Number Experience

Section I: Purpose of the Review

Section II: The History of Mathematics Education

Section III: The Need for Reform

Section IV: The Benefits

Section V: The Challenge: Make it Work!

Section VI: "Quadraliterature"

Section VII: Personal Commentary: Review of Literature, Observations, and

Section VIII: Works Cited

Section IX: Sample Lesson: A Remainder of One

Section X: Sample Lesson: "Human Place Value"

to name the stars."

As educators continue to search for the most effective approach to teaching mathematics, they face the monumental challenge of meeting the national call for reform. The rapid advances in knowledge and technology and the need for a better means of preparing children for today’s challenging world have led educators to examine new ways of actively engaging students in their mathematics learning, primarily through it’s integration with literature. By providing a context through which students can construct meaning, it is the goal of educators to subsequently foster and develop students mathematical thinking and reasoning using what they have learned to solve problems both in school and in real-world contexts. The purpose of this current review is to critically examine and discuss recent literature and research concerning the integration of mathematics and literature at the elementary school level, as a way of exploring and investigating mathematical concepts, providing the reader with a sense of how this literature reflects the current views on this topic. For while there continues to be changes in the most effective ways of providing students with meaningful mathematical instruction; no one disputes the significance of providing learning environments in which all students have the opportunity to learn, grow, and reach their maximum potential.

While the study of mathematics as a process for communicating data and examining pattern and order, has existed for as long as recorded history, its scope has changed over the centuries, progressing from a static field of study to its current dynamic status of universal applicability (O’Banion, 1997). In the past, the mathematics curriculum was isolated from all other disciplines and was designed to provide basic computational skills, emphasizing the rote memorization of rules and procedures. Students mastered these skills using paper and pencil drill, textbooks, and the memorization of addition, subtraction, multiplication, and division facts. In mathematics, opinions on how and what should be learned shifted rapidly, from an emphasis on basic skills mastered through precision and rigor, to a process-driven hands-on approach using manipulatives, and then back to the basics attitude, with "basics" never precisely defined or agreed upon. A valid concern about the basic skills and knowledge of our students and the adjustments necessary in mathematics education has lead to the current shift toward a broader view of mathematical instruction reflected in the National Council of Teachers of Mathematics (NCTM) Standards for the elementary school level (Gailey, 1993).

The complexity of today’s society requires all citizens of different cultures and backgrounds to be well prepared in the area of mathematics, a need that far exceeds basic computational skills. Although the rote learning of math facts and processes do not adequately prepare students for life in today’s world, these computational skills are still valuable tools for understanding our number system and providing a necessary and efficient method to perform computational functions.

In an effort to keep up with students in other advanced nations and to help students see connections between mathematics and their world, educators must seek new and creative methods to motivate students and provide them with real-life applications of mathematical concepts. With the publication of the National Council of Teachers of Mathematics (NCTM) Standards, many mathematics teachers and educators have become especially interested in making mathematical connections, such as those found between math and children’s literature (Leitze, 1997). This logical union between math and literature provides a natural way for teachers to allow students to see mathematics in everyday society, to give it meaning, and to make it come alive. Similarly, it provides students the opportunity to observe the interaction of mathematics with other disciplines and with daily life. The overarching goal of these standards is the integration of mathematics into contexts that give its symbols and processes practical meaning (Leitze, 1997).

The inclusion of literature in mathematics is one of the changes recommended by the National Council of Teachers of Mathematics, which enables a more authentic approach to math. These standards underscore the constructive nature of mathematical understanding and stress the need for students to communicate mathematical ideas. According to curriculum standards, communication helps students "construct links between their informal, intuitive notions and the abstract language and symbolism of mathematics; it also plays a key role in helping children make important connections among physical, pictorial, graphic, symbolic, verbal, and mental representations of mathematical ideas (Lewis, Long, & MacKay, 1993). The message of NCTM’s teaching standards is that "computational algorithms, manipulation of equations, and paper-pencil drill must no longer dominate school mathematics. In mathematical reasoning, problem solving, communication, and connections are central" (Lewis et al., 1993). A critical look at the abundance of research which supports the integration of math and literature examines the opportunities provided by children’s books to develop mathematical power in a natural and meaningful way.

The benefits of the math-literature link are rooted in its inherent connection, integrating the learning of mathematical concepts into contexts that are meaningful to children (Raymond, 1995). According to Raymond (1995), children’s literature provides a stepping stone to mathematical understanding. Its ability to motivate students to learn mathematics illustrates the notion that it does not have to be learned "in isolation" from other subject areas. By eliminating the barriers created by the constraints of time and formal math instruction, both students and teachers benefit, provided with more time and the smooth, gradual flow of interdisciplinary activities (Lightsey, 1996). Trade books portray mathematics in a different light, as an everyday human activity, rather than as the rules and procedures that children "have to learn" which do not seem applicable to life situations. Through the math-literature connection, "it is hoped that…students begin to view mathematics…as a natural part of everyday life" (Raymond, 1995).

