefs. For example, a teacher’s approach to praise, whether it is about intellect or nonintellect behaviors can lead to a positive or negative attitude. Boys and girls receive the same overall feedback about their intellect but student performance, behavior, neatness, and speaking clearly can differ by gender. They conclude that boys see their intellect as their strength while girls see nonintellectual behaviors (neatness and being good) as their strength. These gender differences begin as early as early elementary school. Many researchers have stated that teachers’ attitudes toward math can affect their students’ math attitude and achievement, but few have directly tested this relation (Akin, & Kurbanoglu, 2011; Midgley, Feldlaufer, & Eccles, 1989). Beilcok, Gunderson, Ramirez, and Levine (2010) found that female teachers’ math anxiety was related to female student math achievement. Findings suggested that teachers might show evidence of the dislike of math and confirm the stereotype for students. Teachers with low math teaching selfefficacy and high math anxiety could have behavior tendencies that reflect their perspectives in their classroom (Swars, Daane, & Geisen, 2010). Girls might be more aware of attitudes from their teacher and be influenced by the similarity in gender and viewing the teacher as a role model (Bussey & Bandura, 1984). These studies were the first steps in bringing forth the idea that teachers could be a main source of math anxiety and female negative attitudes toward math. It may be true, though, that the teacher who has low math anxiety and high teaching selfefficacy can break down these stereotypes for students. 45 Students will place high value, be motivated to engage in learning activities, and have high expectations for success in classroom settings that provide opportunities for them to fulfill their developmental needs; however, they tend to disengage from learning in classrooms that do not provide such opportunities (Wang, 2012). Supportive teacherstudent relationships and classrooms where students are provided a variety of motivation and engagement opportunities have shown to have a positive effect on students (Ryan & Deci, 2002; Wentzel, 1998; Wigfield, Byrnes, & Eccles, 2006). Positive teacherstudent relationships along with student sense of belonging or relatedness lead to successful development in school for learners (Furrer & Skinner, 2003). Teachers characterized as trusting, caring, and respectful of students provide the emotional support students need in order to approach, engage, and persist on academic learning tasks (Roeser & Eccles, 1998) which can lead to positive academic selfefficacy and values (Crosnoe, Johnson, & Elder, 2004). When students perceived teachers as being supportive, students are more likely to view themselves as academically competent and set higher educational goals (Wigfield, 2006). Additionally, students who perceive their teachers as caring have higher levels of interest and enjoyment in their schoolwork (Midgley, Feldlaufer, & Eccles, 1989), more positive academic ability (Ryan & Patrick, 2001), and greater expectancies for success in the classroom (Goodenow, 1993). Teacher student relationships that are healthy and appropriate can be considered one of the most important aspects of classroom environment (Doyle, 1986). Student perceptions of teacher interpersonal behavior are strongly related to student motivation and achievement in all subjects (den Brok, Brekelmans, & Wubbels, 2004; Wubbels & Brekelmans, 1998). Research on teacher student interpersonal behavior has suggested that teachers in science and mathematics class are perceived less favorably by students than teachers of other subjects (den Brok, Taconis, 46 & Fisher, 2010; Spinner & Fraser, 2005). Wubbles and Levy (1993) believed that the negative perception toward these subjects is due to instructional choices made by the teachers including wholeclass teaching and small problemsolving tasks which require correcting behavior which results in less favorable perceptions by students. Mathematics classes have also been perceived by students as passive, inflexible, and having dominant and intimidating teachers with lack of supportive academic atmosphere (Fauzan, Slettenharr, & Plomp, 2002). Multiple studies conducted show a positive relationship between interpersonal behavior and subjectrelated attitudes (Telli, den Brok, Cakiroglu, 2007; den Brok, Fisher, & Koul, 2005a). Teachers categorized as leading, helpful/friendly, and understanding were considered to have more positive ratings than teachers who were uncertain, dissatisfied, and admonishing (Maulana, Opdenakker, den Brok, & Bosker, 2011). A healthy interpersonal relationship may be more important for mathematics teachers than for any other subject because math teachers tend to be rated less favorably than other content area teachers. Conclusions Math anxiety is a great problem in our society. It has become expected and causes a lack of achievement for many individuals. These attitudes can come from many different aspects in an individual’s environment, including school experiences and home experiences (Akin & Kurbanoglu, 2011). When a student is in a classroom with a teacher who has a negative attitude toward mathematics, it can be transferred into the instruction, discussion, and time management decisions that are made by the teacher. Students, especially girls, pick up on these clues inadvertently given by the teacher and take it on as their own. Parents can reinforce this attitude at home in discussion with the child, as well as priorities aligned with the family (Ambrose, 2004). When attitudes are developed to negatively think about math, achievement suffers. The 47 negative emotion sends negative signals to the brain and therefore blocks out learning of math. Students begin to develop their attitudes toward learning starting in elementary school, but the crucial time period to develop student positive attitudes of mathematics is in junior high and solidifies in high school. Removing choice, timed tests, and emphasis on getting the right answer, versus emphasis on the thinking and cognition behind their answer, create negative attitudes toward mathematics in students (Akin & Kurbanoglu, 2011). Additionally, classroom environment has been researched extensively, as well as selfefficacy, but very few studies have looked at the relationship between the two (Spinner & Fraser, 2005; Wang, 2012). This study aims to examine this potential relationship. In Chapter 3, the research methodology is explained. In Chapter 4, the data collected is analyzed and results of the analysis are explained. In Chapter 5, the data are explained and applied to implications of a classroom setting. 48 Chapter 3 METHOD OF PROCEDURE In order for students to have strong skills in mathematics and the opportunity to pursue mathematics in their future, they must have a strong selfefficacy in that subject matter (Schunk & Pajares, 2004). The purpose of this study was to compare students’ perception of their classroom environment and their selfefficacy in mathematics. Classroom environment has been shown to be one of the most significant factors in students’ learning and attitudes in math and science (Fraser & Kahle, 2007). The classroom environment is a critical context for promoting the development of students’ educational and career interests (Simpkins, DavisKean, & Eccles, 2006). Classroom environment that promotes a positive selfefficacy could lead to increased success for more students. Few studies have been conducted comparing student selfefficacy to perceived classroom environment (Spinner & Fraser, 2005; Wang, 2012). Selfefficacy can be assumed to be a motivating factor and is correlated with characteristics of the learning environment such as goal orientation, high cohesion, satisfaction, and a low level of disorder and conflict (Anderson, Hamilton, & Hattie, 2004). Selfefficacy was found to affect goal level, task performance, goal commitment, and choice to set specific goals (Patrick, Kaplan, & Ryan, 2011). This finding also supported Bandura’s (1982) theory that past performance determines selfefficacy (Patrick et al., 2011). Selfefficacy has been found to be positively related to mastery goal structure, personal mastery goal orientation, effort, not cheating, satisfaction with learning, schoolrelated effort, and achievement (Ames & Archer, 1988; Anderman, 1999; Kaplan & Midgley, 1999; Murdock, Hale, & Weber, 2001). Pajares (1996) found that higher selfefficacy scores lead to better performance and persistence in engineering courses. Selfefficacy beliefs are powerful predictors of the choices that individuals make on a daily basis, the 49 level of effort that they put on the task, and their persistence toward facing challenges (Multon, Brown, & Lent, 1991). Research Design This quantitative study sought to describe the connection between classroom environment and students’ selfefficacy in mathematics. The researcher determined if a relationship exists between students’ mathematics selfefficacy and their perceived mathematics classroom environment. The collected data were scores provided by the individual participant’s answers to the My Classroom Inventory (MCI) (Fraser, Anderson, & Walberg, 1982) classroom environment questionnaire and selected selfefficacy items from the Patterns of Adaptive Learning Survey (PALS) (Midgley et al., 2000). Students in grades 4 through 12 in a small school district in North Texas completed two questionnaires. During November and December 2013, students were given the classroom environment assessment (My Classroom Inventory MCI) during their regular school day to determine how they perceive their mathematics classroom environment. Approximately 7 to 10 days later, students took the selfefficacy assessment (Patterns of Adaptive Learning SurveyPALS). Data were taken from both of these questionnaires and analyzed using the statistics program Statistical Program for Social Sciences (SPSS). Data collected from students included the items from both surveys and demographics. A multiple regression was used to answer Research Questions 1 and 2 to determine if the five different dimensions of classroom environment could predict high and low math selfefficacy. 50 This dissertation study addressed the following questions: 1. Which dimensions of classroom environment (cohesiveness, friction, satisfaction, difficulty, or competitiveness) are the best predictors of high mathematics selfefficacy for students? 2. Which dimensions of classroom environment (cohesiveness, friction, satisfaction, difficulty, or competitiveness) are the best predictors of low math selfefficacy for students? Population and Sample Participants included students enrolled in a math class from grades 4 through 12 in a single North Texas school district. The school district was chosen as a convenience sample. Parental permission and student consent forms were collected in November and data were collected during December 2013. Parental permission slips were available to parents electronically on the school website as well as through email. Students were also given a paper copy by their teacher and asked to take it home to have their parents sign. The researcher received the permission slips from the teachers and office staff members who collected the slips from students. The student assent letter was available to students the day they took both of the surveys. The researcher collected the student assent letters from the teachers who gave the surveys. All grades 4 through 12 students enrolled in a math course in the fall of 2013 took the two surveys but only those who had parent permission and student assent were included in the study. The school district superintendent had given prior permission to the researcher to collect the data (see Appendix K). The district includes students who are 73% White, 17% Hispanic, 6% Black, and 4% Other. This population also includes 20% low socioeconomic status. All students enrolled in a math 51 class were able to participate including those in special education or any having been retained. There were approximately 400 participants used in this research. Instrumentation In order to collect information from students’ perspectives, two surveys were given to the sample being studied. Students provided data on how they perceived their mathematics classroom environment as well as insight into their personal attitudes toward mathematics. My Classroom Inventory (MCI) Classroom climate instruments are used to describe naturalistic classrooms (Trickett & Moos, 1974), compare student perceptions of their current and ideal classroom (Sinclair & Fraser, 2002), compare classrooms that differ (Waxman, Anderson, Huang, & Weinstein, 1997), evaluate effectiveness of different types of interventions (Johnson & Johnson, 1983), and compare perceived classroom climate by gender (Sinclair & Fraser, 2002). In this study, the My Classroom Inventory (Fraser et al., 1982) (see Appendix A) was used to collect data regarding how students perceived their mathematics classroom environment. My Classroom Inventory (MCI) was developed as a simplified version of the Learning Environment Inventory (LEI) to be used for primary grades, but is also found to be useful for students at the junior high level (Fraser, 2011). This instrument has been used for providing teachers with feedback about their classrooms as well as the effects of classroom climate on student learning. MCI was originally given as a paper and pencil survey; however, this study presented the survey in an electronic format. Students took the survey as a class in their school computer lab. The survey included 38 items and the estimated time for completion was about 30 minutes. 52 My Classroom Inventory measures five dimensions of social climate and was carefully developed and extensively field tested (Fraser et al., 1982). The five dimensions include cohesiveness, friction, satisfaction, difficulty, and competitiveness. Each item in the five dimensions is answered with a simple yes or no and uses age appropriate wording. Cohesion is the extent to which students know, help, and are friendly toward each other and was measured using six items. Friction measures that amount of tension and quarreling among students and was measured using eight items. Satisfaction is the extent to how satisfied students are in the classroom and was measured using nine items. Difficulty is the extent to which students find difficulty with the work of the class and was measured using eight items. Competition includes the emphasis on students competing with each other and was measured using seven items. MCI was used in 2002, 2005, and 2008 by Barry Fraser in many different locations and subject areas in school to compare student actual and preferred classroom environment as well as to compare the different dimensions among the students who participated. MCI has been used to measure classroom environment in multiple cultures, ages and subject areas. MCI makes it possible for teachers to obtain reliable feedback information about the climate of their own classroom as perceived by their students. This instrument has been found to be reliable and valid in many different school settings and it is especially applicable for ethnically and culturally diverse students (Waxman & Chen, 2006). Patterns of Adaptive Learning Scales (PALS) The Patterns of Adaptive Learning Scales (see Appendix B) was used to collect data on student efficacy in mathematics. The student survey assesses personal achievement goal orientations, perception of teacher goals, perceptions for the goal structures in the classroom, achievementrelated beliefs, attitudes and strategies, and perceptions of parent and home life 53 (Midgley et al., 2000). PALS focuses on goal orientation theory and examines the relationship between learning environment, student motivation, affect, and behavior. Scales within the instrument are based on mastery and performance goals associated with maladaptive patterns of learning (Ames, 1992; Dweck, 1986; Nicholls, 1984). There are two parts of this survey, a student section and a teacher section; however, only portions of the 72 item student section were used for this research study. The items are measured with a 5point Likert scale including 1 not at all, 3 somewhat true, and 5 very true. While students completed the entire instrument, only mastery goal orientation and academic efficacy were analyzed to focus this instrument on high and low selfefficacy. A score for high math selfefficacy was computed as the mean of mastery goal orientation and academic efficacy items, while a score for low math selfefficacy was computed as the mean of academic selfhandicapping strategy items. The PALS instrument as a whole is a tool used to collect data on a variety of aspects