
THE IMPACT OF FLIPPED INSTRUCTION ON MIDDLE SCHOOL MATHEMATICS ACHIEVEMENT A Dissertation by AMANDA GRACE MARTIN 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 August 2015 THE IMPACT OF FLIPPED INSTRUCTION ON MIDDLE SCHOOL MATHEMATICS ACHIEVEMENT A Dissertation by AMANDA GRACE MARTIN Approved by: Advisor: Melissa Arrambide Committee: Katy Denson Chuck Holt Head of Department: Chuck Holt Dean of the College: Timothy Letzring Dean of Graduate Studies: Arlene Horne iii Copyright © 2015 Amanda Grace Martin iv ABSTRACT THE IMPACT OF FLIPPED INSTRUCTION ON MIDDLE SCHOOL MATHEMATICS ACHIEVEMENT Amanda G. Martin, EdD Texas A&M UniversityCommerce, 2015 Advisor: Melissa Arrambide, EdD The purpose of this causal comparative quantitative research study was to examine the effectiveness of flipped instruction on middle school mathematics achievement when compared to the traditional classroom. The effectiveness of the flipped classroom in closing the existing achievement gap among students of various ethnic subpopulations, socioeconomic statuses, and in the instruction of students within preAP mathematics classes was investigated in this study. Propensity score matching was used to match students taught by the same teacher within control and treatment groups using 1:1 nearest neighbor matching with a caliper of 0.25 SD. The matched student data were analyzed using multilevel modeling facilitated by the mixed models linear program in SPSS. The results indicated that no significant differences existed between the STAAR Mathematics scale scores of students within flipped or traditional classrooms. The researcher failed to reject the null hypotheses of no significant differences between scores of African American, Hispanic, White, Other, economically disadvantaged, noneconomically disadvantaged, and preAP mathematics students in flipped or traditional classrooms. v ACKNOWLEDGEMENTS I am truly grateful for the support of my family, friends, advisor, committee members, and colleagues. Without your encouragement, this journey would not be possible. I am thankful for my time spent at Texas A&M UniversityCommerce. The faculty and staff are helpful, and I am proud to call it my alma mater. Thank you, committee members, for your support and guidance. I appreciate the time and effort you devoted to my journey. Dr. Arrambide, you gave encouragement when it was needed most. Dr. Denson, I am forever indebted to you for the time you generously shared and I admire your expertise. Dr. Holt, I appreciate your sound advice and participation. All of you have made this a rewarding experience, and I thank you. My family, friends, and colleagues have played an incredible role as my support system. I am delighted to have my husband by my side, and my family cheering me on. Thank you for always knowing what to say and do. I do not have words to express my gratitude for your love, time, support, and encouragement. You are truly my biggest fans and I love you. I know that God has great things in store for our lives, and I am excited to see what He has planned for us. vi TABLE OF CONTENTS LIST OF TABLES ...................................................................................................................... x LIST OF FIGURES ................................................................................................................... xi CHAPTER 1. INTRODUCTION ..................................................................................................... 1 Statement of the Problem .................................................................................... 5 Purpose of the Study ........................................................................................... 8 Research Questions and Hypotheses .................................................................. 9 Significance of the Study .................................................................................. 11 Method of Procedure ......................................................................................... 12 Selection of Sample ................................................................................... 12 Collection of Data ...................................................................................... 16 Treatment of the Data ................................................................................ 16 Propensity Score Matching .................................................................. 17 Multilevel Modeling ........................................................................... 20 Definitions of Terms ......................................................................................... 21 Limitations ........................................................................................................ 23 Delimitations ..................................................................................................... 23 Assumptions ...................................................................................................... 24 Organization of Dissertation Chapters .............................................................. 24 2. REVIEW OF THE LITERATURE ......................................................................... 26 Theoretical Background of Mathematics Achievement ................................... 27 Federal Mandates ....................................................................................... 27 vii CHAPTER State Mandates ........................................................................................... 28 The Mathematics Achievement Gap Among Student Groups .......................... 29 National Mathematics ................................................................................ 30 Texas Mathematics .................................................................................... 31 Instructional Technology .................................................................................... 31 Curriculum Integration ............................................................................... 32 Impact of Technology on Student Achievement ........................................ 33 Differentiated Instruction .................................................................................. 34 Meeting Student Needs Through Differentiation ....................................... 35 Impact of Differentiation on Student Achievement ................................... 36 Flipped Instruction ............................................................................................ 37 The Flipped Classroom .............................................................................. 37 History of the Flipped Classroom .............................................................. 39 Flipped Instruction in High School Courses .............................................. 41 Flipped Instruction in Higher Education Courses ...................................... 41 Flipped Instruction Survey Research ......................................................... 46 Benefits and Challenges of Flipped Instruction ......................................... 47 Summary ........................................................................................................... 49 3. METHOD OF PROCEDURE ................................................................................... 51 Selection of Participants ................................................................................... 51 Instrumentation ................................................................................................. 54 STAAR Mathematics ................................................................................. 54 viii CHAPTER Middle School Mathematics Flipped Instruction Survey .......................... 57 Data Collection ................................................................................................. 57 Data Analysis .................................................................................................... 60 Propensity Score Matching ............................................................................... 61 Constructing the Data Set ................................................................................. 65 Multilevel Modeling ......................................................................................... 68 Research Question 1 .................................................................................. 72 Research Question 2 .................................................................................. 72 Research Question 3 .................................................................................. 72 Research Question 4 .................................................................................. 73 Summary ........................................................................................................... 73 4. PRESENTATION OF DATA ................................................................................... 76 Data Set ...................................................................................................... 77 Data Analyses ................................................................................................... 78 Propensity Score Matching ........................................................................ 79 Restructuring the Data ............................................................................... 84 Multilevel Modeling .................................................................................. 85 Null Model ........................................................................................... 85 Growth Rate Model ............................................................................. 88 Treatment Model .................................................................................. 89 Model with Level 1 Student Variables ............................................... 89 Model with Level 2 Class Variables ................................................... 90 ix CHAPTER Model with Interactions with Treatment ............................................. 91 Research Questions ........................................................................................... 91 Research Question 1 .................................................................................. 91 Research Question 2 .................................................................................. 92 Research Question 3 .................................................................................. 93 Research Question 4 .................................................................................. 93 Summary ........................................................................................................... 94 5. SUMMARY OF THE STUDY AND THE FINDINGS, CONCLUSIONS, IMPLICATIONS, AND RECOMMENDATIONS FOR FUTURE RESEARCH .. 96 Findings ............................................................................................................. 97 Conclusions ..................................................................................................... 100 Implications ..................................................................................................... 103 Recommendations for Future Research .......................................................... 105 REFERENCES ....................................................................................................................... 108 VITA ...................................................................................................................................... 116 x LIST OF TABLES TABLE 1. Percentage of Texas students meeting expectations on 2013 STAAR Mathematics ...... 7 2. Percentage of Texas and Suburban ISD students meeting expectations on 2013 STAAR Grade 7 Mathematics ........................................................................................ 13 3. Student Characteristics of Grade 8 Regular Mathematics Students Original and Matched Samples ........................................................................................................... 80 4. Student Characteristics of Grade 8 PreAP Mathematics Students Original and Matched Samples ........................................................................................................... 81 5. Standardized Differences in Characteristics of Treatment and Control Groups by Level of Instruction, Regular or PreAP ........................................................................ 84 6. Parameter Estimates for Five Models Examining the Differences Between Traditional and Flipped Instruction with Covariate Influence ....................................... 87 xi LIST OF FIGURES FIGURE 1. Summary of steps to construct the matched flipped and traditional classroom sample .. 19 2. Data collection for data analysis ...................................................................................... 59 3. Steps to construct the matched flipped and traditional classroom sample ....................... 63 4. Distribution of propensity scores for Grade 8 students in regular mathematics classes .. 82 5. Distribution of propensity scores for Grade 8 students in preAP mathematics classes .. 83 1 Chapter 1 INTRODUCTION In education, student achievement is paramount. Administrators encounter the challenge of leading instructional programs and choosing instructional strategies that enhance and increase student achievement. In a time of intense accountability, educational systems face “severe challenges to meet bottom line results while external pressures from federal, state, and local mandates are compelling educational leaders to drive enhanced student achievement” (Onorato, 2013, p. 33). Instructional leaders face this challenge as they build effective learning environments for students and teachers. Instructional leaders also strive to improve teacher quality with an ultimate goal of raising student achievement (Pansiri, 2008). The quality of learning depends on the strategies implemented by teachers and administrators. The quality teacher uses various teaching practices and instructional strategies to impact student success (Anderson, 2007). The intentional selection of these instructional strategies is important to consider. Instructional strategies are needed to maximize instructional time and offer flexibility for the teacher to meet student needs and increase achievement (Bergmann & Sams, 2012). Varying student needs provoke the necessity for a variety of strategies to employ in the classroom. Students deserve instruction that meets their needs in multiple ways, and teachers need more time to conduct small group instruction and work with students one at a time to impact student achievement (Flumerfelt & Green, 2013). Time is a valuable resource, and strategies are needed to increase learning and teaching time. Educational leaders can impact student achievement through the selection and implementation of instructional strategies (Onorato, 2013). It is essential for educational leaders to choose instructional strategies that positively impact the learning environment. Flipped instruction, or the flipped classroom, is an 2 instructional approach that is gaining momentum and attention in the learning community and could be selected by educational leaders to positively influence student achievement, specifically mathematics achievement (Love, Hodge, Grandgenett, & Swift, 2014). The purpose of the study was to examine the flipped classroom and its effect on student learning. The flipped classroom allows educators to “radically rethink how they use class time” (Tucker, 2012, p. 82). The flipped classroom essentially ‘flips’ what is traditionally done in class and what is traditionally done as homework. The activities that are completed at home and at school are inverted in the flipped classroom, which is an “inverted approach in which the students’ homework is to view a recording of the lecture, and class time is used for active problemsolving activities with instructor guidance” (DeMaio & Oakes, 2014, p. 340). In the flipped classroom, students learn content outside of class time. Students can view instructional videos, take notes to learn content at home, and then practice the content during class with the guidance of the teacher. Class time is devoted to “practice assignments, targeted remedial help, or activities designed to promote higher order thinking skills” (Davies, Dean, & Ball, 2013, p. 564). In the traditional mathematics classroom, students listen to the instructional lecture during class time and practice mathematics problems in the time remaining at school and finish at home. In contrast, in the flipped mathematics classroom, students view instructional lecture videos at home and practice mathematics problems during class time. The flipped classroom could offer a solution for teachers and administrators who want to maximize the use of class time to increase student achievement (DeMaio & Oakes, 2014). Student experiences in the traditional classroom are often more passive in nature. In traditional classroom lecture, “the teacher is doing the active work and the students are passively listening” (Fulton, 2012, p. 21). In the flipped classroom, students watch teachercreated lecture 3 videos and learn about the concepts and skills outside of class time. They take notes and prepare questions or discussion topics for the next class. Teachers employing the flipped instructional approach expect students to watch the lecture video and hold them accountable for watching the instructional video by checking their notes and questions (DeMaio & Oakes, 2014). This strategy allows class time to be devoted to solving problems, working collaboratively, extending the learning, and ensuring high levels of thinking. Class time is valuable, and this instructional time is maximized using the flipped instructional approach. The flipped classroom “redefines class time as a studentcentered environment” (Sams & Bergmann, 2013, p. 17). Students and teachers can use class time to work together, and students have the benefit of having the certified teacher assist them with their practice instead of struggling with new content outside of class. In the flipped classroom “students learn by doing, and ... the doing is happening within a handraise of the teacher. Students are no longer at home in isolation and unsupported while they do the difficult work of learning” (Fulton, 2012, p. 22). When students watch lecture videos prepared by their teacher outside of class time, they are prepared to engage in meaningful practice during class. This also allows the teacher to differentiate for students and work with individual students or small groups each day. Differentiated instruction points to “achievement gains on standardized tests, including mathematics assessments” (Chamberlin & Powers, 2010, p. 116). Teachers can engage students in learning activities tailored to their needs and “most importantly, all aspects of instruction can be rethought to best maximize the scarcest learning resource – time” (Tucker, 2012, p. 82). Time for practice and solving problems is valuable, and using technology maximizes learning time in the flipped classroom. 4 Technology also plays a large role in the implementation of the flipped classroom. Many teachers and educational leaders believe that students should be engaged in learning with technology (Hepplestone, Holden, Irwin, Parkin, & Thorpe, 2011). The flipped classroom allows for this engagement. Technology tools can be employed in the flipped classroom to enhance learning opportunities. The flipped classroom “relies on technology to introduce students to course content outside of the classroom so that students can engage that content at a deeper level inside the classroom” (Strayer, 2012, p. 171). Using technology, students in the flipped classroom can have more time to complete the rigorous learning tasks expected of them. The teacher becomes the facilitator of learning and can be available to help students and differentiate activities as needed (Love et al., 2014). Students in flipped classrooms also “see value in helping each other learn with a cooperative approach” (Strayer, 2012, p. 183). This cooperative approach is advantageous in learning, and students in flipped classrooms are “more willing to work together and engage in activity in the classroom than the students in the traditional classroom” (Strayer, 2012, p. 188). These students are also more eager to participate in class and struggling students can get the help they need. Teachers credit the flipped classroom with “fostering better relationships, greater student engagement, and higher levels of motivation” (Tucker, 2012, p. 82). Increased class time, fewer student failures, energized teachers, more opportunities for differentiated instruction, and engaged students are just some of the benefits (Bergmann & Sams, 2012). In an “experimental flipped class, the students increased their online engagement and homework rates from 75% to 100%,” which resulted in an “elimination of all students’ class failures” (Flumerfelt & Green, 2013, p. 364). Because of the many possible benefits, educational leaders could choose the flipped classroom as an instructional strategy to impact student achievement. 5 In this study, the implementation of flipped instruction in middle school mathematics classrooms was examined to determine the impact on student achievement. This instructional strategy was also analyzed to assess its potential to close the achievement gap that exists between students of various ethnicities and socioeconomic statuses. Additional research was needed “to assess the direct effect of the flipped classroom on student learning outcomes” (DeMaio & Oakes, 2014). Therefore, this quantitative research study focused on the impact of flipped instruction on middle school mathematics achievement as measured by state assessment scores and its effectiveness in closing the existing achievement gap among students of various ethnic subpopulations and socioeconomic statuses. Statement of the Problem Educational leaders seek strategies to increase class time, student engagement, and overall student achievement. Teachers need an approach that allows them to meet the unique learning needs of students (Anderson, 2007). Educational leaders must make instructional decisions that impact the learning environment, as they are “expected to be instructional leaders” (Vornberg, Hickey, & Borgemenke, 2012, p. 128). Purposeful selection and implementation of instructional strategies is necessary in the learning environment. Flipped instruction was examined to determine its effectiveness as an instructional approach. The flipped classroom allows for increased time in class for differentiation and student engagement that “has been empirically related to achievement test scores and grades” (Young, 2010, p. 4). This quantitative research study was conducted to determine the effect of the flipped instructional approach on student achievement in middle school mathematics when compared to the traditional instructional approach. 6 The accountability system in Texas is rigorous and holds districts, administrators, teachers, and students to high standards. Students in the state of Texas are evaluated annually for performance on the State of Texas Assessment of Academic Readiness (STAAR). Texas students must perform satisfactorily on STAAR assessments. School districts in Texas must ensure that all students learn required content and must look carefully at achievement gaps between students of various ethnicities and socioeconomic statuses (Texas Education Agency, 2010). In the state of Texas, 79% of students in all grades met expectations on the 2013 State of Texas Assessment of Academic Readiness (STAAR) Mathematics assessment. However, an achievement gap exists between ethnic subpopulations, as shown in Table 1. White students outperform their African American and Hispanic peers. In addition, students who are economically disadvantaged perform slightly lower than noneconomically disadvantaged peers. 7 Table 1 Percentage of Texas Students Meeting Expectations on 2013 STAAR Mathematics Note. From “20122013 Texas Performance Reporting System: Report for State,” by Texas Education Agency, 2013b. Efforts must be made to close the achievement gap. Teachers are looking for innovative ways “to instruct technology age students, administrators are seeking new ways to lead teachers in an age of increasingly uncertain resource allocations, and district officers are looking for new ways to train instructional leaders for the 21st century” (Smith & Addison, 2013, p. 135). As new instructional strategies are needed to close the achievement gap and engage students, flipped instruction was examined. In addition, teachers are faced with meeting the unique learning modes of students in basic classes, regular classes, preadvanced placement (preAP) classes, and gifted/talented (GT) classes. Students within these classes have varied learning and readiness levels. Teachers and administrators can work collaboratively to impact student achievement through the selection of effective instructional strategies (Pansiri, 2008). In addition, “we know challenge, rigor, high Characteristic Percent African American 68 Hispanic 76 White 88 Economically Disadvantaged 72 NonEconomically Disadvantaged 89 All Students 79 8 standards, and expectations are critical to improved student achievement” (Swanson, 2006, p. 23). Teachers must keep high expectations for students in all classes in order to attain increased student achievement. It is critical to note that “minority and lowincome students benefit from advanced curricula and instructional strategies that challenge them” (Swanson, 2006, p. 11). While teachers are faced with the challenge of teaching and reaching every student at his or her ability level, little quantitative research has been conducted in the area of the flipped classroom (Love et al., 2014). An effective instructional approach is needed to positively impact student achievement, and the flipped classroom was investigated in this quantitative research study. Purpose of the Study The purpose of this quantitative study was to examine the effects of the flipped classroom on middle school mathematics achievement when compared to the traditional classroom. Another aim was to determine the effectiveness of the flipped classroom as an instructional approach in closing the existing achievement gap among identified student groups, including African American, Hispanic, White, and economically disadvantaged and noneconomically disadvantaged. The effectiveness of the flipped classroom in the instruction of students within preAP classrooms was also examined. To measure student achievement, scale scores from the STAAR Grade 8 Mathematics and STAAR Grade 7 Mathematics, used as a covariate, were reported, collected, and analyzed. Flipped instruction is a new instructional strategy used in the classroom with little research regarding its effectiveness. In addition, the results of the study can inform educational leaders as they choose effective instructional strategies to implement in the learning environment. 9 Research Questions and Hypotheses The causal comparative quantitative study analyzed the flipped instructional strategy and its impact on the mathematics achievement of Grade 8 students in one suburban independent school district. Data from students who received instruction in the flipped classroom and the traditional classroom were compared and analyzed. The following questions guided the research study: 1. To what extent does the flipped classroom increase student achievement on the STAAR Grade 8 Mathematics assessment when compared to the traditional classroom? a. Ho1: There is no significant difference between the mathematics scores of students receiving instruction in the flipped classroom and the mathematics scores of students receiving instruction in the traditional classroom. b. Ha1: There is a significant difference between the mathematics scores of students receiving instruction in the flipped classroom and the mathematics scores of students receiving instruction in the traditional classroom. 2. To what extent does the flipped classroom increase mathematics scores of economically disadvantaged students when compared to the traditional classroom? a. Ho2: There is no significant difference between the mathematics scores of economically disadvantaged students receiving instruction in the flipped classroom and the mathematics scores of economically disadvantaged students receiving instruction in the traditional classroom. b. Ha2: There is a significant difference between the mathematics scores of economically disadvantaged students receiving instruction in the flipped 10 classroom and the mathematics scores of economically disadvantaged students receiving instruction in the traditional classroom. 3. To what extent does the flipped classroom close the achievement gap between students of ethnic subpopulations when compared to the traditional classroom? a. Ho3: There is no significant difference between the mathematics scores of White, African American, and Hispanic students receiving instruction in the flipped classroom and the mathematics scores of the White, African American, and Hispanic students receiving instruction in the traditional classroom. b. Ha3: There is a significant difference between the mathematics scores of White, African American, and Hispanic students receiving instruction in the flipped classroom and the mathematics scores of White, African American, and Hispanic students receiving instruction in the traditional classroom. 4. To what extent does the flipped classroom increase mathematics scores of students in preAP and regular mathematics when compared to the traditional classroom? a. Ho2: There is no significant difference between the scores of students in pre AP and regular mathematics classes receiving instruction in the flipped classroom and the scores of students in preAP and regular mathematics classes receiving instruction in the traditional classroom. b. Ha2: There is a significant difference between the scores of students in preAP and regular mathematics classes receiving instruction in the flipped classroom and the scores of students in preAP and regular mathematics classes receiving instruction in the traditional classroom. 