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Content Analysis of Mathematical Concepts in Children's Literature An Honors Thesis Jessica John Submitted to the Texas A&M UniversityCommerce Honors Committee in partial fulfi llment of the Program of Honors Study leading to the degree of Bachelor of fnterdisciplinary Studies Directed by Dr. Susan Szabo & Dr. Laverne Raine Assistant Professors Department of Curriculum and Instruction April23, 2012 Approved: Advisor 11tUu .d~ lli . fvob:::; Department Head QJ9' ervices Content Analysis of Mathematical Concepts in Children's Literature 1 Content Analysis of Mathematical Concepts in Children's Literature Jessica John Texas A&M UniversityCommerce Content Analysis of Mathematical Concepts in Children's Literature 2 Abstract Mathematics is an important aspect of education and daily life. However, many students do not see mathematics as relevant to their everyday living, thus the anxiety and disinterest in mathematics. Effective teachers should use captivating literature as a tool to capture student's interest and introduce and teach math concepts that are critical to academic success and daily living. This paper details what measures can be taken by teachers to analyze the text and illustrations to ensure the children's book chosen will have a positive impact on students in the classroom. A rubric is also incorporated into this study as a visual aide that was used to analyze and judge book's mathematical and literary components. Content Analysis of Mathematical Concepts in Children's Literature 3 Content Analysis of Mathematical Concepts in Children's Literature Introduction: Student attitudes and perspectives towards math have been negative in the classroom (Mitchell, 1999), and research has revealed that students are suffering from math anxiety as well as believing mathematics is not relevant to their life (Geist, 201 0). These student beliefs have caused teachers of mathematics some anxiety, as math is not only relevant in real life but is also tested at many grade levels. Therefore, it is important that mathematics teachers find ways to motivate and encourage students to become more engaged while learning mathematical concepts. Studies have shown that teachers can help students have a more positive experience if they use children's books (Harper, Boggan, and Tucker, 2008). Children's literature helps to teach number concepts in a connected, interactive, and meaningful way so that the learning moves to longterm memory (Raymond, 1995). In addition, math scores have also been shown to increase when math strategies are combined with literature (Jennings, 1992). Therefore, it appears that teachers can effectively teach mathematic concepts using literature as a vehicle to obtain and retain students· interest and motivation while learning math concepts. Purpose of Study The purpose of this content analysis is to provide a list of good children's books that teach mathematical concepts correctly. It is believed that these books will capture student's interest, alleviate math anxiety, teach mathematical concepts in a way that is relevant to their lives and in a meaningful context, and prepare students to be successful in mathematics. Content Analysis of Mathematical Concepts in Children's Literature 4 Methods and Procedure To begin this project, the math Texas Essential Skills and Knowledge (TEKS) for elementary grades (Kindergarten5th grade) were reviewed. The Math TEKS lists the mathematical concepts that should be included in the curriculum, when teachers should start introducing that concept, and the grade level in which students should master each specific mathematical concept. The TEKS are specific to grade level, and students must master the concept in order to be considered successful. Second, ten math literature books were read and the mathematical concepts presented in the book were aligned with the appropriate math TEKS. In addition, in order to assess the effectiveness of the literature, a list of all the concepts found in the books were listed and an extensive research on the concepts was done. The history of the concept (where it came from and why it was brought about, how the concept can be applied to everyday living, and the various ways it can be taught) was determined when possible. Third, the text was analyzed for accuracy of its presentation in each of the children's literature books. The students must be able to comprehend the literature content as well as the mathematical concept that is being presented. Words must be simple and understandable to the age group it is trying to convey the message to. For example, if the concept introduced is whole numbers and it is introduced in Kindergarten, the text must be uncomplicated and plain so that five year olds can follow along and make meaning of what is being taught. Any discrepancies in the text will cause confusion for the child causing frustration and further driving their negative attitude towards mathematics. Other aspects of the children's books to analyze are if the book '·fulfills its intended purpose, if it holds the attention ofthe reader, and ifthe child will find Content Analysis of Mathematical Concepts in Children's Literature pleasure in reading the book" (Farr, 1979, p. 101 ). The books chosen were evaluated based on the criteria mentioned above, and the evaluation forms can be found in Appendix A. 5 Fourth, after the best books had been selected that correctly illustrated the concept for children, the books were reread to find vocabulary words that must be pretaught to students in order for them to successfully learn and understand the mathematical concept. The vocabulary words that need to be pretaught may or may not have a mathematical foundation; they are simply words that students must know before they are acquainted with the text. That way, the vocabulary words do not hinder the student's ability to grasp the concept that had been taught. Fifth, an extensive research was conducted on how the reading ability of students impacts success in mathematics and how teaching vocabulary words before the concept is introduced will allow students to be successful in fully comprehending the math concept. Effective Math Instruction Anyone can teach, but it takes a knowledgeable teacher of both math skills and teaching pedagogy to teach math effectively (O'Donnell, 2009). Teachers need to examine the Texas Essential Knowledge and Skills (TEKS) that students are expected to master by grade level. In addition, National Council ofTeachers of Mathematics (NCTM) has identified three crucial math concepts that need to be addressed in each grade. State standards are derived from these focal points and are used to provide mathematics curriculum for prekindergarten through eighth grade (NCTM 2006). Then, teachers should provide a variety of ways on how these skills get taught. There are many approaches to teaching math, and teachers should learn a variety of ways and strive for a balance between them (Protheroe, 2007). Shellard and Moyer (2002) identify Content Analysis of Mathematical Concepts in Children's Literature 6 three critical components of effective mathematical instruction: "Teaching for conceptual understanding, developing children's procedural literacy, and promoting strategic competence through meaningful problemsolving investigations·' (p. 52). Another way to help students' understanding is by presenting the topics sequentially as well as making sure it is appropriate for the developmental level of the students (Reyes et at., 1999). In addition, NCTM has developed a timeline for student's mathematical skills development and instruction which can be found at http:/ /standards. nctm.org. Protheroe (2007) lists some ideas that make teachers effective. Teachers must have good class management skills, because effective teaching cannot occur in a classroom that is full of chaos. Teachers must use differentiated instruction to reach to the learning needs of all their students. Other aspects include active engagement of students (Wood, Williams, & McNeal, 2006), efficient use of time, logical procession of lessons (Reyes et al., 1999), effective use of assessment, and time management (O'Donnell. 2009). In addition, there must be an effective mathematics environment where there is an acceptance of divergent ideas from students. Teachers need to challenge students to think deeper and to explain their thinking and their logic. When students are challenged, the challenge develops their selfconfidence in their mathematical abilities and they gain a deeper grasp of what the concept is about. Students' curiosity should be welcomed and questions answered. Teachers who have positive attitudes about math relay that attitude to their students. In addition, teachers should have a clear understanding that all students can do well in math. Integrating crosscurricular activities into math lessons so that students can see that math can be used everywhere is also important, as math in the ·'real world" is not segmented out like math classes. Content Analysis of Mathematical Concepts in Children's Literature 7 Teachers should allow student~ to work in groups or in pairs, in order to solve problems together. Group work emphasizes the importance of working together and collaborating to find a solution. Great math instruction gives students as many chances as possible to communicate mathematically. How a student communicates mathematically can be up to them, whether they draw a picture, write in journals, or have discussions. Last but not least, manipulatives should be used in the classroom (Farr, 1979). Research clearly shows that students learn more effectively when handson activities are used, and interest and positive attitudes towards mathematics can be achieved. Manipulatives are used to explore, represent, and communicate mathematical ideas (Nelson and Sassi, 2006). Effective teachers demonstrate proper use of manipulatives, allows time for students to explore personally, and encourages participation from all students. Barbara 0 ' Donnell (2009) studied elementary teachers that promote mathematical learning through problem solving, and identified major themes and related strategies that characterized the practices that effective math teachers had in common. She found that in order to create an inquiry based classroom, the teacher must have high expectations for each child, allow students time to think for themselves, give students responsibility, and accept that some students will not get the answer. In addition, children need to be encouraged to rely on their own thinking and critical skills (Kamii and Warrington, 1999). Too often, teachers answer too readily without giving enough wait time. "Immediate responses prevent students from thinking through issues and concepts thoroughly" (Brooks and Brooks, 1999, p.lO 1 ). When students are given responsibility over a problem, they will take the necessary steps to get through the process and arrive at the correct solution. However, teachers must be able to accept that students may not be able to get the correct answer. This can cause students frustration, but there is a lesson to be Content Analysis of Mathematical Concepts in Children's Literature 8 learned behind getting an incorrect answer, as mathematical problems can require more than just one problem solver and it may take team work to arrive at the correct solution, as well as having practice engagement in ·'looking for relationships, making conjectures, testing conjectures, and explaining and justifying the generalizations they make" (Russell, 1999, p. 136). Struggling with problems may result in confident problem solvers as long as the disequilibrium caused does not reach frustrational level and/or cause cognitive overload which puts the learner in panic or shutdown mode, as some disequilibrium is crucial to a child's intellectual growth (O'Donnell, 2009). As seen above, there are a variety of ways in which teachers can teach math lessons effectively. It is not merely enough for students to memorize math facts and recite them; students must understand the concept that is behind and truly grasp the foundations as math is truly a part of everyday life" (O'Donnell, 2009). Learning Math through Literature Children's books can be a great teaching tool as they provide stories that integrate many mathematical concepts. "Literature that interacts with the curriculum extends the focus to include books and readers along with content area knowing" (Johnson & Giorgis, 2001, p.204). Literature motivates children to learn, provides a meaningful context for math, celebrates math as a language, demonstrates that math develops out of human experience, fosters the development of number sense, and integrates math into other curriculum areas (Whiten & Wilde, 1992, 1995). Many people may wonder how literature invites interaction with math but the connection is actually more natural than one may expect. Concepts such as mathematical shapes can be readily seen and understood when presented using common images and everyday experiences. For example, when a car stops at the stop sign, the big, red, stop sign automatically registers in Content Analysis of Mathematical Concepts in Children's Literature the child's brain as a shape. They may not know that the shape is an octagon, but the mathematical concept of a shape is there. When the family orders a large pizza for dinner, the child may see the pizza as a whole circle, or a pizza slice as a triangle. The connections children's literature makes to mathematical concepts in their everyday settings are natural. Children learn through direct, concrete experiences (Copeland, 1978); therefore, they will be introduced to and learn simple math concepts while doing everyday things such as playing, eating, and communicating with one another. Young children can explore math concepts while they enjoy picture and story books. BarattaLorton (1976) affirms that when we teach mathematics to young children, we must look