of the student, although, this study focused solely on high and low selfefficacy. Only parts of the PALS instrument were used in data analysis in order to emphasize selfefficacy while the other scales were omitted. The PALS instrument was chosen because of its validity and reliability and there was no other appropriate mathematics selfefficacy instrument. Levpuscek and Zupancic (2009) used PALS with Sloven eighth graders and found that selfefficacy predicted students’ math achievement and that selfefficacy is a link to the relationship between teachers’ classroom behavior and students’ academic performance. Bong (2001) used PALS to measure the selfefficacy of 424 Korean middle and high school students. PALS scores were positively correlated with all school subjects for both middle and high school students, and found significant and positive correlation between mastery goal factors and self54 efficacy. Pajares, Britner, and Valiante (2000) used PALS to analyze middle school writing, science and math students. They found that goals were associated with writing selfefficacy and both writing and science selfconcept in middle school students. Furthermore, task goals were positively related to selfefficacy. Smith, Sinclair, and Chapman (2002) used PALS to correlate achievement and selfefficacy in Australian secondary students while also looking at states of depression, anxiety, and stress in students using an alternate tool. This study took place over the course of one year. They found that selfefficacy decreased over the course of the year and was found to be negatively related to ability goal orientation and positively related to task goal orientation. Additionally they found that as selfhandicapping strategies increased, selfefficacy would decrease. Validity and Reliability Both surveys have been measured for reliability and validity in order to ensure that these tools were appropriate for this study. Both instruments were altered only slightly to place the emphasis on mathematics. Items in both surveys were changed to focus on the math class rather than class. No other changes were made to the instruments. This change was very important for the data collection of this study. This study used the second version of MCI due to increased reliability over the previous version. The 1982 version of MCI was standardized with 2,305 seventh grade students in Tasmania, Australia using 100 classes (Fraser, Anderson, & Walberg, 1982). The reliability for cohesiveness was 0.67, friction was 0.67, difficulty was 0.62, satisfaction was 0.78, and competitiveness was 0.71. The alpha coefficient was used as the index of internal consistency reliability and indicates that each MCI scale has satisfactory reliability (Fraser et al., 1982). 55 Fisher and Fraser (1983) explored predictive validity by using a multiple regression analysis. The validity was adequate and was normed before controlling for pretest and general ability (16 and 12.1) and then after controlling for pretest and general ability (6.5 and 4.6) using p<0.05. These values support the instrument’s validity by showing the significant difference in the decrease in the values after controlling for variables in the normed data collection. The Patterns of Adaptive Learning Scale (PALS) has been used in nine school districts in three Midwestern states and administered to elementary, middle and high school levels. The normed population includes students of low and middle socioeconomic status with equal representation of males and females. The manual stated that the teacher and student surveys can be used together or separate (Midgley et al., 2000). PALS reliability was analyzed under the multiple scales included in the instrument and are as follows: mastery goal orientation was 0.85, performance approach goal orientation was 0.89, performanceavoid goal orientation was 0.74, classroom mastery goal structure was 0.76, classroom performance approach goal structure was 0.70, classroom performance avoid goal structure was 0.83, academic efficacy was 0.78, academic press was 0.79, academic selfhandicapping strategies was 0.84, avoiding novelty was 0.78, cheating behavior was 0.87, disruptive behavior was 0.89, selfpresentation of low achievement was 0.78, and skepticism about the relevance of school for future success was 0.83. These alpha coefficients indicate the instrument has an adequate reliability level (Midgley et al., 2000). Ross, Shannon, SalisburyGlennon, and Guarino (2002) found that PALS can successfully be used with students of younger and older grades. Procedures This research study began implementation in October 2013. Permission to move forward with data collection was given by the school district superintendent in May of 2013 and the 56 Texas A&M University Commerce Institutional Review Board (TAMUC IRB) committee in July of 2013. All fourth through twelfth grade students currently taking a math class at the time of the data collection were participants, however only data from students with parental consent and student assent were utilized in the study. The researcher met with the principals and teachers of the three schools housing fourth through twelfth grade students in order to discuss the purpose of this study and inform the educators about their part in supporting the study. In the beginning of the school year, information about the study was communicated in several ways. The researcher provided a video for teachers, parents, and students to watch for information on the study. The parent permission slip was located on the district website, communicated through a variety of emails, and given to students to hand deliver to their parents. Information used to recruit students can be found in Appendices F and G. Students watched an informative video about the study before receiving a parent permission slip. Teachers were asked to collect parent consent forms and administer the surveys. The researcher gained consent from parents before collection of data began. Consent form, assent form, and video script are found in Appendices D, C, and H. In November and December, 2013, students completed two surveys in the campus computer labs. The first survey was the My Classroom Inventory (MCI), which measured perceived classroom environment. Then within 10 days, students completed the Patterns of Adaptive Learning Scale (PALS) to measure student selfefficacy in mathematics. Each survey took participants about 30 minutes to complete. Data from students who did not have parent consent or student assent were not included in the analysis. Students took the surveys during the regular school day at a specified time. The survey was given through a password protected website from a computer program provided by the 57 school district. Students watched an instructional video before taking the surveys to inform them of the purpose of the study, expectations, and to put them at ease about taking the survey. Students were instructed to write their district ID number on both surveys in order to directly correlate the two surveys. Students who did not sign an assent form or have a signed consent form were noted and were deleted from the analyzed data set. Data Gathering The data collected included the MCI survey, PALS survey, and students’ demographics that included ID number, race, age, grade, gender, ethnicity, and math class currently enrolled (for example, fourth grade, Algebra, Calculus). Students took the MCI survey during the regular school day in a computer lab at a specified time and then within the next 10 days, the same students completed the PALS during the regular school day, in the computer lab at a specified time. Students were instructed to enter their district ID number on parent permission slip, student assent, and both surveys. ID numbers were used to match the two surveys and the permission slips in order to analyze only the data with permission. Students who did not sign the assent form and did not have parental permission to be in the study completed both surveys but their data were excluded from the analysis. A list of students who did not give parental permission or student assent was created using student ID number. This list of students was given to a district employee who removed the data of students who did not receive parent or student permission and generated a new coded ID number before providing the data to the researcher. The identity of the participants was protected by keeping the data secured through recoding of the ID numbers to prevent any future confidentiality concerns. The data collected from the survey were accessible only to the researcher and the one district employee. Once the 58 data were collected and analyzed, they were saved on an external hard drive and will be kept in a locked safe in the researcher’s house for three years and then deleted from the external hard drive after that time. Treatment of Data Analysis of the data was completed in the spring of 2014. Data were analyzed using SPSS, conducting multiple regressions to determine which of the dimensions of classroom environment could predict high or low math selfefficacy. The different dimensions of the classroom environment were represented by the independent variables while the high or low math selfefficacy score was the dependent variable. For the classroom environment dimensions, students scored each item as 1 = Yes and 0 = No, therefore, mean scores ranged from 0 to 1. Statements categorized as mastery goal orientation and academic efficacy were grouped to represent high selfefficacy and mean scores were computed. Academic selfhandicapping strategies were categorized as low selfefficacy statements and mean scores were computed. Scores ranged from 1 to 5, with 1 indicating not at all true and 5 indicating very true, therefore, mean scores ranged from 1 to 5. Assumptions were checked for normality, homogeneity of variance and multicollinearity. Effect size was assessed using R2. Summary In order to answer the research questions, fourth through twelfth grade math students in a single North Texas school district completed two surveys. The MCI examined how they perceived their classroom mathematics environment and the PALS measured student selfefficacy in mathematics. The data were analyzed in order to determine if there was a relationship between perceived math classroom environment and high and low math selfefficacy. 59 The results provide teachers with more information about how to approach math students within their classroom. The specific subgroups of classroom environment that are found to predict a positive selfefficacy in math will aid teachers with the most appropriate way to prepare lessons and conduct their class time in order to promote a positive selfefficacy and reduce negative selfefficacy in mathematics. 60 Chapter 4 ANALYSIS OF DATA The personenvironment fit theory states that an individual’s behavior is a function of the person and the environment (Lewin, 1935; Murray, 1938, 1951). Therefore, in a classroom, students are directly impacted by the environment created around them and their personal beliefs about themselves are impacted through it. Selfefficacy has been found to be a strong predictor of student performance in mathematics (Pajares & Miller, 1994). This study sought to determine if different constructs within a classroom environment can predict high and low math selfefficacy. Selfefficacy was measured using selected items from the Patterns of Adaptive Learning Scale (PALS) instrument (Midgley et al., 2000). High selfefficacy was measured using mastery goal orientation and academic efficacy statements from this instrument while low selfefficacy was measured using academic selfhandicapping strategies. Classroom environment was measured using the My Classroom Inventory (MCI) (Fraser, Anderson, & Walberg, 1982) survey, using five dimensions including cohesiveness, competitiveness, friction, difficulty, and satisfaction. All dimensions were created by the instrument authors and stated in the manual. Results Data were analyzed from approximately 400 students in a North Texas school district. The researcher was given permission from the school district, parents, and students to collect and analyze the data. Participants were 53% females (N = 217) and 47% males (N = 192). The sample included grades 412 with 46% of participants being fourth and fifth graders, 22% were in seventh and eighth grades, and 19% were high school students in ninth to 12th grade. Seventy61 five percent of participants were White, 10% were Hispanic/Latino, 6% were African American, 2% were Asian, and 6% were Other. Multiple regression analyses were used to answer both research questions. The five dimensions of the classroom environment survey—cohesiveness, competitiveness, friction, difficulty, and satisfaction–were used as the predictor variables for both analyses. These five measures were used to predict high math selfefficacy for question 1 and low math selfefficacy for question 2. Assumptions were checked for normality, homogeneity of variance, and multicollinearity. Effect size was assessed using R2. Research Question 1 Research Question 1 asked “Which dimensions of classroom environment (cohesiveness, friction, satisfaction, difficulty, or competitiveness) are the best predictors of high selfefficacy for students in mathematics?” Of the classroom environment dimensions, students scored the highest on satisfaction (mean = 0.67, s.d. = .20) and competitiveness (mean = 0.60, s.d. = .22) (see Table 1). The scores of the classroom environment scale were 0 and 1, therefore the mean falls between 0 and 1, with 1 being the highest score. The mean high selfefficacy score was 3.918 (s.d. = .85). Selfefficacy was scored on a scale of 1 to 5 with 5 being the highest score. Four out of the five predictor variables were significantly correlated with the criterion variable (see Table 1). The only predictor variable that was not significantly correlated to high selfefficacy was competitiveness (r = .068, p = .086). Cohesion, satisfaction, and competitiveness showed a positive correlation with high math selfefficacy, while friction and difficulty were negatively correlated with high math selfefficacy. 62 Table 1 Means, Standard Deviations and Intercorrelations for High SelfEfficacy, Cohesiveness, Friction, Satisfaction, Difficulty, and Competitiveness (N = 409) Predictor Variables Variable Mean SD 1 2 3 4 5 High SelfEfficacy 3.91 0.85 .231*** .318*** .407*** .193*** .068 Predictor variables 1. Cohesiveness 0.49 0.24 .472*** .238*** .036 .043 2. Friction 0.39 0.27 .096* .128** .320*** 3. Satisfaction 0.67 0.20 .119** .173*** 4. Difficulty 0.42 0.17 .179*** 5. Competitiveness 0.60 0.22 *p < .05; **p < .01, ***p < .001. The regression procedure showed that the model significantly predicted high math selfefficacy [F (5, 403) = 30.141, p< .001]. The adjusted R2 of .263 indicated that, of the total variability that existed in high math selfefficacy, 26.3% was associated with variability in cohesiveness, friction, satisfaction, difficulty, and competitiveness. The standardized beta coefficients were all statistically significant except for cohesiveness (see Table 2). Satisfaction had the highest standardized beta value, making it the most significant predictor of high math selfefficacy. Tolerance values indicated that multicollinearity was not a problem in this analysis. 63 Table 2 Multiple Regression Analysis Summary for Variables Predicting High Math SelfEfficacy (N = 409) Variable B Standard Error of B Cohesiveness .074 0.181 .021 Friction .958 0.164 .301*** Satisfaction 1.397 0.189 .334*** Difficulty .684 0.216 .139** Competitiveness .510 0.180 .132** Constant 3.294 0.190 Note. R2 = .263; F (5, 403) = 30.141, p< .001. *p < .05; **p < .01,***p < .001. Research Question 2 Research Question 2 asked “Which dimensions of classroom environment (cohesiveness, friction, satisfaction, difficulty, or competitiveness) are the best predictors of low selfefficacy?” Of the classroom environment dimensions, students scored lowest on friction (mean = 0.39, s.d = 0.27) and difficulty (mean = 0.42, s.d = 0.17) (see Table 3). The mean low selfefficacy score was 2.11 (s.d = 0.97). All of the predictor variables were significantly correlated to low selfefficacy (see Table 3). Cohesiveness and satisfaction showed a negative correlation with low math selfefficacy, while friction, difficulty, and competitiveness were positively correlated with low selfefficacy. 64 Table 3 Means, Standard Deviations and Intercorrelations for Low SelfEfficacy, Cohesiveness, Friction, Satisfaction, Difficulty, and Competitiveness (N = 409) Predictor Variables Variable Mean SD 1 2 3 4 5 Low SelfEfficacy 2.11 0.97
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Title  CLASSROOM ENVIRONMENT INFLUENCE ON STUDENT SELFEFFICACY IN MATHEMATICS 
Author  Croissant, Hillary P. 