11 Significance of the Study The intent of the causal comparative quantitative study was to identify whether the flipped instructional strategy was an effective approach to increase mathematics achievement for middle school students. If educational leaders can determine the factors that can increase student achievement in mathematics, then leaders can implement the instructional strategy to positively impact students. Closing the achievement gap among ethnic subpopulations is a goal for many academic programs (Chamberlin & Powers, 2010). African American and Hispanic students are expected to exemplify success on state assessments at the same level as their White peers, and an instructional approach must be found to close the achievement gap. Mathematics achievement trends “suggest that the gap between some minority and White students persists and may even be widening” (Bol & Berry, 2005, p. 33). Student achievement is paramount, and educational leaders seek effective instructional strategies to employ in the learning environment to close the achievement gap among students of various ethnic subpopulations. In addition, studies reveal that economically disadvantaged students typically perform below their mainstream counterparts and “there is a considerable gap in test performance between students from poor families and those from nonpoor families” (Flores, 2007, p. 30). The potential impact of the flipped classroom cannot be overlooked. The objective of this research study was to examine the flipped instructional strategy as an approach to increase mathematics achievement in middle school students and to examine its potential to close the achievement gap among students of various socioeconomic statuses and ethnicities. This study also provided insight into the strategies that are effective in differentiating instruction for high achieving students in preAP classes. Teachers and administrators need instructional approaches that positively impact student achievement and creatively use valuable instructional time. In the 12 flipped classroom, “teachers spend more actual time teaching and facilitating instead of just lecturing” (Fulton, 2012, p. 22). Being intentional and purposeful with the time devoted to learning can lead to successful learning outcomes. A central theme is that “active learning works best. Telling doesn’t work very well. Doing is the secret. Active student engagement is necessary” (Herreid & Schiller, 2013, p. 65). This study is added to the body of research on the flipped classroom and its impact on middle school mathematics student achievement. Method of Procedure This causalcomparative quantitative study analyzed the effectiveness of the flipped instructional strategy on mathematics achievement of Grade 8 students when compared to the traditional instructional approach. The quantitative data of this study included the STAAR Grade 8 Mathematics scale scores, student ethnicities, socioeconomic status, and level of instruction, regular education or preAP. The independent variable was defined as the type of instruction, flipped instruction or traditional instruction. The dependent variable was mathematics achievement as measured by the STAAR Grade 8 Mathematics scale score, using the STAAR Grade 7 Mathematics scale score as a covariate. The students receiving instruction in the traditional classroom served as the control group, and the students receiving instruction in the flipped classroom served as the treatment group. Selection of Sample The causalcomparative quantitative study was conducted in a suburban independent school district in Texas. The district served students in grades PreKindergarten through 12. The district stretched approximately 60 square miles and has approximately 39,000 students at 47 campuses. This study included the data from all 8 middle school campuses. In the suburban independent school district used in this study, 75% of students met expectations on the 2013 13 State of Texas Assessment of Academic Readiness (STAAR) Grade 7 Mathematics. An achievement gap existed between ethnic subpopulations, as shown in Table 2. Similar to the state, White students outperform their African American and Hispanic peers in the suburban independent school district used in this study. In addition, students who are economically disadvantaged performed lower than noneconomically disadvantaged peers. Table 2 Percentage of District Students Meeting Expectations on 2013 STAAR Grade 7 Mathematics Characteristic Texas Suburban ISD African American 58 64 Hispanic 67 78 White 83 81 Economically Disadvantaged 64 73 NonEconomically Disadvantaged 84 80 All Students 72 75 Note. From “20122013 Texas Performance Reporting System,” by Texas Education Agency, 2013b. The student ethnic makeup of this district included 51.3% Hispanic students, 24.9% African American students, 19.3% White students, and 4.5% other students (Texas Education Agency, 2013a). Currently, 70.3% of students in the suburban district are considered economically disadvantaged (Texas Education Agency, 2013a). Ethnic subpopulations and socioeconomic statuses for the specific students in this study are reported in Chapter 4. 14 All middle school mathematics teachers participated in an introductory 6hour professional development session regarding flipped instruction before the 20132014 academic year began. The professional development session highlighted the benefits and challenges for flipping the classroom. Included in the study were the students of Grade 8 middle school mathematics teachers who attended this training. All Grade 8 mathematics teachers used traditional instruction for the 20122013 academic year. Teachers were given autonomy from their administrators to choose the traditional classroom or the flipped classroom as an instructional approach to implement throughout the 20132014 academic year. Therefore, some teachers chose to implement the flipped instructional approach in their Grade 8 mathematics classes, some chose to use the traditional instructional method, and some chose to use the flipped instructional approach for a shorter period of time. Data from all Grade 8 mathematics teachers were gathered and compared based upon the instructional approach chosen. The middle school mathematics teachers in the suburban independent school district have a locally developed paced curriculum. All teachers followed the same scope and sequence and lesson documents, regardless of whether they chose to use flipped or traditional instruction. The curriculum resources were the same for the 20122013 and 20132014 academic years. Middle school mathematics classes in the district included regular mathematics, where students receive grade level instruction; preAdvanced Placement (AP) mathematics, where students receive grade level instruction with enrichment; gifted and talented (GT) mathematics, where gifted students receive above grade level instruction; and basic mathematics, where students receive special education modified instruction. For the context of this study, only students in regular and preAP mathematics classes were included because they were the eighth graders receiving grade level instruction. For the 20132014 school year, there were 127 classes of Grade 8 students in 15 the district under study with 108 regular mathematics classes and 19 preAP mathematics classes. In addition, only students with both a STAAR Grade 7 Mathematics score and STAAR Grade 8 Mathematics score were included in the study. The number of classes and students included in this study are described in detail in Chapter 4. At the end of the 20132014 academic year, district personnel administered a survey to the Grade 8 mathematics teachers. Permission to access the results of this survey was obtained by the researcher. The results of this survey indicated the teachers who chose to implement the flipped instructional approach during the 20132014 academic year. Through the use of cluster sampling, the student data of Grade 8 teachers who implemented flipped instruction for the duration of the 20132014 academic year served as the treatment group. Once the flipped classroom teachers were identified, their student data from the previous 20122013 academic year served as the control group. This control group received traditional instruction for the 2012 2013 academic year. The 20132014 treatment and 20122013 control group students taught by the same teacher were matched using propensity score matching and were included in this study. The student data of Grade 8 teachers that chose to implement flipped instruction for a shorter period of time were not included in the study. Therefore, the results of the teacher survey determined the number of flipped classrooms in the district under study for the 20132014 academic year. Multilevel modeling was used to analyze data in this study, with the student data as Level 1 and the class data for Level 2. In studies that use multilevel modeling, the researcher can strive for a sample of “about 50 groups with about 20 individuals per group” (Hox, 2010, p. 235). For this study, the groups are classes. Therefore, this quantitative study analyzed student data from the treatment and control group classes with both STAAR Grade 7 Mathematics and STAAR 16 Grade 8 Mathematics scale scores. There were a sufficient number of classes included in this study with about 20 students in each class. Collection of Data The population for this study included Grade 8 students who received flipped instruction during the 20132014 academic year and Grade 8 students who received traditional instruction taught by the same teacher during the 20122013 academic year. Because a multilevel modeling technique was used for data analysis, data were collected for two levels, the student level and the class level. Level 1 student data included the STAAR Grade 8 Mathematics scale scores, STAAR Grade 7 Mathematics scale scores as covariate, and ethnicity, limited English proficiency (LEP) status, gender, special education status, socioeconomic status based on freeor reducedprice lunch status, class code, and teacher code. Students and teachers were given a coded number to maintain anonymity. Level 2 class data were whether the teacher used flipped or traditional instruction and whether the class was a regular or preAP mathematics class. Other classlevel variables were computed by the researcher and discussed in the next section. Once the researcher obtained permission, personnel from the school district retrieved the data for the researcher. All identifying information for the students along with their class and teacher were removed and replaced with a number randomly generated by district personnel to maintain confidentiality and anonymity. The district personnel also paired the teacher number with the type of instruction used so that the students in the treatment and control groups taught by the same teacher could be matched and analyzed. Treatment of the Data The complexity of educational research makes the interpretation of treatment effects difficult because of the lack of true randomization and experimental design in educational 17 settings (Lane, To, Shelley, & Henson, 2012). Therefore, the data were analyzed using propensity score matching strategies described by Thoemmes (2012) and steps outlined by Randolph, Falbe, Manuel, and Balloun (2014), and multilevel modeling techniques described by Rickles (2011). These strategies allowed the researcher to analyze the treatment effect of flipped instruction across students and classes. The propensity score matching and multilevel modeling allowed for “double robustness” in the study (Schafer & Kang, 2008, p. 280). Propensity score matching. Propensity score matching was used to match the students in the control and treatment groups of the causal comparative study. The propensity score is the “probability of receiving the treatment given the observed covariates” (Stuart & Rubin, 2008, p. 281). When random assignment is not possible in a study, propensity score matching can be used to “control for bias in a treatment effect” (Lane et al., 2012, p. 187). A propensity score was calculated for each student based on the probability of receiving flipped instruction based on covariates. The propensity scores were calculated separately among regular students and then preAP students. Students with similar propensity scores were matched from the flipped and traditional classrooms. This created “balance on the covariates that were used to estimate the propensity score” (Thoemmes, 2012, p. 3). The statistical matching of students accounted for the nonrandomization within the study because the students were matched across the treatment and control groups based on the covariates of ethnicity, socioeconomic status, gender, LEP status, special education status, and scale scores for the STAAR Grade 7 Mathematics. The U.S. Department of Education “supports propensity score matching as a method for evidencebased research when group equivalence can be established through the analysis” (Lane et al., 2012, p. 188). The use of propensity score matching aided the researcher in ruling out the possibility that differences between treatment and control groups were due “to systematic 18 differences between the groups at baseline” (Schafer & Kang, 2008, p. 279). To further reduce teacher effect in this study, the students within the treatment and control groups received instruction from the same teacher. The propensity scores were calculated for each student in the study using 1:1 nearest neighbor matching, which means that “a single treated participant is matched to a single untreated participant who has the most similar estimated propensity score” (Thoemmes, 2012, p. 5). A caliper of 0.25 SD, also used by Rickles (2011), allowed for a close match between students of the flipped and traditional instruction groups. This propensity score matching technique allowed the researcher to analyze the differences in treatment and control groups although randomization and true experimental design was not possible. The students within the treatment and control groups were matched based on propensity score, creating pairs of student data. It is important to consider the balance in baseline covariates within the matches (Austin, 2008). Therefore, a standardized differences method recommended by Ho, Imai, King, and Stuart (2007) was used to assess the balance of the differences. The standardized difference is “the absolute difference in sample means divided by an estimate of the pooled standard deviation of the variable” (Austin, 2008, p. 2039). This method assessed the balance within the matched pairs of students and was reported in this research study in Chapter 4. This method allowed for less bias and less variance in the model (Ho et al., 2007). Furthermore, Austin (2008) discussed five recommendations for studies that use propensity score matching. The details of those recommendations are depicted in Chapter 3. In the first step of the propensity score matching process, the 20132014 treatment students who received flipped instruction in regular mathematics classes were matched to 2012 2013 control students in regular mathematics classes that used traditional instruction, taught by the same teacher. A data file was saved for this group. In the next step, the 20132014 treatment 19 students in the preAP mathematics classes were matched to the 20122013 control students in preAP mathematics classes. A data file was saved for this group as well. The propensity score matching technique allowed the matched data to be similar to randomized methods, where treatment and control groups are created randomly and independently (Rickles, 2011). Once the matching process was complete, two data files were created with the matched treatment and control students for regular mathematics classes (M) and the matched treatment and control students for preAP mathematics classes (MC). Then the matched treatment and control students in data file M and MC were used in a 2level multilevel modeling procedure to estimate the treatment effects of receiving instruction in the flipped classroom. The steps to construct the matched control and treatment group sample are summarized in Figure 1, and are described in more detail in Chapter 3. Step Description 1 Estimate the propensity score for each student using the STAAR Grade 7 Mathematics scale score and student demographic characteristics as covariates. 2 For the regular mathematics classes, create data set M by conducting a 1:1 propensity score match without replacement, using a caliper of 0.25 SD of the propensity score logodds with control and treatment students. 3 For the preAP mathematics classes, create data set MC by conducting a 1:1 propensity score match without replacement using a caliper of 0.25 SD of the propensity score logodds with control and treatment students. 4 Export the data files for analyses. Estimate the treatment effect outcome in data sets M and MC using a multilevel linear model. The multilevel model includes the same student characteristics and allows the intercept to vary across the teachers. Figure 1. Summary of steps to construct the matched flipped and traditional classroom sample. Adapted from “A stepbystep guide to propensity score matching in R,” by Justus J. Randolph, Kristina Falbe, Austin Kureethara Manuel, and Joseph L. Balloun, 2014, Practical Assessment, Research & Evaluation, p. 16. 20 Multilevel modeling. Once the propensity scores were calculated for each student, multilevel modeling was used to evaluate the data imported into version 21.0 of the Statistical Package for the Social Sciences (SPSS). “Multilevel modeling provides a powerful framework for analyzing data collected in the school context” (Dettmers, Trautwein, Ludtke, Kunter, & Baumert, 2010, p. 472). Multilevel modeling is a robust model of analysis and was used to analyze the matched pairs of student data. As in most research conducted “in school settings, students in this study are nested within classes. Students within a class are typically more similar to each other than are two students randomly selected from the whole sample” (Dettmers et al., 2010, p. 472). Multilevel modeling considered the nested data within the educational context. For this study, Level 1 student data were nested within the Level 2 class data. For this study, multilevel modeling analyzed the impact of flipped instruction or traditional instruction on the STAAR Grade 8 Mathematics scale score. Level 1 student data were nested within the Level 2 class data. Level 1 student data included the STAAR Grade 8 Mathematics scale score, gender, socioeconomic status, ethnicity, special education status, and LEP status. Using the STAAR Grade 7 Mathematics scale score as the covariate adjusted for initial differences in the flipped instruction and traditional instruction groups. Level 2 class data included the type of instruction (flipped or traditional), level of instruction (regular or preAP), and aggregated class data of percent of economically disadvantaged students, percent of students by ethnic subpopulation, percent of students who are limited English proficient, percent of students who receive special education services, and percent of students by gender. Because teachers and schools used either all flipped classes or no flipped classes, it was not necessary for teacher and school variables to be included in the model. 21 Definitions of Terms Accountability Rating System. As part of the Texas Education Agency’s accountability rating system, campuses and districts are evaluated on performance on state assessments, commended performance, annual dropout rate, completion rate, and the progress of English Language Learners (ELL). Possible ratings are Academically Unacceptable, Academically Acceptable, Recognized, Exemplary, and Not Rated (Texas Education Agency, 2011a). African American. A person originating from the “black racial groups of Africa” (National Center for Education Statistics, 2013, para. 3). Economically Disadvantaged. This term describes students who are reported as eligible for free or reducedprice meals or eligible for other programs of public assistance (Texas Education Agency, 2011a). Ethnicity. “Used to describe groups to which individuals belong, identify with, or belong in the eyes of the community … The designations are used to categorize United States citizens, resident aliens, and other eligible noncitizens” (National Center for Education Statistics, 2013, para. 1). Flipped Classroom. A classroom that uses flipped instruction to deliver content (Bergmann & Sams, 2012). Flipped Instruction. That which is traditionally done is class is now done at home, and that which is traditionally done at home is now completed in class. Students watch teachercreated lecture videos at home, and practice exercises and activities are completed during class (Bergmann & Sams, 2012). Flipped Instructional Strategy. An instructional strategy that uses flipped instruction to deliver content (Bergmann & Sams, 2012). 22 Hispanic. “A person of Cuban, Mexican, Puerto Rican, South or Central American, or other Spanish culture or origin, regardless of race” (National Center for Education Statistics, 2013, para. 3). Instruction. Activities and lessons directly associated with the interaction between teachers and students (Texas Education Agency, 2011a). Percent Score. The number of correctly answered test questions divided by the total number of questions (Texas Education Agency, 2011a). Raw Score. The number of test questions answered correctly (Texas Education Agency, 2011a). Recognized. The second tier in the accountability rating system that includes: Academically Unacceptable, Academically Acceptable, Recognized, Exemplary, and Not Rated (Texas Education Agency, 2011a). Scale score. It converts the raw score onto a scale that is universal to all assessment test forms. It takes into account the complexity level of the specific set of questions and “quantifies a student’s performance relative to the passing standards” and allows “direct comparisons of student performance between specific sets of test questions from different test administrations” (Texas Education Agency, 2012, para. 1). Socioeconomic status. Based on their eligibility for free or reducedpriced meals or for other public assistance programs, students are classified as economically disadvantaged or not (Texas Education Agency, 2011a). Student Groups. Students are classified among the four student groups of African American, Hispanic, White, and economically disadvantaged that are evaluated in the accountability system (Texas Education Agency, 2011a). 23 STAAR. State of Texas Assessments of Academic Readiness (STAAR) is the state assessment program that “includes annual assessments for reading and mathematics at Grades 3 8, writing at Grades 4 and 7, science at Grades 5 and 8, social studies at Grade 8, and endofcourse assessments for English I, English II, Algebra I, biology, and United States history” (Texas Education Agency, 2011b, para. 1). White. “A person having origins in any of the original peoples of Europe, the Middle East, or North Africa” (National Center for Education Statistics, 2013, para. 3). Limitations There are some limitations to this study. The sample of students was drawn from a single suburban independent school district in Texas. Therefore, generalizing the results of the study to all students in school districts in Texas was limited. It is also important to note that classes and class sizes were determined at the campus level. Thus, class sizes included in this study vary. The educational leadership team on each campus assigned the teachers and the students to classes at the campus level. In addition, the individual teacher chose the instructional approach employed in the classroom. One might assume that the teachers who used the flipped instructional strategy chose to do so, and this may have some impact on the delivery of instruction using this strategy. Delimitations For the purpose of this study, the following delimitations were made. The flipped instructional strategy was implemented in the middle school mathematics classes in a single school district in Texas. The study included the Grade 8 students who received grade level instruction and did not include the gifted students who receive above grade level instruction or students who receive modified TEKS instruction in basic mathematics classes. For this study, 24 student achievement in mathematics was analyzed using the STAAR Grade 7 Mathematics scale scores as a baseline, and STAAR Grade 8 Mathematics scale scores to measure achievement. Only students who had a STAAR Grade 7 Mathematics scale score and STAAR Grade 8 Mathematics scale score were included in this study. In addition, this study was conducted during one academic year. Assumptions Assumptions in this study included, but are not limited to, the roles of the students and teachers as indicated. It is assumed that the teachers implemented the flipped instructional strategy and put forth effort in helping the students as they transitioned to the new instructional delivery model. It can also be assumed that students participated effectively and were engaged in their learning. In addition, it is assumed that students gave effort in attempting assignments, watching instructional videos, and completing assessments with accurate responses. Last, it is assumed that the data collected from Texas Education Agency for the STAAR Mathematics exam were accurate and were a reliable and valid measure of student mathematics achievement. Organization of Dissertation Chapters The study consists of five chapters. Chapter 1 contained the introduction, statement of the problem, purpose of the study, research questions, research hypotheses, significance of the study, method of procedure, definitions of terms, limitations, delimitations, assumptions, and organization of the study. Chapter 2 reviews the relevant literature to the study. The review of the literature includes an overview of the existing mathematics achievement gap among students, current research in employing technology in instruction, information about differentiated instruction, and the current research about the flipped instructional strategy. Chapter 3 includes a description of the method used in this study and the collection of the data in the research design. 25 The population sample was identified and the procedures described. Chapter 4 presents the results of the study including the treatment of the data, the descriptive statistics, and the analysis of the statistical tests based on the research questions. The data analysis was interpreted and the findings are presented with a summary of the results. Chapter 5 provides a discussion of the findings, recommendations for further research, and conclusions of the study. 26 Chapter 2 LITERATURE REVIEW The purpose of the study was to determine the impact of flipped instruction on the mathematics achievement of middle school students on the State of Texas Assessment of Academic Readiness (STAAR) Mathematics. An achievement gap exists among the student groups of African American, Hispanic, White, and economically disadvantaged students in the state of Texas and across the nation. The achievement gaps “among racial and ethnic groups and between students from poor and nonpoor families are welldocumented. They are large and have been persistent; this is well known and widely accepted” (Barton, 2003, p. 4). Although the achievement gap exists, educational leaders seek creative solutions to close the achievement gap and increase overall mathematics achievement. In this study, the flipped classroom was examined as a vehicle to increase mathematics achievement for middle school students and to close the achievement gap among student groups. Minimal research has been conducted in the area of the flipped classroom. Existing studies have been conducted in both high school and college settings in the subjects of science, marketing, radiology, and pharmacology. Survey research studies of K12 educators include multiple subjects and grade levels and indicate teacher and student perceptions of the strategy. The flipped classroom model is “gaining recognition in a wide variety of academic settings as an approach to promote studentcentered, active learning” (Pierce & Fox, 2012, p. 4). Educators strive to meet the unique learning needs of students. Through varied learning activities, the flipped classroom promotes studentcentered activities that are tailored to student needs (Bergmann & Sams, 2012). The studentcentered flipped classroom connects active learning and student engagement for effective learning environments. 