at the world through their eyes. Visual representations are crucial to earlylevel instruction, and children's books provide the opportunity for them to see mathematical concepts visually. We take in information by seeing things, and children take in math concepts subconsciously while viewing illustrations in children's books. "Books that show how math works in carefully constructed diagrams and illustrations can help them understand specific concepts better than purely verbal or numerical explorations" (Murphy, 1999, p. 122). Murphy realized through his visits to schools that many children understood difficult mathematical concepts when they were presented within the context of a story and illustrated through diagrams, graphs, and other visual displays. "Bright, colorful illustrations in children's books may be used to help distinguish geometric shapes in familiar objects" (Radebaugh, 1981 ). Many mathematical concept books can provide an interesting, riskfree context for children to explore mathematical concepts (Harper, Boggan and Tucker, 2008). Effective Cchildren's literature can help children relate math to their personal lives, extend their understanding to other contexts, and provide an opportunity to explore mathematic concepts 9 Content Analysis of Mathematical Concepts in Children's Literature 10 further (Shatzer, 2008). When teachers use children's literature to teach math concepts, they help children connect their formal ideas with the abstract language and symbols of mathematics, which also reduces anxiety and negative attitudes towards math (Harper, Boggan and Tucker, 2008). As Radebaugh (1981) so wisely stated, '·using children's literature as a springboard for mathematical experiences allows language and mathematics learning to grow together naturally and imaginatively"(p. 196). Mathematical Concepts in Everyday Life Unfortunately, children do not value mathematics because they do not see it as relevant to their daily lives (Harper, Boggan, and Tucker, 2008). Many students appear to be just memorizing facts and figures to pass a test or to get to the next grade level. They wonder why they need to learn math concepts and question when they are ever going to use the concept in their life. "Presenting mathematical ideas within stories that relate specifically to kids can help answer these questions. Stories, especially illustrated stories, can engage children and help them connect mathematical ideas to their own lives" (Murphy, 1999, p.122). ''Children need vehicles that will help them apply the information they learn to their everyday lives" (Murphy, 1999, p.l22). Storybooks can be the perfect vehicles; when '·children see how people use math [in the storybook] on a daily basis for many purposes, they can then transfer those math concepts to their own lives" (Harper, Boggan, and Tucker, 2008, p. 79). ·'Bright, colorful illustrations in children's books may be used to help distinguish geometric shapes in familiar objects" (Radebaugh, 1981 , p. 902). "Trade books can suggest activities that emerge from the story and that help children see connections to their own lives. They need to try activities for themselves and see what works, discover patterns, and create their own models. They need to be able to take the math out of a book and extend it to a wide variety of authentic Content Analysis of Mathematical Concepts in Children's Literature 11 personal experiences" (Murphy, 1999, p. 122). When students realize that math pertains to their life and can make relevant connections between math concepts and their personal experiences, they are more likely to remember the concept and understand it more deeply. Mirella Rizzo, an ESL teacher, asked her students to use their personal experiences to make sense of the mathematical relationships in the problem after reading a storybook; the fifthgraders made connections between their personal interests, knowledge and experience to key math ideas (Whitin and Whitin, 2006). Shatzer (2008) chose books that connected content to her student's lives so that her students could construct meaning from those books. If you think about your everyday activities, you will realize that you use math constantly. In calculating how long and how much gas or money it takes us to get somewhere. how much longer you get to sleep in without being late, if you' re eating the right amount of calories, how much taller you grew since the last time you were at the doctor's office, money management, and dividing your laundry to see how many loads you need to wash are just a few examples. ·'Books that demonstrate mathematical concepts as part of a story reflect reallife situations" (Murphy, 1999, p.122). Friedman (1997) suggests that students be allowed to write their own stories (similar to the children·s book they had read), encouraging students to be creative and to communicate about math. Thus. students can envision how the mathematical concept was used or can be used in their personal life, and communicate the mathematical concept in a situation that is personal and relevant to their lives. Stories provide an opportunity to emphasize how math concepts are applied to everyday settings that are familiar to children and connect them in some way. Content Analysis of Mathematical Concepts in Children's Literature 12 Reading Ability Affects Math Reading plays an important role in student mathematics achievement (Larwin, 201 0; Rust, 2008). However, many teachers assume the difficulty is with a student's math abilities and not the student's poor reading ability (Draper, Smith, Hall, & Siebert, 2005). However, in the standardized math assessments that are given to students today, questions are in the form of a word problem (U.S. Department of Education, 1996). "Therefore, in practice, poor reading ability automatically undermines a student's likelihood of success on math achievement measures" (Larwin, 1996, p. 133). According to Kintsch and Greeno (1985), the linguistic part of understanding the text of the math problem is crucial to being able to successfully solve the problem. Students must be able to read the word problem at the basic level of phoneme and word recognition and comprehend the words well enough to transfer into a conceptual understanding of the text. Only after a child has been able to decipher the math question can he or she apply their mathematical skills to solve the problem. For students who have low reading ability, advancing beyond word recognition and comprehension is almost impossible. Bull and Johnston (1997) found a direct relationship between math achievement and reading ability. A student's processing speed is limited when they have poor reading skills. Research states that even students with high math abilities cannot succeed if they are not proficient in reading (Larwin, 1996). In addition, research done by Kintsch and Greeno (1985) uphold the findings that solving word problems in mathematics involves a high level of cognitive complexity. Research findings from Youngstown State University disclose that '·56% of the variance in student math achievement can be explained by student's reading ability" (Larwin, 1996, p.l31). Similarly, data utilizing 100 students from India reflect that reading ability directly Content Analysis of Mathematical Concepts in Children's Literature correlates to student performance on math exams (Rangappa, 1993). High ability readers performed better than normal ability readers, and normal ability readers performed better than low ability readers. Majumder (2003) concluded that a strong predictor of a student's ability to solve math word problems was reading comprehension. 13 Current findings reveal that the strong linkage found in elementary age children is sustained till high school years; therefore, reading problems should be addressed at all grade levels in order to prevent students from being unsuccessful in their mathematics achievement in later years. What Makes a Children's Book Effective? In recent years, the trend for children·s literature with mathematical concepts has increased (Farr, 1979). Unfortunately, mixed in between quality books are books of little to no value (Hellwig et al., 2000). It is the critical role of teachers to select quality literature for their students. With instructional time restraints imposed on teachers, it is inefficient to use a trade book for instruction if it does not contain high mathematical and literary quality. Farr (1979) examined the various approaches books utilized to illustrate specific mathematical concept to evaluate the book's effectiveness. First, does the book fulfill its intended purpose? ln order for the book to fulfill its intended purpose, the information presented in the book must be accurate and precise. In addition, "the concepts must follow a logical procession towards increased complexity" (Farr, 1979, p.l 01 ). Any discrepancies in the text or illustration will confuse the reader, thus taking away the intended objective of the book. Therefore, "to enhance mathematics literature, teachers should not be afraid to add mathematical annotations and vocabulary" (Hunsader, 2004, p.619). Content Analysis of Mathematical Concepts in Children's Literature 14 In order to convey the math concept, the book must be captivating and keep the audience's attention. Children's books also have an advantage for visual learners, as the concepts and ideas are represented in a nonthreatening pictorial format (Guiett, 1999). Good books bridge the gap between concrete representations and abstract concepts. The story's plot should be interesting to its audience and students should be able to relate the story to their life, experiences, and the world around them. The role of connecting literature with math is powerful (Columba et al., 2005) and teachers must ensure that the book selected is interactive. Interactive readaJouds are important for developing reader, text, and context connections (Rosenblatt, 1978, 1995). While it is important for teachers to select books of quality, teachers are also responsible during the readaloud to help students make the connection to self, to the text, and to the world (Fountas & Pinnell, 2001), as well as construct meaning from the book (Hyde, 2006). Children's literature that teaches mathematical concepts are more effective "when children are able to see how people use math on a daily basis for many purposes, and can then transfer those math concepts to their own lives'' (Harper, Boggan, and Tucker, 2008, p.78). When numbers and operations are embedded in meaningful realworld contexts as those seen in quality children's literature, children are able to gain knowledge about math and develop a wider view of how math relates to their world (Schiro, 1997). "Quality children's books are appealing, nonthreatening, and related to children's lives" (Harper, Boggan, and Tucker, 2008, p.78). Effective books provide a riskfree environment for students to explore mathematical concepts and extend their knowledge to other contexts. The National Council of Teachers for Mathematics (NCTM) emphasizes the importance of communicating mathematically and developing connections between their informal Content Analysis of Mathematical Concepts in Children's Literature 15 knowledge and abstract symbolism of math concepts. '·Many children's books present interesting problems and illustrate how other children solve them. Through these books students see mathematics in a different context while they use reading as a form of communication" (National Council ofTeachers of Mathematics, 1989, p.27). There are many critical components of children's literature that must be evaluated in order to assess the effectiveness of the book. Hellwig eta/ (2000) stated that accuracy, verbal and visual appeal, connections, audience, and the "wow" factor as criteria for quality children's literature. However, Farr (1979) believes that the most critical requirement for any type of quality literature is that the child should find pleasure in reading or hearing it. When selecting and using children's literature to find natural mathematics connections, teachers create a learning environment that is supported by both the National Council of Teachers of English (NCTE) and the NCTM (Moyer, 2000; Taylor, 1999). Quality children's books will benefit students by allowing them to develop their language and math skills simultaneously (Hellwig et al., 2000). Content Analysis of Mathematical Concepts in Children's Literature 16 References BarattaLorton, M. ( 1976). Math Their Way. Menlo Park, CA: AddisonWesley. Beard, L.A. (2003). 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(2000). Communicating Mathematically: Cruldren's literature as a natural connection. The Reading Teacher, 54, 246255. Murphy, Stuart J. (1999). Learning Math through Stories. School Library Journal, 122 123. Natjonal Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author. National Council ofTeachers of Mathematics. (2006) Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. Retrieved from www. Nctm.org/focalpoints. Content Analysis of Mathematical Concepts in Children's Literature Nelson, B.S. & Sassi, A. (2006). What to Look for in Your Math Classrooms. National Association for Elemenrary School Principles, 4649. O'Donnell, B. (2009). What effective math teachers have in common. Teaching Children Mathematics, 16, 118125. Protheroe, N. (2007). What Does Good Math Instruction Look Like? National Association for Elementary School Principles, 5154. Radebaugh, M.R. (1981 ). 