Subject  Education; Mathematics education 
Abstract  CLASSROOM ENVIRONMENT INFLUENCE ON STUDENT SELFEFFICACY IN MATHEMATICS A Dissertation by HILLARY P. CROISSANT Submitted to the Office of Graduate Studies of Texas A&M UniversityCommerce in partial fulfillment of the requirements for the degree of DOCTOR OF EDUCATION May 2014 CLASSROOM ENVIRONMENT INFLUENCE ON STUDENT SELFEFFICACY IN MATHEMATICS A Dissertation by HILLARY P. CROISSANT Approved by: Advisor: Gilbert Naizer Committee: Tami Morton Katy Denson Head of Department: Martha Foote Dean of the College: Gail Johnson Dean of Graduate Studies: Arlene Horne iii Copyright © 2014 Hillary P. Croissant iv ABSTRACT CLASSROOM ENVIRONMENT INFLUENCE ON STUDENT SELFEFFICACY IN MATHEMATICS Hillary P. Croissant, EdD Texas A&M UniversityCommerce, 2014 Advisor: Gilbert Naizer, PhD This study aimed to find the characteristics of public school math classrooms and how they influence selfefficacy of students. Data were collected on math students in grades 4 through 12 in a North Texas school district. Two surveys were administered to students in the district. Within 10 days, the students completed a classroom environment survey, followed by a selfefficacy survey. Both surveys were electronic and administered during the school day. Student data were analyzed by conducting a simple linear regression in order to determine if a relationship existed between classroom environment and student selfefficacy. A multiple regression was used in order to determine which dimensions under classroom environment could predict a high or low selfefficacy. Data analysis was unable to generalize low selfefficacy in mathematics and classroom environment correlation due to a small effect size. High selfefficacy in mathematics was found to increase as cohesion and satisfaction would increase and high selfefficacy in mathematics would increase as friction and difficulty would decrease. v ACKNOWLEDGEMENTS “Teaching is a work of the heart” is a sign I have up in my classroom that reminds me that not only as a teacher can I make a difference, but I am impacted by all kinds of teachers throughout my life. I want to thank the many mentors and supporters from whom I have had the opportunity to be influenced by and taught. You have encouraged me, supported me, and given me the strength to complete this journey. I would like to thank my closest friends for supporting me throughout this journey. First, to my friend Wendy Ulrich for encouraging me to continue on this path while being my work spouse by ensuring me that I could be a teacher and student at the same time. Also, to Laura Ahrens for reminding me how fortunate I am to be on this adventure and keeping me passionate about the knowledge that I was gaining. My inspiration comes from my teachers from the past. This great idea started with my professors from Austin College—Jane White, Julia Shahid, and Barbara Sylvester—and my goal to be like them someday. I appreciate my mentors and support from administration and fellow teachers in my school district for their extended support. A special thanks goes out to my advisor Dr. Gilbert Naizer who has read and reread through my work, emailed and conferenced, and helped me make sure that I am the best that I could be. Also thank you to Katy Denson and Tami Morton for being a part of my dissertation committee and supporting my statistical and literary efforts. Jane Braddock and Kelli Knight for bringing snacks to class and being the perfect support system for this doctoral stage of life. Lastly I would like to thank my family for their continued support. My mom and dad for always being my number one fan as well as my parentsinlaw who support any crazy idea I come up with and ensure I have everything I need to be successful. Most of all I want to thank vi my husband Eric for putting up with the late nights, study sessions, and tears that come with the crazy life of being a doctoral student. You are my greatest supporter and sounding board, and I could not have done it without your continued love and motivation. Weston better be ready for a wild ride as a part of this family. This dissertation is dedicated to students who strongly dislike math in the hope that one day they will be positively impacted by a classroom or a teacher who instills the love of math in them so that it becomes a subject to be passionate about rather than despised. vii TABLE OF CONTENTS LIST OF TABLES ...........................................................................................................................x LIST OF FIGURES ....................................................................................................................... xi CHAPTER 1. INTRODUCTION .........................................................................................................1 Statement of the Problem .........................................................................................1 Purpose of the Study ................................................................................................3 Research Questions ..................................................................................................3 Research Hypotheses ...............................................................................................4 Theoretical Framework ............................................................................................4 Significance of the Problem ...................................................................................10 Method of Procedure..............................................................................................11 Definitions of Terms ..............................................................................................13 Limitations .............................................................................................................14 Delimitations ..........................................................................................................15 Assumptions ...........................................................................................................15 Organization of the Study ......................................................................................16 2. REVIEW OF THE LITERATURE .............................................................................17 Math Anxiety .........................................................................................................17 Classroom Environment.........................................................................................20 SelfEfficacy and Classroom Environment ..........................................................25 SelfEfficacy and Math ..........................................................................................30 SelfEfficacy and Achievement .............................................................................32 viii Student Attitudes and Achievement.......................................................................38 Anxiety and Achievement......................................................................................39 Teacher Attitudes ...................................................................................................42 Conclusions ............................................................................................................46 3. METHOD OF PROCEDURE......................................................................................48 Research Design.....................................................................................................49 Population and Sample ..........................................................................................50 Instrumentation ......................................................................................................51 Procedures ..............................................................................................................55 Data Gathering .......................................................................................................57 Treatment of Data ..................................................................................................58 Summary ................................................................................................................58 4. ANALYSIS OF DATA................................................................................................60 Results ....................................................................................................................60 Summary ................................................................................................................65 5. SUMMARY OF THE STUDY AND THE FINDINGS, CONCLUSIONS, IMPLICATIONS, AND RECOMMENDATIONS FOR FUTURE RESEARCH ......66 Summary of the Study ...........................................................................................66 Summary of the Findings .......................................................................................66 Conclusions ............................................................................................................67 Implications............................................................................................................71 Recommendations for Further Research ................................................................74 Summary ................................................................................................................75 ix REFERENCES ..............................................................................................................................76 APPENDICES .............................................................................................................................107 Appendix A. My Classroom Inventory .....................................................................................108 B. Patterns of Adaptive Learning Survey .................................................................111 C. Parent Permission Form .......................................................................................115 D. Child/Minor Agreement to Be in a Research Study ............................................119 E. District Agreement ...............................................................................................122 F. Parent and Student Recruitment Letters ..............................................................125 G. Demographic Survey ...........................................................................................127 H. Video Script .........................................................................................................129 I. Spanish Translation of Parent Letter....................................................................132 J. Spanish Translation of Parent Permission Form ..................................................134 K. Signed Site Letter .................................................................................................138 L. Tables 14.............................................................................................................141 VITA ...........................................................................................................................................144 x LIST OF TABLES TABLE 1. Means, Standard Deviations and Intercorrelations for High SelfEfficacy, Cohesiveness, Friction, Satisfaction, Difficulty, and Competitiveness .....................................................62 2. Multiple Regression Analysis Summary for Variables Predicting High Math SelfEfficacy ..............................................................................................................................63 3. Means, Standard Deviations and Intercorrelations for Low SelfEfficacy, Cohesiveness, Friction, Satisfaction, Difficulty, and Competitiveness .....................................................64 4. Multiple Regression Analysis Summary for Variables Predicting Low Math SelfEfficacy...........................................................................................................................................65 xi LIST OF FIGURES FIGURE 1. Theoretical Framework ........................................................................................................5 1 Chapter 1 INTRODUCTION Starting at a young age, people are very impressionable through interactions in their environment including at home, at school, and with peers. These impressions can be reinforced or changed throughout the student’s life. An impression that has been an epidemic in our society is the negative attitude toward mathematics. Having a negative attitude in mathematics can lead to lower achievement in mathematics and lack of interest in continuing to develop a knowledge base of this topic. This study aimed to examine existing research and add to the body of knowledge in order to create an environment for students that leads to an increase in mathematics selfefficacy and ultimately improves attitudes and achievement in mathematics. Statement of the Problem A 2005 Associated Press poll found that nearly 40% of adults strongly disliked mathematics in school, twice the percentage of adults who disliked other subjects (Philipp, 2007). The way individuals see mathematics can negatively or positively impact their attitude toward the subject. While students learn mathematics, they acquire skills, understand math’s value, how it is learned, who should learn it, and what is needed for engagement in mathematics understanding. Heller stated, “Be careful how you interpret the world; it is like that” (McFague, 2001, p. 39). This implies that the way that an individual makes sense of the world, not only defines the person for the world, but also the world for that person. The importance and need for math are emphasized in many areas of the world around us and in our life and workplace. Math is a significant part of the scientific and technical community our society has become, as well as our cultural heritage (National Council of Teachers of Mathematics [NCTM], 2000). The increase in the complexity of our everyday life 2 has raised the importance and significance of mathematics and the role it has in our society. Unfortunately, the level of difficulty and abstractness of math are a large reason why people have developed a negative view, attitude, or affect toward mathematics (Adeyemi, 2012). This negative view of educators can trickle down to students and lead to unsatisfactory achievement and participation in mathematics (Malmivuori, 2008). Lack of intrinsic motivation can lead to resistance toward mathematics and the learners’ selfperception will decline and difficulties in mathematics will increase (Royer & Walles, 2007). Students who have difficulties in math often have lower confidence in math and lower achievement in mathematics. Selfefficacy is defined by Bandura (1986) as “people’s judgments of their capabilities to organize and execute courses of action required to attain designated types of performances” (p. 391) and can be easily confused with attitudes. Attitudes toward math have been defined as “a liking or disliking of mathematics, a tendency to engage in or avoid mathematics activities, a belief that one is good or bad at mathematics, and a belief that mathematics is useful or useless” (Neale, 1969, p. 623). While both strongly reflect an individual’s feelings toward an area of focus, in this case mathematics, they are different through the fact that selfefficacy has a greater emphasis on the performance that is associated with the attitude rather than just the feeling. It is crucial that educators create learning environments that build students into adults that approach challenging math and science tasks with full force. Times where students shy away from these tasks should be limited. Educators need to be sure that they present environments where students are getting a positive feeling about how they do mathematics and want to do more. When students feel successful in a school setting, they are more likely to want to explore it further into their adult life. Classroom environment is a topic that needs to be explored so we can not only prevent students from avoiding math, but also encourage them to take it further. 3 Purpose of the Study The purpose of the study was to examine how a classroom and the environment created by the teacher and classmates can impact how students feel about their ability to do and be successful in mathematics. It focused on how students perceived their classroom environment and measured student attitudes toward mathematics in order to determine relationships between the two. The relationship between how the students perceived their classroom environment and their attitudes toward math was analyzed. The quantitative data collected gave insight into the classroom environment characteristics that foster negative and/or positive students’ selfefficacy in mathematics classrooms. This study determined how different characteristics of a classroom correlates to student selfefficacy in mathematics. The researcher sought to find what characteristics in a classroom environment are predictors of negative and/or positive attitudes toward mathematics. Emphasis was placed on examining how students feel about the environment created in a mathematics classroom and how their feelings toward mathematics were affected. Another emphasis of this research was to examine which classroom environment dimensions impact negative and positive student selfefficacy in mathematics. Research Questions This study addressed the following questions: 1. Which dimensions of classroom environment (cohesiveness, friction, satisfaction, difficulty, or competitiveness) are the best predictors of high selfefficacy for students in mathematics? 4 2. Which dimensions of classroom environment (cohesiveness, friction, satisfaction, difficulty, or competitiveness) are the best predictors of low selfefficacy for students in mathematics? Research Hypotheses The following null hypotheses reflect the research questions: 1. No relationship exists among the dimensions of classroom environment (cohesiveness, friction, satisfaction, difficulty, or competitiveness) and students’ high selfefficacy in mathematics. 2. No relationship exists among the dimensions of classroom environment (cohesiveness, friction, satisfaction, difficulty, or competitiveness) and students’ low selfefficacy in mathematics. Theoretical Framework Individuals’ behaviors and attitudes are caused by multiple variables including their environment, peer interactions, feedback from authority figures, and their personal experiences (Battistich, Solomon, Kim, Watson, & Schaps, 1995). In a classroom, all of these variables impact students and their behavior as well as selfefficacy toward the subject being taught. The following historical and current theories support these findings. These theories include the social cognitive theory, attribution theory, selfefficacy theory, person environment fit theory, and the expectancyvalue theory. Each theory supports different variables in this study. Figure 1 shows a visual representation of how each theory is directly connected to the current study. Selfefficacy is connected to the social cognitive theory, attribution theory, and expectancyvalue theory. Classroom environment is supported by the personenvironment fit theory. The social cognitive 5 theory is thinking about and reflecting over your behavior. Selfefficacy is impacted by the social cognitive theory because thinking leads to judgments created about oneself which impact individual future performance. The attribution theory causes individuals to think about why they succeed or fail and these ideas can lead to future behaviors and performance. Expectancyvalue theory involves individual motivation in an area based on its value according to that individual. This can impact future performance from that individual, as well as selfefficacy. Personenvironment fit theory is based on how the environment impacts behavior. This directly connects to how a classroom is conducted, and the culture created within it can impact the students in it. Social Cognitive Theory Social cognitive learning theorists view human functioning as reciprocal interactions among behaviors of individuals, environmental variables, cognition, and personal factors (Bandura, 1986). When individuals perform a task, the perceived importance of the task is a large part of the result of the outcome expectation the individual has for the task. Bandura (1986) stated that beliefs determine expectations; therefore people generally value what they feel 6 capable of accomplishing and do not value the activities in which they have little confidence. Through selfreflection, individuals evaluate their own experiences and thought processes, which powerfully influences how they will behave in future tasks (Pajares, 1996). Bandura’s (1997) social cognitive theory proposed that selfefficacy is strongly affected by previous performance and influenced by observing others, verbal persuasion, and interpretation of physiological states, with possibilities that student perceptions of their learning environment also affect their efficacy. People are selforganizing, proactive, selfreflecting, selfregulating, nonreactive beings easily influenced by their environmental or inner impulses. People interpret their own behavior, which impacts their environment and personal impulses and can therefore alter their subsequent behavior. Pajares (2002) supported the idea that teachers can work to improve their students’ perception of school and students’ emotional state in order to selfcorrect false selfbeliefs and develop habits to improve their academic skill and selfregulatory practices. Additionally, society constructs values and standards that impact the ways students view themselves, depending on their approach and success with given tasks in the education system (Hickey & Granade, 2004). The social cognitive theory is based on the idea that people purposefully engage in their own development and can make things happen through their actions. Attribution Theory The attribution theory emphasizes the thought that for individuals who believe success is due to high ability and failure is due to lack of effort, motivation will remain constant. However, students who believe success is luck and failure is expected are less likely to be motivated (Diener & Dweck, 1978). Students or others who have always failed in the past in a specific task, attribute that failure to themselves, especially if they see others succeeding (Weiner, 2004). 