27 The review of the literature presented in this chapter describes the theoretical framework of mathematics achievement and the existing achievement gap among student groups. Flipped instruction uses instructional technology for increased class time and student engagement with differentiated instruction. Therefore, a review of the previous research on (a) instructional technology, (b) differentiated instruction, and (c) flipped instruction is presented within the review of the literature. The review focuses on scholarly articles relevant to flipped instruction, differentiated instruction, instructional technology, mathematics achievement, and the achievement gap. A summary concludes this section. Theoretical Background of Mathematics Achievement Federal Mandates Congress passed the No Child Left Behind (NCLB) Act in 2001 and it was signed into law in 2002. It reauthorized the Elementary and Secondary Education Act (ESEA) in a way that “dramatically expanded the historically limited scope and scale of federal involvement in K12 schooling” (Dee & Jacob, 2011, p. 420). The goal of the No Child Left Behind Act is to improve education in public schools by establishing high expectations, assessing student performance, and implementing an accountability system for student performance on standards (Krieg, 2011). Accountability through highstakes testing is now customary in public schools as a result of No Child Left Behind, and this legislation has expanded federal influence over the nation’s public schools (Dee & Jacob, 2011). Schools and school districts are accountable for academic performance improvement of all students and must make adequate yearly progress (AYP). For a school to meet AYP, the percentage of students at a school in each ethnic subgroup and students who are categorized as economically disadvantaged, ELL, and special education must demonstrate proficiency on the state test and must meet expectations as determined by the state 28 (Krieg, 2011). The accountability system is robust and school districts across the nation strive to improve instructional programs. The No Child Left Behind Act holds districts within each state accountable for student performance on state mandated assessments. State Mandates The Texas Education Agency (TEA) holds school districts accountable for the performance of students on the State of Texas Assessment of Academic Readiness (STAAR). The first administration of STAAR appeared in Spring 2012 and replaced the former state standardized assessment, Texas Assessment of Knowledge and Skills (TAKS). The STAAR measures mathematics in Grades 38, reading in Grades 38, science in Grades 5 and 8, writing in Grades 4 and 7, and social studies in Grade 8. The STAAR also includes high school End of Course (EOC) testing for English, Algebra, Biology, and History (Texas Education Agency, 2011b). Texas school districts must ensure that students learn required content and must look carefully at achievement gaps between students of various ethnic subpopulations and socioeconomic statuses (Texas Education Agency, 2010). Educational leaders seek instructional strategies that increase student achievement and have lasting and positive effects on student learning. Schools strive to “continuously challenge current instructional practices in order to produce improvement, not just change for change’s sake, but by engaging in value added improvement” (Flumerfelt & Green, 2013, p. 364). State and federal mandates require schools to meet and exceed performance standards. Schools are charged with the responsibility of meeting student needs and preparing them to perform satisfactorily on state assessments. The federal mandate, No Child Left Behind Act gives direction to the states that all students achieve proficiency in mathematics and reading and also institutes “sanctions and rewards based on each school’s AYP status” (Dee & Jacob, 2011, p. 29 418). As a result, schools face rewards and consequences based on annual student performance results. The Mathematics Achievement Gap Among Student Groups A mathematics achievement gap exists among student groups of African American, Hispanic, White students in Texas and across the nation. At the time of the passage of the No Child Left Behind Act, one of the stated goals was to “eliminate the achievement gap between students of different races” (Krieg, 2011, p. 664). However, the study conducted by Dee and Jacob (2011) found that NCLB had “limited contributions to reducing achievement gaps” (p. 442). Many schools focus efforts and funds toward the student groups that are in danger of not meeting AYP standards. In fact, Krieg (2011) found that “administrators focus their efforts on racial groups that have trouble making AYP” which causes a “diminution in academic performance of students in successful racial groups” (p. 663). Krieg (2011) argues that schools participate in “strategic instruction” which focuses on the subjects that are tested and focuses on the student groups that require increased performance to meet AYP standards (p. 655). In addition, students of various ethnic subpopulations and socioeconomic statuses are underrepresented in highlevel mathematics classes. In fact, “students of color and economically disadvantaged students still are not enrolled in AP courses in the percentages equal to their percentage in their local school’s population” (Clark, Moore, & Slate, 2012, p. 266). Furthermore, teacher perceptions may have a part in this underrepresentation (Clark et al., 2012). It is imperative for educational leaders to face the challenge of closing the achievement gap among student groups and seek ways to accomplish this task. 30 National Mathematics The National Assessment of Educational Progress (NAEP) was designed in the 1960s as a national “tool for monitoring student achievement” (Rutledge, Kloosterman, & Kenney, 2009). The NAEP offers mathematics assessments every 2 to 4 years and is given to a sample of students across the nation. Rutledge et al. (2009) determined the extent to which mathematics skills have changed over 25 years. They discovered that the scores for 9yearold students and 13yearolds have climbed, but the scores for seventeenyearold students “have been relatively stable throughout the history of NAEP” (p. 446). They also found that the “ethnicity gaps are much larger: the whiteblack gap ranges from 21 to 38 points, and the whiteHispanic gap ranges from 2027 points” (Rutledge et al., 2009, p. 446). The achievement gap among students of various ethnicities is evident across the nation. In addition, the NAEP has been predominantly important for “measuring change in achievement over time for national cohorts of fourth, eighth, and twelfth graders. These data have shown that significant differences exist among racial and ethnic groups” (Robinson, 2010, p. 265). The findings show that minority students become further behind in reading and mathematics during the middle grades, when the achievement gap is largest (Robinson, 2010). Positively, the results suggest that students of all ethnicities are increasing scores over time and heading in the same direction. However, the scores of the White students are moving faster (Robinson, 2010). Closing this achievement gap is crucial for student learning and “reducing the racial/ethnic achievement gap is perhaps the most important method for bringing about equality within the United States” (as cited in Robinson, 2010, p. 264). The achievement gap exists across the nation and reducing this gap is critical for equality in learning. 31 Texas Mathematics The achievement gap exists in Texas as well. Student groups of African American, Hispanic, White, and economically disadvantaged must meet state standards, and an achievement gap exists between them. There are performance differences on “national and state mathematics tests between different groups of students, the most commonly examined comparisons being by ethnic group and income level” (Flores, 2007, p. 29). These differences equate to a systemic issue in schools today. Educational leaders have the challenge to close the achievement gap and meet the learning needs of students. The achievement gap is not an occurrence that appears at the summation of a student’s academic career. School achievement differences “among subgroups of the population have deep roots. They arrive early and stay late – beginning before the cradle and continuing through to graduation” (Barton, 2003, p. 4). There are several factors that impact the achievement gap. Knowing these factors can help educational leaders combat the existing gap. Barton’s (2003) report identifies 14 factors that affect the academic achievement of students and the school can only impact 6 of these factors. They include the rigor of the curriculum, class size, teacher preparation, teacher experience and attendance, school safety, and technologyassisted instruction (Barton, 2003). Knowing these factors, educators can work to unravel and understand the existing achievement gap and find solutions. Instructional Technology As educators seek solutions for optimizing student achievement, technology has the potential to enhance student engagement and increase achievement (Hepplestone et al., 2011). Employing technology can promote active learning and student excitement for learning. Technologyenhanced learning experiences also can help students develop 21st century 32 competencies such as problem solving, digital literacy, and selfdirected learning (Shapley, 2011). Lessons supported by technology can involve realworld problems and “research shows that students learn more when they are engaged in meaningful, relevant, and intellectually stimulating work” (as cited in Shapley, 2011, p. 299). With technology, students can engage with authentic and relevant topics that challenge them to use problemsolving skills. In addition, “engaged learning and engaged learners are increasingly cited as critical factors in producing significant learning” (Young, 2010, p. 1). Therefore, student engagement can positively impact learning. Curriculum Integration Technology devices are a part of the lives of students. McNulty (2013) recognizes that most students cannot identify with life before laptops and cell phones. Yet many educators “still do not take full advantage of it in their teaching” (McNulty, 2013, p. 41). Implementing instructional technology into the classroom requires the teacher to facilitate the learning environment. Technologyinfused models “suit all types of curricula … which leads the way in applied learning by keeping current with technological advances across disciplines” (McNulty, 2013, p. 41). In an effort to meet student needs, flipped classrooms, blended classrooms, and distance learning classrooms are being employed. These models “change the educator’s role, but they do not negate it” (McNulty, 2013, p. 43). Instructional technology is being employed to maximize student learning. Educators must “seek ways to engage all types of learners so they can succeed not only in the world they live in now, but also in the one they are only beginning to dream up” (McNulty, 2013, p. 43). Instructional technology can aid the educator as they design activities to support reallife applications. 33 As students work collaboratively on practical applications, instructional technology can be employed. Research suggests “that technology yields the greatest learning benefits when it is used in learnercentered ways” (Burns, 2013, p. 42). A studentcentered environment sets the tone for learning and “the creation of learning environments that remain at the heart of why we use technology and for which we strive cannot be attained by technology alone, though technology can aid in this endeavor” (Burns, 2013, p. 44). Instructional technology can enhance learning. Students can put instructional technology devices to use as they learn new concepts and create products for evaluation. Students who used “computer tutorials in mathematics, natural science, or social science scored significantly higher in these subjects compared to traditional approaches” (Burns, 2013, p. 40). Using technology to enhance learning leads to student achievement. Ultimately, it is not the technology alone that makes the students successful because “teachers, not technology, are essential to student learning” (Burns, 2013, p. 41). The teacher facilitates the integration of technology into the curriculum and makes the learning relevant and appropriate for students. Impact of Technology on Student Achievement Not only can technology engage students, it can also impact student achievement in mathematics. Taj and Sivalingam (2013) studied the effectiveness of computerassisted instruction over the traditional method in teaching mathematics. They found that the “mean achievement score, of the students learning with computer assisted instruction, is better than students taught through traditional instruction only” (Taj & Sivalingam, 2013, p. 4). Technology can enhance mathematics instruction and lead to student success. Students in the study found “computer assisted instruction to be an effective method of learning” (Taj & Sivalingam, 2013, p. 4). Employing technology to enhance instruction can lead to student engagement and 34 achievement in mathematics. With increasing efforts of integrating technology into the classroom, students can flourish in learning mathematical content with computers and other instructional technology devices (Taj & Sivalingam, 2013). The use of technology enhances learning. Teachers are choosing to employ “digital resources when building, implementing, and engaging students in classroom experiences” (Thiele, 2013, p. 44). Using this digital content allows the teacher to engage students with instructional technology in various ways. Teachers can “infuse technology into the classroom most successfully when they find new ways to enhance current practices, leveraging technology’s ability to help them connect, collaborate, and enrich” (Gullen & Zimmerman, 2013, p. 66). Technology can be used to enhance instruction in a number of ways. Two ways in which “technology can be extremely valuable are presenting content and assessing achievement” (Davies et al., 2013, p. 565). Teachers can use technology in the classroom to maximize the presentation of content and also in assessment tasks. Differentiated Instruction The teacher can facilitate differentiated instruction to meet the learning needs of students and promote engagement. In fact, “one way to improve learning is to differentiate instruction. The purpose of differentiation is to meet the learning needs of individual students” (Davies et al., 2013, p. 566). Differentiated instruction refers to the delivery of instruction by teachers that consistently adjust instruction and curriculum “in response to student readiness, interest, and learning profile” (Tomlinson et al., 2003, p. 131). Each student possesses a unique learning style and ability. It is the teacher’s role to meet the unique learning needs of each student. Readiness refers to the “knowledge, understandings, and skills” that a student brings to the learning (Santangelo & Tomlinson, 2012, p. 312). Activities designed in response to student readiness 35 are appropriately challenging for the student. Interest refers to the topics or processes that “evoke curiosity and inspire passion” (Santangelo & Tomlinson, 2012, p. 312). Activities geared toward student interest promote engagement and motivation. These activities help students connect to prior knowledge. Learning profile refers to the “ways in which students learn most naturally and efficiently” (Santangelo & Tomlinson, 2012, p. 313). Grouping techniques, learning styles, and classroom environment preferences are examples of learning profile elements. As teachers develop knowledge about differentiated instruction, they begin to tailor instruction to student needs based on interest, readiness, and learning profile. Teachers can also differentiate instruction based on process, product, content, and learning environment. Content refers to the concepts being taught, and process refers to the way that students think about the learning (Santangelo & Tomlinson, 2012). Products are performancebased and demonstrate what students have learned, and the learning environment “consists of the routines, procedures, and physical arrangement of the classroom, as well as the overall tone or mood that exists among and between the students and teacher” (Santangelo & Tomlinson, 2012, p. 314). Creating a positive environment for learning is part of the differentiated classroom. Meeting Student Needs Through Differentiation Differentiated instruction is often delivered to small groups of students, rather than whole group settings. Small group instruction opportunities “give teachers the flexibility to address learner variance more appropriately than does sole reliance on wholeclass instruction” (Tomlinson et al., 2003, p. 132). Differentiated instruction allows the teacher to meet the learning goals of students. Students can be grouped according to interest, readiness, or learning profile. Differentiated instruction increases the variety of instructional activities, learning tools, and class structure. The goal of this instructional approach is to maximize the learning 36 experiences in response to student needs. Through differentiation, the student’s unique learning needs are met and the student successfully demonstrates learning. Differentiated instruction leads to standardized test achievement in mathematics (Chamberlin & Powers, 2010). Teachers can have flexibility in using various learning tools, technology, projects, handson learning, and high levels of discussion. Research studies “indicate that students in these differentiated classrooms achieve better outcomes than students in classrooms with a more singlesize approach to instruction” (Tomlinson et al., 2003, p. 127). Differentiated instruction has the potential to improve student learning outcomes. Impact of Differentiation on Student Achievement Studies in classrooms employing differentiated instruction have seen achievement gains for students of various ethnic subpopulations and socioeconomic groups (Chamberlin & Powers, 2010). The increased class time allows the teacher to meet student needs more effectively through differentiated instructional activities, varied class structure, and learning tools. The benefits of “differentiated instruction includes an increased motivation and enthusiasm for learning” (Chamberlin & Powers, 2010, p. 116). Motivation is a key factor in learning and it is enhanced in the classroom that uses differentiated instruction. More research suggests when “differentiated instruction is implemented with fidelity, it has significant and meaningful benefits for diverse populations of students” (as cited in Santangelo & Tomlinson, 2012, p. 310). The classroom is filled with diverse students of various learning abilities and readiness levels. Differentiated instruction can help meet these individual learning needs. Through differentiated instruction, each student’s learning potential and outcomes are maximized (Santangelo & Tomlinson, 2012). In differentiated classrooms, “all students are engaged in instruction and participating in their own learning” and differentiated thinking 37 “empowers teachers to be responsive rather that reactive to the unique and individual personalities, backgrounds, and abilities found within students” (Anderson, 2007, p. 52). Instruction can be tailored to student needs, and student engagement can be increased in the differentiated classroom. Additionally, “a major drawback of traditional instruction is that many teachers ‘teach to the middle’, which means that the needs of a growing number of students will go unmet” (Rock, Gregg, Ellis, & Gable, 2008, p. 32). Students and teachers share the responsibility of learning in the differentiated classroom and learning tasks are designed for students based on their learning needs. Flipped Instruction The Flipped Classroom The flipped classroom is an instructional strategy that actually ‘flips’ the activities that are traditionally practiced in the classroom and at home. In the flipped classroom, “what is normally done in class and what is normally done as homework is switched or flipped” (Herreid & Schiller, 2013, p. 62). In other words, the instructional lecture and homework practice components are inverted. In traditional lecture, the teacher is active as the students passively listen (Fulton, 2012, p. 21). In the flipped classroom, teachers use instructional technology devices to create lecture videos. Students watch these videos to learn about the concepts and skills outside of class time. Class time is then reserved for solving problems, working collaboratively, extending the learning, and ensuring high levels of thinking (Bull, Ferster, & Kjellstrom, 2013). Teachers restructure class time to meet student needs in the flipped classroom. Using the flipped instructional strategy provides teachers with “the flexibility to create learning groups based on student needs” and it allows the instructional leaders to “select lecture 38 content creation based on strength of delivery by teacher expertise” (Flumerfelt & Green, 2013, p. 364). As teachers create instructional lecture videos, they work to deliver content to students in a concise and clear manner. A traditional classroom lecture that could take an entire class period is being condensed to a 10minute lecture video with the exact information that students need (Bergmann & Sams, 2012). In the flipped classroom, teachers are challenged to refine their lecture and use technology to engage students with content. In addition, instructional videos are subject to pause, rewind, fastforward, and can be played again to meet the learning style and needs of the student (Bergmann & Sams, 2012). In the flipped classroom, “there is an opportunity to reconsider and perhaps reshape the structure of time, communication, collaboration, expectations, and the physical space of the classroom” (Thiele, 2013, p. 44). Learning takes place outside and inside of the flipped classroom, which increases learning time. Meeting student needs is the responsibility of the teacher. “Enabling teachers in the classroom to ‘flip’ lecture time into time for higher level engagement by students and teachers” allows for increased class time (Flumerfelt & Green, 2013, p. 363). This allows “students to increase processing time substantially and to do so in an environment in the classroom, where teacher and peer support is available” (Flumerfelt & Green, 2013, p. 363). Using flipped instruction allows teachers to facilitate differentiated activities for students to practice mathematical concepts, ask questions, and apply mathematics to realworld situations and projects with the teacher readily nearby. Flipped classroom teachers can spend more time with struggling students, employing differentiated instruction to meet learning needs. Parents of struggling students can watch instructional videos to further help their student with content as well. The flipped classroom is “a framework that enables teachers to effectively personalize the education of each student” 39 (Bergmann & Sams, 2012, p. 7). Students can be engaged with concepts and be motivated to complete activities. The flipped classroom allows teachers to meet student needs through differentiated instruction and increase learning time (Bergmann & Sams, 2012). All students learn differently, and the flipped classroom allows students to have access to differentiated instruction from their teacher. The teacher is “engaged in continual formative assessment, diagnosing on the spot each student’s understanding and modifying instruction for each student as needed” (Sams & Bergmann, 2013, p. 18). The flipped classroom offers flexibility for the teacher to meet the specific learning needs of students. Education is for everyone, but the way we deliver education – and the way students receive it – is not the same for everyone. A flipped classroom gives teachers the flexibility to meet the learning needs of all their students, and it gives students the flexibility to have their needs met in multiple ways. By doing so, it creates a classroom that is truly studentcentered. (Sams & Bergmann, 2013, p. 20) As students complete the difficult part of learning in the classroom with the teacher, they have a greater chance of success and mastery than practicing alone without guidance at home (Gullen & Zimmerman, 2013). Studies in classrooms using differentiated instruction, like in flipped classrooms, have seen achievement gains “for all students and across all racial and socioeconomic groups” (Chamberlin & Powers, 2010, p. 116). Furthermore, the flipped classroom has the potential to enhance student achievement. History of the Flipped Classroom Lage, Platt, and Treglia (2000) are thought to be the first to publish a study on the inverted classroom. Using videotaped lectures, reading assignments, and PowerPoint slides about the lecture, students could access the Economics course content outside of class time. 40 Students reviewed the material outside of class time and “students were expected to come to class prepared to discuss relevant material” (Lage et al., 2000, p. 33). The instructors would quickly answer questions about the content and then meaningful practice with experiments, labs, and handson activities would follow. The instructors wanted to meet student needs in a variety of ways, and the inverted classroom afforded them the opportunity to accommodate various learning styles. They used class time more efficiently using the inverted instructional approach. Evidence suggests that students “generally preferred the inverted classroom to a traditional lecture and would prefer to take future economics classes using the same format” (Lage et al., 2000, p. 41). The first inverted classroom was successful by rethinking the way class time was used. Lage et al. (2000) used the technology available at the time in their inverted economics course. The approach became more prominent as access to technology increased. “In the shadow of Colorado’s Pike’s Peak, veteran Woodland Park High School chemistry teachers Jonathan Bergmann and Aaron Sams stumbled onto an idea” (Tucker, 2012, p. 82). They struggled to find a way to deliver course content to absent students and created videos and screencasts to post online. The absent students benefited from these videos and soon other students accessed the online content to review and reinforce concepts. Bergmann and Sams recognized that they could structure their class time differently in the flipped classroom (Tucker, 2012). Bergmann and Sams (2012) currently lead the charge for flipped instruction, author books, and host conferences regarding the benefits of implementing flipped instruction and integrating technology in the flipped classroom. Although the inverted approach has been successfully employed for years, technology has enhanced the current models of flipped classrooms. 41 Flipped Instruction in High School Courses In a flipped high school geometry class, a teacher recorded his lessons and posted the videos to YouTube for students to view online to prepare for class the next day. This means “spending 4560 minutes taping lessons after school, it saves [the teacher] from teaching that same lesson four times, and the video becomes a resource for years to come” (Gullen & Zimmerman, 2013, p. 64). In addition, the teacher can engage students during class time in higherlevel activities and give them “individual feedback and coach them as they work with concepts they’ve just learned” (Gullen & Zimmerman, 2013, p. 64). The teacher noted the videotaped lessons allow him to be less exhausted, more consistent in instruction, and aware of student progress (Gullen & Zimmerman, 2013). The students in the flipped high school geometry class find that flipped instruction meets their needs, and they can “review the lesson multiple times if needed” (Gullen & Zimmerman, 2013, p. 65). This review time and practice time is important for student learning. Flipped Instruction in Higher Education Courses In a study accomplished by Pierce and Fox (2012), the students in the renal pharmacology course “expressed a consistently high preference for the flipped classroom instructional model relative to the traditional instructorled lecture model” and the study “supports the notion that the quality, not necessarily the quantity, of studentteacher interaction is a compelling force in improving student performance” (p. 4). The students in the study recognized the importance of viewing lecture content before class and being prepared for discussions and projects. The flipped classroom implementation in this study “accompanied improved student performance and generated positive student attitudes towards the experience” (Pierce & Fox, 2012, p. 5). Assessment scores increased with the use of flipped instruction. 42 In another college study, Garver and Roberts (2013) found that a common problem in traditional college instruction “is that many straight lecture classes reach only the two lowest levels – knowledge and comprehension of Bloom’s taxonomy of learning” (p. 17). This does not reach higher levels of thinking and learning and does not focus on student engagement and active learning. The dilemma is that there is “not enough time to cover the material and do active learning exercises to achieve higherorder learning” (Garver & Roberts, 2013, p. 17). After implementing the flipped classroom and clicker response systems in the college marketing class, Garver and Roberts (2013) experienced student success; over 90% of class time is dedicated to higherorder learning, and student interest and engagement in the subject has “dramatically increased” (p. 19). Before the implementation of the flipped classroom, only 5% of students scored an A on the 2006 exam in contrast to the 38% that scored an A on the exam in 2011. The study also determined that students believe “learning is greatly improved and more enjoyable as compared to a traditional class format” (Garver & Roberts, 2013, p. 17). Davies et al. (2013) found that the technologyenhanced flipped classroom was found to be “both effective and scalable; it better facilitated learning than the simulationbased training and students found this approach to be more motivating in that it allowed for greater differentiation of instruction” (p. 563). The college level introductory spreadsheet course used flipped instruction because so many students come to the course with varied levels of experiences with spreadsheets. Students review the content before arriving to class, and the instructors can customize instruction to the needs of students. The learning is not “limited to the classroom, and students can move at their own pace and direct their efforts based on their own individual needs, thus personalizing instruction” (Davies et al., 2013, p. 565). The college course instructors were able to create lesson videos that “were as effective at motivating students 43 about the subject matter as the instructors delivering the regular approach” (Davies et al., 2013, p. 578). When students were asked about how much they learned in class, their evaluation of the instructors, their assessment of the value of the class, and if they would recommend the course to another student, the “mean scores for the flipped approach were slightly more favorable than those of the regular approach” (Davies et al., 2013, p. 577). Therefore, the flipped instructional approach proved to be advantageous for college level learners in the introductory spreadsheet course. DeMaio and Oakes (2014) discovered that students in a radiography college course prefer the flipped classroom to traditional lecture. Students view screencasts that are approximately 15 20 minutes in length and then during the next class meeting, “they work in small groups to solve the problems with the instructor providing direct assistance as necessary” (DeMaio & Oakes, p. 341). Students would normally struggle with solving the problems in isolation outside of class time, and are finding success with the flipped classroom. For the professors of the college course, the flipped classroom is a convenient way to offer students additional support, and “flipping allows for more productive inclass time because the instructor can coach students as they work, improving understanding and performance” (DeMaio & Oakes, 2014, p. 342). It is important for students to watch the screencasts ahead of time, so they are ready for solving problems in class. A radiologic science professor found that the flipped classroom has many benefits. Clark (2014) found that flipped instruction promotes active learning, meets individual learning needs through formative assessment and feedback, and provides opportunities for more interaction with students. Another benefit of the flipped classroom is the “promotion of teamwork skills” (Clark, 2014, p. 687). Students learn essential teamwork skills to be successful in their future radiologic 44 science profession. In addition, Clark (2014) found that “collaboration among students in the flipped classroom improves participation, builds confidence, and promotes a sense of teamwork” (p. 687). Collaboration is improved when the flipped instructional strategy is employed. A physical therapist preparation program employed flipped instruction at a Texas university. A comparison was made between students assigned to flipped instruction and traditional instruction sections of the course. The students receiving flipped instruction for a full year experienced no student failures on the examinations, and “this was considered noteworthy, as it was an atypical experience” (Boucher, Robertson, Wainner, & Sanders, 2013, p. 75). The students within the course found that flipped instruction increased time to practice the difficult concepts of physical therapy. Furthermore, the flipped classroom “produced improved learning outcomes as measured by course grades, student surveys, and faculty response” (Boucher et al., 2013, p. 76). Students and professors perceived the flipped instructional approach positively. Chemistry professors also experienced success with the flipped classroom. The seat time of a large lecture university class that met three times per week was reduced by “twothirds while lectures were shifted online” (Baepler, Walker, & Driessen, 2014, p. 235). The students enrolled in the large class were split into three sections that met one day per week. The other two days were spent watching lecture videos and engaged in online discussion of questions and topics. The reduced time in class was used “in an active learning classroom where students worked with each other to solve problem sets, answer clicker questions, listen to spot explanations of key concepts, and watch short demonstrations” (Baepler et al., 2014, p. 235). The students within the college chemistry class benefited from the flipped instructional approach. Although the class seat time was reduced by twothirds, the students “achieved learning outcomes that were in one case superior to, and in the other case statistically equal to, to outcomes from the traditional 45 classroom” (Baepler et al., 2014, p. 235). The traditional classroom kept the lecture format and met three times per week. The flipped instructional approach allowed students to achieve positive learning results with less seat time. Millard (2012) studied more reasons to consider the flipped classroom in college instruction. Professors have found that it increases student engagement and that “students love this system because they’re not listening to some old lecture. They’re interacting and debating, and that makes them feel involved” (Millard, 2012, p. 27). Student engagement is enhanced in the flipped classroom due to the active learning that happens in the classroom and the passive learning that transpires outside of the classroom. This type of learning environment also strengthens teambased skills and “higher education is succeeding with flipped classrooms, because it adjusts the delivery style to the students” (Millard, 2012, p. 28). Teambased activities allow the students to compete with learning groups and engage in active learning. The flipped classroom also allows for personalized student guidance, because “instructors are able to provide personalized instruction to some degree” (Millard, 2012, p. 28). In large college courses, it can be difficult for professors to monitor student progress each day. The use of clickers helps to gauge student answers and progress with the course materials. Students can get “instant feedback about their understanding” (Millard, 2012, p. 28). The flipped classroom was also found to focus classroom discussion and provide faculty freedom. The professors can “concentrate on inclass rich learning activities” (Millard, 2012, p. 29). It also allows for flexibility in instruction because the professor can tailor learning activities to the needs of students. Overall, university professors in the study enjoy the flipped classroom and see the advantages for using this instructional strategy. 