In a study conducted by Jennings, Jennings, Richey, and Dixon-Krauss (1992), it was found that the use of children’s literature to teach mathematics concepts to kindergarten children improved math achievement test scores, and increased both their interest in mathematics, and the number of times they used mathematical vocabulary during free play. Research conducted supported the idea that using children’s literature to teach math provides teachers with the opportunity for creativity, a vital component of successful teaching, while resulting in increased student interest and achievement in the area of mathematics. The Jennings et al.(1992) study examines the importance of providing meaningful experiences that actively involve children in their learning. The benefits of these developmentally appropriate activities lie in their ability to act as prerequisites for the eventual application of concepts and principles to real-life problems, the motivation for both teachers and students provided through the integration of real-life problem solving situations, and the facilitation of discussion fostered by these activities, a necessary part of understanding and applying mathematics to new situations.

The challenge of providing experiences that are meaningful for each individual student faces educators everyday, as they strive to meet the needs of a diverse group of students. The integration of math and literature provides the ideal opportunity for tapping into the talents of all students no matter what their ability levels may be. As stated by Thrailkill (1994), "the line between ‘good’ readers and ‘good’ mathematicians begins to blur and children are more likely to build their confidence in each area focusing less upon what they see as their strengths and weaknesses in school subjects."

Trade books, especially picture books, can be integrated into any lesson because of their short format. Presenting similar information as textbooks, children’s literature provides a more interesting format as well as issues and themes that are of interest to various age levels. They act as vehicles that help children to apply the information they learn to their own lives as opposed to textbooks which often include activities that are based on things that kids don’t do, can’t do, or don’t want to do (Murphy, 1999). In a society inundated with visuals, picture books provide a more meaningful avenue for understanding difficult concepts. Books portray specific concepts through diagrams and illustrations, which, for visual learners, can be much more meaningful than purely verbal or numerical explorations. In picture books by Mitsumasa Anno, for example, math concepts become clear without the use of a single word (Murphy, 1999). They can be used to introduce a specific concept, develop interest, provide background information and expand understanding of a lesson (Goerss, 1998). The problem solving process of both literature and mathematics provides a dual opportunity for enhancing thinking both in comprehending a piece of children’s literature and in the broader, more meaningful assessment of student’s thinking in mathematics, which is more powerful than assessing either reading comprehension or mathematical understanding separately (Thiessen, 1996).

The use of children’s books in mathematics enriches overall learning. Mathematics and language skills develop together as students listen, read, write, and talk about mathematical ideas. While enhancing mathematics learning, children’s books also enhance reading skills, providing students more opportunities to experience literature as it pertains to different content areas (Gailey, 1993).

The greatest risk in integrating literature with math; in fact, the greatest risk in integrating any areas of the curriculum is inappropriately doing so. What is meant by "appropriate" is not specifically defined but basically means that the literature used has a specific purpose and is not used as a means of teaching a specific skill. The best books are obviously those related to the math being taught, the ones with which extensions can be made, such as to other areas of the curriculum (i.e. dramatic arts), and those that motivate children to subsequently explore with the books themselves.

"Appropriate" also means that the developmental levels and previous literacy experiences of children must be considered when using children’s literature to teach mathematics. Listening to children’s responses to a story and incorporating these into teacher planning are absolutely crucial for developing understanding, interest, and motivation in mathematics (Jennings, Richey, & Dixon-Krauss, 1997). When teachers fail to learn from their students, their students fail to learn.

When children are guided in learning, and subsequently allowed to make their own investigations and decisions, the math and literature connection will equal learning. Ultimately, Jacobs and Rak (1997) state, "mathematics should flow from and be a natural part of the book."

The "language" of mathematics can be divided into four categories of children’s books: counting books, storybooks, number books, and concept books. While not limited to these categories, Gailey (1993) offers these to teachers to better classify that which the books are intended to teach.

Counting books, as their name implies, reinforce number concepts and can be used to teach any of the arithmetic functions of addition, subtraction, multiplication, and division. Widely used in first grade to review the numerals from 1-10, counting books actively engage students in learning. Moja Means One: Swahili Counting Book, by Marjorie Feelings, uses African people in native dress to illustrate the numerals from one to ten. As a multi-cultural extension, it also teaches children the Swahili word for each numeral. Teachers can use the book with children to count such things in the classroom as boys, girls, children wearing red, etc. Thus the children while learning to count, subsequently learn to classify sets of objects and different representations of numbers.