7 The attribution theory is based on causal attributions that people make about the success or failure of their actions that will influence how they feel and how they expect to perform on future tasks or activities of the same nature (Weiner, 1986). The effect of children’s own perceptions of their ability to achieve success has a direct impact on their personal attitude toward math. Attributions influence motivation and performance through the meditational role of selfefficacy (Bandura, 1995; Schunk, 1991). SelfEfficacy Individuals’ selfefficacy influences how people feel, think, motivate themselves, and behave. Bandura (1997) described four major processes that are impacted by selfefficacy including cognitive, motivational, affective, and selection processes. Major focuses of cognition included the impact of comparing, feedback, and amount of control over a situation. Additionally, individuals that believe they will perform well will tend to perform well, while those that feel inferior will perform poorly. Students with high selfefficacy seem to participate more readily, work harder, persist longer, and achieve higher results. Bandura (1986) defined selfefficacy as “people’s judgments of their capabilities to organize and execute courses of action required to attain designated types of performances” (p. 391). Selfefficacy impacts almost every aspect of people’s lives and is the core of human motivation, wellbeing, and personal accomplishment. It influences individual choices, goals, emotional reactions, efforts, coping, and persistence (Gist, Mitchell, & Mitchell, 1992). When individuals are faced with adversity, selfefficacy determines their behavior (Pajares, 2002). Selfefficacy impacts motivation, affect, and actions based on the interaction of what the individual believes rather than what is actually true (Bandura, 1997). 8 Selfefficacy influences the choices that people make and how much effort they put into the tasks, their thought patterns, and their emotional reactions (Pajares, 2002). There are four different sources through which selfefficacy can be developed including mastery experience, vicarious experience, social persuasions, and somatic and emotional states. Mastery experience is the most influential source and is the act of individuals engaging in the actual task or activity and then interpreting the results of their actions. These interpretations are then used to develop a personal belief about their capability to perform the task or activity and then act in line with the beliefs they have created (Pajares, 2002). Researchers have shown that selfefficacy is related to the career path and choices made by individuals along with other decisional behaviors (Betz & Hackett, 1981, 1983; Lent, Brown, & Larkin, 1987). Also, selfefficacy can predict success and persistence in certain academic majors and is strongly related to achievement status (Multon, Brown, & Lent, 1991). Person Environment Fit Theory The personenvironment fit theory (Lewin, 1935; Murray, 1938, 1951) emphasizes the idea that behavior is a function of the person and the environment. There is a mutual relationship between the environment and person such that the environment influences behavior. Hunt (1975) emphasized the need for a match between the person and the environment in the course of learning. Early adolescents have an increase in a need for higher quality interactions with adults, sense of autonomy, and a sense of belonging (Eccles, et al., 1993; Kuperminc, Leadbeater, & Blatt, 2001; Midgley, Feldlaufer, & Eccles, 1989; Osterman, 2000). There is dual emphasis on the person and the environment and behavior, attitudes, and wellbeing are determined by both the person and the environment. Within the research under personenvironment fit theory, the feeling gained by the individual arises not from the person or environment but rather by his or 9 her fit or congruence with one another (Edwards, Caplan, & Harrison, 1998). Classroom environments have a culture of their own created by the people within and surrounding it. The environment created has an impact on the individuals that are a part of it, which include the students. This theory supports the concept that the environment created has an impact on the behavior of those that are a part of the environment, in this case, with emphasis on the students. Expectancyvalue Theory The expectancy value theory emphasizes how motivation is a primary result of an individual’s belief about the outcome of a specific activity and the importance placed on that outcome (Atkinson, 1957; McClelland, 1985; Rotter, 1982). Individuals will be motivated to participate in tasks if they find value in the outcome of that particular task and will not be motivated to take part in a task if they do not find value in the outcome. Researchers have agreed that competence in completing a task plays a crucial role if the task will be valued by the individual (Eccles, 1983; Wigfield & Eccles, 1992). Bandura (1986) emphasized that outcome expectation will have a stronger influence on the motivation and predicting behavior of the task performed. Bandura stated that personal judgments of the individual’s competence are different than the individual’s judgment of the likely outcome from the task. Those who expect success will behave in such a way in order to achieve that goal. The opposite is also true; if individuals expect failure, they will be more likely to fulfill that belief (Pajares, 1996). According to Eccles (2009), achievement related behaviors like course selection and occupational aspiration are most directly influenced by the individual’s expectation for success. Research has indicated that students who are most likely to take math courses and to aspire to math focused careers place higher value and have greater confidence in their math abilities than those who do not (Eccles, 2007). 10 The expectancyvalue theory also shows that the feedback students receive on their academic performance influences their motivational beliefs and academic choices (Eccles, 2009). Wang (2012) concurred; he found that students who earned higher grades in math also reported higher math expectancies and subjective task values, and were more likely to continue with course work in math and have mathrelated jobs in the future. Significance of the Problem Students in our colleges are straying away from majoring in mathematics intensive fields because of the lack of selfefficacy in this area (Committee on Science, Engineering, and Public Policy, 2007). This shortage of math majors and graduates has put the United States behind in mathematics, science, and technology development. The Industrial Revolution spawned a multitude of engineering endeavors that spring boarded the economy in the United States (Committee on Science, Engineering, and Public Policy, 2007). Many areas of our life including transportation, communication, agriculture, education, health, defense, and employment opportunities are available due to the investment in scientific research and engineering (Popper & Wagner, 2002). The United States has been considered a leader in science and engineering activities since the early 1900s with 30% of the world’s scientists and engineers as well as 17 of the world’s top 20 universities (Freeman, 2005). With the reputation so high in the US, other countries have stepped up and increased their competitiveness with the US over the past 20 years. This changing global market requires the US to produce not only more engineers, but higher quality engineers that are needed to be worldwide leaders in this hightech production market. High school graduates pursuing engineering degrees are declining (Noeth, Cruce, & Harmston, 2003), and less than half the freshmen who begin college with engineering as their major finishing with an engineering degree (BesterfieldSacre, Atman, & Shuman, 1997). One 11 attempt to solve this problem is to increase the number of students choosing to study engineering (Fantz, Siller, & Demiranda, 2011). Mathematics is a crucial piece of many fields, including the engineering field. Without mathematics, problem solving, process formation, and application would find disconnect within this field of study. This research study helps to determine what characteristics of classrooms can lead to a low or high selfefficacy in mathematics. Using this information, educators will be able to determine what they can do in their classroom to encourage high mathematics selfefficacy in their students and eliminate characteristics that tend to form a lower selfefficacy. This will lead to improved math interest and achievement as well as an increase in students in mathematic career fields. This boost in mathematics in America could jump start the society with improvement in areas like Science, Technology, Engineering, and Mathematics (STEM) fields. Method of Procedure This research study sought to determine what characteristics of the mathematic classroom environment could predict high or low student selfefficacy in mathematics. Two surveys were administered to participants in order to collect data. The data were then analyzed using multiple regression. Selection of Sample Participants for this study included students in fourth through 12th grade in a small North Texas school district. Only participants with parent permission and student assent were included in the data analysis. The school district superintendent gave prior permission for the researcher to collect the student data. Approximately 400 students participated in this study. 12 Instrumentation The Patterns of Adaptive Learning Scale (PALS) (Midgley et al., 2000) instrument as a whole is a tool used to measure a variety of learning aspects of the student. This study focused solely on high and low selfefficacy, therefore, only parts of the PALS instrument were used in data analysis to emphasize selfefficacy rather than the other student scales. The PALS instrument was chosen because of its validity and reliability and there was no other appropriate mathematics selfefficacy instrument. Selfhandicapping is associated with maladaptive behavior which leads to low selfefficacy (Patrick, Kaplan, & Ryan, 2011), therefore low selfefficacy was measured using the statements under “academic selfhandicapping strategies” (p. 368). Selfefficacy also has been found to be positively related to mastery goal structure, personal mastery goal orientation, effort, not cheating, satisfaction with learning, schoolrelated effort, and achievement (Ames & Archer, 1988; Anderman, 1999; Kaplan & Midgley, 1999; Murdock, Hale, & Weber, 2001). Therefore, high selfefficacy was measured by analyzing the statements that fall under “mastery goal orientation” and “academic efficacy”. Students also took the My Classroom Inventory (MCI) (Fraser, Anderson, & Walberg, 1982) which measured students’ perception of the classroom environment in their mathematics classroom. The MCI measures five dimensions of social climate, including cohesiveness, friction, satisfaction, difficulty, and competitiveness. Collection of Data Students took the two separate surveys, in an electronic version, during the regular school day in their computer lab, the MCI. My Classroom Inventory (MCI) and the selected items from the Patterns of Adaptive Learning Survey (PALS) (Midgley et al., 2000) were used to collect and 13 analyze data from the students. Students entered some demographic information on both surveys, including their ID number in order for their surveys to be matched by a district employee for analysis. The ID number is a school district issued number that students are familiar with and use on a daily basis. Student ID numbers were removed before data were given to the researcher. Treatment of the Data The data were collected and analyzed using Statistical Program for Social Sciences (SPSS) through conducting two multiple regressions to determine which dimensions of classroom environment can predict a high or low math selfefficacy. Student demographics were reported. Definitions of Terms The following terms are used in the present study: Classroom environment. Classroom environment involves interpersonal relationships with peers, relationships between students and their teacher, the relationship between students, the subject studied and teaching methods, in addition to student perceptions of structural characteristics of the class (Fraser et al., 1982). In this study, classroom environment was measured by My Classroom Inventory (MCI) (Fraser et al., 1982). The five subscales under classroom environment are listed below: Cohesiveness extent to which students, know, help and are friendly toward each other; Friction amount of tension and quarrelling among students; Satisfaction extent of enjoyment of class work; Difficulty the extent to which students find difficulty with the work of the class; and Competitiveness emphasis is placed on students competing with each other. 14 High selfefficacy. High selfefficacy is defined as mastery goal orientation and academic efficacy. High selfefficacy was measured by Patterns of Adaptive Learning Survey (PALS) (Midgley et al., 2000) using the “mastery goal orientation” and “academic efficacy” scales. Low selfefficacy. Low selfefficacy is defined as looking at student attribution through “academic selfhandicapping strategies”. Low selfefficacy was measured by Patterns of Adaptive Learning Survey (PALS) (Midgley et al., 2000) using the academic selfhandicapping scale. Mathematics selfefficacy. Selfefficacy of students specifically in the mathematics classroom and academic area of math (Bagaka, 2011). Mathematics classroom. Mathematics classrooms ranged from a selfcontained elementary classroom to a dual credit calculus classroom. Selfefficacy. Selfefficacy was defined by Albert Bandura (1994) as “the belief in one’s capabilities to organize and execute the courses of action required to manage prospective situations” (p. 72). It measures how people think, feel, and behave in certain situations and their personal opinion of how they can succeed in that environment. Students. Students are defined as children from fourth through 12th grades who were approximately age 9 to 19. Limitations The limitations of this study were as follows: 1. The district selected has a small population and limited subgroups (ethnicity, socioeconomic status, languages spoken). 2. The sampled participants were not an exact representation of the population of the 15 school district due to the requirements needed for students to participate. 3. Students completed the surveys on a computerbased survey system that could cause students to make mistakes by incorrectly clicking an answer they do not want. 4. Previous experiences and events that occur prior to students taking the surveys were not controlled by the researcher and could impact the results of the survey. Delimitations The delimitations of this study were as follows: 1. The data were collected from one school district. 2. The data were collected with limited student subgroups. 3. Only the student section of the PALS survey was used to measure students’ perception of classroom environment in mathematics classrooms. No data were collected using the teacher portion of the instrument. 4. The data were collected within a 10day time period which could cause some difference in data collection and change in attitudes of the participants. 5. Only grades four through 12 were analyzed. 6. The researcher chose the order in which the students completed the surveys. Assumptions This study is based on the following assumptions: 1. Students responded accurately and honestly. 2. Teachers administrating the surveys did not impact student responses. 3. Math teachers did not alter their teaching in order to gain specific results from the data collected. 16 4. Both instruments are valid and reliable and the two surveys did not influence each other. Organization of the Study This dissertation is organized into five chapters. Chapter 1 includes a statement of the problem, purpose of the study, research questions, research hypotheses, theoretical framework, significance of the study, definitions of terms, limitations, delimitations, and assumptions. Chapter 2 includes related professional literature regarding selfefficacy and classroom environment in mathematics. In Chapter 3 is a discussion of the research methodology. Chapter 4 includes the analysis of the data; Chapter 5 includes a discussion of the findings and applications to education. 17 Chapter 2 LITERATURE REVIEW This study aimed to determine what dimensions of classroom environment predict high selfefficacy and low selfefficacy in mathematics. Students in a North Texas school district participated in taking two surveys. One survey measured their perception of the classroom environment of their math class while the other measured the high and low selfefficacy in mathematics. Data were analyzed using a multiple regression in order to determine what characteristics of the math class could predict high and low selfefficacy in mathematics. Selfefficacy plays a major role in individuals’ everyday lives. Many different variables can impact each individual’s selfefficacy, especially in the area of mathematics (Hackett & Betz, 1989). Students’ attitudes are influenced by many different things including parents, peers, school, teacher, and classroom environment (Klassen & Usher, 2010). This literature review examines the importance of a positive selfefficacy in students at all ages in the area of mathematics and explains why classroom environment, in regard to selfefficacy, needs to be studied further. Math Anxiety Mathematic anxiety is a worldwide concern. The root of the problem is in schools, where students are developing negative attitudes toward mathematics at a very early age (Ashcraft, 2002). Math anxiety can be described as “a feeling of tension that interferes with the manipulations of numbers and the solving of mathematical problems in academic and ordinary life situations” (Sousa, 2008, p. 171). Math anxiety has been defined as the feeling of tension, helplessness, mental disorganization and dread when one is required to work and manipulate math problems (Ashcraft & Faust, 1994). Math anxiety can conjure up feelings of apprehension, 18 dislike, fear and dread (McLeod, 1994). It can prevent students from interacting with situations that are math intensive and these students avoid upper level math courses (Akin & Kurbanoglu, 2011). Lazarus (1974) believed that mathematic anxiety developed in elementary and secondary grades. Researchers have shown that negative math experiences can start around third or fourth grade (Ashcraft & Ridley, 2005; Beilock, Gunderson, Ramirez, & Levine, 2010). Math anxiety occurs in people from all different race, gender, and age group and can be a product of the home, school, or society. Burns (1998) estimated that 60% of adults have a fear of mathematics. Students develop a fear of mathematics (math anxiety) through negative experiences in math classes or having a lack of selfconfidence with numbers (Sousa, 2008). These experiences and lack of confidence usually lead to fear of calculation, failure, and difficulty in mathematics. The fear causes their minds to go blank and then causes frustration, which leads to additional amnesia. Fear and anxiety is increased when time limits are added to the mathematics activity. Students who have developed math anxiety need help to replace the memory of failure with the possibility for success (Ashcraft, 2002). The most obvious consequence of math anxiety is poor achievement and poor grades in mathematics (Sousa, 2008). Poor performance can be caused by a chemical change happening in the brain through the biology of the body. Any kind of anxiety causes the body to release cortisol into the bloodstream. Cortisol is a hormone that refocuses the brain on the anxiety to determine what action to take to relieve the stress. While this is happening, the frontal lobe is no longer interested in learning or processing the mathematical operation while the brain is dealing with a threat to the individual’s safety. Therefore, the student cannot focus and has to cope with the frustration of inattention. As well as their inability to manipulate and retain numbers and expressions due to a disruption in the working memory (Ashcraft & Kirk, 2001). 