46 Flipped Instruction Survey Research In a survey of more than 500 teachers, Classroom Window found that “nearly 90% of respondents who had tried flipping their classroom reported improved job satisfaction; nearly 70% reported increases in student standardized test scores; and 80% reported improved student attitudes” (Brunsell & Horejsi, 2013, p. 8). In addition, flipped instruction is efficient, improves the life of the teacher, strengthens relationships, improves the quality of teaching, increases collaboration, and provides the time to differentiate instruction (Brunsell & Horejsi, 2013). Flipped instruction has many benefits and has impacted the learning environment. More survey research has been conducted in the area of flipped instruction. A survey of the National Center for Case Study Teaching in Science Listserv members conducted by Herreid and Schiller (2013) identified 200 teachers that implement the flipped classroom and found these motives for doing so: There is more time to spend with students on authentic research; students get more time working with scientific equipment that is only available in the classroom; students who miss class for debate/sports/etc. can watch the lectures while on the road; the method promotes thinking inside and outside of the classroom; students are more actively involved in the learning process; and they also really like it. (p. 62) The respondents to the survey also preferred that students watch “online videos over reading material to accomplish the goal of preparing students out of class for inclass active learning. Their students prefer video too” (Herreid & Schiller, 2013, p. 64). The flipped classroom allows for the flexibility of learning that many learners need, and instructors are eager to meet the learning needs of students. 47 Benefits and Challenges of Flipped Instruction Science teachers that responded to the survey by the National Center for Case Study Teaching in Science conducted by Herreid and Schiller (2013) also identified two major problems. They found that students new to the flipped classroom might be “initially resistant because it requires that they do work at home rather than be first exposed to the subject matter in school” (Herreid & Schiller, 2013, p. 63). Students may come to class unprepared. Teachers resolve this by administering a quiz or requiring note taking homework that can only be completed by watching the video or reading the material (Herreid & Schiller, 2013). The other pitfall of implementing the flipped classroom is the homework videos or readings “must be carefully tailored for the students in order to prepare them for the inclass activities” and this takes additional time (Herreid & Schiller, 2013, p. 63). Ultimately, the benefits outweigh the problems. The flipped classroom, “with its use of videos that engage and focus student learning, offers us a new model for teaching, combining active, studentcentered learning with content mastery that can be applied to solving realworld problems. It’s a winwin” (Herreid & Schiller, 2013, p. 65). The flipped classroom allows educators to meet the unique learning needs of students through engaging and active learning. The survey research shows that many educators implement the flipped classroom with success and have found that the flipped classroom offers a new model for teaching and learning (Herreid & Schiller, 2013). The flipped classroom can positively influence student perceptions and learning outcomes. Some teachers are resistant to blended or flipped learning environments because challenges exist. “Finding time for professional learning, fear of change or giving up control, and rapidly changing expectations” are some fears that educators have in regards to the flipped 48 classroom (Thiele, 2013, p. 44). Students must have access to the Internet and a device that can display instructional videos. These components are necessary to the flipped classroom, and some students do not have access at home. Schools must be creative in allowing students the access they need. Allowing students to watch instructional videos on campus before and after school has been a popular solution. Schools must provide sufficient network infrastructure, bandwidth, and wireless access at school in order to foster success in the flipped classroom. Despite the challenges to flipped instruction, teachers are finding ways to incorporate this strategy in their instruction (Thiele, 2013). Implementing the flipped classroom takes time, ingenuity, and patience. Since the flipped classroom concept “is relatively new and still evolving, little research is available to guide best practices” (Bull et al., 2013, p. 11). Videos for the flipped classroom generally span 10 minutes and cover one concept. This allows students to study them one at a time. “A considerable body of research suggests that distributed learning can contribute to more meaningful learning than massed practice” which is fostered in the flipped classroom (Bull et al., 2013, p. 11). Students can also watch the videos at their own pace and when they are ready for learning. “Digital equity is one issue that educators must address during implementation of flipped classrooms” and schools must be creative when students have limited access to Internet and digital tools (Bull et al., 2013, p. 11). Providing materials on a CD or keeping computer labs available before and after school can help alleviate some issues. These issues can be resolved and using flipped instruction “allows teachers to leverage technology to increase interaction with students” (Bergmann & Sams, 2012, p. 25). Leveraging technology in the flipped classroom, students watch lecture videos online and have the “opportunity to hit rewind and view again a section they don’t understand or fastforward through material they have already mastered” 49 (Horn, 2013, p. 78). Students can take ownership of their learning and can decide when to watch the instructional videos. The technology frees up time in class for students to “practice problems, discuss issues, or work on specific projects” (Horn, 2013, p. 78). The instructional technology allows the teacher to guide students to apply online learning in an active learning environment. Summary Educational leaders are charged with the responsibility of student performance on statemandated assessments (Dee & Jacob, 2011). The accountability system is robust and tied to student achievement. Educational leaders and teachers are searching for creative solutions to close the existing achievement gap among student groups (Robinson, 2010). The existing achievement gap persists across the nation, and educational leaders seek solutions to close the gap. Employing technology is a creative solution that can enhance student learning (Shapley, 2011). These technological devices are put to use in the flipped classroom. The flipped classroom has many benefits, and educators are beginning to understand the amount of time that can be saved and devoted to student learning. Traditional classroom lecture does not elevate higherorder thinking and problem solving skills (Garver & Roberts, 2013). Students passively listen to the lecture, and this takes an increased amount of class time. Students are then held responsible for the active part of learning and practice outside of class time. The flipped classroom essentially flips these passive and active components of learning. Active learning and student engagement are enhanced in the flipped classroom (Bergmann & Sams, 2012). Little quantitative research has been conducted in the area of flipped instruction (Bull et al., 2013). It is a relatively new phenomenon that deserves investigation. Throughout this review of the literature, the background was discussed in regards to mathematics achievement 50 and the existing achievement gap among student groups. The use of instructional technology and differentiated instruction was also explored. Flipped instruction was discussed along with existing survey research and research studies conducted in secondary and postsecondary courses. A flipped classroom investigation has not been explored in middle school mathematics and its impact on a state assessment. In this causal comparative quantitative study, the flipped classroom was researched on its impact on student achievement in middle school mathematics as measured by the STAAR, and its ability to close the achievement gap among student groups. 51 Chapter 3 METHOD OF PROCEDURE The primary goal of this causal comparative quantitative research study was to determine the impact of flipped instruction on middle school mathematics achievement as measured by the student scale scores on the State of Texas Assessment of Academic Readiness (STAAR) Grade 8 Mathematics. Another aim of this study was to determine the effectiveness of flipped instruction on closing the existing achievement gap among the student groups of African American, Hispanic, White, economically disadvantaged and noneconomically disadvantaged. Data from students in regular and preAP mathematics classes were also analyzed. The quantitative study used a causal comparative research design with a betweengroups experimental approach. Causal comparative research design is also known as “ex post facto (after the fact) research” (Lunenburg & Irby, 2008, p. 45). This study used the causal comparative research design because the researcher did not manipulate variables or randomize the groups within the study. Causal comparative research does “not manipulate the dependent variable since it has already occurred” (Lunenburg & Irby, 2008, p. 46). The method used to test the research questions is presented in this chapter. The chapter is organized into four sections: (a) selection of participants, (b) instrumentation, (c) data collection, and (d) data analysis. Selection of Participants The quantitative study was conducted in a suburban independent school district in Texas. The public school district educates approximately 39,000 students each year. The school district is comprised of 32 elementary campuses, eight middle school campuses, five high school campuses, and two alternative education campuses, for a total of 47 campuses. This study was 52 centered upon the mathematics achievement of middle school students. Four of the eight middle school campuses are considered Title 1 campuses. Half of the middle school campuses have Grade 6, 7, and 8 students and the other four campuses have Grade 7 and 8 students. A principal and two assistant principals lead each of the eight middle school campuses. Middle school mathematics students are scheduled into various mathematics classes depending on ability and readiness. Eighth grade students can be enrolled in a regular mathematics class and receive grade level instruction; preAdvanced Placement (preAP) mathematics and receive grade level instruction with enrichment; gifted and talented (GT) mathematics and receive above grade level instruction; or basic mathematics and receive special education modified instruction. The focus for this study included the student population for Grade 8 students who received grade level instruction. Therefore, the target population for this study included the students enrolled in Grade 8 mathematics and Grade 8 preAP mathematics. Each middle school campus has certified teachers assigned to deliver instruction to these students, and the classes and class sizes are determined at the campus level by administrators and registrars. The suburban district has a locally developed and paced curriculum, where teachers across the district access the same scope and sequence, lessons, and curriculum resources. The curriculum resources were the same for the 20122013 and the 20132014 academic years. Common district assessments are administered at each campus across all classrooms, and teachers across the district maintain consistent pacing. All Grade 8 mathematics teachers employed traditional instruction during the 20122013 academic year. In August of 2013, prior to the start of the 20132014 academic year, middle school mathematics teachers from Grades 6, 7, and 8 attended an introductory staff development 53 regarding flipped instruction. Teachers learned about the strategy along with the benefits and challenges of implementation. Teachers also learned about technology applications that could assist with the implementation of the flipped classroom, and the teachers learned about those technology applications through practice. Administrators gave teachers autonomy to choose the flipped classroom or the traditional classroom for the 20132014 academic year. The middle school mathematics teachers of this suburban district employed either flipped instruction or traditional instruction to deliver Grade 8 mathematics curriculum resources for the duration of the academic year, and some teachers chose to employ flipped instruction for a shorter time period. When using the traditional method of instruction, teachers chose to instruct students during class time and provide practice time at school and home. The teachers who selected to implement the flipped instructional method of instruction chose to instruct students through instructional videos outside of class time and engage in practice during class time. The goal of this study was to determine the impact of flipped instruction on middle school mathematics achievement. The target population for the study included the students of teachers that delivered Grade 8 mathematics instruction to Grade 8 students in regular and pre AP classes using flipped instruction for the duration of the 20132014 academic year. The students of teachers that chose to implement flipped instruction for a shorter time period were not included in the study. The teachers that implemented flipped instruction needed to be identified. The mathematics curriculum department administered a district survey in May 2014 to determine the teachers that implemented flipped instruction during the 20132014 academic year. In this survey, teachers indicated the strategy used and the duration it was employed. The survey is discussed in more detail in Instrumentation. Permission to access the results of the survey was obtained by the researcher. 54 The classes selected for the study were determined by cluster sampling. In cluster sampling, the process includes “selecting groups, not individuals” (Lunenburg & Irby, 2008, p. 172). The clusters of classrooms were selected once the teachers that implemented the flipped classroom for the full academic year were identified. Eleven 20132014 flipped classroom teachers were identified, and then six flipped classroom teachers that also taught Grade 8 mathematics using traditional instruction during 20122013 were included in the study. The control group included the students of teachers that used traditional instruction during the 2012 2013 academic year and the treatment group consisted of the students of teachers that subsequently used flipped instruction during the 20132014 academic year. The students within the treatment and control groups received instruction by the same teacher, so this reduced the teacher effect differences within the research model. To allow for a sufficient sample of clusters, all 46 target population classrooms were included in the study. Instrumentation STAAR Mathematics This quantitative study used the student scale score for STAAR Grade 8 Mathematics as the measure of mathematics achievement, the dependent variable, and the STAAR Grade 7 Mathematics scale score as a covariate. The scale score is “a conversion of the raw score onto a scale that is common to all test forms for that assessment. Scale scores allow for direct comparisons of student performance between specific sets of test questions from different test administrations” (Texas Education Agency, 2012). The scale score accounts for the difficulty level of the assessment and quantifies the performance of the student (Texas Education Agency, 2012). For the treatment group, the dependent variable was the 2014 STAAR Grade 8 Mathematics scale score, with the 2013 STAAR Grade 7 Mathematics scale score as the 55 covariate. For the control group, the dependent variable was the 2013 STAAR Grade 8 Mathematics scale score, with the 2012 STAAR Grade 7 Mathematics scale score as the covariate. The State of Texas Assessment of Academic Readiness (STAAR) was introduced in Spring 2012. It replaced the former state assessment, Texas Assessment of Knowledge and Skills (TAKS). The STAAR Mathematics assessment is administered in Grades 38 and includes a STAAR End of Course (EOC) assessment for Algebra I (Texas Education Agency, 2010). The mathematics assessments are rigorous and evaluate the skills mastered by students and were “developed using three major design attributes: focus, clarity, and depth” (Texas Education Agency, 2010, p. 25). The assessments are offered in a paperandpencil format and consist primarily of multiplechoice questions, as well as some openended griddable items (Texas Education Agency, 2010). The STAAR assessments are administered in the second semester of each academic year for mathematics in Grades 38 and Algebra I. It is important that the STAAR Mathematics be an accurate and appropriate measure for student achievement in mathematics. The reliability and validity of the assessment score is paramount. “Reliability is the degree to which an instrument consistently measures whatever it is measuring” and the alignment of the test was central to the reliability of the assessment (Lunenburg & Irby, 2008, p. 182). It is important to verify the “extent to which STAAR adequately measures the knowledge and skills specified in the [Texas Essential Knowledge and Skills] TEKS and the extent to which STAAR includes items that cover the full range of achievement standards” (Texas Education Agency, 2010, p. 32). The test must be narrowly aligned to the content standards of the gradelevel and every item included on a STAAR assessment is reviewed by Texas Education Agency, 40 independent Texas educators, and its 56 testing contractor (Texas Education Agency, 2010). The validity is also considered for the STAAR and “validity is the degree to which an instrument measures what it purports to measure” (Lunenburg & Irby, 2008, p. 181). The use of STAAR assessment data is supported by validity evidence, “by correlating the STAAR assessments with other tests or measures of student performance” (Texas Education Agency, 2010, p. 43). Comparisons with national and international assessments were used to establish validity. The National Assessment of Educational Progress (NEAP) is a national assessment and Trends in International Mathematics and Science Study (TIMSS) is an international assessment used to evaluate validity (Texas Education Agency, 2010). External validity evidence was collected and scores on each assessment are associated across grades to performance on other same subject assessments (Texas Education Agency, 2010). The STAAR Grade 8 Mathematics assessment consists of 56 items, including four griddable items (Texas Education Agency, 2011c). The assessment evaluates the application of knowledge and skills in 11 readiness standards and 22 supporting standards. The readiness standards comprise approximately 60%65% of the assessment and supporting standards comprise approximately 35%40% of the assessment (Texas Education Agency, 2011c). Seven process standards are woven throughout at least 75% of the STAAR in the form of dualcoded items, which included a process standard and either a readiness or supporting standard. The STAAR Grade 8 Mathematics included 11 items in Numbers, Operations, and Quantitative Reasoning; 14 items in Patterns, Relationships, and Algebraic Reasoning; eight items in Geometry and Spatial Reasoning; 13 items in Measurement; and 10 items in Probability and Statistics (Texas Education Agency, 2011c). The STAAR Mathematics assessment was scored by the Texas Education Agency. Data were reported to the school district for each student. The 57 STAAR Grade 8 Mathematics assessment had an initial administration and students had two more opportunities to take and meet expectations on the assessment if needed. For the purpose of this study, only the first administration results were analyzed. The student data results and demographics were documented in the suburban district’s Eduphoria database. Middle School Mathematics Flipped Instruction Survey The middle school mathematics teachers in the suburban school district under study completed the Middle School Mathematics Flipped Instruction Survey. The district mathematics curriculum department personnel administered the survey in May 2014. The survey included seven questions to assess the use of flipped instruction. Responses from all middle school mathematics teachers from Grades 6, 7, and 8 in the suburban school district were recorded. Teachers answered questions about the use of flipped instruction and the month they began and ended the use of the strategy. Teachers also reported the classes that received flipped instruction, how often the strategy was used, and if they would employ flipped instruction in the future. Permission to access the results of the survey was obtained by the researcher to determine the Grade 8 classes that received instruction in the flipped classroom. Data Collection Through the results of the Middle School Mathematics Flipped Instruction Survey, the Grade 8 mathematics teachers that employed the flipped method of instruction and their students were determined. Students with both a 2013 STAAR Grade 7 Mathematics scale score and a 2014 STAAR Grade 8 Mathematics scale score were included in the study’s treatment group. Students with both a 2012 STAAR Grade 7 Mathematics scale score and a 2013 STAAR Grade 8 Mathematics scale score were included in the study’s control group. Permission to access the 58 district survey results and access the state assessment student data in the Eduphoria database was obtained by the researcher. Once the researcher obtained permission, personnel from the school district retrieved the data for the researcher. All identifying information for the teachers and students was removed. Confidentiality was maintained. The data that were obtained for the Grade 8 students within the suburban school district are listed in Figure 2. 59 Data Categories: Reported As: Teacher Number 1 – 30 Class Number 1 – 200 Student Number 1 – 7000 Type of Instruction 0 Traditional 1 Flipped Ethnicity 1 African American 2 Hispanic 3 White 4 Other Gender 0 Male 1 Female SocioEconomic Status 0 NonEconomically Disadvantaged 1 Economically Disadvantaged Special Education Status 0 No Special Education Services 1 Special Education Services LEP Status 0 Not LEP 1 LEP Level of Instruction 1 Regular mathematics class 2 PreAP mathematics class Class percentages by Ethnicity 0.00 – 100.0 Class percentage by Gender 0.00 – 100.0 Class percentage Economically Disadvantaged 0.00 – 100.0 Class percentage Special Education 0.00 – 100.0 Class percentage LEP 0.00 – 100.0 2013 STAAR Grade 7 Math Scale Score (treatment) 984 – 2189 (TEA, 2012) 2014 STAAR Grade 8 Math Scale Score (treatment) 1034 – 2231 (TEA, 2012) 2012 STAAR Grade 7 Math Scale Score (control) 985 – 2185 (TEA, 2012) 2013 STAAR Grade 8 Math Scale Score (control) 1036 – 2233 (TEA, 2012) Figure 2. Data collection for data analysis. The teacher and student identification numbers were replaced with numbers randomly generated by the district. The district personnel also paired the teacher number with the type of instruction used. The data remained anonymous to the researcher. The existing data were collected for the 20132014 flipped classrooms, which served as the treatment group. The 60 control group included the 20122013 traditional classrooms that were taught by the teachers that chose flipped instruction for the 20132014 academic year. The student data of teachers that implemented flipped instruction for a shorter period of time were deleted from the data set. In addition, the student data of flipped classroom teachers that did not have 20122013 control group student data were also deleted from the data set. It was important for each student in the treatment group to have a STAAR Grade 7 Mathematics scale score as a covariate variable and a STAAR Grade 8 Mathematics scale score as the dependent variable. Students without both scores were deleted from the data set. Class data were also collected for the treatment and control groups. The percentage of students in the classes who were LEP, economically disadvantaged, and received special education services were included in the data set. The class data also included the percentage of male and female students as well as the percentage of students in the classes who were African American, Hispanic, White, and Other. Data from 23 control group classes and from 23 flipped classes were collected, which included data from 1025 students. The data set was entered as a spreadsheet and inputted into version 21.0 of SPSS for analysis. Data Analysis Experimental design is “historically the only approach for estimating true treatment effects and making causal inferences” (Lane et al., 2012, p. 187). However, research in educational settings does not always lend itself to true randomization and experimental design (Lane et al., 2012). A true experimental research design is difficult to implement in educational settings, particularly when there are multiple schools involved and selection procedures may not be the same at each school (Kim & Seltzer, 2007). 61 Because randomization was not possible for this study, the data were analyzed using propensity score matching (PSM) described by Thoemmes (2012) with steps depicted by Randolph et al. (2014), and a multilevel modeling (MLM) approach described by Rickles (2011). Propensity score methods are used “so that balance on observed covariates is achieved through careful matching on a single score—the estimated propensity of selecting the treatment, or simply the propensity score” (Thoemmes, 2012, p. 2). This PSM allowed the researcher to study the differences in treatment and control groups, although randomization and true experimental design was not possible. Another complication when estimating the effects of educational programs was that the treatment itself may vary across sites. “Variation in the treatment conditions across schools [in this study, across classes] can result in a break of the stableunittreatment value assumption (SUTVA)” or what is sometimes “referred to as treatment enactment variation due to an organization effect” (Rickles, 2013, p. 253254). Rickles (2013) and others advocate investigating effect differences through multilevel modeling. For this study, after the data were preprocessed using PSM, the treatment effect for flipped instruction was analyzed with descriptive statistics and multilevel linear models (Rickles, 2011) to estimate variation in the treatment effect across students and classes. Propensity Score Matching A propensity score matching SPSS procedure developed by Thoemmes (2012) was used to establish an equivalent baseline between the treatment and control groups in the causal comparative study. As outlined by Thoemmes (2012), the first step in PSM was to select pretest covariates based on previous research and theory. This step was vital “as the credibility of the propensity score analysis hinges on the selection of proper covariates” (Thoemmes, 2012, p. 4). For this study, the covariates were gender, ethnicity, socioeconomic status, special education 62 status, and LEP status, as shown in Figure 2. Each student’s STAAR Grade 7 Mathematics scale score was the pretest covariate for the control and treatment groups. Based on this set of covariates, a propensity score was estimated in SPSS using the covariates as predictor variables and the treatment status (0 = traditional, 1= flipped) as the outcome variable. A logistic regression estimation algorithm was used, discarding units outside the common area of support. Selecting this option can “improve balance on covariates and can avoid extrapolation of units in one group that were so dissimilar on their covariates that no comparable units in the other group were found” (Thoemmes, 2012, p. 9). The nearest neighbor 1:1 matching algorithm was used with a 0.25 SD caliper, as used by Rickles (2011). A caliper “is a maximum distance that two units can be apart from each other and is defined in units of standard deviations of the logit of the estimated propensity score” (Thoemmes, 2012, p. 10). The resulting propensity score was the probability of being in a flipped classroom. After matching for regular and preAP mathematics students by teacher was complete, descriptive statistics were run on all covariates for the treatment and control groups to verify balance on the covariates. These statistics are reported in Chapter 4. In this study, the steps indic
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Title  The Impact of Flipped Instruction on Middle School Mathematics Achievement 
Author  Martin, Amanda Grace 
Subject  Educational leadership; Educational administration; Education 