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Presented at the AMA TYC Conference. Schiro, M. ( 1997). integrating children 's literature and mathematics in the classroom: Content Analysis of Mathematical Concepts in Children's Literature 20 Children as meaning makers, problem solvers, and literary critics. New York: Teachers College Press. Shatzer. J. (2008) Picture Book Power: Connecting Children's Literature and Mathematics. The Reading Teacher, 61 , 64953. Shellard, E. & P.S. Moyer. (2002). What Principals Need to Know about Teaching Math. Alexandria, Va.: National Association of Elementary School Principals and Education Research Service. Taylor, G.M. (1999). Reading, writing, arithmeticMaking connections. Teaching Children Mathematics, 6, 190197. U.S. Department of Education {1996). Reading Literacy in the United States: Findings From the lEA Reading Literacy Study. National Center for Education Statistics, Washington, D.C. Whitin, D.J ., & Wilde, S. ( 1992). Read any good math lately? Children's books for mathematical/earning, K6. Portsmouth, NH: Heinemann. Whitin, D.J., & Wilde, S. (1995). It 's the story that counts: More children's books for mathemalicallearning, K6. Portsmouth, NH: Heinemann. Whitin, P. and Whitin, D. (2006) Making Connections through MathRelated Book Pairs. Teaching Children Mathematics, 13, 196202. Wood, T., Williams, G. & McNeal, B. (2006). Children's Mathematical Thinking in Different Classroom Cultures. Journal for Research in Mathematics Education 37, 222 255 Content Analysis of Mathematical Concepts in Children's Literature Appendix A Evaluation of Mathematical Concepts in Children's Literature Evaluator:  Date: _______________ _ Book Name: Author: Mathematical concept(s) in book: Targeted Audience (circle all that apply): PreK K How effective is the book from a mathematical perspective? 2 Not effective somewhat effective 3 effective How effective is the book from a literary perspective? Not effective General Comments: 2 somewhat effective 3 effective Mathematical Principles Is the math concept found in the book correct and accurate? optimally Comments: 2 partially 3 poorly Is the math vocabulary defined correctly in the book? 2 3 optimally partially poorly Comments: 2 3 4 5 4 highly effective 4 highly effective 21 Content Analysis of Mathematical Concepts in Children's Literature Does the illustration correctly portray the concept? 1 optimally Comments: 2 partially 3 poorly Does the book encourage student involvement in mathematics? optimally Comments: 2 partially 3 poorly Literary Principles Does the book attract its intended audience? optimally Comments: 2 partially Is the book interactive and engaging? optimally Comments: 2 partiaJly 3 poorly 3 poorly 22 Content Analysis of Mathematical Concepts in Children's Literature Do the book's plot and the illustrations complement each other? optimally Comments: 2 partially 3 poorly Is the book developmentally appropriate for its intended audience? optimally Comments: 2 partially 3 poorly 23 Content Analysis of Mathematical Concepts in Children's Literature Appendix B: Mathematical Concept Children's Literature Book Summaries Leedy, L. (2008). The Action of Subtraction. Minneapolis: Millbrook Press. Mathematical Concept Book is Teaching: Subtraction Grade Level and Grade Level TEKS this Book Could be Used for: 24 Kindergarten (b) ( 4) Number, operation, and quantitative reasoning. The student models addition (joining) and subtraction (separating). The student is expected to model and create addition and subtraction problems in real situations with concrete object. First Grade (b) 3(A) model and create addition and subtraction problem situations with concrete objects and write corresponding number sentences; and (B) use concrete and pictorial models to apply basic addition and subtraction facts (up to 9 + 9 = 18 and 18  9 = 9). Second Grade (b) 3 (A) recaJI and apply basic addition and subtraction facts (to 18);(B) model addition and subtraction of twodigit numbers with objects, pictures, words, and numbers; Summary of Book: The Action of Subtraction is an informational book about the concept of subtraction. The book is ideal for students in Kindergartenthird grade. Relevant definitions are mentioned in this book, and the animated images help students see the action of subtraction happening. The book is long enough to cover the essential skills of subtraction, but short enough to keep the reader's interest. The font ofthe text is animated and helps to connect to the pictures. The text is simple to read and the font is the perfect size. The numbers in a subtraction problem are a different color than the font which will assist students in visualizing the numbers when the story is being read. The book shows a variety of ways subtraction can be shown (diagonally and vertically), and it also mentions the various ways to tell subtraction is happening (minus, less than, fewer, etc.). The book extends subtraction problems to more than just two numbers; it allows students to think even more critically by subtracting more numbers in just one problem (Ex: 122=1 0, 10 5=5). Vocabulary Words to Work On: Action something being done or performed. Hornets bugs that can sting you. Discomfort not comforting Bent curved, crooked. Amount the sum total Fewer less than Shrinking getting smaJier Content Analysis of Mathematical Concepts in Children's Literature 25 Demi. ( 1997). One Grain of Rice: A Mathematical Folktale. New York: Scholastic Press. Mathematical Concept Book is Teaching: Multiplication Grade Level and Grade Level TEKS this Book Could be Used for: Second Grade (b) 4 (A) model, create, and describe multiplication situations in which equivalent sets of concrete objects are joined; Third Grade (b) 4 (A) learn and apply multiplication facts through 12 by 12 using concrete models and objects; (B) solve and record multiplication problems (up to two digits times one digit); and Fourth Grade (b) 4 (A) model factors and products using arrays and area models; (B) represent multiplication and division situations in picture, word, and number form; (C) recall and apply multiplication facts through 12 x 12; (D) use multiplication to solve problems (no more than two digits times two digits without technology) Summary of Book: A mathematical folktale that is sure to captivate students with its detailed illustrations, vivid colors, cultural background, and life learning moral. The large amounts of white space with a splash of deep color in the book allow a regal feel. The illustrations also depict one type of Indian culture, and the vocabulary is quite uncommon. Teachers can also use this book to introduce the varied types of government. Students will not realize they are learning a math lesson till they get into the meat of the story, and by then, they are already hooked. The book focuses on a young girl. s smarts; I would emphasize that anyone can make a difference regardless of age. The book details how many rice she gets (as her reward) per day, and also estimates what that amount of rice will fill up. For example. students may not know that approximately 4,000 grains of rice will only fill up a bowl. The extended pages with images illustrating how much rice the young girl was rewarded is a visual representation of how multiplication works. There is also a calendar at the very end of the book that shows how much rice the girl received per day, and teachers can make a similar calendar or table that is half done, and let students finish the chart to assess understanding and mathematical skill. Vocabulary Words to Work On: India a country in the continent of Asia Raja  King Wi e very mart Province a part of a country Decreed to give orders Storehouses places to store things Famine a time of no food Royal blood line Troubled worried Fulfill to finish, follow Ministers people that work with the king imploredbegged Feast a huge meal Village a small town Trickle a very little amount Clever very smart Halt to stop Deedsomething that is done Plentifu l to have lots of something Modest not flashy Content Analysis of Mathematical Concepts in Children's Literature Murphy, S. J. (1997). Betcha! New York: Harper Collins Publisher Inc. Mathematical Concept Book is Teaching: Estimation, Prediction Grade Level and Grade Level TEKS this Book Could be Used for: First Grade (b) (4) Patterns. relationships, and algebraic thinking. The student uses repeating patterns and additive patterns to make predictions. The student is expected to identify, describe, and extend concrete and pictorial patterns in order to make predictions and solve problems. 26 Second Grade (b)(6) Patterns, relationships, and algebraic thinking. The student uses patterns to describe relationships and make predictions. The student is expected to: (A) generate a list of paired numbers based on a reallife situation such as number of tricycles related to number of wheels; (B) identify patterns in a list of related number pairs based on a reallife situation and extend the list; and (C) identify, describe, and extend repeating and additive patterns to make predictions and solve problems. Third Grade (b) (6) Patterns, relationships, and algebraic thinking. The student uses patterns to solve problems. The student is expected to: (A) identify and extend wholenumber and geometric patterns to make predictions and solve problems; (B) identify patterns in multiplication facts using concrete objects, pictorial models, or technology; and (C) identify patterns in related multiplication and division sentences (fact families) such as 2 x 3 = 6, 3 x 2 = 6, 6 ~ 2 = 3, 6 ~ 3 = 2. Betcha! is a book that many students will be able to relate to because many librarians or even classroom teachers have a jar of marbles set out to teach their students about prediction and estimation. My favorite aspect of this book is that it has two boys as the main characters, and they are hoping to win tickets to a sporting game by using math! It also shows that friends can compete in a fair and fun manner. When the boys are figuring out how many things are in a set, the illustrations show their thinking so students can see how the characters come up with an answer. This will help visual learners. The book has simple text that allows the teacher to read the sentence, and then gives time for students to reflect on the picture and make estimations on their own. Addition, money, estimation, and prediction are the concepts mentioned in this book. Vocabulary Words to Work On: Contest a challenge Guess to think, believe, or suppose something Content Analysis of Mathematical Concepts in Children's Literature 27 Burns, M. (2008). The Greedy Triangle. New York: Scholastic. Mathematical Concept Book is Teaching: Shapes, Angles Grade Level and Grade Level TEKS this Book Could be Used fo r: Kindergarten (b) (8) Geometry and spatial reasoning. The student uses attributes to determine how objects are alike and different. The student is expected to: (A) describe and identify an object by its attributes using informal language: (B) compare two objects based on their attributes; and (C) sort a variety of objects including two and threedimensional geometric figures according to their attributes and describe how the objects are sorted. (9) Geometry and spatial reasoning. The student recognizes attributes of twoand threedimensional geometric figures. The student is expected to: (A) describe and compare the attributes of reallife objects such as balls, boxes, cans, and cones or models of threedimensional geometric figures; (B) recognize shapes in reallife threedimensional geometric figures or models of threedimensional geometric figures; and (C) describe, identify, and compare circles, triangles, rectangles, and squares (a special type of rectangle). First Grade (b) (6) Geometry and spatial reasoning. The student uses attributes to identify two and threedimensional geometric figures. The student compares and contrasts two and threedimensional geometric figures or both. The student is expected to: (A) describe and identify twodimensional geometric figures, including circles, triangles, rectangles, and squares (a special type of rectangle); (B) describe and identify threedimensional geometric figures, including spheres, rectangular prisms (including cubes), cylinders, and cones; (C) describe and identify two and threedimensional geometric figures in order to sort them according to a given attribute using informal and formal language; and (D) use concrete models to combine twodimensional geometric figures to make new geometric figures. The Greedy Triangle is a fun, lively, and creative book to teach about shapes and angles. This book goes through the names of shapes with up to ten angles, and demonstrates how the shapes and angles can be used in everyday situations. The pages are covered in color from top to bottom, and the emotionalfilled pictures will capture student's attention and allow the audience to feel what the triangle feels. The book has great examples of how shapes are everywhere and how angles can be used in the real world. The illustrations are also made from the various shapes and stand out. Student's vocabulary list will be extended with the numerous vocabulary words found in this book. Although the book is very colorful and busy, the borders around the illustrations keep it simple. Not only can this text be used to teach math, it is also great for lessons on adjectives, emotions, and vocabulary. Vocabulary Words to Work On: Supporting helping Symphony orchestra a group of people playing music together Dissatisfied not happy Grumbled mumbling, muttering unhappily Nonagon a shape with nine sides Decagon a shape with ten sides Screeching a loud cry Colliding bumping into Terrify scaring Shapeshifter a person who can change a shape Quadrilateral a shape with four sides Pentagon a shape with five sides Hexagon a shape with six sides Socket an opening Boltsscrews Wrench a type of tool Restless always moving Heptagon a shape with seven sides Octagona shape with eight sides Content Analysis of Mathematical Concepts in Children's Literature 28 Miranda, A. (1999). Monster Math. Florida: Harcourt, Inc. Mathematical Concept Book is Teaching: Addition and Subtraction Grade Level and Grade Level TEKS this Book Could be Used for: Kindergarten (b) (4) Number, operation, and quantitative reasoning. The student models addition Gaining) and subtraction (separating). The student is expected to model and create addition and subtraction problems in real situations with concrete