Incorporating language arts into the mathematics curriculum: a literature survey.
Many educators today describe themselves as whole language teachers. According to Reutzel and Cooter (1992), whole language teachers are those who believe in reading literature in the classroom and who attempt to integrate listening, speaking, reading, and writing across the curriculum. Literature and language skills, however, are often neglected in the mathematics area of the curriculum. Educators are now discovering ways to incorporate reading into mathematics through the use of children's literature.
Stories Provide Meaningful Contexts
Books are advantageous because they help students explore mathematical ideas in natural, familiar, and meaningful contexts (Griffiths & Clyne, 1991; Whitin, 1994). Literature can spark students' interest in a math lesson, if the story is first read and enjoyed for its literary content (Whitin & Gary, 1994). If students can relate to and enjoy the plot, setting, and characters of a story, the new math skill will be associated with the meaningful contexts.
Several educators refer to the picture book, The Doorbell Rang, by Pat Hutchins (1986) as a valuable resource for math teachers (Conaway & Midkiff, 1994; Hopkins & Dorsey, 1992; Nichols, 1993; Thrailkill, 1994). This story puts the mathematical concept of division into the familiar context of sharing. Two children are preparing to share a dozen cookies when the doorbell rings and two more children enter the house. As soon as the four children decide how many cookies each person will get, the doorbell rings once more, and the cookies have to be divided again. The pattern continues until the book's surprise ending. Thus, the book introduces students to the mathematics concept of division in the familiar context of sharing and eating cookies. After hearing the story, students can practice division in similar situations. The Doorbell Rang is one example of how picture books can be useful for putting mathematical concepts into a meaningful context for students.
Stories Model Mathematical Ideas
Griffiths and Clyne (1991) suggested that children can take math ideas from stories and use them in their own situations, and that stories pose problems that children are intrinsically interested in solving. One example given by Conaway and Midkiff (1994) demonstrates how picture books can be effective in modeling fractional concepts. Children are attracted to the pictures in the book Eating Fractions, by Bruce McMillan (1991), because there are photographs of children eating fractional parts of foods, such as halves of a banana and fourths of a pizza. Simple recipes for the foods shown in the pictures are located in the back of the book. Therefore teachers can help students model fractions in a fun and enjoyable way, using the same portions of foods mentioned by the children in the book (Conaway & Midkiff). Stories can provide a literature link to math by modeling concepts in ways that can be recreated using objects or manipulatives shown in books. In addition to modeling math ideas, Eating Fractions also puts the fraction concept into a meaningful context.
Stories Challenge Students
Ohanian (1989) asserted that A Grain of Rice by Helena Clare (1992) is a story that develops a meanful concept. In this tale, a farmer saves the life of the emperor's daughter. He asks that his reward be one grain of rice on the first day, and for the amount to be doubled each succeeding day. After predicting how many grains of rice the farmer would have received by the 25th day, students might feel challenged to solve the problem for themselves. They would be quite surprised to learn that on the 25th day, the emperor would pay the farmer 16,777,216 grains of rice (Ohanian). Griffiths and Clyne (1991) described a similar story, King Kaid of India, in which the king wishes to reward the man who invented the game of chess. The inventor asks for one grain of corn on the first square of the chessboard, double that on the second square, double that on the third square, and so on. While students are attempting to solve the problem of how much corn will be needed to pay the reward, they are involved in a number of mathematical processes, such as developing and testing hypotheses, searching for patterns, utilizing various methods of recording, multiplying, adding, and using calculators (Griffiths & Clyne). The King's Chessboard by David Birch (1993) is another retelling of this story which might also be used to introduced this challenge to students (Ohanian).
Literature Encourages Investigation
Children's literature gives students the opportunity to test important mathematical concepts in a nonthreatening arena. Counting on Frank by Rod Clement (1990) tells of a boy who explores his environment in a humorous and mathematically inclined way (Whitin & Gary, 1994). Students are intrigued by Frank's calculations that ten humpback whales would fit into his house, but that only one-tenth of his father would fit inside a portable television (Griffiths & Clyne, 1991). If children are encouraged to question these calculations, their investigations will require hypothesizing, estimating, measuring, and computing. These investigations could possibly lead students to create and solve new problems of their own.