Abstract  THE IMPACT OF FLIPPED INSTRUCTION ON MIDDLE SCHOOL MATHEMATICS ACHIEVEMENT A Dissertation by AMANDA GRACE MARTIN 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 August 2015 THE IMPACT OF FLIPPED INSTRUCTION ON MIDDLE SCHOOL MATHEMATICS ACHIEVEMENT A Dissertation by AMANDA GRACE MARTIN Approved by: Advisor: Melissa Arrambide Committee: Katy Denson Chuck Holt Head of Department: Chuck Holt Dean of the College: Timothy Letzring Dean of Graduate Studies: Arlene Horne iii Copyright © 2015 Amanda Grace Martin iv ABSTRACT THE IMPACT OF FLIPPED INSTRUCTION ON MIDDLE SCHOOL MATHEMATICS ACHIEVEMENT Amanda G. Martin, EdD Texas A&M UniversityCommerce, 2015 Advisor: Melissa Arrambide, EdD The purpose of this causal comparative quantitative research study was to examine the effectiveness of flipped instruction on middle school mathematics achievement when compared to the traditional classroom. The effectiveness of the flipped classroom in closing the existing achievement gap among students of various ethnic subpopulations, socioeconomic statuses, and in the instruction of students within preAP mathematics classes was investigated in this study. Propensity score matching was used to match students taught by the same teacher within control and treatment groups using 1:1 nearest neighbor matching with a caliper of 0.25 SD. The matched student data were analyzed using multilevel modeling facilitated by the mixed models linear program in SPSS. The results indicated that no significant differences existed between the STAAR Mathematics scale scores of students within flipped or traditional classrooms. The researcher failed to reject the null hypotheses of no significant differences between scores of African American, Hispanic, White, Other, economically disadvantaged, noneconomically disadvantaged, and preAP mathematics students in flipped or traditional classrooms. v ACKNOWLEDGEMENTS I am truly grateful for the support of my family, friends, advisor, committee members, and colleagues. Without your encouragement, this journey would not be possible. I am thankful for my time spent at Texas A&M UniversityCommerce. The faculty and staff are helpful, and I am proud to call it my alma mater. Thank you, committee members, for your support and guidance. I appreciate the time and effort you devoted to my journey. Dr. Arrambide, you gave encouragement when it was needed most. Dr. Denson, I am forever indebted to you for the time you generously shared and I admire your expertise. Dr. Holt, I appreciate your sound advice and participation. All of you have made this a rewarding experience, and I thank you. My family, friends, and colleagues have played an incredible role as my support system. I am delighted to have my husband by my side, and my family cheering me on. Thank you for always knowing what to say and do. I do not have words to express my gratitude for your love, time, support, and encouragement. You are truly my biggest fans and I love you. I know that God has great things in store for our lives, and I am excited to see what He has planned for us. vi TABLE OF CONTENTS LIST OF TABLES ...................................................................................................................... x LIST OF FIGURES ................................................................................................................... xi CHAPTER 1. INTRODUCTION ..................................................................................................... 1 Statement of the Problem .................................................................................... 5 Purpose of the Study ........................................................................................... 8 Research Questions and Hypotheses .................................................................. 9 Significance of the Study .................................................................................. 11 Method of Procedure ......................................................................................... 12 Selection of Sample ................................................................................... 12 Collection of Data ...................................................................................... 16 Treatment of the Data ................................................................................ 16 Propensity Score Matching .................................................................. 17 Multilevel Modeling ........................................................................... 20 Definitions of Terms ......................................................................................... 21 Limitations ........................................................................................................ 23 Delimitations ..................................................................................................... 23 Assumptions ...................................................................................................... 24 Organization of Dissertation Chapters .............................................................. 24 2. REVIEW OF THE LITERATURE ......................................................................... 26 Theoretical Background of Mathematics Achievement ................................... 27 Federal Mandates ....................................................................................... 27 vii CHAPTER State Mandates ........................................................................................... 28 The Mathematics Achievement Gap Among Student Groups .......................... 29 National Mathematics ................................................................................ 30 Texas Mathematics .................................................................................... 31 Instructional Technology .................................................................................... 31 Curriculum Integration ............................................................................... 32 Impact of Technology on Student Achievement ........................................ 33 Differentiated Instruction .................................................................................. 34 Meeting Student Needs Through Differentiation ....................................... 35 Impact of Differentiation on Student Achievement ................................... 36 Flipped Instruction ............................................................................................ 37 The Flipped Classroom .............................................................................. 37 History of the Flipped Classroom .............................................................. 39 Flipped Instruction in High School Courses .............................................. 41 Flipped Instruction in Higher Education Courses ...................................... 41 Flipped Instruction Survey Research ......................................................... 46 Benefits and Challenges of Flipped Instruction ......................................... 47 Summary ........................................................................................................... 49 3. METHOD OF PROCEDURE ................................................................................... 51 Selection of Participants ................................................................................... 51 Instrumentation ................................................................................................. 54 STAAR Mathematics ................................................................................. 54 viii CHAPTER Middle School Mathematics Flipped Instruction Survey .......................... 57 Data Collection ................................................................................................. 57 Data Analysis .................................................................................................... 60 Propensity Score Matching ............................................................................... 61 Constructing the Data Set ................................................................................. 65 Multilevel Modeling ......................................................................................... 68 Research Question 1 .................................................................................. 72 Research Question 2 .................................................................................. 72 Research Question 3 .................................................................................. 72 Research Question 4 .................................................................................. 73 Summary ........................................................................................................... 73 4. PRESENTATION OF DATA ................................................................................... 76 Data Set ...................................................................................................... 77 Data Analyses ................................................................................................... 78 Propensity Score Matching ........................................................................ 79 Restructuring the Data ............................................................................... 84 Multilevel Modeling .................................................................................. 85 Null Model ........................................................................................... 85 Growth Rate Model ............................................................................. 88 Treatment Model .................................................................................. 89 Model with Level 1 Student Variables ............................................... 89 Model with Level 2 Class Variables ................................................... 90 ix CHAPTER Model with Interactions with Treatment ............................................. 91 Research Questions ........................................................................................... 91 Research Question 1 .................................................................................. 91 Research Question 2 .................................................................................. 92 Research Question 3 .................................................................................. 93 Research Question 4 .................................................................................. 93 Summary ........................................................................................................... 94 5. SUMMARY OF THE STUDY AND THE FINDINGS, CONCLUSIONS, IMPLICATIONS, AND RECOMMENDATIONS FOR FUTURE RESEARCH .. 96 Findings ............................................................................................................. 97 Conclusions ..................................................................................................... 100 Implications ..................................................................................................... 103 Recommendations for Future Research .......................................................... 105 REFERENCES ....................................................................................................................... 108 VITA ...................................................................................................................................... 116 x LIST OF TABLES TABLE 1. Percentage of Texas students meeting expectations on 2013 STAAR Mathematics ...... 7 2. Percentage of Texas and Suburban ISD students meeting expectations on 2013 STAAR Grade 7 Mathematics ........................................................................................ 13 3. Student Characteristics of Grade 8 Regular Mathematics Students Original and Matched Samples ........................................................................................................... 80 4. Student Characteristics of Grade 8 PreAP Mathematics Students Original and Matched Samples ........................................................................................................... 81 5. Standardized Differences in Characteristics of Treatment and Control Groups by Level of Instruction, Regular or PreAP ........................................................................ 84 6. Parameter Estimates for Five Models Examining the Differences Between Traditional and Flipped Instruction with Covariate Influence ....................................... 87 xi LIST OF FIGURES FIGURE 1. Summary of steps to construct the matched flipped and traditional classroom sample .. 19 2. Data collection for data analysis ...................................................................................... 59 3. Steps to construct the matched flipped and traditional classroom sample ....................... 63 4. Distribution of propensity scores for Grade 8 students in regular mathematics classes .. 82 5. Distribution of propensity scores for Grade 8 students in preAP mathematics classes .. 83 1 Chapter 1 INTRODUCTION In education, student achievement is paramount. Administrators encounter the challenge of leading instructional programs and choosing instructional strategies that enhance and increase student achievement. In a time of intense accountability, educational systems face “severe challenges to meet bottom line results while external pressures from federal, state, and local mandates are compelling educational leaders to drive enhanced student achievement” (Onorato, 2013, p. 33). Instructional leaders face this challenge as they build effective learning environments for students and teachers. Instructional leaders also strive to improve teacher quality with an ultimate goal of raising student achievement (Pansiri, 2008). The quality of learning depends on the strategies implemented by teachers and administrators. The quality teacher uses various teaching practices and instructional strategies to impact student success (Anderson, 2007). The intentional selection of these instructional strategies is important to consider. Instructional strategies are needed to maximize instructional time and offer flexibility for the teacher to meet student needs and increase achievement (Bergmann & Sams, 2012). Varying student needs provoke the necessity for a variety of strategies to employ in the classroom. Students deserve instruction that meets their needs in multiple ways, and teachers need more time to conduct small group instruction and work with students one at a time to impact student achievement (Flumerfelt & Green, 2013). Time is a valuable resource, and strategies are needed to increase learning and teaching time. Educational leaders can impact student achievement through the selection and implementation of instructional strategies (Onorato, 2013). It is essential for educational leaders to choose instructional strategies that positively impact the learning environment. Flipped instruction, or the flipped classroom, is an 2 instructional approach that is gaining momentum and attention in the learning community and could be selected by educational leaders to positively influence student achievement, specifically mathematics achievement (Love, Hodge, Grandgenett, & Swift, 2014). The purpose of the study was to examine the flipped classroom and its effect on student learning. The flipped classroom allows educators to “radically rethink how they use class time” (Tucker, 2012, p. 82). The flipped classroom essentially ‘flips’ what is traditionally done in class and what is traditionally done as homework. The activities that are completed at home and at school are inverted in the flipped classroom, which is an “inverted approach in which the students’ homework is to view a recording of the lecture, and class time is used for active problemsolving activities with instructor guidance” (DeMaio & Oakes, 2014, p. 340). In the flipped classroom, students learn content outside of class time. Students can view instructional videos, take notes to learn content at home, and then practice the content during class with the guidance of the teacher. Class time is devoted to “practice assignments, targeted remedial help, or activities designed to promote higher order thinking skills” (Davies, Dean, & Ball, 2013, p. 564). In the traditional mathematics classroom, students listen to the instructional lecture during class time and practice mathematics problems in the time remaining at school and finish at home. In contrast, in the flipped mathematics classroom, students view instructional lecture videos at home and practice mathematics problems during class time. The flipped classroom could offer a solution for teachers and administrators who want to maximize the use of class time to increase student achievement (DeMaio & Oakes, 2014). Student experiences in the traditional classroom are often more passive in nature. In traditional classroom lecture, “the teacher is doing the active work and the students are passively listening” (Fulton, 2012, p. 21). In the flipped classroom, students watch teachercreated lecture 3 videos and learn about the concepts and skills outside of class time. They take notes and prepare questions or discussion topics for the next class. Teachers employing the flipped instructional approach expect students to watch the lecture video and hold them accountable for watching the instructional video by checking their notes and questions (DeMaio & Oakes, 2014). This strategy allows class time to be devoted to solving problems, working collaboratively, extending the learning, and ensuring high levels of thinking. Class time is valuable, and this instructional time is maximized using the flipped instructional approach. The flipped classroom “redefines class time as a studentcentered environment” (Sams & Bergmann, 2013, p. 17). Students and teachers can use class time to work together, and students have the benefit of having the certified teacher assist them with their practice instead of struggling with new content outside of class. In the flipped classroom “students learn by doing, and ... the doing is happening within a handraise of the teacher. Students are no longer at home in isolation and unsupported while they do the difficult work of learning” (Fulton, 2012, p. 22). When students watch lecture videos prepared by their teacher outside of class time, they are prepared to engage in meaningful practice during class. This also allows the teacher to differentiate for students and work with individual students or small groups each day. Differentiated instruction points to “achievement gains on standardized tests, including mathematics assessments” (Chamberlin & Powers, 2010, p. 116). Teachers can engage students in learning activities tailored to their needs and “most importantly, all aspects of instruction can be rethought to best maximize the scarcest learning resource – time” (Tucker, 2012, p. 82). Time for practice and solving problems is valuable, and using technology maximizes learning time in the flipped classroom. 4 Technology also plays a large role in the implementation of the flipped classroom. Many teachers and educational leaders believe that students should be engaged in learning with technology (Hepplestone, Holden, Irwin, Parkin, & Thorpe, 2011). The flipped classroom allows for this engagement. Technology tools can be employed in the flipped classroom to enhance learning opportunities. The flipped classroom “relies on technology to introduce students to course content outside of the classroom so that students can engage that content at a deeper level inside the classroom” (Strayer, 2012, p. 171). Using technology, students in the flipped classroom can have more time to complete the rigorous learning tasks expected of them. The teacher becomes the facilitator of learning and can be available to help students and differentiate activities as needed (Love et al., 2014). Students in flipped classrooms also “see value in helping each other learn with a cooperative approach” (Strayer, 2012, p. 183). This cooperative approach is advantageous in learning, and students in flipped classrooms are “more willing to work together and engage in activity in the classroom than the students in the traditional classroom” (Strayer, 2012, p. 188). These students are also more eager to participate in class and struggling students can get the help they need. Teachers credit the flipped classroom with “fostering better relationships, greater student engagement, and higher levels of motivation” (Tucker, 2012, p. 82). Increased class time, fewer student failures, energized teachers, more opportunities for differentiated instruction, and engaged students are just some of the benefits (Bergmann & Sams, 2012). In an “experimental flipped class, the students increased their online engagement and homework rates from 75% to 100%,” which resulted in an “elimination of all students’ class failures” (Flumerfelt & Green, 2013, p. 364). Because of the many possible benefits, educational leaders could choose the flipped classroom as an instructional strategy to impact student achievement. 5 In this study, the implementation of flipped instruction in middle school mathematics classrooms was examined to determine the impact on student achievement. This instructional strategy was also analyzed to assess its potential to close the achievement gap that exists between students of various ethnicities and socioeconomic statuses. Additional research was needed “to assess the direct effect of the flipped classroom on student learning outcomes” (DeMaio & Oakes, 2014). Therefore, this quantitative research study focused on the impact of flipped instruction on middle school mathematics achievement as measured by state assessment scores and its effectiveness in closing the existing achievement gap among students of various ethnic subpopulations and socioeconomic statuses. Statement of the Problem Educational leaders seek strategies to increase class time, student engagement, and overall student achievement. Teachers need an approach that allows them to meet the unique learning needs of students (Anderson, 2007). Educational leaders must make instructional decisions that impact the learning environment, as they are “expected to be instructional leaders” (Vornberg, Hickey, & Borgemenke, 2012, p. 128). Purposeful selection and implementation of instructional strategies is necessary in the learning environment. Flipped instruction was examined to determine its effectiveness as an instructional approach. The flipped classroom allows for increased time in class for differentiation and student engagement that “has been empirically related to achievement test scores and grades” (Young, 2010, p. 4). This quantitative research study was conducted to determine the effect of the flipped instructional approach on student achievement in middle school mathematics when compared to the traditional instructional approach. 6 The accountability system in Texas is rigorous and holds districts, administrators, teachers, and students to high standards. Students in the state of Texas are evaluated annually for performance on the State of Texas Assessment of Academic Readiness (STAAR). Texas students must perform satisfactorily on STAAR assessments. School districts in Texas must ensure that all students learn required content and must look carefully at achievement gaps between students of various ethnicities and socioeconomic statuses (Texas Education Agency, 2010). In the state of Texas, 79% of students in all grades met expectations on the 2013 State of Texas Assessment of Academic Readiness (STAAR) Mathematics assessment. However, an achievement gap exists between ethnic subpopulations, as shown in Table 1. White students outperform their African American and Hispanic peers. In addition, students who are economically disadvantaged perform slightly lower than noneconomically disadvantaged peers. 7 Table 1 Percentage of Texas Students Meeting Expectations on 2013 STAAR Mathematics Note. From “20122013 Texas Performance Reporting System: Report for State,” by Texas Education Agency, 2013b. Efforts must be made to close the achievement gap. Teachers are looking for innovative ways “to instruct technology age students, administrators are seeking new ways to lead teachers in an age of increasingly uncertain resource allocations, and district officers are looking for new ways to train instructional leaders for the 21st century” (Smith & Addison, 2013, p. 135). As new instructional strategies are needed to close the achievement gap and engage students, flipped instruction was examined. In addition, teachers are faced with meeting the unique learning modes of students in basic classes, regular classes, preadvanced placement (preAP) classes, and gifted/talented (GT) classes. Students within these classes have varied learning and readiness levels. Teachers and administrators can work collaboratively to impact student achievement through the selection of effective instructional strategies (Pansiri, 2008). In addition, “we know challenge, rigor, high Characteristic Percent African American 68 Hispanic 76 White 88 Economically Disadvantaged 72 NonEconomically Disadvantaged 89 All Students 79 8 standards, and expectations are critical to improved student achievement” (Swanson, 2006, p. 23). Teachers must keep high expectations for students in all classes in order to attain increased student achievement. It is critical to note that “minority and lowincome students benefit from advanced curricula and instructional strategies that challenge them” (Swanson, 2006, p. 11). While teachers are faced with the challenge of teaching and reaching every student at his or her ability level, little quantitative research has been conducted in the area of the flipped classroom (Love et al., 2014). An effective instructional approach is needed to positively impact student achievement, and the flipped classroom was investigated in this quantitative research study. Purpose of the Study The purpose of this quantitative study was to examine the effects of the flipped classroom on middle school mathematics achievement when compared to the traditional classroom. Another aim was to determine the effectiveness of the flipped classroom as an instructional approach in closing the existing achievement gap among identified student groups, including African American, Hispanic, White, and economically disadvantaged and noneconomically disadvantaged. The effectiveness of the flipped classroom in the instruction of students within preAP classrooms was also examined. To measure student achievement, scale scores from the STAAR Grade 8 Mathematics and STAAR Grade 7 Mathematics, used as a covariate, were reported, collected, and analyzed. Flipped instruction is a new instructional strategy used in the classroom with little research regarding its effectiveness. In addition, the results of the study can inform educational leaders as they choose effective instructional strategies to implement in the learning environment. 9 Research Questions and Hypotheses The causal comparative quantitative study analyzed the flipped instructional strategy and its impact on the mathematics achievement of Grade 8 students in one suburban independent school district. Data from students who received instruction in the flipped classroom and the traditional classroom were compared and analyzed. The following questions guided the research study: 1. To what extent does the flipped classroom increase student achievement on the STAAR Grade 8 Mathematics assessment when compared to the traditional classroom? a. Ho1: There is no significant difference between the mathematics scores of students receiving instruction in the flipped classroom and the mathematics scores of students receiving instruction in the traditional classroom. b. Ha1: There is a significant difference between the mathematics scores of students receiving instruction in the flipped classroom and the mathematics scores of students receiving instruction in the traditional classroom. 2. To what extent does the flipped classroom increase mathematics scores of economically disadvantaged students when compared to the traditional classroom? a. Ho2: There is no significant difference between the mathematics scores of economically disadvantaged students receiving instruction in the flipped classroom and the mathematics scores of economically disadvantaged students receiving instruction in the traditional classroom. b. Ha2: There is a significant difference between the mathematics scores of economically disadvantaged students receiving instruction in the flipped 10 classroom and the mathematics scores of economically disadvantaged students receiving instruction in the traditional classroom. 3. To what extent does the flipped classroom close the achievement gap between students of ethnic subpopulations when compared to the traditional classroom? a. Ho3: There is no significant difference between the mathematics scores of White, African American, and Hispanic students receiving instruction in the flipped classroom and the mathematics scores of the White, African American, and Hispanic students receiving instruction in the traditional classroom. b. Ha3: There is a significant difference between the mathematics scores of White, African American, and Hispanic students receiving instruction in the flipped classroom and the mathematics scores of White, African American, and Hispanic students receiving instruction in the traditional classroom. 4. To what extent does the flipped classroom increase mathematics scores of students in preAP and regular mathematics when compared to the traditional classroom? a. Ho2: There is no significant difference between the scores of students in pre AP and regular mathematics classes receiving instruction in the flipped classroom and the scores of students in preAP and regular mathematics classes receiving instruction in the traditional classroom. b. Ha2: There is a significant difference between the scores of students in preAP and regular mathematics classes receiving instruction in the flipped classroom and the scores of students in preAP and regular mathematics classes receiving instruction in the traditional classroom. 