19 Beilock, Gunderson, Ramirez, and Levine (2010) focused on how math anxiety can impact students, specifically girls. This study looked at how female elementary teacher’s math anxiety influences the female student’s achievement and how that compared to the male students. Students were first and second grade students who were given math assessments throughout the school year. Students were told two gender neutral stories about students who were good at math and the other was good at reading and then the students drew a picture of what each looked like. The pictures were coded and correlated with the math assessment finding that girls who had confirmed gender ability roles (boys are good at math, and girls are good at reading) performed worse on the math assessment than girls who did not. These girls also performed worse than the boys with these differences related to the anxiety that the teacher had about math. Harper and Daane (1998) studied the causes of math anxiety in preservice elementary teachers and found that the cause usually stemmed from elementary school and included fear of making mistakes, having the right answer, amount of time given for a task, word problems, and problem solving. Philippous and Christou (2003) studied preservice teachers in Greece and found that teachers with negative attitudes toward mathematics were slightly positively impacted when they understood the usefulness of the skill while the deeply rooted anxieties about mathematics did not seem to change. Ma (1999) found that there is a significant relationship between math anxiety and math achievement. Bretscher, Dwindell, Hey, and Higbee (1989) posited that students who learned math because they wanted to, had higher math achievement, therefore the motivation toward performing math increased the student achievement. Norwood (1994) found that the elements of math anxiety included a mixture of truancy, poor selfimage, poor coping skills, teacher attitude, and the emphasis on learning math through drill practice rather than understanding. Zakaria and 20 Nordin (2008) found that students who had a high math anxiety also had a low math achievement as well as the students with low math anxiety had high math achievement. Classroom Environment The term classroom environment refers to the social and psychological surroundings of the classroom (Fraser, 1991). The teacher is a part of and contributes to the classroom environment which influences choices and norms of the classroom (Shuell, 1996). Research has shown that the quality of classroom environment is a significant determinant of student learning (Fraser, 1994, 1998b). Early seminal work by Lewin (1935, 1936) and Murray (1938) recognized that both the environment and its interaction with personal characteristics of the individual are determinants of the human behavior. Students learn better when they perceive the classroom environment positively (Dorman, 2003). Research on classroom environment has been diverse and varied, but began with the work of Walberg (1979) and Moos (1974), who spawned additional research programs all over the world. While questionnaires were used greatly in the beginning of the classroom environment research, both quantitative and qualitative methods are the more typical route of researchers. The majority of classroom environment research has been done in science classrooms and very few have involved mathematics classrooms (Spinner & Fraser, 2005). Classroom environment has been shown to be the most significant factor in students’ learning and attitudes in math and science (Fraser & Kahle, 2007). The classroom environment is a critical context for promoting the development of students’ educational and career interests (Simpkins, DavisKean, & Eccles, 2006). There is evidence to suggest that classroom environment influences how well students achieve a range of desirable outcomes (Fraser, 2007). Research has supported the fact that the social environment of classrooms can significantly 21 impact students’ motivated behavior, specifically the level of friendship students feel for each other measured by students getting to know each other, helping each other, and working together (Fraser & Fisher, 1983; Trickett & Moos, 1974). Students have been found to achieve better in the types of classroom environments that they prefer (Fraser & Fisher, 1983). Teacher techniques that include the focus on memorization rather than understanding the concept are among the main sources of math anxiety. Math anxiety also stems from a classroom culture that searches for one right answer with no recognition or appreciation for the thinking the student goes through or their cognitive process. Flewelling and Higginson (2001) found that students who have rewarding and successful learning experiences with math were able to overcome their math anxiety. Math classrooms and teachers who focus on making sense of that mathematical process and not memorizing or being correct cultivate students who avoid math anxiety. Having a positive classroom environment is a valuable goal of education (Fraser, 2001). Describing the class through the actual participants, students are in a good position to make judgments about classrooms because they have experienced many different learning environments and have spent enough time in the class to form accurate opinions. While teachers can be inconsistent in daily behavior, there is usually a consistent picture of the traditions and features of the classroom environment. While observation is a strategy used to collect data on classroom environments, it does not tell the whole story about the students’ perspective. Classroom environment includes the relationships between students, teachers, and subject material (Fraser et al., 1982). Five components of classroom environment will be emphasized in this research including cohesiveness, friction, satisfaction, difficulty, and competitiveness. 22 Sinclair and Fraser (2002) conducted research that looked into three areas of classroom environment. They worked on developing an instrument (Middle School Inventory of Classroom Environments or ICE), collecting quantitative and qualitative data on typical classroom environments, and used the information so teachers could positively impact their classroom and students. Data were collected from about 745 students on their perceived and preferred classroom environments, along with data collected from ten teachers on their perceived and preferred classroom environments. Sinclair and Fraser also took part in classroom observations of the participating teachers. Analysis of the data collected compared the teacher and student preferred and perceptions of the classroom environment. A oneway analysis of variance (ANOVA) was used in order to analyze the data for each scale within the instrument. After initial scores were collected on the teachers and students, the researchers met with the teachers to share the information and determine what areas that the teacher wanted to improve upon in order to increase student perceived classroom environment. One teacher aimed to improve her students’ perceptions of involvement and teacher empathy in her class. The teacher worked on including students in the science lab preparation as well as assistance with class pet maintenance. Research done on classroom social climates has shown that classrooms characterized by cohesiveness, satisfaction, and goal directions are preferred by students and are associated with positive outcomes for students (Fraser, 1991). Students’ sense of autonomy and participation in decision making has also been shown to have positive effects for children (Lewin, Lippitt, & White, 1939). Having a caring environment conveys a set of values such as mutual respect, valuing individual members’ contributions, and obligation of each member to meet the needs of the community (Battistich, Solomon, Kim, Watson, & Schaps, 1995). Fraser (1998a), with 23 support from Goh, Young, and Fraser (1995) found associations between students’ perception of the classroom environment in mathematical classes and established that students with greater cohesiveness were linked to higher achievement for math and teacher support: task orientation and equity were linked with more positive attitudes and selfesteem. Cooperative classroom strategies are associated with improved peer relations and supporting mutual respect (Anderson, 2004). Johnson and Johnson (1991) found that cooperative learning environments lead to productive classrooms where students exert high effort to achieve positive and supportive relationships and psychologically healthy and socially competent students. In a teachercentered mathematics classroom that is controlled by rules, routines, and individual drilling, there is little room for student autonomy or social belonging within the mathematic learning. Studentcentered classrooms with teamwork and emphasis on meaning making give students many opportunities to have students’ needs met through a variety of approaches (Hannula, 2006). The degree to which a classroom is challenging can also influence academic selfefficacy. Challenging is defined as an environment where students are given progressively difficult tasks as their proficiency increases. Some researchers have suggested that challenging students can lead to a stronger belief in the student’s personal academic abilities (Battistich et al., 1995; Pajares, 1996). One of the essential ways to improve middle grade education is to establish a safe and healthy school environment (Jackson & Davis, 2000). Students can be placed at academic risk of failure because of the quality of their school and classroom learning environment (Montgomery & Rossi, 1994). Ineffective and dysfunctional classrooms and instructional learning environments have been uncovered in multiple middle schools (Midgley, Eccles, & 24 Feldlaufer, 1991; MacIver & Epstein, 1993; Waxman, Huang, & Padron, 1995). Middle schools are usually structured, formal, and less personal than elementary schools and students frequently become bored and alienated with an increase in teacher talk and lack of student involvement (Waxman et al., 1995). Middle school classes tend to be more teachercentered and discipline focused where teacher student relations and student decision making are not a focus (Feldlaufer, Midgley, & Eccles, 1988). Additionally, middle schools often do not encourage personal relationships even though caring and supportive environments are critical for students (Baker, 1998; Roeser, Midgley, & Urdan, 1996). Classroom environment needs to be a focus in the middle grades in order to increase student cognitive and affective outcomes (Fraser, 1998; Haertel, Walberg, & Haertel, 1981). Researchers have shown that cohesiveness, student satisfaction, and teacher support are positively related to student increase in academic achievement (Waxman, Read, & Garcia, 2008). Research has been devoted to comparing the perception students have of their classroom as one which is performance based or encourages mastery (Patrick, Kaplan, & Ryan, 2011). Classrooms structured around mastery goals focus on effort put into a task as well as the intrinsic value of learning. This is compared to the performancebased classroom that focuses on competition and natural ability. Previous research has found that classrooms based around the mastery goal model have higher academic selfefficacy (Friedel, Cortina, Turner, & Midgley, 2007). The degree to which students perceive their classroom as a caring environment also has an influence on selfefficacy. Teachers in these classrooms express personal interest in the students, provide emotional support, and create a comfortable atmosphere. Murdock and Miller (2003) suggested that students who perceive their teachers as caring are more likely to view themselves as more academically capable, set higher goals for themselves, and have significantly 25 higher selfefficacy. The effect of emotional support on math achievement was larger than on quantity of math instruction. Roeser et al. (1996) found that a greater sense of school belonging, along with an emphasis on effort, understanding, and beliefs that all students can learn, were associated with academic selfefficacy. Cowen, Work, Hightower, Wyman, Parker, & Lotyczewski (1991) found those students who perceive high levels of classroom competition, friction, and difficulty, felt less efficacy when approached with an academic challenge. McMahon, Wernsman, and Rose (2009) examined 149 fourth and fifth graders from diverse backgrounds in California that completed two selfreports on their perceived classroom environment. The MCI (My Classroom Inventory) was used to collect data from the students on their perceived classroom environment, school belongingness was measured using the Psychological Sense of School Membership Scale, and selfefficacy in language arts and math was also measured using a The Academic SelfEfficacy Scale. They found that satisfaction, cohesion, and school belonging were significantly and positively correlated along with difficulty, competitiveness and friction. Additionally, classroom environment and school belonging predict selfefficacy and lower difficulty predicted higher math and science selfefficacy. School belonging and satisfaction and cohesion did not significantly predict math and science selfefficacy. SelfEfficacy and Classroom Environment Consistent and convincing research gives evidence that the quality of the classroom environment is a significant determinant of student learning (Fraser, 1994). A positive learning environment can influence student academic achievement and attitudes (Fisher, Henderson, & 26 Fraser, 1995). Fraser (1994) indicated that student perceptions of learning environments are an important factor in explaining their cognitive and affective outcomes. In terms of selfefficacy and classroom climate, these factors play important roles in the learning environment (Pitkaniemi & Vanninen, 2012). Students are more likely to have greater expectancy values in math which can lead to students taking more math courses and pursuing a career in mathematics. These students can then encourage, cooperate, interact, and help their classmates and view the curriculum and teaching as meaningful and relevant to their lives when they perceive their teacher as understanding and supportive while having high expectations for their learning achievement (Wang, 2012). Teacher and school practices that promote students’ mathematical selfefficacy may not only promote mathematic achievements, but also could narrow the achievement gaps in mathematics as found by gender, socioeconomic status, and minority status (Bagaka, 2011). Selfefficacy predicts students’ math achievement, and there are reasons to suspect that the relationship between teachers’ classroom behavior and students’ academic performance are also positively correlated (Weinstein & McKown, 1998). Students carefully observe teacher’s verbal and nonverbal behaviors while developing selfbeliefs and academic behaviors based on these observations (Weinstein & McKown, 1998). When educators demonstrate a direct interest in student care and concern, as well as respect for their thoughts, opinions, and ideas, the outcome supports a decrease in student depressive symptoms and an increase in selfesteem (Reddy, Rhones, & Mulhall, 2003). Further et al. (1998) determined that affective teacher behavior including listening, respect, recognition, and fair treatment significantly influenced young adolescent motivation. Muller, Katz, and Dance (1999) established that students 818 years of age desire a personal connection with their teacher and yearn for the instructor to 27 maintain high academic expectations. Fairness is an additional characteristic that students retain from their educator in the classroom. Students identify with different ways teachers treat students associated with success and ability (Weinstein & McKown, 1998). The powerful relationship that grows between the teacher and student in the classroom plays a crucial role in developing the emotional, motivational, and academic behaviors of the student. Teacher support correlates directly with youth adjustment, achievement, social, and motivational development. While educators have a specialized focus of specific academic content, there needs to be an equal focus on student affect and socialemotional needs (Osterman, 2000). Through selfrecorded data, students show a decline in teacher support throughout school years (Reddy et al., 2003) as well as a decline in a sense of belonging over time (Anderman, 2003). The data from the mathematics selfreports suggest that students feel less valuable and see a lower persistence in middle school years. A supportive teaching style has been positively linked to student achievement. It has been found that if teachers’ academic support (the teacher cares about their learning, tries to help them learn, and wants them to do their best), academic press (the teacher checks for understanding and engagement), and mastery goal (the teacher emphasizes learning and understanding, focuses on student development) are all implemented in the classroom, student achievement improves (Goodenow, 1993; Kaplan & Midgley, 1999; Wentzel, 1994, 1997). Students who perceive that their math teachers take into account student relatedness and competence, and enforce positive demands on students’ academic work show more positive motivational beliefs and achieve higher grades. Students who perceive their teacher as responsive, helpful and recognizant of good work tend to perform better than their peers whose teachers are perceived as less supportive (Ambrose, 2004). These results support Slovene’s 28 findings of early adolescents’ perceptions of their teachers and motivational beliefs (selfefficacy and intrinsic motivation) (Puklek, 2001; Puklek, 2004). Selfefficacy beliefs are created through the individual’s interpretation of information from different internal and external sources (Bandura, 1997; Pajares, 2002). An external source of selfefficacy beliefs is verbal judgments that others provide about their capabilities. Teachers are a crucial element of the classroom environment. Students’ perception of affective teacher support can influence their enjoyment in mathematics. Math and science selfefficacy were significantly negatively correlated with difficulty, and positively correlated with language arts selfefficacy (Pajares, 2002). Predictors of selfefficacy include satisfaction and cohesiveness; difficulty, competitiveness, and friction, and school belonging. In terms of math and science selfefficacy, difficulty was the sole predictor when a selfefficacy test was given for the second time. Other variables that can impact selfefficacy are parental influence, teacherstudent and studentstudent interaction, teacher instructional techniques, and appropriate teacher support. Kaplan, Gheen, and Midgley (2002) suggested that students are more likely to have positive selfefficacy from mastering a subject rather than from performing a standard. This could explain the finding that perceived difficulty predicted math and science selfefficacy. When students have a perceived high academic selfefficacy, they exhibit a positive behavioral adjustment and social competence, greater selfconcept, and stronger relationships with peers and parents (Kuperminc, Blatt, & Leadbeater, 1997). Student academic selfefficacy is a strong predictor of academic engagement, persistence, academic effort and performance (Linenbrink & Pintrich, 1997). School environment significantly influences a student’s selfefficacy. 