object. First Grade (b) 3(A) model and create addition and subtraction problem situations with concrete objects and write corresponding number sentences; and (B) use concrete and pictorial models to apply basic addition and subtraction facts (up to 9 + 9 = 18 and 18  9 = 9). Second Grade (b) 3 (A) recall and apply basic addition and subtraction facts ( to 18); (B) model addition and subtraction of twodigit numbers with objects, pictures, words, and numbers; What a book to help relieve students who are frightened of monsters and teach math! Monster Math will help students in counting, skip counting, and subtraction. Monsters come into the house in large amounts, and the little girl monster wants to shoo them away because there are too many! I love this book because it uses awesome adjectives to describe the monsters, and it can be used as a Language Arts lesson as well. The pages are not too busy; they are illustrated in a simple manner, kept in a frame on each page. The silly images will make students giggle and the pattern of adding 10 monsters will come to them easily. Students will be able to relate to the monsters' activities such as blowing out birthday candles, chasing friends, jumping on beds, taking pictures, and such. Vocabulary Words to Work On: Silly funny Wiggling moving around, not staying still Starved very hungry for food Monstrous very great Budge move Wreck a mess Frosted something that has frosting on it Devoured gobbled up, finished. Exhausted very tired Content Analysis of Mathematical Concepts in Children's Literature 29 Murphy, S.J. (1997). Divide and Ride. New York: Harper Collins Publisher Inc. Mathematical Concept Book is Teaching: Division Grade Level and Grade Level TEKS this Book Could be Used for: First Grade (b) (4) Number, operation, and quantitative reasoning. The student models multiplication and division. The student is expected to: (A) model, create, and describe multiplication situations in which equivalent sets of concrete objects are joined; and (B) model, create, and describe division situations in which a set of concrete objects is separated into equivalent sets. Second Grade (b) 4 (B) model, create, and describe division situations in which a set of concrete objects is separated into equivalent sets. Third Grade ( b) 4 (C) use models to solve division problems and use number sentences to record the solutions. Go on the ride of your life with this swirling, invigorating, and mindbogging adventure that will be sure to get your brain working! Divide and Ride teaches the obvious concept: division! Students will get excited for their field day or their field trip while viewing the images as they read along with the story. The characters in the book are at a carnival, and need to figure out how to make equal groups so that everyone will be able to ride the fun rides and roller coasters. The group has an odd number of members, and they need to find an extra friend (or two) at times to fill up seats for an amusement ride. This book is helpful in that it shows verbally, numerically, and pictorially how they can divide up into equal groups. The number sentence along with the picture is an asset. Many students will be able to relate to this storybook and use it as a guide during field trips. They can use the strategies found in the book to divide things into equal groups almost anywhere! Vocabulary Words to Work On: Divide to separate into two or more groups Jolt a sudden, jerky movement Raftsomething put together for transportation on water Content Analysis of Mathematical Concepts in Children's Literature DeRubertis, B. ( 1999). Deena 's Lucky Penny. The Kane Press. Mathematical Concept Book is Teaching: Counting money, monetary value Grade Level and Grade Level TEKS this Book Could be Used for: First Grade (b) I (C) identify individual coins by name and value and describe relationships among them; 30 Second Grade (b) 3 (D) determine the value of a collection of coins up to one dollar; and(E) describe how the cent symbol, dollar symbol, and the decimal point are used to name the value of a collection of coins. Deena needs money to buy her mother a birthday present, and thanks to a lucky penny, she was able to scrounge around and ftnd the right amount needed. Although the book's title is about the lucky penny, this book details the penny, nickel, dime, and quarter. I love how this book depicts the coins and value in a variety of ways. At the bottom of the page, there is a visual image of the coin and how much it is worth. The visual images show what the coins look like on both sides. There is also the cent sign and the dollar sign which help students make the connection to money. The addition sentence also shows how many of each coin you need to add together to get another coin, and it reveals the importance of including signs (such as the money sign in this number problem). Deena also has choices to make; would she rather have a penny or a nickel? A valuable lesson to teach to any grade level is about making good choices. Classes can brainstorm why Deena choose one coin over several of the same coins, and the teacher can faci litate classroom discussion to topics besides money. The book also can be used to introduce students to responsibility and the importance of saving. The piggy bank icon next to the money addition sentence is also a great visual reminder for savings. Vocabulary Words to Work On: Lucky the feeling when something good happens to you Handfula small amount that can fit in your hand Tradeto give something in exchange for something else Lonely to feel alone or by yourself Stack to put things on top of each other Twinklea sparkle or a shine Abracadabra a word used for magic to happen Content Analysis of Mathematical Concepts in Children's Literature 31 Sloat, T. (1998). There Was an Old Lady Who Swallowed a Trout. Canada: Henry Holt and Company. Mathematical Concept Book is Teaching: Order of Events, Sequencing, Ordinal Positions Grade Level and Grade Level TEKS this Book Could be Used for: Kindergarten (b) (2) Number, operation, and quantitative reasoning. The student describes order of events or objects. The student is expected to: (A) use language such as before or after to describe relative position in a sequence of events or objects; and (B) name the ordinal positions in a sequence such as first, second, third, etc. A twist to the familiar poem of'·There Was an Old Lady Who Swallowed a Fly", this book captures the wondrous wildlife that is seen in the Pacific Northwest. The lady swallows many animals, and it is easy to keep up with the order of the animals that she swallows thanks to patterns! Children love listening to this poem, and after they hear it a few times, can readily repeat the story due to the repitition and alliteration. This poem can also be used to teach ordinal numbers. Which animal did the lady swallow first? Second? Third? Vocabulary Words to Work On: Trout a kind offish Thrashflop Salmon another kind of fish Ottera mammal that lives in the water. It has webbed feet and a flattened tail Sealanother animal that lives in the water but can also live on land. Squeal to shriek Porpoisean animal that lives in water that looks like a small dolphin Walrusa large animal that has flippers, a pair of large tusks, and a tough, wrinkled skin. Fussnoisy argument Whale one of the biggest mammals that live in the water; fins, gills, breathes oxygen Ocean a very large body of water Commotion lots of loud noises, arguments. Swirlto move around fast Content Analysis of Mathematical Concepts in Children's Literature Pinczes, E. J. (2001). Jnchworm and a Half New York: Houghton Mifflin Company. Mathematical Concept Book is Teaching: Measurement, Fractions Grade Level and Grade Level TEKS this Book Could be Used for: 32 Kindergarten (b) (3) Number, operation, and quantitative reasoning. The student recognizes that there are quantities less than a whole. The student is expected to: (A) share a whole by separating it into two equal parts; and (B) explain why a given part is half of the whole. (I 0) Measurement. The student directly compares the attributes of length, area, weight/mass, capacity, and/or relative temperature. The student uses comparative language to solve problems and answer questions (A) compare and order two or three concrete objects according to length (longer/shorter than, or the same); (B) compare the areas of two flat surfaces of twodimensional figures (covers more, covers less, or covers the same); First Grade (b) (2) Number, operation, and quantitative reasoning. The student uses pairs of whole numbers to describe fractional parts of whole objects or sets of objects. The student is expected to: (A) separate a whole into two, three, or four equal parts and use appropriate language to describe the parts such as three out of four equal parts (7) Measurement. The student directly compares the attributes of length, area, weight/mass, capacity, and temperature. The tudent uses comparative language to solve problems and an wer questions. The student selects and uses nonstandard units to describe length. The student is expected to: (A) estimate and measure length using nonstandard units such as paper clips or sides of color tiles; (B) compare and order two or more concrete objects according to length (from longest to shortest); (C) describe the relationship between the size of the unit and the number of units needed to measure the length of an object An inchwonn is off to measure things that surround her, but gets confused when things are not exactly an inch. What's there to do when it' s smaller than an inch? The little wonns in this book explain the concept of an halfinch, a onefourth inch, and a third inch. This book can also be used to teach vocabulary. The text is full of beautiful words that can be used in everyday setting. The pictures in the frames are colorful and lively, and the wonns are sure to capture student's attention. Although the text is small, it goes along with the smallness of the worms and it's fitting. The dotted lines (loops) is a great visual reminder of how much an inch is as well, and the students can count how many loops there are to see how many inches a certain thing is. The book also clearly states the definition of a fraction: equal parts of a whole. This is crucial because students need to learn the foundations. The way the wonns measure an object is also a way to teach students how to read the fraction (One ... and a half!). Vocabulary Words to Work On: Nibbles to bite off in small pieces Trea ures something very important and valuable Results the end of something, the answer Cinch something easy Unthinkable something you can't even Imagine Fraction equal parts of a whole Spry active Trio group of three Occurred happened Accuracy being exact, correct Ease free from concerns Content Analysis of Mathematical Concepts in Children's Literature 33 Sierra, J. (1997). Counting Crocodiles. Florida: Harcourt Inc. Mathematical Concept Book is Teaching: Number Sense; counting from 11 0 and counting backwards Grade Level and Grade Level TEKS this Book Could be Used for: Kindergarten (b) (1) Number, operation, and quantitative reasoning. The student uses numbers to name quantities. (A) use onetoone correspondence and language such as more than, same number as, or two less than to describe relative sizes of sets of concrete objects; (B) use sets of concrete objects to represent quantities given in verbal or written form (through 20); and (C) use numbers to describe how many objects are in a set (through 20) using verbal and symbolic descriptions. (6) Patterns, relationships, and algebraic thinking. The student uses patterns to make predictions. The student is expected to: (A) use patterns to predict what comes next, including causeandeffect relationships; and (B) count by ones to 100. An amusing and entertajning book that will have children counting along with you! The text in Counting Crocodiles is an asset to the classroom because it provides children with a numerous amount ofrich vocabulary, rhyming patterns, emotions, and entertajnment. The illustrations are lively and they correctly depict the number of crocodiles on each page. The colors are beautiful on the pages and seem to jump out at you! Students can relate to the emotions of the crocodiles and the monkey, and some of the actions that the crocodiles are involved in. The book also helps readers learn how to count backwards, which is another essential skill children need to know. Each page depicts one number, which allows students to focus on that number and associate the illustrations with the number. Vocabulary Words to Work On: Island an area of land surrounded by water Clever smart Sauteed cooked Pureed food blended together Puckered wrinkled Delectable yummy, delicious Privatepersonal, not belonging to everyone Vicious mean Feastingeating Suspiciousquestionable, wonder Crusty rude Lurking sneaking around, waiting Galore many Hunch guess Cavorting prancing Impatient does not like to wait Scold to get in trouble Scurry to move quickly Content Analysis of Mathematical Concepts in Children's Literature *A call was made to Barnes and Nobles Customer Service on Saturday, April28, 2012 concerning the copyright ofthe images ofthe book covers. It was stated that displaying images of the book's cover was not a copyright issue. 34
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Title  Content Analysis of Mathematical Concepts in Children's Literature 
Author  Jessica John 
Directed by  Dr. Susan Szabo; Dr. Laverne Raine 
Department  Curriculum and Instruction 
Date  20120423 
Subject  Mathematics; Children's literature; 
Publisher of Collection  Texas A&M UniversityCommerce 
Type  Text 
Format  
Language  eng 
Rights  All rights to materials within this collection are held by respective holding institutions or individuals with the exception of public domain items. The materials contained within this collection are made available online for educational and/or personal research purposes only. 