11 Significance of the Study The intent of the causal comparative quantitative study was to identify whether the flipped instructional strategy was an effective approach to increase mathematics achievement for middle school students. If educational leaders can determine the factors that can increase student achievement in mathematics, then leaders can implement the instructional strategy to positively impact students. Closing the achievement gap among ethnic subpopulations is a goal for many academic programs (Chamberlin & Powers, 2010). African American and Hispanic students are expected to exemplify success on state assessments at the same level as their White peers, and an instructional approach must be found to close the achievement gap. Mathematics achievement trends “suggest that the gap between some minority and White students persists and may even be widening” (Bol & Berry, 2005, p. 33). Student achievement is paramount, and educational leaders seek effective instructional strategies to employ in the learning environment to close the achievement gap among students of various ethnic subpopulations. In addition, studies reveal that economically disadvantaged students typically perform below their mainstream counterparts and “there is a considerable gap in test performance between students from poor families and those from nonpoor families” (Flores, 2007, p. 30). The potential impact of the flipped classroom cannot be overlooked. The objective of this research study was to examine the flipped instructional strategy as an approach to increase mathematics achievement in middle school students and to examine its potential to close the achievement gap among students of various socioeconomic statuses and ethnicities. This study also provided insight into the strategies that are effective in differentiating instruction for high achieving students in preAP classes. Teachers and administrators need instructional approaches that positively impact student achievement and creatively use valuable instructional time. In the 12 flipped classroom, “teachers spend more actual time teaching and facilitating instead of just lecturing” (Fulton, 2012, p. 22). Being intentional and purposeful with the time devoted to learning can lead to successful learning outcomes. A central theme is that “active learning works best. Telling doesn’t work very well. Doing is the secret. Active student engagement is necessary” (Herreid & Schiller, 2013, p. 65). This study is added to the body of research on the flipped classroom and its impact on middle school mathematics student achievement. Method of Procedure This causalcomparative quantitative study analyzed the effectiveness of the flipped instructional strategy on mathematics achievement of Grade 8 students when compared to the traditional instructional approach. The quantitative data of this study included the STAAR Grade 8 Mathematics scale scores, student ethnicities, socioeconomic status, and level of instruction, regular education or preAP. The independent variable was defined as the type of instruction, flipped instruction or traditional instruction. The dependent variable was mathematics achievement as measured by the STAAR Grade 8 Mathematics scale score, using the STAAR Grade 7 Mathematics scale score as a covariate. The students receiving instruction in the traditional classroom served as the control group, and the students receiving instruction in the flipped classroom served as the treatment group. Selection of Sample The causalcomparative quantitative study was conducted in a suburban independent school district in Texas. The district served students in grades PreKindergarten through 12. The district stretched approximately 60 square miles and has approximately 39,000 students at 47 campuses. This study included the data from all 8 middle school campuses. In the suburban independent school district used in this study, 75% of students met expectations on the 2013 13 State of Texas Assessment of Academic Readiness (STAAR) Grade 7 Mathematics. An achievement gap existed between ethnic subpopulations, as shown in Table 2. Similar to the state, White students outperform their African American and Hispanic peers in the suburban independent school district used in this study. In addition, students who are economically disadvantaged performed lower than noneconomically disadvantaged peers. Table 2 Percentage of District Students Meeting Expectations on 2013 STAAR Grade 7 Mathematics Characteristic Texas Suburban ISD African American 58 64 Hispanic 67 78 White 83 81 Economically Disadvantaged 64 73 NonEconomically Disadvantaged 84 80 All Students 72 75 Note. From “20122013 Texas Performance Reporting System,” by Texas Education Agency, 2013b. The student ethnic makeup of this district included 51.3% Hispanic students, 24.9% African American students, 19.3% White students, and 4.5% other students (Texas Education Agency, 2013a). Currently, 70.3% of students in the suburban district are considered economically disadvantaged (Texas Education Agency, 2013a). Ethnic subpopulations and socioeconomic statuses for the specific students in this study are reported in Chapter 4. 14 All middle school mathematics teachers participated in an introductory 6hour professional development session regarding flipped instruction before the 20132014 academic year began. The professional development session highlighted the benefits and challenges for flipping the classroom. Included in the study were the students of Grade 8 middle school mathematics teachers who attended this training. All Grade 8 mathematics teachers used traditional instruction for the 20122013 academic year. Teachers were given autonomy from their administrators to choose the traditional classroom or the flipped classroom as an instructional approach to implement throughout the 20132014 academic year. Therefore, some teachers chose to implement the flipped instructional approach in their Grade 8 mathematics classes, some chose to use the traditional instructional method, and some chose to use the flipped instructional approach for a shorter period of time. Data from all Grade 8 mathematics teachers were gathered and compared based upon the instructional approach chosen. The middle school mathematics teachers in the suburban independent school district have a locally developed paced curriculum. All teachers followed the same scope and sequence and lesson documents, regardless of whether they chose to use flipped or traditional instruction. The curriculum resources were the same for the 20122013 and 20132014 academic years. Middle school mathematics classes in the district included regular mathematics, where students receive grade level instruction; preAdvanced Placement (AP) mathematics, where students receive grade level instruction with enrichment; gifted and talented (GT) mathematics, where gifted students receive above grade level instruction; and basic mathematics, where students receive special education modified instruction. For the context of this study, only students in regular and preAP mathematics classes were included because they were the eighth graders receiving grade level instruction. For the 20132014 school year, there were 127 classes of Grade 8 students in 15 the district under study with 108 regular mathematics classes and 19 preAP mathematics classes. In addition, only students with both a STAAR Grade 7 Mathematics score and STAAR Grade 8 Mathematics score were included in the study. The number of classes and students included in this study are described in detail in Chapter 4. At the end of the 20132014 academic year, district personnel administered a survey to the Grade 8 mathematics teachers. Permission to access the results of this survey was obtained by the researcher. The results of this survey indicated the teachers who chose to implement the flipped instructional approach during the 20132014 academic year. Through the use of cluster sampling, the student data of Grade 8 teachers who implemented flipped instruction for the duration of the 20132014 academic year served as the treatment group. Once the flipped classroom teachers were identified, their student data from the previous 20122013 academic year served as the control group. This control group received traditional instruction for the 2012 2013 academic year. The 20132014 treatment and 20122013 control group students taught by the same teacher were matched using propensity score matching and were included in this study. The student data of Grade 8 teachers that chose to implement flipped instruction for a shorter period of time were not included in the study. Therefore, the results of the teacher survey determined the number of flipped classrooms in the district under study for the 20132014 academic year. Multilevel modeling was used to analyze data in this study, with the student data as Level 1 and the class data for Level 2. In studies that use multilevel modeling, the researcher can strive for a sample of “about 50 groups with about 20 individuals per group” (Hox, 2010, p. 235). For this study, the groups are classes. Therefore, this quantitative study analyzed student data from the treatment and control group classes with both STAAR Grade 7 Mathematics and STAAR 16 Grade 8 Mathematics scale scores. There were a sufficient number of classes included in this study with about 20 students in each class. Collection of Data The population for this study included Grade 8 students who received flipped instruction during the 20132014 academic year and Grade 8 students who received traditional instruction taught by the same teacher during the 20122013 academic year. Because a multilevel modeling technique was used for data analysis, data were collected for two levels, the student level and the class level. Level 1 student data included the STAAR Grade 8 Mathematics scale scores, STAAR Grade 7 Mathematics scale scores as covariate, and ethnicity, limited English proficiency (LEP) status, gender, special education status, socioeconomic status based on freeor reducedprice lunch status, class code, and teacher code. Students and teachers were given a coded number to maintain anonymity. Level 2 class data were whether the teacher used flipped or traditional instruction and whether the class was a regular or preAP mathematics class. Other classlevel variables were computed by the researcher and discussed in the next section. Once the researcher obtained permission, personnel from the school district retrieved the data for the researcher. All identifying information for the students along with their class and teacher were removed and replaced with a number randomly generated by district personnel to maintain confidentiality and anonymity. The district personnel also paired the teacher number with the type of instruction used so that the students in the treatment and control groups taught by the same teacher could be matched and analyzed. Treatment of the Data The complexity of educational research makes the interpretation of treatment effects difficult because of the lack of true randomization and experimental design in educational 17 settings (Lane, To, Shelley, & Henson, 2012). Therefore, the data were analyzed using propensity score matching strategies described by Thoemmes (2012) and steps outlined by Randolph, Falbe, Manuel, and Balloun (2014), and multilevel modeling techniques described by Rickles (2011). These strategies allowed the researcher to analyze the treatment effect of flipped instruction across students and classes. The propensity score matching and multilevel modeling allowed for “double robustness” in the study (Schafer & Kang, 2008, p. 280). Propensity score matching. Propensity score matching was used to match the students in the control and treatment groups of the causal comparative study. The propensity score is the “probability of receiving the treatment given the observed covariates” (Stuart & Rubin, 2008, p. 281). When random assignment is not possible in a study, propensity score matching can be used to “control for bias in a treatment effect” (Lane et al., 2012, p. 187). A propensity score was calculated for each student based on the probability of receiving flipped instruction based on covariates. The propensity scores were calculated separately among regular students and then preAP students. Students with similar propensity scores were matched from the flipped and traditional classrooms. This created “balance on the covariates that were used to estimate the propensity score” (Thoemmes, 2012, p. 3). The statistical matching of students accounted for the nonrandomization within the study because the students were matched across the treatment and control groups based on the covariates of ethnicity, socioeconomic status, gender, LEP status, special education status, and scale scores for the STAAR Grade 7 Mathematics. The U.S. Department of Education “supports propensity score matching as a method for evidencebased research when group equivalence can be established through the analysis” (Lane et al., 2012, p. 188). The use of propensity score matching aided the researcher in ruling out the possibility that differences between treatment and control groups were due “to systematic 18 differences between the groups at baseline” (Schafer & Kang, 2008, p. 279). To further reduce teacher effect in this study, the students within the treatment and control groups received instruction from the same teacher. The propensity scores were calculated for each student in the study using 1:1 nearest neighbor matching, which means that “a single treated participant is matched to a single untreated participant who has the most similar estimated propensity score” (Thoemmes, 2012, p. 5). A caliper of 0.25 SD, also used by Rickles (2011), allowed for a close match between students of the flipped and traditional instruction groups. This propensity score matching technique allowed the researcher to analyze the differences in treatment and control groups although randomization and true experimental design was not possible. The students within the treatment and control groups were matched based on propensity score, creating pairs of student data. It is important to consider the balance in baseline covariates within the matches (Austin, 2008). Therefore, a standardized differences method recommended by Ho, Imai, King, and Stuart (2007) was used to assess the balance of the differences. The standardized difference is “the absolute difference in sample means divided by an estimate of the pooled standard deviation of the variable” (Austin, 2008, p. 2039). This method assessed the balance within the matched pairs of students and was reported in this research study in Chapter 4. This method allowed for less bias and less variance in the model (Ho et al., 2007). Furthermore, Austin (2008) discussed five recommendations for studies that use propensity score matching. The details of those recommendations are depicted in Chapter 3. In the first step of the propensity score matching process, the 20132014 treatment students who received flipped instruction in regular mathematics classes were matched to 2012 2013 control students in regular mathematics classes that used traditional instruction, taught by the same teacher. A data file was saved for this group. In the next step, the 20132014 treatment 19 students in the preAP mathematics classes were matched to the 20122013 control students in preAP mathematics classes. A data file was saved for this group as well. The propensity score matching technique allowed the matched data to be similar to randomized methods, where treatment and control groups are created randomly and independently (Rickles, 2011). Once the matching process was complete, two data files were created with the matched treatment and control students for regular mathematics classes (M) and the matched treatment and control students for preAP mathematics classes (MC). Then the matched treatment and control students in data file M and MC were used in a 2level multilevel modeling procedure to estimate the treatment effects of receiving instruction in the flipped classroom. The steps to construct the matched control and treatment group sample are summarized in Figure 1, and are described in more detail in Chapter 3. Step Description 1 Estimate the propensity score for each student using the STAAR Grade 7 Mathematics scale score and student demographic characteristics as covariates. 2 For the regular mathematics classes, create data set M by conducting a 1:1 propensity score match without replacement, using a caliper of 0.25 SD of the propensity score logodds with control and treatment students. 3 For the preAP mathematics classes, create data set MC by conducting a 1:1 propensity score match without replacement using a caliper of 0.25 SD of the propensity score logodds with control and treatment students. 4 Export the data files for analyses. Estimate the treatment effect outcome in data sets M and MC using a multilevel linear model. The multilevel model includes the same student characteristics and allows the intercept to vary across the teachers. Figure 1. Summary of steps to construct the matched flipped and traditional classroom sample. Adapted from “A stepbystep guide to propensity score matching in R,” by Justus J. Randolph, Kristina Falbe, Austin Kureethara Manuel, and Joseph L. Balloun, 2014, Practical Assessment, Research & Evaluation, p. 16. 20 Multilevel modeling. Once the propensity scores were calculated for each student, multilevel modeling was used to evaluate the data imported into version 21.0 of the Statistical Package for the Social Sciences (SPSS). “Multilevel modeling provides a powerful framework for analyzing data collected in the school context” (Dettmers, Trautwein, Ludtke, Kunter, & Baumert, 2010, p. 472). Multilevel modeling is a robust model of analysis and was used to analyze the matched pairs of student data. As in most research conducted “in school settings, students in this study are nested within classes. Students within a class are typically more similar to each other than are two students randomly selected from the whole sample” (Dettmers et al., 2010, p. 472). Multilevel modeling considered the nested data within the educational context. For this study, Level 1 student data were nested within the Level 2 class data. For this study, multilevel modeling analyzed the impact of flipped instruction or traditional instruction on the STAAR Grade 8 Mathematics scale score. Level 1 student data were nested within the Level 2 class data. Level 1 student data included the STAAR Grade 8 Mathematics scale score, gender, socioeconomic status, ethnicity, special education status, and LEP status. Using the STAAR Grade 7 Mathematics scale score as the covariate adjusted for initial differences in the flipped instruction and traditional instruction groups. Level 2 class data included the type of instruction (flipped or traditional), level of instruction (regular or preAP), and aggregated class data of percent of economically disadvantaged students, percent of students by ethnic subpopulation, percent of students who are limited English proficient, percent of students who receive special education services, and percent of students by gender. Because teachers and schools used either all flipped classes or no flipped classes, it was not necessary for teacher and school variables to be included in the model. 21 Definitions of Terms Accountability Rating System. As part of the Texas Education Agency’s accountability rating system, campuses and districts are evaluated on performance on state assessments, commended performance, annual dropout rate, completion rate, and the progress of English Language Learners (ELL). Possible ratings are Academically Unacceptable, Academically Acceptable, Recognized, Exemplary, and Not Rated (Texas Education Agency, 2011a). African American. A person originating from the “black racial groups of Africa” (National Center for Education Statistics, 2013, para. 3). Economically Disadvantaged. This term describes students who are reported as eligible for free or reducedprice meals or eligible for other programs of public assistance (Texas Education Agency, 2011a). Ethnicity. “Used to describe groups to which individuals belong, identify with, or belong in the eyes of the community … The designations are used to categorize United States citizens, resident aliens, and other eligible noncitizens” (National Center for Education Statistics, 2013, para. 1). Flipped Classroom. A classroom that uses flipped instruction to deliver content (Bergmann & Sams, 2012). Flipped Instruction. That which is traditionally done is class is now done at home, and that which is traditionally done at home is now completed in class. Students watch teachercreated lecture videos at home, and practice exercises and activities are completed during class (Bergmann & Sams, 2012). Flipped Instructional Strategy. An instructional strategy that uses flipped instruction to deliver content (Bergmann & Sams, 2012). 22 Hispanic. “A person of Cuban, Mexican, Puerto Rican, South or Central American, or other Spanish culture or origin, regardless of race” (National Center for Education Statistics, 2013, para. 3). Instruction. Activities and lessons directly associated with the interaction between teachers and students (Texas Education Agency, 2011a). Percent Score. The number of correctly answered test questions divided by the total number of questions (Texas Education Agency, 2011a). Raw Score. The number of test questions answered correctly (Texas Education Agency, 2011a). Recognized. The second tier in the accountability rating system that includes: Academically Unacceptable, Academically Acceptable, Recognized, Exemplary, and Not Rated (Texas Education Agency, 2011a). Scale score. It converts the raw score onto a scale that is universal to all assessment test forms. It takes into account the complexity level of the specific set of questions and “quantifies a student’s performance relative to the passing standards” and allows “direct comparisons of student performance between specific sets of test questions from different test administrations” (Texas Education Agency, 2012, para. 1). Socioeconomic status. Based on their eligibility for free or reducedpriced meals or for other public assistance programs, students are classified as economically disadvantaged or not (Texas Education Agency, 2011a). Student Groups. Students are classified among the four student groups of African American, Hispanic, White, and economically disadvantaged that are evaluated in the accountability system (Texas Education Agency, 2011a). 23 STAAR. State of Texas Assessments of Academic Readiness (STAAR) is the state assessment program that “includes annual assessments for reading and mathematics at Grades 3 8, writing at Grades 4 and 7, science at Grades 5 and 8, social studies at Grade 8, and endofcourse assessments for English I, English II, Algebra I, biology, and United States history” (Texas Education Agency, 2011b, para. 1). White. “A person having origins in any of the original peoples of Europe, the Middle East, or North Africa” (National Center for Education Statistics, 2013, para. 3). Limitations There are some limitations to this study. The sample of students was drawn from a single suburban independent school district in Texas. Therefore, generalizing the results of the study to all students in school districts in Texas was limited. It is also important to note that classes and class sizes were determined at the campus level. Thus, class sizes included in this study vary. The educational leadership team on each campus assigned the teachers and the students to classes at the campus level. In addition, the individual teacher chose the instructional approach employed in the classroom. One might assume that the teachers who used the flipped instructional strategy chose to do so, and this may have some impact on the delivery of instruction using this strategy. Delimitations For the purpose of this study, the following delimitations were made. The flipped instructional strategy was implemented in the middle school mathematics classes in a single school district in Texas. The study included the Grade 8 students who received grade level instruction and did not include the gifted students who receive above grade level instruction or students who receive modified TEKS instruction in basic mathematics classes. For this study, 24 student achievement in mathematics was analyzed using the STAAR Grade 7 Mathematics scale scores as a baseline, and STAAR Grade 8 Mathematics scale scores to measure achievement. Only students who had a STAAR Grade 7 Mathematics scale score and STAAR Grade 8 Mathematics scale score were included in this study. In addition, this study was conducted during one academic year. Assumptions Assumptions in this study included, but are not limited to, the roles of the students and teachers as indicated. It is assumed that the teachers implemented the flipped instructional strategy and put forth effort in helping the students as they transitioned to the new instructional delivery model. It can also be assumed that students participated effectively and were engaged in their learning. In addition, it is assumed that students gave effort in attempting assignments, watching instructional videos, and completing assessments with accurate responses. Last, it is assumed that the data collected from Texas Education Agency for the STAAR Mathematics exam were accurate and were a reliable and valid measure of student mathematics achievement. Organization of Dissertation Chapters The study consists of five chapters. Chapter 1 contained the introduction, statement of the problem, purpose of the study, research questions, research hypotheses, significance of the study, method of procedure, definitions of terms, limitations, delimitations, assumptions, and organization of the study. Chapter 2 reviews the relevant literature to the study. The review of the literature includes an overview of the existing mathematics achievement gap among students, current research in employing technology in instruction, information about differentiated instruction, and the current research about the flipped instructional strategy. Chapter 3 includes a description of the method used in this study and the collection of the data in the research design. 25 The population sample was identified and the procedures described. Chapter 4 presents the results of the study including the treatment of the data, the descriptive statistics, and the analysis of the statistical tests based on the research questions. The data analysis was interpreted and the findings are presented with a summary of the results. Chapter 5 provides a discussion of the findings, recommendations for further research, and conclusions of the study. 26 Chapter 2 LITERATURE REVIEW The purpose of the study was to determine the impact of flipped instruction on the mathematics achievement of middle school students on the State of Texas Assessment of Academic Readiness (STAAR) Mathematics. An achievement gap exists among the student groups of African American, Hispanic, White, and economically disadvantaged students in the state of Texas and across the nation. The achievement gaps “among racial and ethnic groups and between students from poor and nonpoor families are welldocumented. They are large and have been persistent; this is well known and widely accepted” (Barton, 2003, p. 4). Although the achievement gap exists, educational leaders seek creative solutions to close the achievement gap and increase overall mathematics achievement. In this study, the flipped classroom was examined as a vehicle to increase mathematics achievement for middle school students and to close the achievement gap among student groups. Minimal research has been conducted in the area of the flipped classroom. Existing studies have been conducted in both high school and college settings in the subjects of science, marketing, radiology, and pharmacology. Survey research studies of K12 educators include multiple subjects and grade levels and indicate teacher and student perceptions of the strategy. The flipped classroom model is “gaining recognition in a wide variety of academic settings as an approach to promote studentcentered, active learning” (Pierce & Fox, 2012, p. 4). Educators strive to meet the unique learning needs of students. Through varied learning activities, the flipped classroom promotes studentcentered activities that are tailored to student needs (Bergmann & Sams, 2012). The studentcentered flipped classroom connects active learning and student engagement for effective learning environments. 