Number books, as their name implies, reinforce a particular number. Examples include My Six Book, by Jane Moncure, and Jeffrey Moss’s Five People in My Family. This math-literature connection is vital in teaching beginning readers the importance of labeling. Students will soon strengthen understanding that "6" is the same as "six" is the same as "a picture of six cows." Lightsey (1996) recommends several songs and rhymes to accompany number books, aiding in their understanding of specific numbers. The song "This Old Man" lends itself to this goal, as children learn and can even act it out. The students have fun and are motivated to learn more, subsequently establishing stronger connections.

To introduce or reinforce mathematical concepts, storybooks can also be used. Fairy tales, folk tales, or any other stories in which the author touches on a mathematical concept can be used. Two Ways to Count to Ten, by Dee may be used as a way to introduce alternative counting methods. In the story, King Lear holds a spear-throwing contest to find an heir to his throne. The first animal to count to ten before his spear hits the ground wins. Finally, an antelope discusses counting by even numbers is quicker and he is made heir to the throne. Students will also come up with other ways such as counting by 5’s, laying the foundation for basic discussion. A Remainder of One (see attached lesson) is one of my favorites. In the story, poor Joe is always being left out of his squadron of twenty-five ants as they rearrange themselves into lines of two by twelve, three by eight, and four by six. This story illustrates multiplication and division using different arrangements of ants, which can later be reinforced, with the creation of fact families.

Lastly, concept books (informational books) are useful in exploring specific mathematical concepts such as money, time, "a million", and fractions. They usually have interesting formats and convey excitement in exploring various mathematical ideas. Schwartz’s How Much is a Million is popular in classrooms to teach the concept of large numbers. When teaching basic place value and then introducing this book, students are motivated to discuss this "imaginary" number and what exactly it is. One Grain of Rice (see attached lesson) by Demi provides the basis for a lesson on place value as a review of the tens, hundreds, ones, tenths, and hundredths places of a multi-digit numeral. Eating Fractions, by Bruce McMillan is similarly motivating to students when introducing the concept of fractions. McMillan shows real children manipulating food to show different fractions. Since the text is simple, emergent readers will enjoy reading and re-reading the book. Similarly students love to make their own food fractions, sharing, and counting them with their classmates.

This presents an overview of how children’s books fit into categories, better assisting the teacher in making this appropriate integration. While it is not necessary to categorize every book, it is imperative that these books are appropriately used within a mathematics curriculum to ensure student understanding.

As a future elementary/special educator, I found this analysis of past and current literature on the math-literature connection to be an extremely rewarding experience that has helped me to see just how valuable the integration of children’s literature with mathematical concepts can be, especially at a time where elementary testing does not blur their distinction. Each of the articles addressed key issues surrounding math and literature in a clear and concise manner, with the author making his/her purpose known to the reader in the introduction. The remainder of each article followed wholly and essentially from the introductory paragraph providing the reader with distinct sections and issues to compare and contrast as well as examples of activities involving math and literature. Research findings indicate both the benefits and the challenges of creating meaningful and effective math-literature connections. For only when this teaching strategy is used appropriately, can it be a positive experience for the entire community of learners.

Harris Hill Elementary School in Penfield, NY holds a firm belief in the need to actively involve students in meaningful, hands-on, real-life experiences involving a variety of learning modalities. In an observation of Mrs. Wostl’s second grade classroom, I was fortunate enough to be able to watch an amazing teacher connect mathematics and literature using the class’s very own garden to create the interest, motivation, inquiry, and excitement, which facilitate true learning. With the class garden right outside the door of the classroom in the school’s courtyard, Mrs. Wostl’s class had the responsibilities of planting seeds and watering the plants, while also graphing the locations of the different plants/vegetables, and their continuous growth. The students saw the results of their efforts as they watched seeds bloom into flowers and plants grow into vegetables, which eventually became a part of their afternoon snack. Using Ehlert’s book, Planting a Rainbow, Mrs. Wostl complemented the mathematics involved in the students’ gardening experience with literature, nurturing the students’ enthusiasm prior to the actual planting experience. In the children’s gardening, mental math, numbers and operations, and measurements were involved in mathematical ideas such as the number of seeds in each package, how many flowers bloomed on each plant, the size of the garden needed to plant a given number of plants, the number of days each group of flowers takes to bloom (compare groups), the size of the plants, the length of the rows, and the area of the garden. By appropriately connecting math and literature and even science, Mrs. Wostl was able to use children’s books and a garden as avenues to explore the mathematical linkages offered, motivating her students with real-world experiences, and fostering meaningful connections.