29 The relationship between academic effort and academic achievement in middle school is important because it has been found to predict math achievement in high school, which will directly impact the student in college (Wang & Goldschmidt, 2003). Previous theory and research suggested a positive relation between academic selfefficacy beliefs and academic outcomes of students (Bandura, 1997; Pajares & Graham, 1999). Lorsbach and Jinks (1999) suggested that student perceptions of their learning environment are influenced by student academic selfefficacy and can lead to an appreciation of what is happening in classrooms. As expected, students who reported a greater sense of belonging in their mathematics classroom were likely to report higher academic enjoyment (Wang, 2012). Researchers did not find any statistical significance between academic enjoyment and academic hopelessness, or between academic enjoyment and academic selfefficacy. Academic enjoyment proved to be a powerful connection with academic effort. Students who reported higher teacher affective support were likely to report lower academic hopelessness, which was associated with greater academic selfefficacy (Pekrun, Goetz, Frenzel, Barchfeld, & Perry, 2011). Academic hopelessness did negatively predict academic effort through its detrimental effect on academic selfefficacy. Students who reported high academic hopelessness were likely to report low academic selfefficacy belief and related to lower academic effort. Students who report higher academic selfefficacy tended to report greater academic success in mathematics. There was a positive correlation between teacher academic press and student motivational beliefs; students’ selfefficacy and mastery goal orientation in math were positively related to their math grade. Results also showed that level of parental involvement would predict student math grades, while the math teaching measures were the most powerful predictors of student selfefficacy in math (Battistich et al., 1995). The students’ ratings of math teachers’ 30 academic support contributed to student mastery goal orientation and math achievement. The perceptions of teacher academic press predicted student selfefficacy and mastery goal orientation in math and their math grade (Anderson, Hamilton, & Hattie, 2004). Overall, it was found that classroom environment does have an impact on student academic selfefficacy and the many different variables that can impact these relate to students and their experiences (Weinstein & McKown, 1998). SelfEfficacy and Math Selfefficacy in mathematics has been studied, but not in great detail. Math selfefficacy is a strong predictor of math performance (Pajares & Miller 1994, 1995). The selfefficacy theory states that perceived selfefficacy influences and is influenced by thought patterns, affective arousal, and choice behavior as well as task performance (Bandura, 1977, 1986). According to the social learning theory, selfefficacy expectations are an important factor in influencing math attitudes and math anxiety (Bandura, 1977; Hackett & Betz, 1981). Bandura (1986), Pajares (1996), and Schunk (1991) found that selfefficacy beliefs predict student performance in mathematics. Selfefficacy can also influence math performance as strongly as general mathematics ability (Pajares & Kranzler, 1995). Across ability levels, students who have high selfefficacy are more accurate in their mathematical computation and are more persistent when faced with a challenge when compared to students with low selfefficacy (Collins, 1985). Lloyd, Walsh, and Yailagh (2005) analyzed fourth and seventh graders in order to compare their math grades, math foundation skills, performance attributions, and selfefficacy looking specifically at gender differences. They found that boys and girls equally attributed their success to effort and fourth graders were more likely to attribute their success to effort when compared to seventh graders. Ability was the attribution that the majority of students believed 31 lead to success. Fourth graders were also more likely than seventh graders to attribute their success to help from their teachers than seventh graders. Fourth graders were more efficacious than seventh graders and girls tended to be underconfident while boys were overconfident; however, girls’ achievement met or exceeded boys’ achievement. Akin and Kurbanoglu (2011) examined the relationship between math anxiety and selfefficacy. Participants included 372 university students in Turkey who took the assessment RMARS (Revised Mathematics Anxiety Rating Scale) to measure anxiety, Mathematics Attitudes Scale to measure mathematic attitudes, and Motivated Strategies for Learning Questionnaire (MSLQ) to measure selfefficacy. They found that selfefficacy is a proximal determinant of math attitudes and selfefficacy and that math anxiety was predicted by negative selfefficacy. Overall, the stronger the selfefficacy, the more active are the individual’s efforts and the longer they will persist. Additionally, selfefficacy predicted negative attitudes and positive attitudes. Pajares and Miller (1996) found that math selfefficacy has stronger direct effects on mathematics problem solving than selfconcept, perceived usefulness, or prior experience. Judgments of individuals’ ability to solve math problems should be more strongly able to predict their ability to solve those problems than their confidence in their ability on math related tasks. Similarly, judgments of their ability to succeed in math related courses should predict their choice to enroll in math courses than should their confidence in their ability to solve specific problems or perform math tasks (Pajares, 1996). Schunk (1981) showed that teacher modeling increased persistence and accuracy on division problems by arising student selfefficacy, which had a direct effect on skill. Additionally, he found that student effort was attributed to feedback of prior performance. This behavior raised student selfefficacy expectations in elementary 32 students. Later, he also discovered that ability feedback had a stronger effect on selfefficacy and performance (Schunk & Gunn, 1986). SelfEfficacy and Achievement Selfefficacy contributes to personal goals individuals set for themselves, how much effort they will exert in order to perform a task, how long an individual will persevere when facing a challenge, and how resilient the individual is toward failures. Bandura (1982) found that selfefficacy is more strongly related to future and actual task performance than past performance. Selfefficacy is not concerned with specific skills an individual has but the judgments and selfbelief of what one can do with the skills they possess (Bandura, 1982). Several studies have established the strong positive connection between student selfefficacy and their academic performance (Pajares, 1996; Pajares & Graham, 1999). Selfefficacy has been shown to predict achievement outcomes in a variety of content areas including mathematics, science, and writing (Klassen & Usher, 2010; Pajares, 1996; Pajares & Urdan, 2006). Selfefficacy is also a powerful predictor of student achievement (AlHarthy, Was, & Isaacson, 2010; Andrew, 1998; Bandura, 1993; Barkly, 2006; Paulsen & Gentry, 1995; Schunk, 1989; Zimmerman, 2000). Bandura (1977, 1997) and Pajares (1996) found that higher selfefficacy scores leads to better performance and persistence in engineering courses. Selfefficacy is a taskspecific capability (Gist, Mitchell, & Mitchell, 1992) and a dynamic construct. The selfefficacy judgment from the individual changes over time as new information and experiences are gained (Bandura, 1989). Personal efficacy beliefs help individuals determine how much effort people will spend on an activity, for how long they will persevere when faced with a challenge, and how resilient they are when the odds are not in their favor (Pajares, 1996). Selfefficacy also 33 influences the thought patterns and emotional reactions of individuals. Selfefficacy beliefs are powerful predictors of the choices that individuals make on a daily basis, the level of effort that they put on the task, and their persistence toward facing challenges (Multon, Brown, & Lent, 1991). Individuals with low selfefficacy may view a challenge and think that it is more difficult than it really is, impacting their stress level, depression, and ability to best solve the problem. In contrast, high selfefficacy helps individuals create a feeling of confidence when approaching difficult tasks and activities (Pajares, 1996). Pekrun et al. (2011) found that focusing on academic enjoyment in a college classroom positively impacted selfefficacy, intrinsic and extrinsic motivation, academic effort, selfregulation, and academic performance. There are four factors that influence selfefficacy: mastery experience, vicarious experience, social persuasions, and somatic emotional state. Mastery experience, interpreting one’s own performance, is the most potent source of selfefficacy (Bandura, 1986, 1997). Prior experience will affect students’ initial belief in their personal capabilities. Those who perform well on the activity believe they are capable of furthering their abilities in that area. Individuals who experience challenge and difficulties may doubt their capabilities (Schunk, 1989). Actions perceived by the individual as successful typically raise selfefficacy and perceived failure lowers it. Positive feedback can enhance selfefficacy but can be short lived if efforts following the feedback are poor as students are generally not motivated to behave in ways that they believe will result in negative outcomes (Schunk, 1989). Research shows that mastery goal orientation is linked to positive, adaptive pattern of attributions, whereas a performance goal orientation was linked to a maladaptive, helpless pattern of attributions (Ames, 1992b; Dweck & Leggett, 1988). Under mastery goal orientation, students are more likely to see a strong link between effort and outcomes and make more effort attributions for success and failure (Schunk, Meece, & Pintrich, 34 2014). Students with performance goal orientation see effort and ability as inversely related, as opposed to the positive relation under mastery goal (Schunk et al., 2014). Selfefficacy has been found to be related to goal orientation and found that people with mastery goals have higher selfefficacy and better task performance than people with performance goals (Locke, Frederick, Lee, & Bobko, 1984; Locke & Latham, 1990; Wood, Bandura, & Bailey, 1990). Researchers have found links between mastery goals and judgments of selfefficacy are generally positive (Sakiz, 2011). As mastery goals were formed, Dweck and Leggett (1988) performed laboratory research that showed that students oriented toward mastery and learning maintained positive and adaptive selfefficacy beliefs and perceptions of competence in the face of difficult tasks. Mastery goals related positively to selfefficacy in college students enrolled in statistics courses (Bandalos, Finney, & Geske, 2003). Bong (2009), Kaplan and Midgley (1997), Middleton and Midgley (1997), Sakiz (2011), and Thorkildsen and Nicholls (1998) have also shown the same general pattern. Vicarious experience, observing the actions of others, is also another way that individuals obtain information about what they can do (Bandura, 1997; Schunk, 1987). Students who observe similar peers perform a task may believe that they are capable as well. This source of selfefficacy is not as strong as mastery experience, but when individuals are uncertain of their abilities or have little prior experience, they become more sensitive to it (Pajares, 2002). Selfefficacy can also be created through the result of social persuasions received from others in their environment. Efficacy will increase when individuals are being told they are capable by a trustworthy source. This can include verbal judgments from peers or adults and play an important role in the development of an individual’s selfbeliefs. Individuals compare themselves to others in their environment around them and evaluate themselves with those who 35 are similar in ability (Festinger, 1954). Lastly, anxiety, stress, arousal, and mood states fall under that category of somatic and emotional states and can influence selfefficacy. Strong emotional reactions to a task can foreshadow the anticipated success or failure of the outcome (Pajares, 2002). Bandura (1997) found that people live in psychic environments that are of their own making, so therefore, individuals have the capability to alter their own thinking and feeling to enhance their selfefficacy beliefs. Selfefficacy can change as a result of learning, experience, and feedback (Gist et al., 1992). Selfefficacy can affect individuals’ psychological wellbeing and performance while exerting some influence over their lives through the environments they select and environments they create. Personal efficacy affects each individual’s choices of activities to take part in. Those who believe they are not capable of a task will avoid it, but the same individual will be willing to take on an alternate activity they feel they are capable of completing or accomplishing (Wood & Bandura, 1989). Perceived selfefficacy also has an impact on the choice of the individual’s career path with stronger selfefficacy connecting to more career options they consider to be possible (Betz & Hackett, 1986; Lent & Hackett, 1987). Selfefficacy also enhances students’ memory performance by enhancing persistence (Berry, 1987). Academic selfefficacy can be seen as a part of student motivation and is defined as students’ beliefs about their ability to learn or perform specific tasks (Bandura, 1986, 1997). Students with high selfefficacy attempt difficult tasks and activities regularly and tend to achieve higher than students with low selfefficacy (Pajares, 1996; Schunk, 1991). Students with low selfefficacy generally give up on a learning activity when the results of success are not as they preferred, which can lead to lower success, and a further reduced sense of academic selfefficacy. High selfefficacy has been linked to higher grade point averages, standardized test 36 scores, persistence on a challenging task, and enrollment in upperlevel math courses (Pajares, 1996; Pintrich & Schunk, 2002). Students with high selfefficacy have a variety of characteristics that help them increase their achievement and success in the classroom (Schunk, 1981). These students try harder, and persevere longer than their lower selfefficacy counterparts (Bandura, 1982; Bandura, 1986; Pajares, 2003; Pajares & Schunk, 2001) while having a strong sense of responsibility. They are more concerned with the subject, deeply involved in the classroom activities, and try different strategies when they meet difficulties, which lead to greater effort and success (Morgan & Jinks, 1999). Students with high selfefficacy set high expectations for themselves and produce behaviors to perform well (Maxwell, 1998) along with being comfortable and confidently approaching tasks (Schunk, 1991; Bandura, 1993). When these students are faced with a challenge, they put forth greater effort to overcome obstacles (Bandura, 1986, 1997) and spend more energy when encountering difficulties (Schunk, 1990) while being more relaxed and efficient when faced with a challenge (Bandura, 1993; Schunk, 1991). Students with higher math selfefficacy persist longer on difficult tasks and are more accurate in computations compared to students with lower math selfefficacy (Collins, 1985; Hoffman & Schraw, 2009). The students with low selfefficacy in writing were easily distracted from activities, wandered around the room, avoided writing tasks, gave up easily, and took a lot of time to write (Kim & Lorsbach, 2005). Other characteristics of low selfefficacy include a lack of strong achievement (Schunk, 1981), giving up easily and that leads to lower success (Morgan & Jinks, 1999). These students also may avoid specific choices (Bandura, 1982) and experience stress and ineffectiveness when faced with a challenge (Bandura, 1986, 1997). 37 Efficacy cues include performance outcomes where success in a task raises the selfefficacy and failure will lower it. Individuals can perceive their success or failure using attribution cues such as ability, effort, task difficulty, or luck (Frieze, 1980; Weiner, 1985). Bodily symptoms like sweating and trembling can symbolize physiological cues for determining efficacy. Selfefficacy can also be assumed to be a motivating factor and is correlated with characteristics of the learning environment such as goal orientation, high cohesion, satisfaction, and a low level of disorder and conflict (Anderson et al., 2004). Bandura (1997), Nichols (1996), and Pajares (1997) argued that student perceptions of selfefficacy have a positive impact on student motivation and achievement. Selfefficacy determines individual’s level of motivation which is reflected in how much effort they will exert and how long they will persevere. The stronger their selfefficacy, the more persistence, effort, and accomplishment they have (Bandura & Cervone, 1983, 1986; Weinberg, Gould, & Jackson, 1979). Selfefficacy can lead to selfaiding or selfhindering thought patterns, as well as personal goal setting. The higher their selfefficacy, the higher goals are set and the firmer the commitments to those goals (Locke et al., 1984; Taylor, Locke, Lee, & Gist, 1984). Student perceived selfefficacy affects their academic interest and motivation as well as management of stress (Bassi, Steca, Fave, & Caprara, 2007) while mediating the effect of skill, previous experience, mental ability, or other selfbeliefs on subsequent achievement (Pajares & Schunk, 2001). Additionally, Eccles, Midgley, Wigfield, Buchanan, Reuman, Flanagan, and MacIver (1993) suggested that achievement related activities selected by individuals are influenced by social contexts of the individual, like the classroom and family. 38 Student Attitudes and Achievement Student achievement in mathematics is impacted by environmental factors including the emotional response to math (Sousa, 2008). Math and reading have been the standard in the United States to determine the academic abilities of students. Over time, society has accepted the stigma that particular individuals are not able to achieve in the area of mathematics. This stigma stems from the interactions between parent, peer, and teacher (Sousa, 2008). Latterell (2005) surveyed students and found that most feel it is much more embarrassing to make nonmathematical mistakes than mathematical mistakes, therefore lessening the value of mathematic achievement and success among students. Despite the push to encourage females in the mathematical field, they still rate themselves less confident than their male peers (Morge, 2005). Researchers have shown that attitudes predict performance and students with positive attitudes about what they are learning achieve more than students with poor attitudes (Singh, Granville, & Dika, 2002). Ma and Kishor (1997) conducted a metaanalysis to investigate the relationship between student attitudes toward mathematics and student achievement in mathematics. They concluded that the results were statistically significant, but not enough for educational practice. Attitudes toward math and achievement were not strong in the elementary level, while the junior high level tended to be the most important period during which students shape their attitudes toward mathematics and then stabilize in high school (Ma & Kishor, 1997). Achievement can be predicted by socioeconomic status, aptitude, and prior achievement (Ma & Wilkins, 2007). Researchers have shown that there is a strong relationship between mathematics coursework and mathematics achievement (Campbell, Hombo, & Mazzeo, 2000; Meyer, 1998; Schmidt et al., 2001; U.S. Department of Education, 1997). Pajares (1996) stated 39 that students underestimating their mathematic capabilities, not their lack of skill, can lead to student avoidances of mathematic courses and careers. Students claim that their academic performance can be caused by certain factors within themselves (ability, effort, traits and disposition) or factors outside themselves (luck, ease, difficulty of the task, and help from the teacher) (Pajares, 1996). It is better for students to attribute their success to ability rather than effort because ability is more strongly related to motivation, selfefficacy, and skill development (Schunk & Gunn, 1986). Achievement affects interest; students who feel more competent may become more interested in the subject taught (Koller, Baumert, & Schnabel, 2001). Interest in mathematics clearly decreases from grade 7 to grade 12 (Baumert & Koller, 1998; Gottfried, Fleming, & Gottfried, 2001). Students who have mathematical accomplishments frequently also have higher levels of mathematics selfefficacy than students with fewer accomplishments. Researchers who have examined the correlation between teacher support and its effect on students have found that when teachers are perceived as supportive, students have greater academic achievement, higher student engagement, less problem behaviors, and more positive peer relations (Birch & Ladd, 1997; Hamre & Pianta, 2001: Skinner, Furrer, Marchand, & Kindermann, 2008). Perceived support from teachers positively contributes to students’ classroom functioning, motivation, and attitudes toward school (Ryan, Stiller, & Lynch, 1994; Wentzel, 1997, 1998). A study conducted by Malecki and Demaray (2006) focusing on 7th and 8th grade students found that perceived teacher support was strongly related to grade point average for students who were lower socioeconomic status (SES) then higher SES students. Anxiety and Achievement Math anxiety negatively affects students’ success (Thomas & Higbee, 1999) and learning processes (Aiken, 1970, 1976; McLeod, 1988; Sloan, Daane, & Geisen, 2002; Vinson, 2001). 