27 The review of the literature presented in this chapter describes the theoretical framework of mathematics achievement and the existing achievement gap among student groups. Flipped instruction uses instructional technology for increased class time and student engagement with differentiated instruction. Therefore, a review of the previous research on (a) instructional technology, (b) differentiated instruction, and (c) flipped instruction is presented within the review of the literature. The review focuses on scholarly articles relevant to flipped instruction, differentiated instruction, instructional technology, mathematics achievement, and the achievement gap. A summary concludes this section. Theoretical Background of Mathematics Achievement Federal Mandates Congress passed the No Child Left Behind (NCLB) Act in 2001 and it was signed into law in 2002. It reauthorized the Elementary and Secondary Education Act (ESEA) in a way that “dramatically expanded the historically limited scope and scale of federal involvement in K12 schooling” (Dee & Jacob, 2011, p. 420). The goal of the No Child Left Behind Act is to improve education in public schools by establishing high expectations, assessing student performance, and implementing an accountability system for student performance on standards (Krieg, 2011). Accountability through highstakes testing is now customary in public schools as a result of No Child Left Behind, and this legislation has expanded federal influence over the nation’s public schools (Dee & Jacob, 2011). Schools and school districts are accountable for academic performance improvement of all students and must make adequate yearly progress (AYP). For a school to meet AYP, the percentage of students at a school in each ethnic subgroup and students who are categorized as economically disadvantaged, ELL, and special education must demonstrate proficiency on the state test and must meet expectations as determined by the state 28 (Krieg, 2011). The accountability system is robust and school districts across the nation strive to improve instructional programs. The No Child Left Behind Act holds districts within each state accountable for student performance on state mandated assessments. State Mandates The Texas Education Agency (TEA) holds school districts accountable for the performance of students on the State of Texas Assessment of Academic Readiness (STAAR). The first administration of STAAR appeared in Spring 2012 and replaced the former state standardized assessment, Texas Assessment of Knowledge and Skills (TAKS). The STAAR measures mathematics in Grades 38, reading in Grades 38, science in Grades 5 and 8, writing in Grades 4 and 7, and social studies in Grade 8. The STAAR also includes high school End of Course (EOC) testing for English, Algebra, Biology, and History (Texas Education Agency, 2011b). Texas school districts must ensure that students learn required content and must look carefully at achievement gaps between students of various ethnic subpopulations and socioeconomic statuses (Texas Education Agency, 2010). Educational leaders seek instructional strategies that increase student achievement and have lasting and positive effects on student learning. Schools strive to “continuously challenge current instructional practices in order to produce improvement, not just change for change’s sake, but by engaging in value added improvement” (Flumerfelt & Green, 2013, p. 364). State and federal mandates require schools to meet and exceed performance standards. Schools are charged with the responsibility of meeting student needs and preparing them to perform satisfactorily on state assessments. The federal mandate, No Child Left Behind Act gives direction to the states that all students achieve proficiency in mathematics and reading and also institutes “sanctions and rewards based on each school’s AYP status” (Dee & Jacob, 2011, p. 29 418). As a result, schools face rewards and consequences based on annual student performance results. The Mathematics Achievement Gap Among Student Groups A mathematics achievement gap exists among student groups of African American, Hispanic, White students in Texas and across the nation. At the time of the passage of the No Child Left Behind Act, one of the stated goals was to “eliminate the achievement gap between students of different races” (Krieg, 2011, p. 664). However, the study conducted by Dee and Jacob (2011) found that NCLB had “limited contributions to reducing achievement gaps” (p. 442). Many schools focus efforts and funds toward the student groups that are in danger of not meeting AYP standards. In fact, Krieg (2011) found that “administrators focus their efforts on racial groups that have trouble making AYP” which causes a “diminution in academic performance of students in successful racial groups” (p. 663). Krieg (2011) argues that schools participate in “strategic instruction” which focuses on the subjects that are tested and focuses on the student groups that require increased performance to meet AYP standards (p. 655). In addition, students of various ethnic subpopulations and socioeconomic statuses are underrepresented in highlevel mathematics classes. In fact, “students of color and economically disadvantaged students still are not enrolled in AP courses in the percentages equal to their percentage in their local school’s population” (Clark, Moore, & Slate, 2012, p. 266). Furthermore, teacher perceptions may have a part in this underrepresentation (Clark et al., 2012). It is imperative for educational leaders to face the challenge of closing the achievement gap among student groups and seek ways to accomplish this task. 30 National Mathematics The National Assessment of Educational Progress (NAEP) was designed in the 1960s as a national “tool for monitoring student achievement” (Rutledge, Kloosterman, & Kenney, 2009). The NAEP offers mathematics assessments every 2 to 4 years and is given to a sample of students across the nation. Rutledge et al. (2009) determined the extent to which mathematics skills have changed over 25 years. They discovered that the scores for 9yearold students and 13yearolds have climbed, but the scores for seventeenyearold students “have been relatively stable throughout the history of NAEP” (p. 446). They also found that the “ethnicity gaps are much larger: the whiteblack gap ranges from 21 to 38 points, and the whiteHispanic gap ranges from 2027 points” (Rutledge et al., 2009, p. 446). The achievement gap among students of various ethnicities is evident across the nation. In addition, the NAEP has been predominantly important for “measuring change in achievement over time for national cohorts of fourth, eighth, and twelfth graders. These data have shown that significant differences exist among racial and ethnic groups” (Robinson, 2010, p. 265). The findings show that minority students become further behind in reading and mathematics during the middle grades, when the achievement gap is largest (Robinson, 2010). Positively, the results suggest that students of all ethnicities are increasing scores over time and heading in the same direction. However, the scores of the White students are moving faster (Robinson, 2010). Closing this achievement gap is crucial for student learning and “reducing the racial/ethnic achievement gap is perhaps the most important method for bringing about equality within the United States” (as cited in Robinson, 2010, p. 264). The achievement gap exists across the nation and reducing this gap is critical for equality in learning. 31 Texas Mathematics The achievement gap exists in Texas as well. Student groups of African American, Hispanic, White, and economically disadvantaged must meet state standards, and an achievement gap exists between them. There are performance differences on “national and state mathematics tests between different groups of students, the most commonly examined comparisons being by ethnic group and income level” (Flores, 2007, p. 29). These differences equate to a systemic issue in schools today. Educational leaders have the challenge to close the achievement gap and meet the learning needs of students. The achievement gap is not an occurrence that appears at the summation of a student’s academic career. School achievement differences “among subgroups of the population have deep roots. They arrive early and stay late – beginning before the cradle and continuing through to graduation” (Barton, 2003, p. 4). There are several factors that impact the achievement gap. Knowing these factors can help educational leaders combat the existing gap. Barton’s (2003) report identifies 14 factors that affect the academic achievement of students and the school can only impact 6 of these factors. They include the rigor of the curriculum, class size, teacher preparation, teacher experience and attendance, school safety, and technologyassisted instruction (Barton, 2003). Knowing these factors, educators can work to unravel and understand the existing achievement gap and find solutions. Instructional Technology As educators seek solutions for optimizing student achievement, technology has the potential to enhance student engagement and increase achievement (Hepplestone et al., 2011). Employing technology can promote active learning and student excitement for learning. Technologyenhanced learning experiences also can help students develop 21st century 32 competencies such as problem solving, digital literacy, and selfdirected learning (Shapley, 2011). Lessons supported by technology can involve realworld problems and “research shows that students learn more when they are engaged in meaningful, relevant, and intellectually stimulating work” (as cited in Shapley, 2011, p. 299). With technology, students can engage with authentic and relevant topics that challenge them to use problemsolving skills. In addition, “engaged learning and engaged learners are increasingly cited as critical factors in producing significant learning” (Young, 2010, p. 1). Therefore, student engagement can positively impact learning. Curriculum Integration Technology devices are a part of the lives of students. McNulty (2013) recognizes that most students cannot identify with life before laptops and cell phones. Yet many educators “still do not take full advantage of it in their teaching” (McNulty, 2013, p. 41). Implementing instructional technology into the classroom requires the teacher to facilitate the learning environment. Technologyinfused models “suit all types of curricula … which leads the way in applied learning by keeping current with technological advances across disciplines” (McNulty, 2013, p. 41). In an effort to meet student needs, flipped classrooms, blended classrooms, and distance learning classrooms are being employed. These models “change the educator’s role, but they do not negate it” (McNulty, 2013, p. 43). Instructional technology is being employed to maximize student learning. Educators must “seek ways to engage all types of learners so they can succeed not only in the world they live in now, but also in the one they are only beginning to dream up” (McNulty, 2013, p. 43). Instructional technology can aid the educator as they design activities to support reallife applications. 33 As students work collaboratively on practical applications, instructional technology can be employed. Research suggests “that technology yields the greatest learning benefits when it is used in learnercentered ways” (Burns, 2013, p. 42). A studentcentered environment sets the tone for learning and “the creation of learning environments that remain at the heart of why we use technology and for which we strive cannot be attained by technology alone, though technology can aid in this endeavor” (Burns, 2013, p. 44). Instructional technology can enhance learning. Students can put instructional technology devices to use as they learn new concepts and create products for evaluation. Students who used “computer tutorials in mathematics, natural science, or social science scored significantly higher in these subjects compared to traditional approaches” (Burns, 2013, p. 40). Using technology to enhance learning leads to student achievement. Ultimately, it is not the technology alone that makes the students successful because “teachers, not technology, are essential to student learning” (Burns, 2013, p. 41). The teacher facilitates the integration of technology into the curriculum and makes the learning relevant and appropriate for students. Impact of Technology on Student Achievement Not only can technology engage students, it can also impact student achievement in mathematics. Taj and Sivalingam (2013) studied the effectiveness of computerassisted instruction over the traditional method in teaching mathematics. They found that the “mean achievement score, of the students learning with computer assisted instruction, is better than students taught through traditional instruction only” (Taj & Sivalingam, 2013, p. 4). Technology can enhance mathematics instruction and lead to student success. Students in the study found “computer assisted instruction to be an effective method of learning” (Taj & Sivalingam, 2013, p. 4). Employing technology to enhance instruction can lead to student engagement and 34 achievement in mathematics. With increasing efforts of integrating technology into the classroom, students can flourish in learning mathematical content with computers and other instructional technology devices (Taj & Sivalingam, 2013). The use of technology enhances learning. Teachers are choosing to employ “digital resources when building, implementing, and engaging students in classroom experiences” (Thiele, 2013, p. 44). Using this digital content allows the teacher to engage students with instructional technology in various ways. Teachers can “infuse technology into the classroom most successfully when they find new ways to enhance current practices, leveraging technology’s ability to help them connect, collaborate, and enrich” (Gullen & Zimmerman, 2013, p. 66). Technology can be used to enhance instruction in a number of ways. Two ways in which “technology can be extremely valuable are presenting content and assessing achievement” (Davies et al., 2013, p. 565). Teachers can use technology in the classroom to maximize the presentation of content and also in assessment tasks. Differentiated Instruction The teacher can facilitate differentiated instruction to meet the learning needs of students and promote engagement. In fact, “one way to improve learning is to differentiate instruction. The purpose of differentiation is to meet the learning needs of individual students” (Davies et al., 2013, p. 566). Differentiated instruction refers to the delivery of instruction by teachers that consistently adjust instruction and curriculum “in response to student readiness, interest, and learning profile” (Tomlinson et al., 2003, p. 131). Each student possesses a unique learning style and ability. It is the teacher’s role to meet the unique learning needs of each student. Readiness refers to the “knowledge, understandings, and skills” that a student brings to the learning (Santangelo & Tomlinson, 2012, p. 312). Activities designed in response to student readiness 35 are appropriately challenging for the student. Interest refers to the topics or processes that “evoke curiosity and inspire passion” (Santangelo & Tomlinson, 2012, p. 312). Activities geared toward student interest promote engagement and motivation. These activities help students connect to prior knowledge. Learning profile refers to the “ways in which students learn most naturally and efficiently” (Santangelo & Tomlinson, 2012, p. 313). Grouping techniques, learning styles, and classroom environment preferences are examples of learning profile elements. As teachers develop knowledge about differentiated instruction, they begin to tailor instruction to student needs based on interest, readiness, and learning profile. Teachers can also differentiate instruction based on process, product, content, and learning environment. Content refers to the concepts being taught, and process refers to the way that students think about the learning (Santangelo & Tomlinson, 2012). Products are performancebased and demonstrate what students have learned, and the learning environment “consists of the routines, procedures, and physical arrangement of the classroom, as well as the overall tone or mood that exists among and between the students and teacher” (Santangelo & Tomlinson, 2012, p. 314). Creating a positive environment for learning is part of the differentiated classroom. Meeting Student Needs Through Differentiation Differentiated instruction is often delivered to small groups of students, rather than whole group settings. Small group instruction opportunities “give teachers the flexibility to address learner variance more appropriately than does sole reliance on wholeclass instruction” (Tomlinson et al., 2003, p. 132). Differentiated instruction allows the teacher to meet the learning goals of students. Students can be grouped according to interest, readiness, or learning profile. Differentiated instruction increases the variety of instructional activities, learning tools, and class structure. The goal of this instructional approach is to maximize the learning 36 experiences in response to student needs. Through differentiation, the student’s unique learning needs are met and the student successfully demonstrates learning. Differentiated instruction leads to standardized test achievement in mathematics (Chamberlin & Powers, 2010). Teachers can have flexibility in using various learning tools, technology, projects, handson learning, and high levels of discussion. Research studies “indicate that students in these differentiated classrooms achieve better outcomes than students in classrooms with a more singlesize approach to instruction” (Tomlinson et al., 2003, p. 127). Differentiated instruction has the potential to improve student learning outcomes. Impact of Differentiation on Student Achievement Studies in classrooms employing differentiated instruction have seen achievement gains for students of various ethnic subpopulations and socioeconomic groups (Chamberlin & Powers, 2010). The increased class time allows the teacher to meet student needs more effectively through differentiated instructional activities, varied class structure, and learning tools. The benefits of “differentiated instruction includes an increased motivation and enthusiasm for learning” (Chamberlin & Powers, 2010, p. 116). Motivation is a key factor in learning and it is enhanced in the classroom that uses differentiated instruction. More research suggests when “differentiated instruction is implemented with fidelity, it has significant and meaningful benefits for diverse populations of students” (as cited in Santangelo & Tomlinson, 2012, p. 310). The classroom is filled with diverse students of various learning abilities and readiness levels. Differentiated instruction can help meet these individual learning needs. Through differentiated instruction, each student’s learning potential and outcomes are maximized (Santangelo & Tomlinson, 2012). In differentiated classrooms, “all students are engaged in instruction and participating in their own learning” and differentiated thinking 37 “empowers teachers to be responsive rather that reactive to the unique and individual personalities, backgrounds, and abilities found within students” (Anderson, 2007, p. 52). Instruction can be tailored to student needs, and student engagement can be increased in the differentiated classroom. Additionally, “a major drawback of traditional instruction is that many teachers ‘teach to the middle’, which means that the needs of a growing number of students will go unmet” (Rock, Gregg, Ellis, & Gable, 2008, p. 32). Students and teachers share the responsibility of learning in the differentiated classroom and learning tasks are designed for students based on their learning needs. Flipped Instruction The Flipped Classroom The flipped classroom is an instructional strategy that actually ‘flips’ the activities that are traditionally practiced in the classroom and at home. In the flipped classroom, “what is normally done in class and what is normally done as homework is switched or flipped” (Herreid & Schiller, 2013, p. 62). In other words, the instructional lecture and homework practice components are inverted. In traditional lecture, the teacher is active as the students passively listen (Fulton, 2012, p. 21). In the flipped classroom, teachers use instructional technology devices to create lecture videos. Students watch these videos to learn about the concepts and skills outside of class time. Class time is then reserved for solving problems, working collaboratively, extending the learning, and ensuring high levels of thinking (Bull, Ferster, & Kjellstrom, 2013). Teachers restructure class time to meet student needs in the flipped classroom. Using the flipped instructional strategy provides teachers with “the flexibility to create learning groups based on student needs” and it allows the instructional leaders to “select lecture 38 content creation based on strength of delivery by teacher expertise” (Flumerfelt & Green, 2013, p. 364). As teachers create instructional lecture videos, they work to deliver content to students in a concise and clear manner. A traditional classroom lecture that could take an entire class period is being condensed to a 10minute lecture video with the exact information that students need (Bergmann & Sams, 2012). In the flipped classroom, teachers are challenged to refine their lecture and use technology to engage students with content. In addition, instructional videos are subject to pause, rewind, fastforward, and can be played again to meet the learning style and needs of the student (Bergmann & Sams, 2012). In the flipped classroom, “there is an opportunity to reconsider and perhaps reshape the structure of time, communication, collaboration, expectations, and the physical space of the classroom” (Thiele, 2013, p. 44). Learning takes place outside and inside of the flipped classroom, which increases learning time. Meeting student needs is the responsibility of the teacher. “Enabling teachers in the classroom to ‘flip’ lecture time into time for higher level engagement by students and teachers” allows for increased class time (Flumerfelt & Green, 2013, p. 363). This allows “students to increase processing time substantially and to do so in an environment in the classroom, where teacher and peer support is available” (Flumerfelt & Green, 2013, p. 363). Using flipped instruction allows teachers to facilitate differentiated activities for students to practice mathematical concepts, ask questions, and apply mathematics to realworld situations and projects with the teacher readily nearby. Flipped classroom teachers can spend more time with struggling students, employing differentiated instruction to meet learning needs. Parents of struggling students can watch instructional videos to further help their student with content as well. The flipped classroom is “a framework that enables teachers to effectively personalize the education of each student” 39 (Bergmann & Sams, 2012, p. 7). Students can be engaged with concepts and be motivated to complete activities. The flipped classroom allows teachers to meet student needs through differentiated instruction and increase learning time (Bergmann & Sams, 2012). All students learn differently, and the flipped classroom allows students to have access to differentiated instruction from their teacher. The teacher is “engaged in continual formative assessment, diagnosing on the spot each student’s understanding and modifying instruction for each student as needed” (Sams & Bergmann, 2013, p. 18). The flipped classroom offers flexibility for the teacher to meet the specific learning needs of students. Education is for everyone, but the way we deliver education – and the way students receive it – is not the same for everyone. A flipped classroom gives teachers the flexibility to meet the learning needs of all their students, and it gives students the flexibility to have their needs met in multiple ways. By doing so, it creates a classroom that is truly studentcentered. (Sams & Bergmann, 2013, p. 20) As students complete the difficult part of learning in the classroom with the teacher, they have a greater chance of success and mastery than practicing alone without guidance at home (Gullen & Zimmerman, 2013). Studies in classrooms using differentiated instruction, like in flipped classrooms, have seen achievement gains “for all students and across all racial and socioeconomic groups” (Chamberlin & Powers, 2010, p. 116). Furthermore, the flipped classroom has the potential to enhance student achievement. History of the Flipped Classroom Lage, Platt, and Treglia (2000) are thought to be the first to publish a study on the inverted classroom. Using videotaped lectures, reading assignments, and PowerPoint slides about the lecture, students could access the Economics course content outside of class time. 40 Students reviewed the material outside of class time and “students were expected to come to class prepared to discuss relevant material” (Lage et al., 2000, p. 33). The instructors would quickly answer questions about the content and then meaningful practice with experiments, labs, and handson activities would follow. The instructors wanted to meet student needs in a variety of ways, and the inverted classroom afforded them the opportunity to accommodate various learning styles. They used class time more efficiently using the inverted instructional approach. Evidence suggests that students “generally preferred the inverted classroom to a traditional lecture and would prefer to take future economics classes using the same format” (Lage et al., 2000, p. 41). The first inverted classroom was successful by rethinking the way class time was used. Lage et al. (2000) used the technology available at the time in their inverted economics course. The approach became more prominent as access to technology increased. “In the shadow of Colorado’s Pike’s Peak, veteran Woodland Park High School chemistry teachers Jonathan Bergmann and Aaron Sams stumbled onto an idea” (Tucker, 2012, p. 82). They struggled to find a way to deliver course content to absent students and created videos and screencasts to post online. The absent students benefited from these videos and soon other students accessed the online content to review and reinforce concepts. Bergmann and Sams recognized that they could structure their class time differently in the flipped classroom (Tucker, 2012). Bergmann and Sams (2012) currently lead the charge for flipped instruction, author books, and host conferences regarding the benefits of implementing flipped instruction and integrating technology in the flipped classroom. Although the inverted approach has been successfully employed for years, technology has enhanced the current models of flipped classrooms. 41 Flipped Instruction in High School Courses In a flipped high school geometry class, a teacher recorded his lessons and posted the videos to YouTube for students to view online to prepare for class the next day. This means “spending 4560 minutes taping lessons after school, it saves [the teacher] from teaching that same lesson four times, and the video becomes a resource for years to come” (Gullen & Zimmerman, 2013, p. 64). In addition, the teacher can engage students during class time in higherlevel activities and give them “individual feedback and coach them as they work with concepts they’ve just learned” (Gullen & Zimmerman, 2013, p. 64). The teacher noted the videotaped lessons allow him to be less exhausted, more consistent in instruction, and aware of student progress (Gullen & Zimmerman, 2013). The students in the flipped high school geometry class find that flipped instruction meets their needs, and they can “review the lesson multiple times if needed” (Gullen & Zimmerman, 2013, p. 65). This review time and practice time is important for student learning. Flipped Instruction in Higher Education Courses In a study accomplished by Pierce and Fox (2012), the students in the renal pharmacology course “expressed a consistently high preference for the flipped classroom instructional model relative to the traditional instructorled lecture model” and the study “supports the notion that the quality, not necessarily the quantity, of studentteacher interaction is a compelling force in improving student performance” (p. 4). The students in the study recognized the importance of viewing lecture content before class and being prepared for discussions and projects. The flipped classroom implementation in this study “accompanied improved student performance and generated positive student attitudes towards the experience” (Pierce & Fox, 2012, p. 5). Assessment scores increased with the use of flipped instruction. 42 In another college study, Garver and Roberts (2013) found that a common problem in traditional college instruction “is that many straight lecture classes reach only the two lowest levels – knowledge and comprehension of Bloom’s taxonomy of learning” (p. 17). This does not reach higher levels of thinking and learning and does not focus on student engagement and active learning. The dilemma is that there is “not enough time to cover the material and do active learning exercises to achieve higherorder learning” (Garver & Roberts, 2013, p. 17). After implementing the flipped classroom and clicker response systems in the college marketing class, Garver and Roberts (2013) experienced student success; over 90% of class time is dedicated to higherorder learning, and student interest and engagement in the subject has “dramatically increased” (p. 19). Before the implementation of the flipped classroom, only 5% of students scored an A on the 2006 exam in contrast to the 38% that scored an A on the exam in 2011. The study also determined that students believe “learning is greatly improved and more enjoyable as compared to a traditional class format” (Garver & Roberts, 2013, p. 17). Davies et al. (2013) found that the technologyenhanced flipped classroom was found to be “both effective and scalable; it better facilitated learning than the simulationbased training and students found this approach to be more motivating in that it allowed for greater differentiation of instruction” (p. 563). The college level introductory spreadsheet course used flipped instruction because so many students come to the course with varied levels of experiences with spreadsheets. Students review the content before arriving to class, and the instructors can customize instruction to the needs of students. The learning is not “limited to the classroom, and students can move at their own pace and direct their efforts based on their own individual needs, thus personalizing instruction” (Davies et al., 2013, p. 565). The college course instructors were able to create lesson videos that “were as effective at motivating students 43 about the subject matter as the instructors delivering the regular approach” (Davies et al., 2013, p. 578). When students were asked about how much they learned in class, their evaluation of the instructors, their assessment of the value of the class, and if they would recommend the course to another student, the “mean scores for the flipped approach were slightly more favorable than those of the regular approach” (Davies et al., 2013, p. 577). Therefore, the flipped instructional approach proved to be advantageous for college level learners in the introductory spreadsheet course. DeMaio and Oakes (2014) discovered that students in a radiography college course prefer the flipped classroom to traditional lecture. Students view screencasts that are approximately 15 20 minutes in length and then during the next class meeting, “they work in small groups to solve the problems with the instructor providing direct assistance as necessary” (DeMaio & Oakes, p. 341). Students would normally struggle with solving the problems in isolation outside of class time, and are finding success with the flipped classroom. For the professors of the college course, the flipped classroom is a convenient way to offer students additional support, and “flipping allows for more productive inclass time because the instructor can coach students as they work, improving understanding and performance” (DeMaio & Oakes, 2014, p. 342). It is important for students to watch the screencasts ahead of time, so they are ready for solving problems in class. A radiologic science professor found that the flipped classroom has many benefits. Clark (2014) found that flipped instruction promotes active learning, meets individual learning needs through formative assessment and feedback, and provides opportunities for more interaction with students. Another benefit of the flipped classroom is the “promotion of teamwork skills” (Clark, 2014, p. 687). Students learn essential teamwork skills to be successful in their future radiologic 44 science profession. In addition, Clark (2014) found that “collaboration among students in the flipped classroom improves participation, builds confidence, and promotes a sense of teamwork” (p. 687). Collaboration is improved when the flipped instructional strategy is employed. A physical therapist preparation program employed flipped instruction at a Texas university. A comparison was made between students assigned to flipped instruction and traditional instruction sections of the course. The students receiving flipped instruction for a full year experienced no student failures on the examinations, and “this was considered noteworthy, as it was an atypical experience” (Boucher, Robertson, Wainner, & Sanders, 2013, p. 75). The students within the course found that flipped instruction increased time to practice the difficult concepts of physical therapy. Furthermore, the flipped classroom “produced improved learning outcomes as measured by course grades, student surveys, and faculty response” (Boucher et al., 2013, p. 76). Students and professors perceived the flipped instructional approach positively. Chemistry professors also experienced success with the flipped classroom. The seat time of a large lecture university class that met three times per week was reduced by “twothirds while lectures were shifted online” (Baepler, Walker, & Driessen, 2014, p. 235). The students enrolled in the large class were split into three sections that met one day per week. The other two days were spent watching lecture videos and engaged in online discussion of questions and topics. The reduced time in class was used “in an active learning classroom where students worked with each other to solve problem sets, answer clicker questions, listen to spot explanations of key concepts, and watch short demonstrations” (Baepler et al., 2014, p. 235). The students within the college chemistry class benefited from the flipped instructional approach. Although the class seat time was reduced by twothirds, the students “achieved learning outcomes that were in one case superior to, and in the other case statistically equal to, to outcomes from the traditional 45 classroom” (Baepler et al., 2014, p. 235). The traditional classroom kept the lecture format and met three times per week. The flipped instructional approach allowed students to achieve positive learning results with less seat time. Millard (2012) studied more reasons to consider the flipped classroom in college instruction. Professors have found that it increases student engagement and that “students love this system because they’re not listening to some old lecture. They’re interacting and debating, and that makes them feel involved” (Millard, 2012, p. 27). Student engagement is enhanced in the flipped classroom due to the active learning that happens in the classroom and the passive learning that transpires outside of the classroom. This type of learning environment also strengthens teambased skills and “higher education is succeeding with flipped classrooms, because it adjusts the delivery style to the students” (Millard, 2012, p. 28). Teambased activities allow the students to compete with learning groups and engage in active learning. The flipped classroom also allows for personalized student guidance, because “instructors are able to provide personalized instruction to some degree” (Millard, 2012, p. 28). In large college courses, it can be difficult for professors to monitor student progress each day. The use of clickers helps to gauge student answers and progress with the course materials. Students can get “instant feedback about their understanding” (Millard, 2012, p. 28). The flipped classroom was also found to focus classroom discussion and provide faculty freedom. The professors can “concentrate on inclass rich learning activities” (Millard, 2012, p. 29). It also allows for flexibility in instruction because the professor can tailor learning activities to the needs of students. Overall, university professors in the study enjoy the flipped classroom and see the advantages for using this instructional strategy. 