Another example of a literature selection which encourages children to investigate their surroundings is The Line-up Book by Marisabina Russo (1986) (Whitin & Gary, 1994). Sam, the main character, makes a line from his room to the kitchen using various objects as measuring tools. Whitin and Gary noticed that during the story, students suggested objects from the illustrations for Sam to use in his line up. Students predicted like readers, while they estimated like mathematicians. Gary, when using this book with her class, encouraged the students to investigate measurements in the classroom, using other objects as the units of measure (Whitin & Gary). Therefore, children's books, such as The Lineup Book and Counting on Frank (Clement, 1990), can prove to be good starting places for exploration and investigation.
Children's Books Illustrate Concepts
Eating Fractions by Bruce McMillan (1991) literally illustrates the concepts of fractions through its pictures (Conaway & Midkiff, 1994). Nichols (1993) asserted that visual images, such as these pictures, can help students see connections between mathematical signs and symbols and the real world. Another book that many teachers value is David M. Schwartz's (1987) book, How Much is a Million?, because it contains wonderful illustrations that depict numbers too large for most students to comprehend. Nichols praised Schwartz's use of humor and everyday experiences to give meaning to numbers that are often mysterious to young people. In her article "Math Concept Books: What We Have, What We Need," Nichols stated that many math concept books are in the picture-book format because visual images help illustrate abstract mathematical principles.
Disadvantages of Using Literature in Math
Despite the many advantages of using children's literature to encourage interest in mathematics, Griffiths and Clyne (1991) admitted that there are concerns that teachers may dissect or trivialize literature for the sake of mathematics. Teachers, however, can give students time to enjoy books for their intrinsic value, then allow the math connections to arise slowly. Whereas some research suggests that children's literature is only useful in the early primary grades, Griffiths and Clyne stated that students in upper grades are also highly motivated by stories. Mathematical connections to literature exist in higher level books and can serve to motivate older students to investigate and explore math concepts.
Conversely, books are limited in their ability to convey three dimensional information. Students learn best by manipulating concrete, three-dimensional objects. Therefore, the math concepts presented in children's literature must be extended through hands-on activities if students are to master them (Nichols, 1993). If teachers combine literature with concrete manipulatives, math instruction becomes more meaningful and exciting for their students. Furthermore, incorporating reading into math is a valuable strategy for improving students' attitudes and increasing their knowledge of mathematical concepts.
Integrating Writing and Mathematics
Integrating writing into mathematics enables students to communicate about math and to help clarify their understanding of various math concepts (Wood, 1992). By requiring reflection, analysis, and synthesis of information, writing involves many of the thought process utilized in mathematics (Davison & Pearce, 1988). Not surprisingly, educators have successfully begun to incorporate different types of writing into the math curriculum.
Writing to Record and Categorize Information
Learning involves the integration of ideas. Writing is often a useful tool in learning because it helps students organize and record information in meaningful ways. Writing can be integrated into the math curriculum in three ways: (a) by creating word webs, (b) by organizing notes in a notebook, and (c) by categorizing concepts on the basis of common clements.
First, a word web is a thought-organization and clarification strategy that can be utilized with students across the curriculum (McGehe, 1991). The value of webbing occurs when students start to associate words and phrases with key math terms and begin to categorize information. Being able to categorize and make connections among related math concepts as essential to learning and retaining information. Consequently, word webs can be useful for introducing a new unit, or reviewing for a test, because the webs help students brainstorm what they already know about a particular math concept (McGehe).
Second, Wood (1992) asserted that a categorization strategy called List-Group-Label and Write (LGLW) is an appropriate way to consolidate learning after a math lesson or unit. This strategy is similar to the webbing activity mentioned previously. After brainstorming all the terms and concepts studied in a previous unit, students work in pairs or small groups to classify the terms by the elements they have in common. After classifying the information, the students choose a category on which to write a paragraph (Wood). While synthesizing the information into a paragraph, students must sequence ideas, develop relationships, and plan solutions. Therefore, the LGLW strategy gives students practice in these critical thinking skills, while at the same time they review important mathematical terms and concepts.
In addition to these strategies, traditional note-taking in an organized notebook can be a simple means of recording information. In fact, word webs and LGLW activities could be recorded along with factual information that has been copied into a notebook for future reference. Davison and Pearce (1988) insisted that note-taking is more effective when students know the notebook will be checked regularly, that it will be helpful as a study tool in preparing for tests, and that they can use the notebook during periodic quizzes. Although requiring fewer processes, this type of writing reminds students of the importance of writing to convey information. This information could be used in additional writing assignments which do involve more steps of the writing process.
Writing to Translate Math Terms and Symbols
Traditionally, most elementary mathematics instruction has been an exact science, where only precise definitions and procedures are acceptable. Yet, in many other curriculum areas, students may use their own words to describe or summarize information in a meaningful way, which they are much more likely to remember than simple memorization of textbook definitions or explanations. Because of this, many math teachers are exploring ways to incorporate writing into math to make mathematical terms and symbols easier for students to understand and remember.