Transcript  Content Analysis of Mathematical Concepts in Children's Literature An Honors Thesis Jessica John Submitted to the Texas A&M UniversityCommerce Honors Committee in partial fulfi llment of the Program of Honors Study leading to the degree of Bachelor of fnterdisciplinary Studies Directed by Dr. Susan Szabo & Dr. Laverne Raine Assistant Professors Department of Curriculum and Instruction April23, 2012 Approved: Advisor 11tUu .d~ lli . fvob:::; Department Head QJ9' ervices Content Analysis of Mathematical Concepts in Children's Literature 1 Content Analysis of Mathematical Concepts in Children's Literature Jessica John Texas A&M UniversityCommerce Content Analysis of Mathematical Concepts in Children's Literature 2 Abstract Mathematics is an important aspect of education and daily life. However, many students do not see mathematics as relevant to their everyday living, thus the anxiety and disinterest in mathematics. Effective teachers should use captivating literature as a tool to capture student's interest and introduce and teach math concepts that are critical to academic success and daily living. This paper details what measures can be taken by teachers to analyze the text and illustrations to ensure the children's book chosen will have a positive impact on students in the classroom. A rubric is also incorporated into this study as a visual aide that was used to analyze and judge book's mathematical and literary components. Content Analysis of Mathematical Concepts in Children's Literature 3 Content Analysis of Mathematical Concepts in Children's Literature Introduction: Student attitudes and perspectives towards math have been negative in the classroom (Mitchell, 1999), and research has revealed that students are suffering from math anxiety as well as believing mathematics is not relevant to their life (Geist, 201 0). These student beliefs have caused teachers of mathematics some anxiety, as math is not only relevant in real life but is also tested at many grade levels. Therefore, it is important that mathematics teachers find ways to motivate and encourage students to become more engaged while learning mathematical concepts. Studies have shown that teachers can help students have a more positive experience if they use children's books (Harper, Boggan, and Tucker, 2008). Children's literature helps to teach number concepts in a connected, interactive, and meaningful way so that the learning moves to longterm memory (Raymond, 1995). In addition, math scores have also been shown to increase when math strategies are combined with literature (Jennings, 1992). Therefore, it appears that teachers can effectively teach mathematic concepts using literature as a vehicle to obtain and retain students· interest and motivation while learning math concepts. Purpose of Study The purpose of this content analysis is to provide a list of good children's books that teach mathematical concepts correctly. It is believed that these books will capture student's interest, alleviate math anxiety, teach mathematical concepts in a way that is relevant to their lives and in a meaningful context, and prepare students to be successful in mathematics. Content Analysis of Mathematical Concepts in Children's Literature 4 Methods and Procedure To begin this project, the math Texas Essential Skills and Knowledge (TEKS) for elementary grades (Kindergarten5th grade) were reviewed. The Math TEKS lists the mathematical concepts that should be included in the curriculum, when teachers should start introducing that concept, and the grade level in which students should master each specific mathematical concept. The TEKS are specific to grade level, and students must master the concept in order to be considered successful. Second, ten math literature books were read and the mathematical concepts presented in the book were aligned with the appropriate math TEKS. In addition, in order to assess the effectiveness of the literature, a list of all the concepts found in the books were listed and an extensive research on the concepts was done. The history of the concept (where it came from and why it was brought about, how the concept can be applied to everyday living, and the various ways it can be taught) was determined when possible. Third, the text was analyzed for accuracy of its presentation in each of the children's literature books. The students must be able to comprehend the literature content as well as the mathematical concept that is being presented. Words must be simple and understandable to the age group it is trying to convey the message to. For example, if the concept introduced is whole numbers and it is introduced in Kindergarten, the text must be uncomplicated and plain so that five year olds can follow along and make meaning of what is being taught. Any discrepancies in the text will cause confusion for the child causing frustration and further driving their negative attitude towards mathematics. Other aspects of the children's books to analyze are if the book '·fulfills its intended purpose, if it holds the attention ofthe reader, and ifthe child will find Content Analysis of Mathematical Concepts in Children's Literature pleasure in reading the book" (Farr, 1979, p. 101 ). The books chosen were evaluated based on the criteria mentioned above, and the evaluation forms can be found in Appendix A. 5 Fourth, after the best books had been selected that correctly illustrated the concept for children, the books were reread to find vocabulary words that must be pretaught to students in order for them to successfully learn and understand the mathematical concept. The vocabulary words that need to be pretaught may or may not have a mathematical foundation; they are simply words that students must know before they are acquainted with the text. That way, the vocabulary words do not hinder the student's ability to grasp the concept that had been taught. Fifth, an extensive research was conducted on how the reading ability of students impacts success in mathematics and how teaching vocabulary words before the concept is introduced will allow students to be successful in fully comprehending the math concept. Effective Math Instruction Anyone can teach, but it takes a knowledgeable teacher of both math skills and teaching pedagogy to teach math effectively (O'Donnell, 2009). Teachers need to examine the Texas Essential Knowledge and Skills (TEKS) that students are expected to master by grade level. In addition, National Council ofTeachers of Mathematics (NCTM) has identified three crucial math concepts that need to be addressed in each grade. State standards are derived from these focal points and are used to provide mathematics curriculum for prekindergarten through eighth grade (NCTM 2006). Then, teachers should provide a variety of ways on how these skills get taught. There are many approaches to teaching math, and teachers should learn a variety of ways and strive for a balance between them (Protheroe, 2007). Shellard and Moyer (2002) identify Content Analysis of Mathematical Concepts in Children's Literature 6 three critical components of effective mathematical instruction: "Teaching for conceptual understanding, developing children's procedural literacy, and promoting strategic competence through meaningful problemsolving investigations·' (p. 52). Another way to help students' understanding is by presenting the topics sequentially as well as making sure it is appropriate for the developmental level of the students (Reyes et at., 1999). In addition, NCTM has developed a timeline for student's mathematical skills development and instruction which can be found at http:/ /standards. nctm.org. Protheroe (2007) lists some ideas that make teachers effective. Teachers must have good class management skills, because effective teaching cannot occur in a classroom that is full of chaos. Teachers must use differentiated instruction to reach to the learning needs of all their students. Other aspects include active engagement of students (Wood, Williams, & McNeal, 2006), efficient use of time, logical procession of lessons (Reyes et al., 1999), effective use of assessment, and time management (O'Donnell. 2009). In addition, there must be an effective mathematics environment where there is an acceptance of divergent ideas from students. Teachers need to challenge students to think deeper and to explain their thinking and their logic. When students are challenged, the challenge develops their selfconfidence in their mathematical abilities and they gain a deeper grasp of what the concept is about. Students' curiosity should be welcomed and questions answered. Teachers who have positive attitudes about math relay that attitude to their students. In addition, teachers should have a clear understanding that all students can do well in math. Integrating crosscurricular activities into math lessons so that students can see that math can be used everywhere is also important, as math in the ·'real world" is not segmented out like math classes. Content Analysis of Mathematical Concepts in Children's Literature 7 Teachers should allow student~ to work in groups or in pairs, in order to solve problems together. Group work emphasizes the importance of working together and collaborating to find a solution. Great math instruction gives students as many chances as possible to communicate mathematically. How a student communicates mathematically can be up to them, whether they draw a picture, write in journals, or have discussions. Last but not least, manipulatives should be used in the classroom (Farr, 1979). Research clearly shows that students learn more effectively when handson activities are used, and interest and positive attitudes towards mathematics can be achieved. Manipulatives are used to explore, represent, and communicate mathematical ideas (Nelson and Sassi, 2006). Effective teachers demonstrate proper use of manipulatives, allows time for students to explore personally, and encourages participation from all students. Barbara 0 ' Donnell (2009) studied elementary teachers that promote mathematical learning through problem solving, and identified major themes and related strategies that characterized the practices that effective math teachers had in common. She found that in order to create an inquiry based classroom, the teacher must have high expectations for each child, allow students time to think for themselves, give students responsibility, and accept that some students will not get the answer. In addition, children need to be encouraged to rely on their own thinking and critical skills (Kamii and Warrington, 1999). Too often, teachers answer too readily without giving enough wait time. "Immediate responses prevent students from thinking through issues and concepts thoroughly" (Brooks and Brooks, 1999, p.lO 1 ). When students are given responsibility over a problem, they will take the necessary steps to get through the process and arrive at the correct solution. However, teachers must be able to accept that students may not be able to get the correct answer. This can cause students frustration, but there is a lesson to be Content Analysis of Mathematical Concepts in Children's Literature 8 learned behind getting an incorrect answer, as mathematical problems can require more than just one problem solver and it may take team work to arrive at the correct solution, as well as having practice engagement in ·'looking for relationships, making conjectures, testing conjectures, and explaining and justifying the generalizations they make" (Russell, 1999, p. 136). Struggling with problems may result in confident problem solvers as long as the disequilibrium caused does not reach frustrational level and/or cause cognitive overload which puts the learner in panic or shutdown mode, as some disequilibrium is crucial to a child's intellectual growth (O'Donnell, 2009). As seen above, there are a variety of ways in which teachers can teach math lessons effectively. It is not merely enough for students to memorize math facts and recite them; students must understand the concept that is behind and truly grasp the foundations as math is truly a part of everyday life" (O'Donnell, 2009). Learning Math through Literature Children's books can be a great teaching tool as they provide stories that integrate many mathematical concepts. "Literature that interacts with the curriculum extends the focus to include books and readers along with content area knowing" (Johnson & Giorgis, 2001, p.204). Literature motivates children to learn, provides a meaningful context for math, celebrates math as a language, demonstrates that math develops out of human experience, fosters the development of number sense, and integrates math into other curriculum areas (Whiten & Wilde, 1992, 1995). Many people may wonder how literature invites interaction with math but the connection is actually more natural than one may expect. Concepts such as mathematical shapes can be readily seen and understood when presented using common images and everyday experiences. For example, when a car stops at the stop sign, the big, red, stop sign automatically registers in Content Analysis of Mathematical Concepts in Children's Literature the child's brain as a shape. They may not know that the shape is an octagon, but the mathematical concept of a shape is there. When the family orders a large pizza for dinner, the child may see the pizza as a whole circle, or a pizza slice as a triangle. The connections children's literature makes to mathematical concepts in their everyday settings are natural. Children learn through direct, concrete experiences (Copeland, 1978); therefore, they will be introduced to and learn simple math concepts while doing everyday things such as playing, eating, and communicating with one another. Young children can explore math concepts while they enjoy picture and story books. BarattaLorton (1976) affirms that when we teach mathematics to young children, we must look at the world through their eyes. Visual representations are crucial to earlylevel instruction, and children's books provide the opportunity for them to see mathematical concepts visually. We take in information by seeing things, and children take in math concepts subconsciously while viewing illustrations in children's books. "Books that show how math works in carefully constructed diagrams and illustrations can help them understand specific concepts better than purely verbal or numerical explorations" (Murphy, 1999, p. 122). Murphy realized through his visits to schools that many children understood difficult mathematical concepts when they were presented within the context of a story and illustrated through diagrams, graphs, and other visual displays. "Bright, colorful illustrations in children's books may be used to help distinguish geometric shapes in familiar objects" (Radebaugh, 1981 ). Many mathematical concept books can provide an interesting, riskfree context for children to explore mathematical concepts (Harper, Boggan and Tucker, 2008). Effective