46 Flipped Instruction Survey Research In a survey of more than 500 teachers, Classroom Window found that “nearly 90% of respondents who had tried flipping their classroom reported improved job satisfaction; nearly 70% reported increases in student standardized test scores; and 80% reported improved student attitudes” (Brunsell & Horejsi, 2013, p. 8). In addition, flipped instruction is efficient, improves the life of the teacher, strengthens relationships, improves the quality of teaching, increases collaboration, and provides the time to differentiate instruction (Brunsell & Horejsi, 2013). Flipped instruction has many benefits and has impacted the learning environment. More survey research has been conducted in the area of flipped instruction. A survey of the National Center for Case Study Teaching in Science Listserv members conducted by Herreid and Schiller (2013) identified 200 teachers that implement the flipped classroom and found these motives for doing so: There is more time to spend with students on authentic research; students get more time working with scientific equipment that is only available in the classroom; students who miss class for debate/sports/etc. can watch the lectures while on the road; the method promotes thinking inside and outside of the classroom; students are more actively involved in the learning process; and they also really like it. (p. 62) The respondents to the survey also preferred that students watch “online videos over reading material to accomplish the goal of preparing students out of class for inclass active learning. Their students prefer video too” (Herreid & Schiller, 2013, p. 64). The flipped classroom allows for the flexibility of learning that many learners need, and instructors are eager to meet the learning needs of students. 47 Benefits and Challenges of Flipped Instruction Science teachers that responded to the survey by the National Center for Case Study Teaching in Science conducted by Herreid and Schiller (2013) also identified two major problems. They found that students new to the flipped classroom might be “initially resistant because it requires that they do work at home rather than be first exposed to the subject matter in school” (Herreid & Schiller, 2013, p. 63). Students may come to class unprepared. Teachers resolve this by administering a quiz or requiring note taking homework that can only be completed by watching the video or reading the material (Herreid & Schiller, 2013). The other pitfall of implementing the flipped classroom is the homework videos or readings “must be carefully tailored for the students in order to prepare them for the inclass activities” and this takes additional time (Herreid & Schiller, 2013, p. 63). Ultimately, the benefits outweigh the problems. The flipped classroom, “with its use of videos that engage and focus student learning, offers us a new model for teaching, combining active, studentcentered learning with content mastery that can be applied to solving realworld problems. It’s a winwin” (Herreid & Schiller, 2013, p. 65). The flipped classroom allows educators to meet the unique learning needs of students through engaging and active learning. The survey research shows that many educators implement the flipped classroom with success and have found that the flipped classroom offers a new model for teaching and learning (Herreid & Schiller, 2013). The flipped classroom can positively influence student perceptions and learning outcomes. Some teachers are resistant to blended or flipped learning environments because challenges exist. “Finding time for professional learning, fear of change or giving up control, and rapidly changing expectations” are some fears that educators have in regards to the flipped 48 classroom (Thiele, 2013, p. 44). Students must have access to the Internet and a device that can display instructional videos. These components are necessary to the flipped classroom, and some students do not have access at home. Schools must be creative in allowing students the access they need. Allowing students to watch instructional videos on campus before and after school has been a popular solution. Schools must provide sufficient network infrastructure, bandwidth, and wireless access at school in order to foster success in the flipped classroom. Despite the challenges to flipped instruction, teachers are finding ways to incorporate this strategy in their instruction (Thiele, 2013). Implementing the flipped classroom takes time, ingenuity, and patience. Since the flipped classroom concept “is relatively new and still evolving, little research is available to guide best practices” (Bull et al., 2013, p. 11). Videos for the flipped classroom generally span 10 minutes and cover one concept. This allows students to study them one at a time. “A considerable body of research suggests that distributed learning can contribute to more meaningful learning than massed practice” which is fostered in the flipped classroom (Bull et al., 2013, p. 11). Students can also watch the videos at their own pace and when they are ready for learning. “Digital equity is one issue that educators must address during implementation of flipped classrooms” and schools must be creative when students have limited access to Internet and digital tools (Bull et al., 2013, p. 11). Providing materials on a CD or keeping computer labs available before and after school can help alleviate some issues. These issues can be resolved and using flipped instruction “allows teachers to leverage technology to increase interaction with students” (Bergmann & Sams, 2012, p. 25). Leveraging technology in the flipped classroom, students watch lecture videos online and have the “opportunity to hit rewind and view again a section they don’t understand or fastforward through material they have already mastered” 49 (Horn, 2013, p. 78). Students can take ownership of their learning and can decide when to watch the instructional videos. The technology frees up time in class for students to “practice problems, discuss issues, or work on specific projects” (Horn, 2013, p. 78). The instructional technology allows the teacher to guide students to apply online learning in an active learning environment. Summary Educational leaders are charged with the responsibility of student performance on statemandated assessments (Dee & Jacob, 2011). The accountability system is robust and tied to student achievement. Educational leaders and teachers are searching for creative solutions to close the existing achievement gap among student groups (Robinson, 2010). The existing achievement gap persists across the nation, and educational leaders seek solutions to close the gap. Employing technology is a creative solution that can enhance student learning (Shapley, 2011). These technological devices are put to use in the flipped classroom. The flipped classroom has many benefits, and educators are beginning to understand the amount of time that can be saved and devoted to student learning. Traditional classroom lecture does not elevate higherorder thinking and problem solving skills (Garver & Roberts, 2013). Students passively listen to the lecture, and this takes an increased amount of class time. Students are then held responsible for the active part of learning and practice outside of class time. The flipped classroom essentially flips these passive and active components of learning. Active learning and student engagement are enhanced in the flipped classroom (Bergmann & Sams, 2012). Little quantitative research has been conducted in the area of flipped instruction (Bull et al., 2013). It is a relatively new phenomenon that deserves investigation. Throughout this review of the literature, the background was discussed in regards to mathematics achievement 50 and the existing achievement gap among student groups. The use of instructional technology and differentiated instruction was also explored. Flipped instruction was discussed along with existing survey research and research studies conducted in secondary and postsecondary courses. A flipped classroom investigation has not been explored in middle school mathematics and its impact on a state assessment. In this causal comparative quantitative study, the flipped classroom was researched on its impact on student achievement in middle school mathematics as measured by the STAAR, and its ability to close the achievement gap among student groups. 51 Chapter 3 METHOD OF PROCEDURE The primary goal of this causal comparative quantitative research study was to determine the impact of flipped instruction on middle school mathematics achievement as measured by the student scale scores on the State of Texas Assessment of Academic Readiness (STAAR) Grade 8 Mathematics. Another aim of this study was to determine the effectiveness of flipped instruction on closing the existing achievement gap among the student groups of African American, Hispanic, White, economically disadvantaged and noneconomically disadvantaged. Data from students in regular and preAP mathematics classes were also analyzed. The quantitative study used a causal comparative research design with a betweengroups experimental approach. Causal comparative research design is also known as “ex post facto (after the fact) research” (Lunenburg & Irby, 2008, p. 45). This study used the causal comparative research design because the researcher did not manipulate variables or randomize the groups within the study. Causal comparative research does “not manipulate the dependent variable since it has already occurred” (Lunenburg & Irby, 2008, p. 46). The method used to test the research questions is presented in this chapter. The chapter is organized into four sections: (a) selection of participants, (b) instrumentation, (c) data collection, and (d) data analysis. Selection of Participants The quantitative study was conducted in a suburban independent school district in Texas. The public school district educates approximately 39,000 students each year. The school district is comprised of 32 elementary campuses, eight middle school campuses, five high school campuses, and two alternative education campuses, for a total of 47 campuses. This study was 52 centered upon the mathematics achievement of middle school students. Four of the eight middle school campuses are considered Title 1 campuses. Half of the middle school campuses have Grade 6, 7, and 8 students and the other four campuses have Grade 7 and 8 students. A principal and two assistant principals lead each of the eight middle school campuses. Middle school mathematics students are scheduled into various mathematics classes depending on ability and readiness. Eighth grade students can be enrolled in a regular mathematics class and receive grade level instruction; preAdvanced Placement (preAP) mathematics and receive grade level instruction with enrichment; gifted and talented (GT) mathematics and receive above grade level instruction; or basic mathematics and receive special education modified instruction. The focus for this study included the student population for Grade 8 students who received grade level instruction. Therefore, the target population for this study included the students enrolled in Grade 8 mathematics and Grade 8 preAP mathematics. Each middle school campus has certified teachers assigned to deliver instruction to these students, and the classes and class sizes are determined at the campus level by administrators and registrars. The suburban district has a locally developed and paced curriculum, where teachers across the district access the same scope and sequence, lessons, and curriculum resources. The curriculum resources were the same for the 20122013 and the 20132014 academic years. Common district assessments are administered at each campus across all classrooms, and teachers across the district maintain consistent pacing. All Grade 8 mathematics teachers employed traditional instruction during the 20122013 academic year. In August of 2013, prior to the start of the 20132014 academic year, middle school mathematics teachers from Grades 6, 7, and 8 attended an introductory staff development 53 regarding flipped instruction. Teachers learned about the strategy along with the benefits and challenges of implementation. Teachers also learned about technology applications that could assist with the implementation of the flipped classroom, and the teachers learned about those technology applications through practice. Administrators gave teachers autonomy to choose the flipped classroom or the traditional classroom for the 20132014 academic year. The middle school mathematics teachers of this suburban district employed either flipped instruction or traditional instruction to deliver Grade 8 mathematics curriculum resources for the duration of the academic year, and some teachers chose to employ flipped instruction for a shorter time period. When using the traditional method of instruction, teachers chose to instruct students during class time and provide practice time at school and home. The teachers who selected to implement the flipped instructional method of instruction chose to instruct students through instructional videos outside of class time and engage in practice during class time. The goal of this study was to determine the impact of flipped instruction on middle school mathematics achievement. The target population for the study included the students of teachers that delivered Grade 8 mathematics instruction to Grade 8 students in regular and pre AP classes using flipped instruction for the duration of the 20132014 academic year. The students of teachers that chose to implement flipped instruction for a shorter time period were not included in the study. The teachers that implemented flipped instruction needed to be identified. The mathematics curriculum department administered a district survey in May 2014 to determine the teachers that implemented flipped instruction during the 20132014 academic year. In this survey, teachers indicated the strategy used and the duration it was employed. The survey is discussed in more detail in Instrumentation. Permission to access the results of the survey was obtained by the researcher. 54 The classes selected for the study were determined by cluster sampling. In cluster sampling, the process includes “selecting groups, not individuals” (Lunenburg & Irby, 2008, p. 172). The clusters of classrooms were selected once the teachers that implemented the flipped classroom for the full academic year were identified. Eleven 20132014 flipped classroom teachers were identified, and then six flipped classroom teachers that also taught Grade 8 mathematics using traditional instruction during 20122013 were included in the study. The control group included the students of teachers that used traditional instruction during the 2012 2013 academic year and the treatment group consisted of the students of teachers that subsequently used flipped instruction during the 20132014 academic year. The students within the treatment and control groups received instruction by the same teacher, so this reduced the teacher effect differences within the research model. To allow for a sufficient sample of clusters, all 46 target population classrooms were included in the study. Instrumentation STAAR Mathematics This quantitative study used the student scale score for STAAR Grade 8 Mathematics as the measure of mathematics achievement, the dependent variable, and the STAAR Grade 7 Mathematics scale score as a covariate. The scale score is “a conversion of the raw score onto a scale that is common to all test forms for that assessment. Scale scores allow for direct comparisons of student performance between specific sets of test questions from different test administrations” (Texas Education Agency, 2012). The scale score accounts for the difficulty level of the assessment and quantifies the performance of the student (Texas Education Agency, 2012). For the treatment group, the dependent variable was the 2014 STAAR Grade 8 Mathematics scale score, with the 2013 STAAR Grade 7 Mathematics scale score as the 55 covariate. For the control group, the dependent variable was the 2013 STAAR Grade 8 Mathematics scale score, with the 2012 STAAR Grade 7 Mathematics scale score as the covariate. The State of Texas Assessment of Academic Readiness (STAAR) was introduced in Spring 2012. It replaced the former state assessment, Texas Assessment of Knowledge and Skills (TAKS). The STAAR Mathematics assessment is administered in Grades 38 and includes a STAAR End of Course (EOC) assessment for Algebra I (Texas Education Agency, 2010). The mathematics assessments are rigorous and evaluate the skills mastered by students and were “developed using three major design attributes: focus, clarity, and depth” (Texas Education Agency, 2010, p. 25). The assessments are offered in a paperandpencil format and consist primarily of multiplechoice questions, as well as some openended griddable items (Texas Education Agency, 2010). The STAAR assessments are administered in the second semester of each academic year for mathematics in Grades 38 and Algebra I. It is important that the STAAR Mathematics be an accurate and appropriate measure for student achievement in mathematics. The reliability and validity of the assessment score is paramount. “Reliability is the degree to which an instrument consistently measures whatever it is measuring” and the alignment of the test was central to the reliability of the assessment (Lunenburg & Irby, 2008, p. 182). It is important to verify the “extent to which STAAR adequately measures the knowledge and skills specified in the [Texas Essential Knowledge and Skills] TEKS and the extent to which STAAR includes items that cover the full range of achievement standards” (Texas Education Agency, 2010, p. 32). The test must be narrowly aligned to the content standards of the gradelevel and every item included on a STAAR assessment is reviewed by Texas Education Agency, 40 independent Texas educators, and its 56 testing contractor (Texas Education Agency, 2010). The validity is also considered for the STAAR and “validity is the degree to which an instrument measures what it purports to measure” (Lunenburg & Irby, 2008, p. 181). The use of STAAR assessment data is supported by validity evidence, “by correlating the STAAR assessments with other tests or measures of student performance” (Texas Education Agency, 2010, p. 43). Comparisons with national and international assessments were used to establish validity. The National Assessment of Educational Progress (NEAP) is a national assessment and Trends in International Mathematics and Science Study (TIMSS) is an international assessment used to evaluate validity (Texas Education Agency, 2010). External validity evidence was collected and scores on each assessment are associated across grades to performance on other same subject assessments (Texas Education Agency, 2010). The STAAR Grade 8 Mathematics assessment consists of 56 items, including four griddable items (Texas Education Agency, 2011c). The assessment evaluates the application of knowledge and skills in 11 readiness standards and 22 supporting standards. The readiness standards comprise approximately 60%65% of the assessment and supporting standards comprise approximately 35%40% of the assessment (Texas Education Agency, 2011c). Seven process standards are woven throughout at least 75% of the STAAR in the form of dualcoded items, which included a process standard and either a readiness or supporting standard. The STAAR Grade 8 Mathematics included 11 items in Numbers, Operations, and Quantitative Reasoning; 14 items in Patterns, Relationships, and Algebraic Reasoning; eight items in Geometry and Spatial Reasoning; 13 items in Measurement; and 10 items in Probability and Statistics (Texas Education Agency, 2011c). The STAAR Mathematics assessment was scored by the Texas Education Agency. Data were reported to the school district for each student. The 57 STAAR Grade 8 Mathematics assessment had an initial administration and students had two more opportunities to take and meet expectations on the assessment if needed. For the purpose of this study, only the first administration results were analyzed. The student data results and demographics were documented in the suburban district’s Eduphoria database. Middle School Mathematics Flipped Instruction Survey The middle school mathematics teachers in the suburban school district under study completed the Middle School Mathematics Flipped Instruction Survey. The district mathematics curriculum department personnel administered the survey in May 2014. The survey included seven questions to assess the use of flipped instruction. Responses from all middle school mathematics teachers from Grades 6, 7, and 8 in the suburban school district were recorded. Teachers answered questions about the use of flipped instruction and the month they began and ended the use of the strategy. Teachers also reported the classes that received flipped instruction, how often the strategy was used, and if they would employ flipped instruction in the future. Permission to access the results of the survey was obtained by the researcher to determine the Grade 8 classes that received instruction in the flipped classroom. Data Collection Through the results of the Middle School Mathematics Flipped Instruction Survey, the Grade 8 mathematics teachers that employed the flipped method of instruction and their students were determined. Students with both a 2013 STAAR Grade 7 Mathematics scale score and a 2014 STAAR Grade 8 Mathematics scale score were included in the study’s treatment group. Students with both a 2012 STAAR Grade 7 Mathematics scale score and a 2013 STAAR Grade 8 Mathematics scale score were included in the study’s control group. Permission to access the 58 district survey results and access the state assessment student data in the Eduphoria database was obtained by the researcher. Once the researcher obtained permission, personnel from the school district retrieved the data for the researcher. All identifying information for the teachers and students was removed. Confidentiality was maintained. The data that were obtained for the Grade 8 students within the suburban school district are listed in Figure 2. 59 Data Categories: Reported As: Teacher Number 1 – 30 Class Number 1 – 200 Student Number 1 – 7000 Type of Instruction 0 Traditional 1 Flipped Ethnicity 1 African American 2 Hispanic 3 White 4 Other Gender 0 Male 1 Female SocioEconomic Status 0 NonEconomically Disadvantaged 1 Economically Disadvantaged Special Education Status 0 No Special Education Services 1 Special Education Services LEP Status 0 Not LEP 1 LEP Level of Instruction 1 Regular mathematics class 2 PreAP mathematics class Class percentages by Ethnicity 0.00 – 100.0 Class percentage by Gender 0.00 – 100.0 Class percentage Economically Disadvantaged 0.00 – 100.0 Class percentage Special Education 0.00 – 100.0 Class percentage LEP 0.00 – 100.0 2013 STAAR Grade 7 Math Scale Score (treatment) 984 – 2189 (TEA, 2012) 2014 STAAR Grade 8 Math Scale Score (treatment) 1034 – 2231 (TEA, 2012) 2012 STAAR Grade 7 Math Scale Score (control) 985 – 2185 (TEA, 2012) 2013 STAAR Grade 8 Math Scale Score (control) 1036 – 2233 (TEA, 2012) Figure 2. Data collection for data analysis. The teacher and student identification numbers were replaced with numbers randomly generated by the district. The district personnel also paired the teacher number with the type of instruction used. The data remained anonymous to the researcher. The existing data were collected for the 20132014 flipped classrooms, which served as the treatment group. The 60 control group included the 20122013 traditional classrooms that were taught by the teachers that chose flipped instruction for the 20132014 academic year. The student data of teachers that implemented flipped instruction for a shorter period of time were deleted from the data set. In addition, the student data of flipped classroom teachers that did not have 20122013 control group student data were also deleted from the data set. It was important for each student in the treatment group to have a STAAR Grade 7 Mathematics scale score as a covariate variable and a STAAR Grade 8 Mathematics scale score as the dependent variable. Students without both scores were deleted from the data set. Class data were also collected for the treatment and control groups. The percentage of students in the classes who were LEP, economically disadvantaged, and received special education services were included in the data set. The class data also included the percentage of male and female students as well as the percentage of students in the classes who were African American, Hispanic, White, and Other. Data from 23 control group classes and from 23 flipped classes were collected, which included data from 1025 students. The data set was entered as a spreadsheet and inputted into version 21.0 of SPSS for analysis. Data Analysis Experimental design is “historically the only approach for estimating true treatment effects and making causal inferences” (Lane et al., 2012, p. 187). However, research in educational settings does not always lend itself to true randomization and experimental design (Lane et al., 2012). A true experimental research design is difficult to implement in educational settings, particularly when there are multiple schools involved and selection procedures may not be the same at each school (Kim & Seltzer, 2007). 61 Because randomization was not possible for this study, the data were analyzed using propensity score matching (PSM) described by Thoemmes (2012) with steps depicted by Randolph et al. (2014), and a multilevel modeling (MLM) approach described by Rickles (2011). Propensity score methods are used “so that balance on observed covariates is achieved through careful matching on a single score—the estimated propensity of selecting the treatment, or simply the propensity score” (Thoemmes, 2012, p. 2). This PSM allowed the researcher to study the differences in treatment and control groups, although randomization and true experimental design was not possible. Another complication when estimating the effects of educational programs was that the treatment itself may vary across sites. “Variation in the treatment conditions across schools [in this study, across classes] can result in a break of the stableunittreatment value assumption (SUTVA)” or what is sometimes “referred to as treatment enactment variation due to an organization effect” (Rickles, 2013, p. 253254). Rickles (2013) and others advocate investigating effect differences through multilevel modeling. For this study, after the data were preprocessed using PSM, the treatment effect for flipped instruction was analyzed with descriptive statistics and multilevel linear models (Rickles, 2011) to estimate variation in the treatment effect across students and classes. Propensity Score Matching A propensity score matching SPSS procedure developed by Thoemmes (2012) was used to establish an equivalent baseline between the treatment and control groups in the causal comparative study. As outlined by Thoemmes (2012), the first step in PSM was to select pretest covariates based on previous research and theory. This step was vital “as the credibility of the propensity score analysis hinges on the selection of proper covariates” (Thoemmes, 2012, p. 4). For this study, the covariates were gender, ethnicity, socioeconomic status, special education 62 status, and LEP status, as shown in Figure 2. Each student’s STAAR Grade 7 Mathematics scale score was the pretest covariate for the control and treatment groups. Based on this set of covariates, a propensity score was estimated in SPSS using the covariates as predictor variables and the treatment status (0 = traditional, 1= flipped) as the outcome variable. A logistic regression estimation algorithm was used, discarding units outside the common area of support. Selecting this option can “improve balance on covariates and can avoid extrapolation of units in one group that were so dissimilar on their covariates that no comparable units in the other group were found” (Thoemmes, 2012, p. 9). The nearest neighbor 1:1 matching algorithm was used with a 0.25 SD caliper, as used by Rickles (2011). A caliper “is a maximum distance that two units can be apart from each other and is defined in units of standard deviations of the logit of the estimated propensity score” (Thoemmes, 2012, p. 10). The resulting propensity score was the probability of being in a flipped classroom. After matching for regular and preAP mathematics students by teacher was complete, descriptive statistics were run on all covariates for the treatment and control groups to verify balance on the covariates. These statistics are reported in Chapter 4. In this study, the steps indic 
Date  2015 
Faculty Advisor  Arrambide, Melissa 
Committee Members 
Denson, Katy Holt, Chuck 
University Affiliation  Texas A&M UniversityCommerce 
Department  EdD Educational Administration 
Degree Awarded  Ed.D. 
Pages  127 
Type  Text 
Format  
Language  eng 
Rights  All rights reserved. 



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