In a study conducted to determine if students could use writing to help them learn math, Evans (1984) required students to write their own definitions for math vocabulary words. Although their definitions lacked the precision of those found in the textbook, the students could understand and could more easily remember the vocabulary words they had defined using familiar terms. Additionally, these definitions provided valuable feedback for the teacher about how well the students understood the concepts being addressed.
Capsule Vocabulary, another strategy, uses writing as a means to learn math vocabulary (Wood, 1992). This strategy was developed to reinforce new vocabulary while promoting participation and communication skills in the classroom. It begins with a list of key terms and concepts, and whole class discussion of each new term's definition. Then, students talk to a partner using as many of the terms as possible. Finally, students compose a paper using the key terms from the lesson (Wood). The synthesis and organization of mathematical ideas into writing foster the development of a broader math vocabulary. Such a vocabulary is necessary to communicate mathematically, one of the primary goals established by the National Council of Teachers of Mathematics (Grossman, Smith, & Miller, 1993).
In addition to the need to understand and to interpret mathematical terms, students must gain an understanding of mathematical symbols. Davison and Pearce (1988) asserted that students should translate mathematical symbols and word problem solutions into writing using complete sentences. Furthermore, students will benefit from writing the problem and describing the steps needed to solve it. The benefit for the students is that they think about what the problem asks and necessary steps for its solution. The teacher also benefits because the written descriptions reflect the students' thought processes, which is especially helpful when students have a misconception about topics or mathematical processes that need teacher clarification.
Writing to Explain Concepts and Processes
The most important reason for integrating writing activities into the math curriculum is that writing helps students learn. Writing directions for other persons and reflecting in a journal how something is done are ways for students to clarify their understanding of a certain concept or process.
When requiring students to explain how to do something, Evans (1984) suggested that students target an uninformed third party. This writing assignment requires students to be more specific and more critical in their thinking processes. Davison and Pearce (1988) also supported how-to writing, viewing it as a way to summarize information. Summarizing information should involve reflecting on mathematical terms and concepts.
Another summarizing activity supported by Davison and Pearce (1988) is journal writing. Journals provide another way of communicating about mathematics, whether by reacting to a topic being studied, posing questions about a particular process, or sharing new insights. Stix (1994) proposed a style of journal writing called Pic-Jour Math, which includes pictures, numbers, symbols, and objects to help students understand mathematical concepts. Stix determined that students developed better understanding and retention of math concepts, less anxiety toward math, and a higher confidence level when using Pic-Jour Math. She also confirmed that students' writing provides valuable feedback to teachers and parents regarding students' thinking, reasoning, and learning styles.
Furthermore, because students often see manipulatives in isolation, journal writing can be a valuable tool to expand their perceptions. By describing in writing, pictures, and numbers the processes used in working with manipulatives, students are more likely to see the connection between the manipulatives and the numbers or symbols they represent (Stix). Thus, journal writing encourages students to think of math concepts logically and to construct understandings that make the concepts meaningful for them. Research has asserted that the most effective method of using writing in mathematics instruction is through the use of journals (Stix).
Another meaningful type of writing which clarifies concepts and processes is an activity called Troubleshooting (Evans, 1984). Troubleshooting requires students to explain, in writing, any errors. in their homework or quizzes using specific details. Such feedback is helpful for students, as well as teachers, to determine if a simple mistake, or a complete lack of understanding, caused the student to miss the problem.
Students and their teacher learn more about how they think and how well they understand mathematical processes when they write about them. Explaining how to do something, describing processes in a journal, or explaining mistakes made during problem solving help students clarify their understanding of various mathematics concepts.
Writing to Create Story Problems
One of the most difficult math tasks for students is solving word problems. Perhaps it is because language has been omitted from the math curriculum for so long that students are intimidated when they see words in math. Fairbairn (1993) offered six simple suggestions to alleviate some of the students' fears. First, he suggested that teachers refer to word problems as story problems and to set the stage for the problems by telling and reading interesting stories aloud to the students. Second, teachers should make story problems appealing to students by including local data and people the students know in place of the problem's original information, without changing the operations to be practiced in the problem. In addition, teachers should encourage group work on story problems and allow students to generate new problems on their own for their peers to solve. Finally, Fairbairn stated that teachers should develop a positive attitude among students and keep the students motivated by using interesting story problems to teach them the needed math skills. These suggestions will not only put students at ease when working with story problems, but will also bring reading and writing into the math curriculum as students endeavor to create their own story problems.