Cchildren's literature can help children relate math to their personal lives, extend their understanding to other contexts, and provide an opportunity to explore mathematic concepts 9 Content Analysis of Mathematical Concepts in Children's Literature 10 further (Shatzer, 2008). When teachers use children's literature to teach math concepts, they help children connect their formal ideas with the abstract language and symbols of mathematics, which also reduces anxiety and negative attitudes towards math (Harper, Boggan and Tucker, 2008). As Radebaugh (1981) so wisely stated, '·using children's literature as a springboard for mathematical experiences allows language and mathematics learning to grow together naturally and imaginatively"(p. 196). Mathematical Concepts in Everyday Life Unfortunately, children do not value mathematics because they do not see it as relevant to their daily lives (Harper, Boggan, and Tucker, 2008). Many students appear to be just memorizing facts and figures to pass a test or to get to the next grade level. They wonder why they need to learn math concepts and question when they are ever going to use the concept in their life. "Presenting mathematical ideas within stories that relate specifically to kids can help answer these questions. Stories, especially illustrated stories, can engage children and help them connect mathematical ideas to their own lives" (Murphy, 1999, p.122). ''Children need vehicles that will help them apply the information they learn to their everyday lives" (Murphy, 1999, p.l22). Storybooks can be the perfect vehicles; when '·children see how people use math [in the storybook] on a daily basis for many purposes, they can then transfer those math concepts to their own lives" (Harper, Boggan, and Tucker, 2008, p. 79). ·'Bright, colorful illustrations in children's books may be used to help distinguish geometric shapes in familiar objects" (Radebaugh, 1981 , p. 902). "Trade books can suggest activities that emerge from the story and that help children see connections to their own lives. They need to try activities for themselves and see what works, discover patterns, and create their own models. They need to be able to take the math out of a book and extend it to a wide variety of authentic Content Analysis of Mathematical Concepts in Children's Literature 11 personal experiences" (Murphy, 1999, p. 122). When students realize that math pertains to their life and can make relevant connections between math concepts and their personal experiences, they are more likely to remember the concept and understand it more deeply. Mirella Rizzo, an ESL teacher, asked her students to use their personal experiences to make sense of the mathematical relationships in the problem after reading a storybook; the fifthgraders made connections between their personal interests, knowledge and experience to key math ideas (Whitin and Whitin, 2006). Shatzer (2008) chose books that connected content to her student's lives so that her students could construct meaning from those books. If you think about your everyday activities, you will realize that you use math constantly. In calculating how long and how much gas or money it takes us to get somewhere. how much longer you get to sleep in without being late, if you' re eating the right amount of calories, how much taller you grew since the last time you were at the doctor's office, money management, and dividing your laundry to see how many loads you need to wash are just a few examples. ·'Books that demonstrate mathematical concepts as part of a story reflect reallife situations" (Murphy, 1999, p.122). Friedman (1997) suggests that students be allowed to write their own stories (similar to the children·s book they had read), encouraging students to be creative and to communicate about math. Thus. students can envision how the mathematical concept was used or can be used in their personal life, and communicate the mathematical concept in a situation that is personal and relevant to their lives. Stories provide an opportunity to emphasize how math concepts are applied to everyday settings that are familiar to children and connect them in some way. Content Analysis of Mathematical Concepts in Children's Literature 12 Reading Ability Affects Math Reading plays an important role in student mathematics achievement (Larwin, 201 0; Rust, 2008). However, many teachers assume the difficulty is with a student's math abilities and not the student's poor reading ability (Draper, Smith, Hall, & Siebert, 2005). However, in the standardized math assessments that are given to students today, questions are in the form of a word problem (U.S. Department of Education, 1996). "Therefore, in practice, poor reading ability automatically undermines a student's likelihood of success on math achievement measures" (Larwin, 1996, p. 133). According to Kintsch and Greeno (1985), the linguistic part of understanding the text of the math problem is crucial to being able to successfully solve the problem. Students must be able to read the word problem at the basic level of phoneme and word recognition and comprehend the words well enough to transfer into a conceptual understanding of the text. Only after a child has been able to decipher the math question can he or she apply their mathematical skills to solve the problem. For students who have low reading ability, advancing beyond word recognition and comprehension is almost impossible. Bull and Johnston (1997) found a direct relationship between math achievement and reading ability. A student's processing speed is limited when they have poor reading skills. Research states that even students with high math abilities cannot succeed if they are not proficient in reading (Larwin, 1996). In addition, research done by Kintsch and Greeno (1985) uphold the findings that solving word problems in mathematics involves a high level of cognitive complexity. Research findings from Youngstown State University disclose that '·56% of the variance in student math achievement can be explained by student's reading ability" (Larwin, 1996, p.l31). Similarly, data utilizing 100 students from India reflect that reading ability directly Content Analysis of Mathematical Concepts in Children's Literature correlates to student performance on math exams (Rangappa, 1993). High ability readers performed better than normal ability readers, and normal ability readers performed better than low ability readers. Majumder (2003) concluded that a strong predictor of a student's ability to solve math word problems was reading comprehension. 13 Current findings reveal that the strong linkage found in elementary age children is sustained till high school years; therefore, reading problems should be addressed at all grade levels in order to prevent students from being unsuccessful in their mathematics achievement in later years. What Makes a Children's Book Effective? In recent years, the trend for children·s literature with mathematical concepts has increased (Farr, 1979). Unfortunately, mixed in between quality books are books of little to no value (Hellwig et al., 2000). It is the critical role of teachers to select quality literature for their students. With instructional time restraints imposed on teachers, it is inefficient to use a trade book for instruction if it does not contain high mathematical and literary quality. Farr (1979) examined the various approaches books utilized to illustrate specific mathematical concept to evaluate the book's effectiveness. First, does the book fulfill its intended purpose? ln order for the book to fulfill its intended purpose, the information presented in the book must be accurate and precise. In addition, "the concepts must follow a logical procession towards increased complexity" (Farr, 1979, p.l 01 ). Any discrepancies in the text or illustration will confuse the reader, thus taking away the intended objective of the book. Therefore, "to enhance mathematics literature, teachers should not be afraid to add mathematical annotations and vocabulary" (Hunsader, 2004, p.619). Content Analysis of Mathematical Concepts in Children's Literature 14 In order to convey the math concept, the book must be captivating and keep the audience's attention. Children's books also have an advantage for visual learners, as the concepts and ideas are represented in a nonthreatening pictorial format (Guiett, 1999). Good books bridge the gap between concrete representations and abstract concepts. The story's plot should be interesting to its audience and students should be able to relate the story to their life, experiences, and the world around them. The role of connecting literature with math is powerful (Columba et al., 2005) and teachers must ensure that the book selected is interactive. Interactive readaJouds are important for developing reader, text, and context connections (Rosenblatt, 1978, 1995). While it is important for teachers to select books of quality, teachers are also responsible during the readaloud to help students make the connection to self, to the text, and to the world (Fountas & Pinnell, 2001), as well as construct meaning from the book (Hyde, 2006). Children's literature that teaches mathematical concepts are more effective "when children are able to see how people use math on a daily basis for many purposes, and can then transfer those math concepts to their own lives'' (Harper, Boggan, and Tucker, 2008, p.78). When numbers and operations are embedded in meaningful realworld contexts as those seen in quality children's literature, children are able to gain knowledge about math and develop a wider view of how math relates to their world (Schiro, 1997). "Quality children's books are appealing, nonthreatening, and related to children's lives" (Harper, Boggan, and Tucker, 2008, p.78). Effective books provide a riskfree environment for students to explore mathematical concepts and extend their knowledge to other contexts. The National Council of Teachers for Mathematics (NCTM) emphasizes the importance of communicating mathematically and developing connections between their informal Content Analysis of Mathematical Concepts in Children's Literature 15 knowledge and abstract symbolism of math concepts. '·Many children's books present interesting problems and illustrate how other children solve them. Through these books students see mathematics in a different context while they use reading as a form of communication" (National Council ofTeachers of Mathematics, 1989, p.27). There are many critical components of children's literature that must be evaluated in order to assess the effectiveness of the book. Hellwig eta/ (2000) stated that accuracy, verbal and visual appeal, connections, audience, and the "wow" factor as criteria for quality children's literature. However, Farr (1979) believes that the most critical requirement for any type of quality literature is that the child should find pleasure in reading or hearing it. When selecting and using children's literature to find natural mathematics connections, teachers create a learning environment that is supported by both the National Council of Teachers of English (NCTE) and the NCTM (Moyer, 2000; Taylor, 1999). Quality children's books will benefit students by allowing them to develop their language and math skills simultaneously (Hellwig et al., 2000). Content Analysis of Mathematical Concepts in Children's Literature 16 References BarattaLorton, M. ( 1976). Math Their Way. Menlo Park, CA: AddisonWesley. Beard, L.A. (2003). The effects of integrated mathematics and children's literature instruction on mathematics achievement and mathematics anxiety by gender. Doctoral dissertation. University of Southern Mississippi, Hattiesburg. Brooks, J.G. & Brooks, M. (1999). In Search of Understanding: The Case for Constructivist Classrooms. Alexandria, VA: Association for Supervision and Curriculum Development. Bull, R., & Johnston, R.S. (1997). Children's arithmetical difficulties. Contributions from processing speed, item identification, and shortterm memory. Journal of Experimental Child Psychology, 65(1), 124. Burns, M. (2005). Lessons by Marilyn Burns. Using Storybooks to Teach Math. Scholastic Instructor, 2730. Burns, M. (2010) As Easy as Pi: Picture Books Are Perfect for Teaching Math. School Library Journal, 3841. Clarke, D. (2002) Making measurement come alive with a children's storybook. Australian Primary Mathematics Classroom, 7. 913. Columba, L., Kim, C.Y., & Moe, A.J. (2005). The power of picture books in teaching math and science: Grade PreK8. Scottsdale, AZ: Holcomb Hathaway. Copeland, R.W. How Children Learn Mathematics. 3rd ed. New York, N.Y.: Macmillan, 1978. Farr, P. L. (1979). Trends in Math Books for Children. School Library Journal26, 99104. Draper, R., Smith, L., Hall, K., & Siebert, D. (2005). What's more important? Choosing Content Analysis of Mathematical Concepts in Children's Literature literacy or content: Confronting the literacycontent dualism. Action in Teacher Education, 27, 1221. Friedman, J.E. (1997). What is the Math Moral of the Story? Childhood Education 74 (1 ), 3335. Fountas, l.C., & Pinnell, G.S. (2001). Guiding readers and writers grade 36: Teaching comprehension, genre, and content literacy. Portsmouth, NH: Heinemann. Geist, E. (20 1 0) The AntiAnxiety Curriculum: Combating Math Anxiety in the Classroom. Journal of Instructional Psychology, 37 (1 ). 2431. Guiett, D. (1999). From alphabet to zebras: Using children;s literature in the mathematics classroom. Ohio Media Spectrum, 51, 3236. Harper, S., Matthew K. B., and Carolyn T. (2008) Using Children's Literature to Teach Math. Southeastern Teacher Education Journal, 1 (1), 7783. Hellwig, S., Monroe., E. E., & Jacobs, J .S. (2000). Making informed choices: Selecting children's trade books for mathematics instruction. Teaching Children Mathematics, 7, 138143. Huber, L. L. and Rosalyn S. L. (2006) Mathematical Concepts Come Alive in PreK and Kindergarten Classrooms. Teaching Children Mathematics, 13, 22630. Hunsader, P.D. (2004). Mathematics trade books: Establishing their value and assessing their quality. international Reading Association, 618629. 