40 Math anxiety is a frequent problem faced by educators (Bursal & Paznokas, 2006; Singh et al., 2002; Zettle & Raines, 2002). Smith (1997) defined math anxiety as students’ restlessness during mathematical operations and their fear or fright of failing exams and experience of physical stress that leads to negative math attitudes or dislike for mathematics (Akin & Kurbanoglu, 2011). Richardson and Suinn (1972) described math anxiety as “the feeling of tension that hampers the use of numbers and solving mathematical operations in individual’s daily life and in their academic ambits” (p. 551). Researchers have shown that math anxiety can seriously harm the performance of an individual of all ages and is negatively related to mathematical performance (Betz, 1978; Chiu & Henry, 1990; Frary & Link, 1983; Lee, 1992; Meece, Wigfield, & Eccles, 1990; Quilter & Harper, 1988). The symptoms of anxiety can make the individual seem as if he or she lacks the skills to perform well (Schunk, 1989) and have been found to be closely related to mathematic attitudes and selfefficacy (Akin & Kurbanoglu, 2011). Math anxiety is predicted negatively by selfefficacy (Hackett, 1985; Pajares & Graham, 1999) and can be considered a result of low selfefficacy, according to the social learning theory. A student who feels anxious about math can almost feel incapable of doing mathematics and vice versa. The stronger the selfefficacy, the more active the individual becomes in putting effort toward the task and the longer they will persist. Therefore, math anxiety can be a predictor of selfefficacy by the fact that higher anxiety in math has been related to lower levels of selfefficacy (Akin & Kurbanoglu, 2011). Students with math anxiety tend to have poor attitudes about math and avoid math courses, therefore the result is lower achievement scores (Beilcok, Gunderson, Ramirez, & Levine, 2010). The influence toward math anxiety is the relationship between the math work, the student, and the math class. When student math work is being assessed, math anxiety is 41 aroused. On the other hand, low achievement scores in math may not be connected to math anxiety, but a deeper connection with test anxiety indicating it was not the material giving them anxiety, it was the testing. Ashcraft and Faust (1994) compared achievement and anxiety as the math problems increased in rigor. As problems became more challenging, student anxiety increased. Anxiety also increased when students were performing the math assessment in an online, timed lab format. Furthermore, advanced math concepts result in increased math anxiety and more negative math attitudes (Betz, 1978). Galla and Wood (2012) researched how anxiety can impair student academic achievement. They included 139 children between the ages of 65 and 144 months old who were interviewed and surveyed about their emotional selfefficacy and anxiety using the Multidimensional Anxiety Scale of Children and SelfEfficacy Scale. Math performance was measured using the Stanford Achievement Test. They found that anxiety is negatively associated with performance on math assessments while revealing that students with a highperceived ability to cope with negative emotions were protected from anxiety related math impairments. High levels of anxiety negatively predicted the performance on the standardized math test. Additionally, this research indicated that high anxiety students who reported high levels of selfefficacy did not have evidence of anxiety during the math test; when students reporting a good emotional selfefficacy, buffered against anxiety related performance on the math exam. Shields (2005) suggested that five areas contribute to students’ math anxiety: teachers’ attitudes, curriculum, instructional strategies, the classroom culture, and assessment. Teacher attitudes greatly influence math anxiety and are the most dominating factor in molding student attitudes about mathematics (Harper & Daane, 1998; Ruffell, Mason, & Allen, 1998). By fourth grade, math anxiety surfaces because of the concrete to abstract curriculum shift (Sousa, 2008). 42 Ashcraft (2002) indicated that student performance in mathematics improves when anxiety is alleviated. Teacher Attitudes Teaching is cultural (Stevenson & Stigler, 1992) and it takes major impacts to make a meaningful change within our education society. Even with a major reform initiative for curriculum change, lasting changes would not occur without sustained professional development designed to change teachers’ beliefs and attitudes (Philipp, 2007). Teachers’ beliefs can be changed by examining students’ mathematical thinking, technology, curriculum, and gender (Philipp, 2007). Elementary teachers tend to have high levels of math anxiety (Brady & Bowd, 2005) and their attitudes toward math have shown to influence their instructional techniques and student attitudes toward math (Fennema, Peterson, Carpenter, & Lubinski 1990; Nespor, 1987). Techniques teachers use to bring math anxiety to the forefront include lecturing, using textbooks, lack of time to teach math, and lack of motivation to change their mathematic techniques (Relich, 1996). Elementary teachers care about children, but not necessarily about mathematics (DarlingHammond & Sclan, 1996). Professional development that aims to help teachers learn about children’s mathematical thinking can help teachers create rich instructional environments. These environments promote mathematical inquiry and understanding which can help decrease student negative attitudes toward math (Philipp, 2007). Ambrose (2004) studied the beliefs of preservice elementary school teachers who were a part of a field experience linked to a mathematics course. Ambrose examined two primary sources for beliefs  emotion packed experiences and cultural transmission. Emotion packed 43 experience includes a negative experience with a mathematical situation while a cultural transmission includes hidden curriculum within the culture of the classroom and society. Ambrose (2004) had preservice teachers interview kindergarten students and analyze their problem solving skills. The preservice teachers were very impressed with the problem solving skills of the kindergarten students and how much they had been taught in the first 2 weeks of school, while in reality, these students had been developing these skills their whole life. All children come to school with previous knowledge that educators build upon. This study indicated that teachers are likely to misinterpret student abilities from the onset. Teacher beliefs also have a great impact on student attitudes toward the content area. What teachers do in their classroom is a direct reflection of their personal beliefs (Cooney, 2001). Teachers’ personal interest in and enjoyment of mathematics will magnify the relationship between student achievement and student competence in mathematics (Harper & Daane, 1998). Teachers with greater enjoyment and interest of mathematics have a greater impact on student achievement and tend to reveal mathematical deficiencies of weaker students, which will reduce their perceived level of competence in mathematics (Bagaka, 2011). Identifying teachers with these characteristics could be one way to improve students’ selfefficacy and therefore, increase their performance in mathematics (Bagaka, 2011). Gunderson, Ramirez, Levine, and Beilock (2011) conducted research under the understanding that gender impacts math performance, math course selection, and math career paths. They believe that girls have a more negative math attitude that has been formed by their parents and teachers. Adult attitudes are likely to influence children and can cause intergenerational transmission of math attitudes. They also found that first grade teachers tend to perceive their best male students as more logical, more competitive, more independent, and 44 liking math more that their best female students. Elementary teachers attribute math success in boys to ability and effort, attribute girls’ failure to lack of ability, and attribute boys’ failure to lack of effort. In addition, they report teacher feedback delivered to students can lead students to formulate their abilities according to the teacher beliefs. For example, a teacher’s approach to praise, whether it is about intellect or nonintellect behaviors can lead to a positive or negative attitude. Boys and girls receive the same overall feedback about their intellect but student performance, behavior, neatness, and speaking clearly can differ by gender. They conclude that boys see their intellect as their strength while girls see nonintellectual behaviors (neatness and being good) as their strength. These gender differences begin as early as early elementary school. Many researchers have stated that teachers’ attitudes toward math can affect their students’ math attitude and achievement, but few have directly tested this relation (Akin, & Kurbanoglu, 2011; Midgley, Feldlaufer, & Eccles, 1989). Beilcok, Gunderson, Ramirez, and Levine (2010) found that female teachers’ math anxiety was related to female student math achievement. Findings suggested that teachers might show evidence of the dislike of math and confirm the stereotype for students. Teachers with low math teaching selfefficacy and high math anxiety could have behavior tendencies that reflect their perspectives in their classroom (Swars, Daane, & Geisen, 2010). Girls might be more aware of attitudes from their teacher and be influenced by the similarity in gender and viewing the teacher as a role model (Bussey & Bandura, 1984). These studies were the first steps in bringing forth the idea that teachers could be a main source of math anxiety and female negative attitudes toward math. It may be true, though, that the teacher who has low math anxiety and high teaching selfefficacy can break down these stereotypes for students. 45 Students will place high value, be motivated to engage in learning activities, and have high expectations for success in classroom settings that provide opportunities for them to fulfill their developmental needs; however, they tend to disengage from learning in classrooms that do not provide such opportunities (Wang, 2012). Supportive teacherstudent relationships and classrooms where students are provided a variety of motivation and engagement opportunities have shown to have a positive effect on students (Ryan & Deci, 2002; Wentzel, 1998; Wigfield, Byrnes, & Eccles, 2006). Positive teacherstudent relationships along with student sense of belonging or relatedness lead to successful development in school for learners (Furrer & Skinner, 2003). Teachers characterized as trusting, caring, and respectful of students provide the emotional support students need in order to approach, engage, and persist on academic learning tasks (Roeser & Eccles, 1998) which can lead to positive academic selfefficacy and values (Crosnoe, Johnson, & Elder, 2004). When students perceived teachers as being supportive, students are more likely to view themselves as academically competent and set higher educational goals (Wigfield, 2006). Additionally, students who perceive their teachers as caring have higher levels of interest and enjoyment in their schoolwork (Midgley, Feldlaufer, & Eccles, 1989), more positive academic ability (Ryan & Patrick, 2001), and greater expectancies for success in the classroom (Goodenow, 1993). Teacher student relationships that are healthy and appropriate can be considered one of the most important aspects of classroom environment (Doyle, 1986). Student perceptions of teacher interpersonal behavior are strongly related to student motivation and achievement in all subjects (den Brok, Brekelmans, & Wubbels, 2004; Wubbels & Brekelmans, 1998). Research on teacher student interpersonal behavior has suggested that teachers in science and mathematics class are perceived less favorably by students than teachers of other subjects (den Brok, Taconis, 46 & Fisher, 2010; Spinner & Fraser, 2005). Wubbles and Levy (1993) believed that the negative perception toward these subjects is due to instructional choices made by the teachers including wholeclass teaching and small problemsolving tasks which require correcting behavior which results in less favorable perceptions by students. Mathematics classes have also been perceived by students as passive, inflexible, and having dominant and intimidating teachers with lack of supportive academic atmosphere (Fauzan, Slettenharr, & Plomp, 2002). Multiple studies conducted show a positive relationship between interpersonal behavior and subjectrelated attitudes (Telli, den Brok, Cakiroglu, 2007; den Brok, Fisher, & Koul, 2005a). Teachers categorized as leading, helpful/friendly, and understanding were considered to have more positive ratings than teachers who were uncertain, dissatisfied, and admonishing (Maulana, Opdenakker, den Brok, & Bosker, 2011). A healthy interpersonal relationship may be more important for mathematics teachers than for any other subject because math teachers tend to be rated less favorably than other content area teachers. Conclusions Math anxiety is a great problem in our society. It has become expected and causes a lack of achievement for many individuals. These attitudes can come from many different aspects in an individual’s environment, including school experiences and home experiences (Akin & Kurbanoglu, 2011). When a student is in a classroom with a teacher who has a negative attitude toward mathematics, it can be transferred into the instruction, discussion, and time management decisions that are made by the teacher. Students, especially girls, pick up on these clues inadvertently given by the teacher and take it on as their own. Parents can reinforce this attitude at home in discussion with the child, as well as priorities aligned with the family (Ambrose, 2004). When attitudes are developed to negatively think about math, achievement suffers. The 47 negative emotion sends negative signals to the brain and therefore blocks out learning of math. Students begin to develop their attitudes toward learning starting in elementary school, but the crucial time period to develop student positive attitudes of mathematics is in junior high and solidifies in high school. Removing choice, timed tests, and emphasis on getting the right answer, versus emphasis on the thinking and cognition behind their answer, create negative attitudes toward mathematics in students (Akin & Kurbanoglu, 2011). Additionally, classroom environment has been researched extensively, as well as selfefficacy, but very few studies have looked at the relationship between the two (Spinner & Fraser, 2005; Wang, 2012). This study aims to examine this potential relationship. In Chapter 3, the research methodology is explained. In Chapter 4, the data collected is analyzed and results of the analysis are explained. In Chapter 5, the data are explained and applied to implications of a classroom setting. 48 Chapter 3 METHOD OF PROCEDURE In order for students to have strong skills in mathematics and the opportunity to pursue mathematics in their future, they must have a strong selfefficacy in that subject matter (Schunk & Pajares, 2004). The purpose of this study was to compare students’ perception of their classroom environment and their selfefficacy in mathematics. Classroom environment has been shown to be one of the most significant factors in students’ learning and attitudes in math and science (Fraser & Kahle, 2007). The classroom environment is a critical context for promoting the development of students’ educational and career interests (Simpkins, DavisKean, & Eccles, 2006). Classroom environment that promotes a positive selfefficacy could lead to increased success for more students. Few studies have been conducted comparing student selfefficacy to perceived classroom environment (Spinner & Fraser, 2005; Wang, 2012). Selfefficacy can be assumed to be a motivating factor and is correlated with characteristics of the learning environment such as goal orientation, high cohesion, satisfaction, and a low level of disorder and conflict (Anderson, Hamilton, & Hattie, 2004). Selfefficacy was found to affect goal level, task performance, goal commitment, and choice to set specific goals (Patrick, Kaplan, & Ryan, 2011). This finding also supported Bandura’s (1982) theory that past performance determines selfefficacy (Patrick et al., 2011). Selfefficacy has been found to be positively related to mastery goal structure, personal mastery goal orientation, effort, not cheating, satisfaction with learning, schoolrelated effort, and achievement (Ames & Archer, 1988; Anderman, 1999; Kaplan & Midgley, 1999; Murdock, Hale, & Weber, 2001). Pajares (1996) found that higher selfefficacy scores lead to better performance and persistence in engineering courses. Selfefficacy beliefs are powerful predictors of the choices that individuals make on a daily basis, the 49 level of effort that they put on the task, and their persistence toward facing challenges (Multon, Brown, & Lent, 1991). Research Design This quantitative study sought to describe the connection between classroom environment and students’ selfefficacy in mathematics. The researcher determined if a relationship exists between students’ mathematics selfefficacy and their perceived mathematics classroom environment. The collected data were scores provided by the individual participant’s answers to the My Classroom Inventory (MCI) (Fraser, Anderson, & Walberg, 1982) classroom environment questionnaire and selected selfefficacy items from the Patterns of Adaptive Learning Survey (PALS) (Midgley et al., 2000). Students in grades 4 through 12 in a small school district in North Texas completed two questionnaires. During November and December 2013, students were given the classroom environment assessment (My Classroom Inventory MCI) during their regular school day to determine how they perceive their mathematics classroom environment. Approximately 7 to 10 days later, students took the selfefficacy assessment (Patterns of Adaptive Learning SurveyPALS). Data were taken from both of these questionnaires and analyzed using the statistics program Statistical Program for Social Sciences (SPSS). Data collected from students included the items from both surveys and demographics. A multiple regression was used to answer Research Questions 1 and 2 to determine if the five different dimensions of classroom environment could predict high and low math selfefficacy. 50 This dissertation study addressed the following questions: 1. Which dimensions of classroom environment (cohesiveness, friction, satisfaction, difficulty, or competitiveness) are the best predictors of high mathematics selfefficacy for students? 2. Which dimensions of classroom environment (cohesiveness, friction, satisfaction, difficulty, or competitiveness) are the best predictors of low math selfefficacy for students? Population and Sample Participants included students enrolled in a math class from grades 4 through 12 in a single North Texas school district. The school district was chosen as a convenience sample. Parental permission and student consent forms were collected in November and data were collected during December 2013. Parental permission slips were available to parents electronically on the school website as well as through email. Students were also given a paper copy by their teacher and asked to take it home to have their parents sign. The researcher received the permission slips from the teachers and office staff members who collected the slips from students. The student assent letter was available to students the day they took both of the surveys. The researcher collected the student assent letters from the teachers who gave the surveys. All grades 4 through 12 students enrolled in a math course in the fall of 2013 took the two surveys but only those who had parent permission and student assent were included in the study. The school district superintendent had given prior permission to the researcher to collect the data (see Appendix K). The district includes students who are 73% White, 17% Hispanic, 6% Black, and 4% Other. This population also includes 20% low socioeconomic status. All students enrolled in a math 51 class were able to participate including those in special education or any having been retained. There were approximately 400 participants used in this research. Instrumentation In order to collect information from students’ perspectives, two surveys were given to the sample being studied. Students provided data on how they perceived their mathematics classroom environment as well as insight into their personal attitudes toward mathematics. My Classroom Inventory (MCI) Classroom climate instruments are used to describe naturalistic classrooms (Trickett & Moos, 1974), compare student perceptions of their current and ideal classroom (Sinclair & Fraser, 2002), compare classrooms that differ (Waxman, Anderson, Huang, & Weinstein, 1997), evaluate effectiveness of different types of interventions (Johnson & Johnson, 1983), and compare perceived classroom climate by gender (Sinclair & Fraser, 2002). In this study, the My Classroom Inventory (Fraser et al., 1982) (see Appendix A) was used to collect data regarding how students perceived their mathematics classroom environment. My Classroom Inventory (MCI) was developed as a simplified version of the Learning Environment Inventory (LEI) to be used for primary grades, but is also found to be useful for students at the junior high level (Fraser, 2011). This instrument has been used for providing teachers with feedback about their classrooms as well as the effects of classroom climate on student learning. MCI was originally given as a paper and pencil survey; however, this study presented the survey in an electronic format. Students took the survey as a class in their school computer lab. The survey included 38 items and the estimated time for completion was about 30 minutes. 