Mayotte and Moore (1992) also made suggestions for encouraging students to write story problems. One strategy they have used is called Math Can Challenge. Students place an original draft of a story problem in a can. At the end of the week the problems are read and revised before being judged by their peers for originality, complexity, and logical information. The winning problem is then solved by a group of students, and the author is revealed. This has proven to be constructive because the students are motivated by pride of authorship and the opportunity to challenge their peers. In addition, Mayotte and Moore encourage students to use characters from literature in their problems, using what they know about the character's experiences in the original book.
Finally, Brown (1993) described a process of story problem writing that focuses on math, reinforces the steps of the writing process, and exemplifies the integrated curriculum philosophy. Brown collected her seventh-grade students' rough drafts of their story problems and evaluated each based on whether the problem illustrated the math operation assigned. Then, the English teacher guided the students' editing and revision process. Once the edited papers were returned, a media specialist supervised while the students used the word processing program in the computer lab to type each of their problems; the problems were later bound into booklets by the curriculum department and shared with each school in the county. As a result, students were more willing to attempt story problems, were more effective in using computers to solve word problems, and were more cognizant of the connection between language arts and math.
Writing to Convey Information
Writing activities such as journal entries and student-created definitions illustrate that one can learn from writing. These types of writing assignments are valuable in the mathematics classroom because they help students clarify information and broaden their personal understanding of various math terms and processes. Another important reason for writing is to convey information to another person. Before information can be shared successfully, it must be pondered, reflected upon, and summarized. These skills reinforce mathematical concepts as they develop higher level thinking and organizational skills.
One example of writing to convey information is a short paper focusing on important people and events in the history of mathematics (Davison & Pearce, 1988). Although this writing assignment may not directly relate to the acquisition of math skills, it does encourage students to explore and convey information related to mathematical concepts. Learning new information through a research project broadens the background experiences students need when dealing with related math concepts in the future.
A second type of writing assignment is called a Reaction Guide (Wood, 1992). During this strategy, students work in pairs or small groups. They are given a series of five to eight statements about a mathematical concept that may be true or false. Students are to find and write down evidence which either confirms or refutes each statement. The guides are then referred to during a class discussion about each statement and later used as study aids.
Mayotte and Moore (1992) described another example of writing to convey information, which they called Technical Writing. They suggested that the class members work together to create a book on how math works. The book would include step-by-step directions to solve various type of problems, such as how to solve simple addition problems or how to check division problems using multiplication. These ideas were compiled in a book patterned after The Way Things Work by David McAuley. Therefore, students were thinking and analyzing mathematical procedures as they described them in writing, which was an effective way to see how well they understood the process about which they were writing.
Finally, students can convey information about math concepts through math limericks. Although this is quite different from technical research writing, limericks provide a fun and creative way for a pair of students to summarize information about a math topic. Again, students have the opportunity to practice the steps of the writing process as they edit and perfect their mathematical limericks. Also, students learn to recall important math concepts as they memorize and recite their own limericks as well as each other's (Mayotte & Moore, 1992).
Despite the fact that writing to convey information often takes the form of a traditional research paper, there are other formats through which students can summarize and share math related information, as well as become more prolific writers.
Using Oral Language Activities in Math
The NCTM asserts that communication helps children construct links between their informal, intuitive notions and the abstract language and symbolism of mathematics (Grossman, Smith, & Miller, 1993). This is in line with the whole language movement which stresses the use of all modes of language. Therefore, in addition to reading and writing in math class, teachers are now discovering ways to incorporate oral language in mathematics as well.
Vacca (1993) emphasized the value of group discussions to help students apply prior knowledge to problem-solving situations while receiving feedback from others. In her article "Teaching and Learning Mathematics through Classroom Discussion," she offered suggestions for teachers about how to create an environment that encourages participation and how to initiate meaningful classroom discussions. The strategies for starting discussions include asking a question, referring to a common experience, introducing a controversial issue, and listing specific concerns about a particular math concept. Once the teacher has established an inviting atmosphere and has learned to initiate meaningful discussions, s/he should focus on teaching students how to learn from discussions in order to benefit from class discussions students need to seek clarification when something is unclear and to be willing to talk about their own ideas. They must also be able to listen to, respond to, and build upon other people's ideas, while being sensitive to their feelings (Vacca). The benefits of talking about math are an increased mathematics vocabulary and a better understanding of the concepts and processes discussed in class. Also, the use of oral language enables students to become active questioners, problem creators, and problem solvers.