17 Hyde, A.A. (2206). Comprehending math: Adapting reading strategies to teach mathematics, K 6. Portsmouth, NH: Heinemann. Jennings, C.M. (1992). Increasing interest and achievement in mathematics through children's literature. Early Childhood Research Quarterly, 7, 263276. Content Analysis of Mathematical Concepts in Children's Literature Johnson, N.J. & Giorgis. C. (2001). Interacting with the curriculum. The Reading Teacher, 55, 204206. Kamji, C. & Warrington, M. (1999). "Teaching Fractions: Fostering Chlldren's Own Reasoning." In Developing Mathematical Reasoning in Grades K12, 1999 18 Yearbook ofthe National Council ofTeachers of Mathematics (NCTM), 8292. Reston, VA: NCTM, 1999. Kintsch, W., & Greeno, J.G. (1985). Understanding and solving word arithmetic problems. Psychological Review, 92, 109129. Larwin, K. (20 1 0) Reading is fundamental in predicting math achievement in 1oth graders. International Electronic Journal of Mathematics Education, 5, 131145. Majumder, S. (2003). Factors in mathematical word problem solving: The role of inhibition. Ph.D. dissertation, York University (Canada), Canada. Mitchell, T. (1999). Changing student attitudes towards mathematics. Primary Educator, 5, 18 Moyer, P.S. (2000). Communicating Mathematically: Cruldren's literature as a natural connection. The Reading Teacher, 54, 246255. Murphy, Stuart J. (1999). Learning Math through Stories. School Library Journal, 122 123. Natjonal Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author. National Council ofTeachers of Mathematics. (2006) Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics. Retrieved from www. Nctm.org/focalpoints. Content Analysis of Mathematical Concepts in Children's Literature Nelson, B.S. & Sassi, A. (2006). What to Look for in Your Math Classrooms. National Association for Elemenrary School Principles, 4649. O'Donnell, B. (2009). What effective math teachers have in common. Teaching Children Mathematics, 16, 118125. Protheroe, N. (2007). What Does Good Math Instruction Look Like? National Association for Elementary School Principles, 5154. Radebaugh, M.R. (1981 ). Using children 's literature to teach mathematics. The Reading Teacher, 34,902906. Rangappa, K.T. (1994). Effect of reading ability on mathematical performance. Psycholingua, 24, 3843. 19 Raymond, A.M. (1995). Engaging young children in mathematical problem solving: Providing a context with children's literature. Contemporary Education, 66, 172174. Reys, R.E., M.N. Suydam, M.M. Lindquist, & N.L. Smith. (1999). Helping Children Learn Mathematics, 5th ed. New York: John Wiley and Sons. Rosenblatt, L.M. (1995) Engaging young children in mathematical problem solving: Providing a context with children· s literature. Contemporary Education, 66, 172174. Russell, N. (1999). "Mathematical Reasoning in the Elementary Grades." In Developing Mathematical Reasoning in Grades K1 2, 1999 Yearbook of the National Council of Teachers of Mathematics (NCTM), 112. Reston, VA: National Council of Teachers of Mathematics. Rust, A. (2008). What does reading have to do with math? (everything!). Presented at the AMA TYC Conference. Schiro, M. ( 1997). integrating children 's literature and mathematics in the classroom: Content Analysis of Mathematical Concepts in Children's Literature 20 Children as meaning makers, problem solvers, and literary critics. New York: Teachers College Press. Shatzer. J. (2008) Picture Book Power: Connecting Children's Literature and Mathematics. The Reading Teacher, 61 , 64953. Shellard, E. & P.S. Moyer. (2002). What Principals Need to Know about Teaching Math. Alexandria, Va.: National Association of Elementary School Principals and Education Research Service. Taylor, G.M. (1999). Reading, writing, arithmeticMaking connections. Teaching Children Mathematics, 6, 190197. U.S. Department of Education {1996). Reading Literacy in the United States: Findings From the lEA Reading Literacy Study. National Center for Education Statistics, Washington, D.C. Whitin, D.J ., & Wilde, S. ( 1992). Read any good math lately? Children's books for mathematical/earning, K6. Portsmouth, NH: Heinemann. Whitin, D.J., & Wilde, S. (1995). It 's the story that counts: More children's books for mathemalicallearning, K6. Portsmouth, NH: Heinemann. Whitin, P. and Whitin, D. (2006) Making Connections through MathRelated Book Pairs. Teaching Children Mathematics, 13, 196202. Wood, T., Williams, G. & McNeal, B. (2006). Children's Mathematical Thinking in Different Classroom Cultures. Journal for Research in Mathematics Education 37, 222 255 Content Analysis of Mathematical Concepts in Children's Literature Appendix A Evaluation of Mathematical Concepts in Children's Literature Evaluator:  Date: _______________ _ Book Name: Author: Mathematical concept(s) in book: Targeted Audience (circle all that apply): PreK K How effective is the book from a mathematical perspective? 2 Not effective somewhat effective 3 effective How effective is the book from a literary perspective? Not effective General Comments: 2 somewhat effective 3 effective Mathematical Principles Is the math concept found in the book correct and accurate? optimally Comments: 2 partially 3 poorly Is the math vocabulary defined correctly in the book? 2 3 optimally partially poorly Comments: 2 3 4 5 4 highly effective 4 highly effective 21 Content Analysis of Mathematical Concepts in Children's Literature Does the illustration correctly portray the concept? 1 optimally Comments: 2 partially 3 poorly Does the book encourage student involvement in mathematics? optimally Comments: 2 partially 3 poorly Literary Principles Does the book attract its intended audience? optimally Comments: 2 partially Is the book interactive and engaging? optimally Comments: 2 partiaJly 3 poorly 3 poorly 22 Content Analysis of Mathematical Concepts in Children's Literature Do the book's plot and the illustrations complement each other? optimally Comments: 2 partially 3 poorly Is the book developmentally appropriate for its intended audience? optimally Comments: 2 partially 3 poorly 23 Content Analysis of Mathematical Concepts in Children's Literature Appendix B: Mathematical Concept Children's Literature Book Summaries Leedy, L. (2008). The Action of Subtraction. Minneapolis: Millbrook Press. Mathematical Concept Book is Teaching: Subtraction Grade Level and Grade Level TEKS this Book Could be Used for: 24 Kindergarten (b) ( 4) Number, operation, and quantitative reasoning. The student models addition (joining) and subtraction (separating). The student is expected to model and create addition and subtraction problems in real situations with concrete object. First Grade (b) 3(A) model and create addition and subtraction problem situations with concrete objects and write corresponding number sentences; and (B) use concrete and pictorial models to apply basic addition and subtraction facts (up to 9 + 9 = 18 and 18  9 = 9). Second Grade (b) 3 (A) recaJI and apply basic addition and subtraction facts (to 18);(B) model addition and subtraction of twodigit numbers with objects, pictures, words, and numbers; Summary of Book: The Action of Subtraction is an informational book about the concept of subtraction. The book is ideal for students in Kindergartenthird grade. Relevant definitions are mentioned in this book, and the animated images help students see the action of subtraction happening. The book is long enough to cover the essential skills of subtraction, but short enough to keep the reader's interest. The font ofthe text is animated and helps to connect to the pictures. The text is simple to read and the font is the perfect size. The numbers in a subtraction problem are a different color than the font which will assist students in visualizing the numbers when the story is being read. The book shows a variety of ways subtraction can be shown (diagonally and vertically), and it also mentions the various ways to tell subtraction is happening (minus, less than, fewer, etc.). The book extends subtraction problems to more than just two numbers; it allows students to think even more critically by subtracting more numbers in just one problem (Ex: 122=1 0, 10 5=5). Vocabulary Words to Work On: Action something being done or performed. Hornets bugs that can sting you. Discomfort not comforting Bent curved, crooked. Amount the sum total Fewer less than Shrinking getting smaJier Content Analysis of Mathematical Concepts in Children's Literature 25 Demi. ( 1997). One Grain of Rice: A Mathematical Folktale. New York: Scholastic Press. Mathematical Concept Book is Teaching: Multiplication Grade Level and Grade Level TEKS this Book Could be Used for: Second Grade (b) 4 (A) model, create, and describe multiplication situations in which equivalent sets of concrete objects are joined; Third Grade (b) 4 (A) learn and apply multiplication facts through 12 by 12 using concrete models and objects; (B) solve and record multiplication problems (up to two digits times one digit); and Fourth Grade (b) 4 (A) model factors and products using arrays and area models; (B) represent multiplication and division situations in picture, word, and number form; (C) recall and apply multiplication facts through 12 x 12; (D) use multiplication to solve problems (no more than two digits times two digits without technology) Summary of Book: A mathematical folktale that is sure to captivate students with its detailed illustrations, vivid colors, cultural background, and life learning moral. The large amounts of white space with a splash of deep color in the book allow a regal feel. The illustrations also depict one type of Indian culture, and the vocabulary is quite uncommon. Teachers can also use this book to introduce the varied types of government. Students will not realize they are learning a math lesson till they get into the meat of the story, and by then, they are already hooked. The book focuses on a young girl. s smarts; I would emphasize that anyone can make a difference regardless of age. The book details how many rice she gets (as her reward) per day, and also estimates what that amount of rice will fill up. For example. students may not know that approximately 4,000 grains of rice will only fill up a bowl. The extended pages with images illustrating how much rice the young girl was rewarded is a visual representation of how multiplication works. There is also a calendar at the very end of the book that shows how much rice the girl received per day, and teachers can make a similar calendar or table that is half done, and let students finish the chart to assess understanding and mathematical skill. Vocabulary Words to Work On: India a country in the continent of Asia Raja  King Wi e very mart Province a part of a country Decreed to give orders Storehouses places to store things Famine a time of no food Royal blood line Troubled worried Fulfill to finish, follow Ministers people that work with the king imploredbegged Feast a huge meal Village a small town Trickle a very little amount Clever very smart Halt to stop Deedsomething that is done Plentifu l to have lots of something Modest not flashy Content Analysis of Mathematical Concepts in Children's Literature Murphy, S. J. (1997). Betcha! New York: Harper Collins Publisher Inc. Mathematical Concept Book is Teaching: Estimation, Prediction Grade Level and Grade Level TEKS this Book Could be Used for: First Grade (b) (4) Patterns. relationships, and algebraic thinking. The student uses repeating patterns and additive patterns to make predictions. The student is expected to identify, describe, and extend concrete and pictorial patterns in order to make predictions and solve problems. 26 Second Grade (b)(6) Patterns, relationships, and algebraic thinking. The student uses patterns to describe relationships and make predictions. The student is expected to: (A) generate a list of paired numbers based on a reallife situation such as number of tricycles related to number of wheels; (B) identify patterns in a list of related number pairs based on a reallife situation and extend the list; and (C) identify, describe, and extend repeating and additive patterns to make predictions and solve problems. Third Grade (b) (6) Patterns, relationships, and algebraic thinking. The student uses patterns to solve problems. The student is expected to: (A) identify and extend wholenumber and geometric patterns to make predictions and solve problems; (B) identify patterns in multiplication facts using concrete objects, pictorial models, or technology; and (C) identify patterns in related multiplication and division sentences (fact families) such as 2 x 3 = 6, 3 x 2 = 6, 6 ~ 2 = 3, 6 ~ 3 = 2. Betcha! is a book that many students will be able to relate to because many librarians or even classroom teachers have a jar of marbles set out to teach their students about prediction and estimation. My favorite aspect of this book is that it has two boys as the main characters, and they are hoping to win tickets to a sporting game by using math! It also shows that friends can compete in a fair and fun manner. When the boys are figuring out how many things are in a set, the illustrations show their thinking so students can see how the characters come up with an answer. This will help visual learners. The book has simple text that allows the teacher to read the sentence, and then gives time for students to reflect on the picture and make estimations on their own. Addition, money, estimation, and prediction are the concepts mentioned in this book. Vocabulary Words to Work On: Contest a challenge Guess to think, believe, or suppose something Content Analysis of Mathematical Concepts in Children's Literature 27 Burns, M. (2008). The Greedy Triangle. New York: Scholastic. Mathematical Concept Book is Teaching: Shapes, Angles Grade Level and Grade Level TEKS this Book Could be Used fo r: Kindergarten (b) (8) Geometry and spatial reasoning. The student uses attributes to determine how objects are alike and different. The student is expected to: (A) describe and identify an object by its attributes using informal language: (B) compare two objects based on their attributes; and (C) sort a variety of objects including two and threedimensional geometric figures according to their attributes and describe how the objects are sorted. (9) Geometry and spatial reasoning. The student recognizes attributes of twoand threedimensional geometric figures. The student is expected to: (A) describe and compare the attributes of reallife objects such as balls, boxes, cans, and cones or models of threedimensional geometric figures; (B) recognize shapes in reallife threedimensional geometric figures or models of threedimensional geometric figures; and (C) describe, identify, and compare circles, triangles, rectangles, and squares (a special type of rectangle). First Grade (b) (6) Geometry and spatial reasoning. The student uses attributes to identify two and threedimensional geometric figures. The student compares and contrasts two and threedimensional geometric figures or both. The student is expected to: (A) describe and identify twodimensional geometric figures, including circles, triangles, rectangles, and squares (a special type of rectangle); (B) describe and identify threedimensional geometric figures, including spheres, rectangular prisms (including cubes), cylinders, and cones; (C) describe and identify two and threedimensional geometric figures in order to sort them according to a given attribute using informal and formal language; and (D) use concrete models to combine twodimensional geometric figures to make new geometric figures. The Greedy Triangle is a fun, lively, and creative book to teach about shapes and angles. This book goes through the names of shapes with up to ten angles, and demonstrates how the shapes and angles can be used in everyday situations. The pages are covered in color from top to bottom, and the emotionalfilled pictures will