52 My Classroom Inventory measures five dimensions of social climate and was carefully developed and extensively field tested (Fraser et al., 1982). The five dimensions include cohesiveness, friction, satisfaction, difficulty, and competitiveness. Each item in the five dimensions is answered with a simple yes or no and uses age appropriate wording. Cohesion is the extent to which students know, help, and are friendly toward each other and was measured using six items. Friction measures that amount of tension and quarreling among students and was measured using eight items. Satisfaction is the extent to how satisfied students are in the classroom and was measured using nine items. Difficulty is the extent to which students find difficulty with the work of the class and was measured using eight items. Competition includes the emphasis on students competing with each other and was measured using seven items. MCI was used in 2002, 2005, and 2008 by Barry Fraser in many different locations and subject areas in school to compare student actual and preferred classroom environment as well as to compare the different dimensions among the students who participated. MCI has been used to measure classroom environment in multiple cultures, ages and subject areas. MCI makes it possible for teachers to obtain reliable feedback information about the climate of their own classroom as perceived by their students. This instrument has been found to be reliable and valid in many different school settings and it is especially applicable for ethnically and culturally diverse students (Waxman & Chen, 2006). Patterns of Adaptive Learning Scales (PALS) The Patterns of Adaptive Learning Scales (see Appendix B) was used to collect data on student efficacy in mathematics. The student survey assesses personal achievement goal orientations, perception of teacher goals, perceptions for the goal structures in the classroom, achievementrelated beliefs, attitudes and strategies, and perceptions of parent and home life 53 (Midgley et al., 2000). PALS focuses on goal orientation theory and examines the relationship between learning environment, student motivation, affect, and behavior. Scales within the instrument are based on mastery and performance goals associated with maladaptive patterns of learning (Ames, 1992; Dweck, 1986; Nicholls, 1984). There are two parts of this survey, a student section and a teacher section; however, only portions of the 72 item student section were used for this research study. The items are measured with a 5point Likert scale including 1 not at all, 3 somewhat true, and 5 very true. While students completed the entire instrument, only mastery goal orientation and academic efficacy were analyzed to focus this instrument on high and low selfefficacy. A score for high math selfefficacy was computed as the mean of mastery goal orientation and academic efficacy items, while a score for low math selfefficacy was computed as the mean of academic selfhandicapping strategy items. The PALS instrument as a whole is a tool used to collect data on a variety of aspects of the student, although, this study focused solely on high and low selfefficacy. Only parts of the PALS instrument were used in data analysis in order to emphasize selfefficacy while the other scales were omitted. The PALS instrument was chosen because of its validity and reliability and there was no other appropriate mathematics selfefficacy instrument. Levpuscek and Zupancic (2009) used PALS with Sloven eighth graders and found that selfefficacy predicted students’ math achievement and that selfefficacy is a link to the relationship between teachers’ classroom behavior and students’ academic performance. Bong (2001) used PALS to measure the selfefficacy of 424 Korean middle and high school students. PALS scores were positively correlated with all school subjects for both middle and high school students, and found significant and positive correlation between mastery goal factors and self54 efficacy. Pajares, Britner, and Valiante (2000) used PALS to analyze middle school writing, science and math students. They found that goals were associated with writing selfefficacy and both writing and science selfconcept in middle school students. Furthermore, task goals were positively related to selfefficacy. Smith, Sinclair, and Chapman (2002) used PALS to correlate achievement and selfefficacy in Australian secondary students while also looking at states of depression, anxiety, and stress in students using an alternate tool. This study took place over the course of one year. They found that selfefficacy decreased over the course of the year and was found to be negatively related to ability goal orientation and positively related to task goal orientation. Additionally they found that as selfhandicapping strategies increased, selfefficacy would decrease. Validity and Reliability Both surveys have been measured for reliability and validity in order to ensure that these tools were appropriate for this study. Both instruments were altered only slightly to place the emphasis on mathematics. Items in both surveys were changed to focus on the math class rather than class. No other changes were made to the instruments. This change was very important for the data collection of this study. This study used the second version of MCI due to increased reliability over the previous version. The 1982 version of MCI was standardized with 2,305 seventh grade students in Tasmania, Australia using 100 classes (Fraser, Anderson, & Walberg, 1982). The reliability for cohesiveness was 0.67, friction was 0.67, difficulty was 0.62, satisfaction was 0.78, and competitiveness was 0.71. The alpha coefficient was used as the index of internal consistency reliability and indicates that each MCI scale has satisfactory reliability (Fraser et al., 1982). 55 Fisher and Fraser (1983) explored predictive validity by using a multiple regression analysis. The validity was adequate and was normed before controlling for pretest and general ability (16 and 12.1) and then after controlling for pretest and general ability (6.5 and 4.6) using p<0.05. These values support the instrument’s validity by showing the significant difference in the decrease in the values after controlling for variables in the normed data collection. The Patterns of Adaptive Learning Scale (PALS) has been used in nine school districts in three Midwestern states and administered to elementary, middle and high school levels. The normed population includes students of low and middle socioeconomic status with equal representation of males and females. The manual stated that the teacher and student surveys can be used together or separate (Midgley et al., 2000). PALS reliability was analyzed under the multiple scales included in the instrument and are as follows: mastery goal orientation was 0.85, performance approach goal orientation was 0.89, performanceavoid goal orientation was 0.74, classroom mastery goal structure was 0.76, classroom performance approach goal structure was 0.70, classroom performance avoid goal structure was 0.83, academic efficacy was 0.78, academic press was 0.79, academic selfhandicapping strategies was 0.84, avoiding novelty was 0.78, cheating behavior was 0.87, disruptive behavior was 0.89, selfpresentation of low achievement was 0.78, and skepticism about the relevance of school for future success was 0.83. These alpha coefficients indicate the instrument has an adequate reliability level (Midgley et al., 2000). Ross, Shannon, SalisburyGlennon, and Guarino (2002) found that PALS can successfully be used with students of younger and older grades. Procedures This research study began implementation in October 2013. Permission to move forward with data collection was given by the school district superintendent in May of 2013 and the 56 Texas A&M University Commerce Institutional Review Board (TAMUC IRB) committee in July of 2013. All fourth through twelfth grade students currently taking a math class at the time of the data collection were participants, however only data from students with parental consent and student assent were utilized in the study. The researcher met with the principals and teachers of the three schools housing fourth through twelfth grade students in order to discuss the purpose of this study and inform the educators about their part in supporting the study. In the beginning of the school year, information about the study was communicated in several ways. The researcher provided a video for teachers, parents, and students to watch for information on the study. The parent permission slip was located on the district website, communicated through a variety of emails, and given to students to hand deliver to their parents. Information used to recruit students can be found in Appendices F and G. Students watched an informative video about the study before receiving a parent permission slip. Teachers were asked to collect parent consent forms and administer the surveys. The researcher gained consent from parents before collection of data began. Consent form, assent form, and video script are found in Appendices D, C, and H. In November and December, 2013, students completed two surveys in the campus computer labs. The first survey was the My Classroom Inventory (MCI), which measured perceived classroom environment. Then within 10 days, students completed the Patterns of Adaptive Learning Scale (PALS) to measure student selfefficacy in mathematics. Each survey took participants about 30 minutes to complete. Data from students who did not have parent consent or student assent were not included in the analysis. Students took the surveys during the regular school day at a specified time. The survey was given through a password protected website from a computer program provided by the 57 school district. Students watched an instructional video before taking the surveys to inform them of the purpose of the study, expectations, and to put them at ease about taking the survey. Students were instructed to write their district ID number on both surveys in order to directly correlate the two surveys. Students who did not sign an assent form or have a signed consent form were noted and were deleted from the analyzed data set. Data Gathering The data collected included the MCI survey, PALS survey, and students’ demographics that included ID number, race, age, grade, gender, ethnicity, and math class currently enrolled (for example, fourth grade, Algebra, Calculus). Students took the MCI survey during the regular school day in a computer lab at a specified time and then within the next 10 days, the same students completed the PALS during the regular school day, in the computer lab at a specified time. Students were instructed to enter their district ID number on parent permission slip, student assent, and both surveys. ID numbers were used to match the two surveys and the permission slips in order to analyze only the data with permission. Students who did not sign the assent form and did not have parental permission to be in the study completed both surveys but their data were excluded from the analysis. A list of students who did not give parental permission or student assent was created using student ID number. This list of students was given to a district employee who removed the data of students who did not receive parent or student permission and generated a new coded ID number before providing the data to the researcher. The identity of the participants was protected by keeping the data secured through recoding of the ID numbers to prevent any future confidentiality concerns. The data collected from the survey were accessible only to the researcher and the one district employee. Once the 58 data were collected and analyzed, they were saved on an external hard drive and will be kept in a locked safe in the researcher’s house for three years and then deleted from the external hard drive after that time. Treatment of Data Analysis of the data was completed in the spring of 2014. Data were analyzed using SPSS, conducting multiple regressions to determine which of the dimensions of classroom environment could predict high or low math selfefficacy. The different dimensions of the classroom environment were represented by the independent variables while the high or low math selfefficacy score was the dependent variable. For the classroom environment dimensions, students scored each item as 1 = Yes and 0 = No, therefore, mean scores ranged from 0 to 1. Statements categorized as mastery goal orientation and academic efficacy were grouped to represent high selfefficacy and mean scores were computed. Academic selfhandicapping strategies were categorized as low selfefficacy statements and mean scores were computed. Scores ranged from 1 to 5, with 1 indicating not at all true and 5 indicating very true, therefore, mean scores ranged from 1 to 5. Assumptions were checked for normality, homogeneity of variance and multicollinearity. Effect size was assessed using R2. Summary In order to answer the research questions, fourth through twelfth grade math students in a single North Texas school district completed two surveys. The MCI examined how they perceived their classroom mathematics environment and the PALS measured student selfefficacy in mathematics. The data were analyzed in order to determine if there was a relationship between perceived math classroom environment and high and low math selfefficacy. 59 The results provide teachers with more information about how to approach math students within their classroom. The specific subgroups of classroom environment that are found to predict a positive selfefficacy in math will aid teachers with the most appropriate way to prepare lessons and conduct their class time in order to promote a positive selfefficacy and reduce negative selfefficacy in mathematics. 60 Chapter 4 ANALYSIS OF DATA The personenvironment fit theory states that an individual’s behavior is a function of the person and the environment (Lewin, 1935; Murray, 1938, 1951). Therefore, in a classroom, students are directly impacted by the environment created around them and their personal beliefs about themselves are impacted through it. Selfefficacy has been found to be a strong predictor of student performance in mathematics (Pajares & Miller, 1994). This study sought to determine if different constructs within a classroom environment can predict high and low math selfefficacy. Selfefficacy was measured using selected items from the Patterns of Adaptive Learning Scale (PALS) instrument (Midgley et al., 2000). High selfefficacy was measured using mastery goal orientation and academic efficacy statements from this instrument while low selfefficacy was measured using academic selfhandicapping strategies. Classroom environment was measured using the My Classroom Inventory (MCI) (Fraser, Anderson, & Walberg, 1982) survey, using five dimensions including cohesiveness, competitiveness, friction, difficulty, and satisfaction. All dimensions were created by the instrument authors and stated in the manual. Results Data were analyzed from approximately 400 students in a North Texas school district. The researcher was given permission from the school district, parents, and students to collect and analyze the data. Participants were 53% females (N = 217) and 47% males (N = 192). The sample included grades 412 with 46% of participants being fourth and fifth graders, 22% were in seventh and eighth grades, and 19% were high school students in ninth to 12th grade. Seventy61 five percent of participants were White, 10% were Hispanic/Latino, 6% were African American, 2% were Asian, and 6% were Other. Multiple regression analyses were used to answer both research questions. The five dimensions of the classroom environment survey—cohesiveness, competitiveness, friction, difficulty, and satisfaction–were used as the predictor variables for both analyses. These five measures were used to predict high math selfefficacy for question 1 and low math selfefficacy for question 2. Assumptions were checked for normality, homogeneity of variance, and multicollinearity. Effect size was assessed using R2. Research Question 1 Research Question 1 asked “Which dimensions of classroom environment (cohesiveness, friction, satisfaction, difficulty, or competitiveness) are the best predictors of high selfefficacy for students in mathematics?” Of the classroom environment dimensions, students scored the highest on satisfaction (mean = 0.67, s.d. = .20) and competitiveness (mean = 0.60, s.d. = .22) (see Table 1). The scores of the classroom environment scale were 0 and 1, therefore the mean falls between 0 and 1, with 1 being the highest score. The mean high selfefficacy score was 3.918 (s.d. = .85). Selfefficacy was scored on a scale of 1 to 5 with 5 being the highest score. Four out of the five predictor variables were significantly correlated with the criterion variable (see Table 1). The only predictor variable that was not significantly correlated to high selfefficacy was competitiveness (r = .068, p = .086). Cohesion, satisfaction, and competitiveness showed a positive correlation with high math selfefficacy, while friction and difficulty were negatively correlated with high math selfefficacy. 62 Table 1 Means, Standard Deviations and Intercorrelations for High SelfEfficacy, Cohesiveness, Friction, Satisfaction, Difficulty, and Competitiveness (N = 409) Predictor Variables Variable Mean SD 1 2 3 4 5 High SelfEfficacy 3.91 0.85 .231*** .318*** .407*** .193*** .068 Predictor variables 1. Cohesiveness 0.49 0.24 .472*** .238*** .036 .043 2. Friction 0.39 0.27 .096* .128** .320*** 3. Satisfaction 0.67 0.20 .119** .173*** 4. Difficulty 0.42 0.17 .179*** 5. Competitiveness 0.60 0.22 *p < .05; **p < .01, ***p < .001. The regression procedure showed that the model significantly predicted high math selfefficacy [F (5, 403) = 30.141, p< .001]. The adjusted R2 of .263 indicated that, of the total variability that existed in high math selfefficacy, 26.3% was associated with variability in cohesiveness, friction, satisfaction, difficulty, and competitiveness. The standardized beta coefficients were all statistically significant except for cohesiveness (see Table 2). Satisfaction had the highest standardized beta value, making it the most significant predictor of high math selfefficacy. Tolerance values indicated that multicollinearity was not a problem in this analysis. 63 Table 2 Multiple Regression Analysis Summary for Variables Predicting High Math SelfEfficacy (N = 409) Variable B Standard Error of B Cohesiveness .074 0.181 .021 Friction .958 0.164 .301*** Satisfaction 1.397 0.189 .334*** Difficulty .684 0.216 .139** Competitiveness .510 0.180 .132** Constant 3.294 0.190 Note. R2 = .263; F (5, 403) = 30.141, p< .001. *p < .05; **p < .01,***p < .001. Research Question 2 Research Question 2 asked “Which dimensions of classroom environment (cohesiveness, friction, satisfaction, difficulty, or competitiveness) are the best predictors of low selfefficacy?” Of the classroom environment dimensions, students scored lowest on friction (mean = 0.39, s.d = 0.27) and difficulty (mean = 0.42, s.d = 0.17) (see Table 3). The mean low selfefficacy score was 2.11 (s.d = 0.97). All of the predictor variables were significantly correlated to low selfefficacy (see Table 3). Cohesiveness and satisfaction showed a negative correlation with low math selfefficacy, while friction, difficulty, and competitiveness were positively correlated with low selfefficacy. 64 Table 3 Means, Standard Deviations and Intercorrelations for Low SelfEfficacy, Cohesiveness, Friction, Satisfaction, Difficulty, and Competitiveness (N = 409) Predictor Variables Variable Mean SD 1 2 3 4 5 Low SelfEfficacy 2.11 0.97 
Date  2014 
Faculty Advisor  Naizer, Gilbert 
Committee Members 
Denson, Katy Morton, Tami 
University Affiliation  Texas A&M UniversityCommerce 
Department  EdD Supervision, Curriculum, and InstructionElementary Education 
Degree Awarded  Ed.D. 
Pages  155 
Type  Text 
Format  
Language  eng 
Rights  All rights reserved. 



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