Capps and Pickreign (1933) supported the use of oral language and classroom discussions to enhance math instruction. They suggested that students should verbalize and discuss ideas aloud when they are working with manipulatives. By talking with and listening to their peers, students will connect their prior knowledge to new mathematical terms and concepts. In addition, when students use manipulatives and talk about what they are doing, teachers have an invaluable opportunity for assessment.
Another way discussion can be used effectively is in developing a math vocabulary. Students learn new math terms when the teacher asks the class to brainstorm what comes to mind when they hear certain vocabulary words. For example, many words used in math, such as plane, degree, or operation, have everyday interpretations quite different from how they are used in math (Capps & Pickreign, 1993). Discussing the multiple meanings of these words helps students understand and use mathematical terms correctly.
Another variation of classroom discussion is to have students involved in paired or group retellings. Wood (1992) suggested that students be grouped in threes, and then each be given a different problem dealing with the same topic or operation. Each student solves his or her problem and talks aloud about the processes involved while pointing to an enlarged, big book version of the problem as other students suggest alternative ways to solve the problem. Therefore, regardless of the number of participants, discussions can facilitate higher level thinking skills and understanding of math concepts, processes, and vocabulary.
Songs, Poems, and Folk Tales
Although a classwide discussion may be the most obvious strategy for incorporating oral language into mathematics, Hurst (1992) suggested that songs, poems, and folk tales can also inspire math activities. Counting songs, such as "The Ants Go Marching," cumulative songs like "The Old Lady who Swallowed a Fly," and action songs like "In a Cabin in a Wood" are wonderful resources for teaching math because their predictability and humor capture students' attention while providing a basis for numerous math activities (Hurst).
Poetry with mathematical connections is another way to incorporate oral language into math class. Hurst (1992) suggested that Jack Prelutsky's poem "The Ants at the Olympics" could be used as the basis for many calculations related to the ant Olympics, such as how long an ant takes to travel one foot, and for various calculations based on actual Olympic records.
Finally, Hurst (1992) promoted the use of folk tales in their original oral form to enhance math instruction. She pointed out that folk tales often include numbers, especially the number three, as in the Three Little Pigs and Three Billy Goats Gruff. These tales can form foundations for mathematical activities and computations.
Although these activities are less structured than some previously mentioned strategies, incorporating music, poetry, and folk tales into math instruction can serve to inspire and motivate students through the use of oral language.
Research on including reading, writing, and oral language in math instruction is very positive. Not only do the students benefit as mathematicians, they develop as readers, writers, and speakers from the additional opportunities to practice these skills. Practicing language arts skills across the curriculum is in line with the whole language movement, as well as with the integrated curriculum approach. The benefits of including literature and reading experiences throughout the curriculum have been expanded upon by whole language researchers. Research by Grossman Smith, and Miller (1993) and Evans (1984) strongly supports the benefits of using writing for improving student performance in mathematics. In order to uphold the NCTM recommendations, students must learn to communicate mathematically, in writing and through oral language (Capps & Pickreign, 1993).
Research supports the benefits of incorporating reading, writing, and oral language into mathematics instruction to help students convey mathematical information in familiar words and to assist them with their thinking processes, as they work through math calculations and problem solving situations. Another reason writing is a valuable asset in mathematics instruction is that the teacher is better able to evaluate students' understanding of math concepts and processes based upon what the children have written. A teacher can also evaluate students by what they say. By including oral language activities in math lessons, students' abilities to communicate mathematically will improve. Thus, a teacher will be better able to evaluate and clarify students' thought processes, while building students' confidence in their own abilities to discuss mathematics. Therefore, based upon the many benefits and the number of emerging strategies for implementing language arts into mathematics instruction, the teacher should begin incorporating reading, writing, and oral language activities into mathematics lessons on a regular basis.
Despite the valuable strategies and teaching techniques now being used, more research needs to be conducted on the benefits of incorporating language arts into the math curriculum, and teachers need more suggestions and additional resources to ensure the success of a language - rich math program.
Finally, because the basis for language arts activities should be literature, the research supports the recommendation by Nichols (1993) that more math concept books, illustrating a wider range of math topics, are needed. In addition, middle school and high school teachers need more math concept books written specifically for students in the upper grades. Such books would provide students with the meaningful contexts and visual representations they need to comprehend the increasingly abstract skills of higher mathematics.
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|Author:||Kolstad, Rosemaire; Briggs, L.D.; Whalen, Karen|
|Date:||Mar 22, 1996|
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