capture student's attention and allow the audience to feel what the triangle feels. The book has great examples of how shapes are everywhere and how angles can be used in the real world. The illustrations are also made from the various shapes and stand out. Student's vocabulary list will be extended with the numerous vocabulary words found in this book. Although the book is very colorful and busy, the borders around the illustrations keep it simple. Not only can this text be used to teach math, it is also great for lessons on adjectives, emotions, and vocabulary. Vocabulary Words to Work On: Supporting helping Symphony orchestra a group of people playing music together Dissatisfied not happy Grumbled mumbling, muttering unhappily Nonagon a shape with nine sides Decagon a shape with ten sides Screeching a loud cry Colliding bumping into Terrify scaring Shapeshifter a person who can change a shape Quadrilateral a shape with four sides Pentagon a shape with five sides Hexagon a shape with six sides Socket an opening Boltsscrews Wrench a type of tool Restless always moving Heptagon a shape with seven sides Octagona shape with eight sides Content Analysis of Mathematical Concepts in Children's Literature 28 Miranda, A. (1999). Monster Math. Florida: Harcourt, Inc. Mathematical Concept Book is Teaching: Addition and Subtraction Grade Level and Grade Level TEKS this Book Could be Used for: Kindergarten (b) (4) Number, operation, and quantitative reasoning. The student models addition Gaining) and subtraction (separating). The student is expected to model and create addition and subtraction problems in real situations with concrete object. First Grade (b) 3(A) model and create addition and subtraction problem situations with concrete objects and write corresponding number sentences; and (B) use concrete and pictorial models to apply basic addition and subtraction facts (up to 9 + 9 = 18 and 18  9 = 9). Second Grade (b) 3 (A) recall and apply basic addition and subtraction facts ( to 18); (B) model addition and subtraction of twodigit numbers with objects, pictures, words, and numbers; What a book to help relieve students who are frightened of monsters and teach math! Monster Math will help students in counting, skip counting, and subtraction. Monsters come into the house in large amounts, and the little girl monster wants to shoo them away because there are too many! I love this book because it uses awesome adjectives to describe the monsters, and it can be used as a Language Arts lesson as well. The pages are not too busy; they are illustrated in a simple manner, kept in a frame on each page. The silly images will make students giggle and the pattern of adding 10 monsters will come to them easily. Students will be able to relate to the monsters' activities such as blowing out birthday candles, chasing friends, jumping on beds, taking pictures, and such. Vocabulary Words to Work On: Silly funny Wiggling moving around, not staying still Starved very hungry for food Monstrous very great Budge move Wreck a mess Frosted something that has frosting on it Devoured gobbled up, finished. Exhausted very tired Content Analysis of Mathematical Concepts in Children's Literature 29 Murphy, S.J. (1997). Divide and Ride. New York: Harper Collins Publisher Inc. Mathematical Concept Book is Teaching: Division Grade Level and Grade Level TEKS this Book Could be Used for: First Grade (b) (4) Number, operation, and quantitative reasoning. The student models multiplication and division. The student is expected to: (A) model, create, and describe multiplication situations in which equivalent sets of concrete objects are joined; and (B) model, create, and describe division situations in which a set of concrete objects is separated into equivalent sets. Second Grade (b) 4 (B) model, create, and describe division situations in which a set of concrete objects is separated into equivalent sets. Third Grade ( b) 4 (C) use models to solve division problems and use number sentences to record the solutions. Go on the ride of your life with this swirling, invigorating, and mindbogging adventure that will be sure to get your brain working! Divide and Ride teaches the obvious concept: division! Students will get excited for their field day or their field trip while viewing the images as they read along with the story. The characters in the book are at a carnival, and need to figure out how to make equal groups so that everyone will be able to ride the fun rides and roller coasters. The group has an odd number of members, and they need to find an extra friend (or two) at times to fill up seats for an amusement ride. This book is helpful in that it shows verbally, numerically, and pictorially how they can divide up into equal groups. The number sentence along with the picture is an asset. Many students will be able to relate to this storybook and use it as a guide during field trips. They can use the strategies found in the book to divide things into equal groups almost anywhere! Vocabulary Words to Work On: Divide to separate into two or more groups Jolt a sudden, jerky movement Raftsomething put together for transportation on water Content Analysis of Mathematical Concepts in Children's Literature DeRubertis, B. ( 1999). Deena 's Lucky Penny. The Kane Press. Mathematical Concept Book is Teaching: Counting money, monetary value Grade Level and Grade Level TEKS this Book Could be Used for: First Grade (b) I (C) identify individual coins by name and value and describe relationships among them; 30 Second Grade (b) 3 (D) determine the value of a collection of coins up to one dollar; and(E) describe how the cent symbol, dollar symbol, and the decimal point are used to name the value of a collection of coins. Deena needs money to buy her mother a birthday present, and thanks to a lucky penny, she was able to scrounge around and ftnd the right amount needed. Although the book's title is about the lucky penny, this book details the penny, nickel, dime, and quarter. I love how this book depicts the coins and value in a variety of ways. At the bottom of the page, there is a visual image of the coin and how much it is worth. The visual images show what the coins look like on both sides. There is also the cent sign and the dollar sign which help students make the connection to money. The addition sentence also shows how many of each coin you need to add together to get another coin, and it reveals the importance of including signs (such as the money sign in this number problem). Deena also has choices to make; would she rather have a penny or a nickel? A valuable lesson to teach to any grade level is about making good choices. Classes can brainstorm why Deena choose one coin over several of the same coins, and the teacher can faci litate classroom discussion to topics besides money. The book also can be used to introduce students to responsibility and the importance of saving. The piggy bank icon next to the money addition sentence is also a great visual reminder for savings. Vocabulary Words to Work On: Lucky the feeling when something good happens to you Handfula small amount that can fit in your hand Tradeto give something in exchange for something else Lonely to feel alone or by yourself Stack to put things on top of each other Twinklea sparkle or a shine Abracadabra a word used for magic to happen Content Analysis of Mathematical Concepts in Children's Literature 31 Sloat, T. (1998). There Was an Old Lady Who Swallowed a Trout. Canada: Henry Holt and Company. Mathematical Concept Book is Teaching: Order of Events, Sequencing, Ordinal Positions Grade Level and Grade Level TEKS this Book Could be Used for: Kindergarten (b) (2) Number, operation, and quantitative reasoning. The student describes order of events or objects. The student is expected to: (A) use language such as before or after to describe relative position in a sequence of events or objects; and (B) name the ordinal positions in a sequence such as first, second, third, etc. A twist to the familiar poem of'·There Was an Old Lady Who Swallowed a Fly", this book captures the wondrous wildlife that is seen in the Pacific Northwest. The lady swallows many animals, and it is easy to keep up with the order of the animals that she swallows thanks to patterns! Children love listening to this poem, and after they hear it a few times, can readily repeat the story due to the repitition and alliteration. This poem can also be used to teach ordinal numbers. Which animal did the lady swallow first? Second? Third? Vocabulary Words to Work On: Trout a kind offish Thrashflop Salmon another kind of fish Ottera mammal that lives in the water. It has webbed feet and a flattened tail Sealanother animal that lives in the water but can also live on land. Squeal to shriek Porpoisean animal that lives in water that looks like a small dolphin Walrusa large animal that has flippers, a pair of large tusks, and a tough, wrinkled skin. Fussnoisy argument Whale one of the biggest mammals that live in the water; fins, gills, breathes oxygen Ocean a very large body of water Commotion lots of loud noises, arguments. Swirlto move around fast Content Analysis of Mathematical Concepts in Children's Literature Pinczes, E. J. (2001). Jnchworm and a Half New York: Houghton Mifflin Company. Mathematical Concept Book is Teaching: Measurement, Fractions Grade Level and Grade Level TEKS this Book Could be Used for: 32 Kindergarten (b) (3) Number, operation, and quantitative reasoning. The student recognizes that there are quantities less than a whole. The student is expected to: (A) share a whole by separating it into two equal parts; and (B) explain why a given part is half of the whole. (I 0) Measurement. The student directly compares the attributes of length, area, weight/mass, capacity, and/or relative temperature. The student uses comparative language to solve problems and answer questions (A) compare and order two or three concrete objects according to length (longer/shorter than, or the same); (B) compare the areas of two flat surfaces of twodimensional figures (covers more, covers less, or covers the same); First Grade (b) (2) Number, operation, and quantitative reasoning. The student uses pairs of whole numbers to describe fractional parts of whole objects or sets of objects. The student is expected to: (A) separate a whole into two, three, or four equal parts and use appropriate language to describe the parts such as three out of four equal parts (7) Measurement. The student directly compares the attributes of length, area, weight/mass, capacity, and temperature. The tudent uses comparative language to solve problems and an wer questions. The student selects and uses nonstandard units to describe length. The student is expected to: (A) estimate and measure length using nonstandard units such as paper clips or sides of color tiles; (B) compare and order two or more concrete objects according to length (from longest to shortest); (C) describe the relationship between the size of the unit and the number of units needed to measure the length of an object An inchwonn is off to measure things that surround her, but gets confused when things are not exactly an inch. What's there to do when it' s smaller than an inch? The little wonns in this book explain the concept of an halfinch, a onefourth inch, and a third inch. This book can also be used to teach vocabulary. The text is full of beautiful words that can be used in everyday setting. The pictures in the frames are colorful and lively, and the wonns are sure to capture student's attention. Although the text is small, it goes along with the smallness of the worms and it's fitting. The dotted lines (loops) is a great visual reminder of how much an inch is as well, and the students can count how many loops there are to see how many inches a certain thing is. The book also clearly states the definition of a fraction: equal parts of a whole. This is crucial because students need to learn the foundations. The way the wonns measure an object is also a way to teach students how to read the fraction (One ... and a half!). Vocabulary Words to Work On: Nibbles to bite off in small pieces Trea ures something very important and valuable Results the end of something, the answer Cinch something easy Unthinkable something you can't even Imagine Fraction equal parts of a whole Spry active Trio group of three Occurred happened Accuracy being exact, correct Ease free from concerns Content Analysis of Mathematical Concepts in Children's Literature 33 Sierra, J. (1997). Counting Crocodiles. Florida: Harcourt Inc. Mathematical Concept Book is Teaching: Number Sense; counting from 11 0 and counting backwards Grade Level and Grade Level TEKS this Book Could be Used for: Kindergarten (b) (1) Number, operation, and quantitative reasoning. The student uses numbers to name quantities. (A) use onetoone correspondence and language such as more than, same number as, or two less than to describe relative sizes of sets of concrete objects; (B) use sets of concrete objects to represent quantities given in verbal or written form (through 20); and (C) use numbers to describe how many objects are in a set (through 20) using verbal and symbolic descriptions. (6) Patterns, relationships, and algebraic thinking. The student uses patterns to make predictions. The student is expected to: (A) use patterns to predict what comes next, including causeandeffect relationships; and (B) count by ones to 100. An amusing and entertajning book that will have children counting along with you! The text in Counting Crocodiles is an asset to the classroom because it provides children with a numerous amount ofrich vocabulary, rhyming patterns, emotions, and entertajnment. The illustrations are lively and they correctly depict the number of crocodiles on each page. The colors are beautiful on the pages and seem to jump out at you! Students can relate to the emotions of the crocodiles and the monkey, and some of the actions that the crocodiles are involved in. The book also helps readers learn how to count backwards, which is another essential skill children need to know. Each page depicts one number, which allows students to focus on that number and associate the illustrations with the number. Vocabulary Words to Work On: Island an area of land surrounded by water Clever smart Sauteed cooked Pureed food blended together Puckered wrinkled Delectable yummy, delicious Privatepersonal, not belonging to everyone Vicious mean Feastingeating Suspiciousquestionable, wonder Crusty rude Lurking sneaking around, waiting Galore many Hunch guess Cavorting prancing Impatient does not like to wait Scold to get in trouble Scurry to move quickly Content Analysis of Mathematical Concepts in Children's Literature *A call was made to Barnes and Nobles Customer Service on Saturday, April28, 2012 concerning the copyright ofthe images ofthe book covers. It was stated that displaying images of the book's cover was not a copyright issue. 34 



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