In my work at Hillside Elementary School in Niskayuna, NY, I have observed the integration of math and literature using the story, The Doorbell Rang by Pat Hutchins. As an introduction to fractions, this first grade teacher provided students with "paper cookies" which could be used to perform math as the book was read aloud. In the story, a mother has made twelve cookies for two children, but the doorbell keeps ringing. As the number of children grows, the number of cookies per child diminishes. Performing the math with manipulatives during the story, the students were able to visualize how _ of 12=6 (cookies per child), _ of 12=3, 1/6 of 12=2, and 1/12 of 12=1. At the end, the doorbell rings one more time and it is Grandma with more cookies.

This book could also be used with other activities to introduce fractions, such as having students role-play the story, write their own stories, or to work out in different ways how many cookies each child would have for various different numbers of children and cookies. Regardless of the method used, these activities use the story as an appealing and meaningful context in which students can develop skills and an understanding of the concept and process of division and fractions. By creating their own similar stories, students are encouraged to both be creative and to communicate about mathematics.

I firmly believe that it is time to stop punishing children with math instruction that involves hours spent on worksheets, flash cards, timed tests, and never-ending algebraic equations. We need to exchange the sweaty palms, the tears, and the attempting of problems over and over again without knowing the meaning or understanding why, for the meaningful, real-world math experiences involving children’s literature, journal writing, cooperative learning, hands-on discoveries, and the creation of their own word problems. With the proper knowledge and skills, we as teachers can put an end to the nightmares that children have experienced with math in the past, providing them with the motivation and tools necessary for success. As educators, we must begin to focus on the individual learner and their special needs, ensuring success for all students. The many alternatives available are necessary and sufficient to meet the needs of a diverse student population and have been proven effective in many educational environments. In an era of such high standards, we must prepare students for the complexity of today's society, which requires all citizens to be well prepared in the area of mathematics. We must see each individual student as a person of value, able to learn and succeed when provided with the appropriate learning environment and activities. When we gamble with math-literature connections without direction, everyone loses. However, when we provide students with motivation, real-world experiences, and meaningful connections, the chances and benefits of success are in everyone’s favor.

Gailey, S.K. (1993). The mathematics-children’s-literature connection. The Arithmetic Teacher, 40, 258-259.

Goerss, B.C. (1998). Incorporating picture books into content classrooms. The Indiana Reading Journal, 30, 30-35.

Jacobs, A., Rak, S. (1997). Mathematics and literature–a winning combination. Teaching Children Mathematics, 4, 156-157.

Jennings, C.M., Jennings, J.E., Richey, J., & Dixon-Krauss, L. (1992). Increasing interest and achievement in mathematics through children’s literature. Early Childhood Research Quarterly,7, 263-276.

Leitze, A.R. (1997). Connecting process problem solving to children’s literature. Teaching Children Mathematics, 3, 398-406.

Lewis, B.A., Long, R., & MacKay, M. (1993). Fostering communication in mathematics using children’s literature. The Arithmetic Teacher, 40, 470-473.

Lightsey, G.E. (1996). Using literature to build first grade math concepts. Reading Horizons, 36, 412-418.

Murphy, S.J. (1999). Learning math through tough stories. School Library Journal, 45, 122-123.

O’Banion, C. (1997). Enhancing math through literature. School Library Media Activities Monthly, 13, 42-44.

Raymond, A.M. (1995). Engaging young children in mathematical problem solving: Providing a context with children’s literature. Contemporary Education, 66, 172-173.

Thiessen, D. (1996). Counting on company row. Teaching Children Mathematics, 12, 34-38.

Thrailkill, C. (1994). Math and literature: A perfect match. Teaching K-8 Mathematics, 6, 64-65.

Name Kristen Jenne Date April 21, 2000

LESSON OPENING [assigned seats]

Name: Kristen Jenne Date: February 13, 2000

Content Area: Mathematics Unit Topic: Place Value

Today’s Lesson: "Human Place Value" Grade Level: Second

New York State Learning Standards for Mathematics, Science, and Technology

1. Students will identify the place value of each digit in a multi-digit numeral.

[Knowledge]

2. Students will identify digits in the tens, hundreds, ones, tenths, and hundredths place. [Knowledge]
3. Students will, holding a paper plate with a number and place value, place their bodies in order to create the numbers dictated by the teacher. [Application]
4. Students will create the largest possible number using a game board and rolling a die. [Comprehension, Application]

Hearing Disability: In order to accommodate the student’s hearing disability, a

Visual Disability: To accommodate a student with a visual disability, the teacher will

Materials: One Grain of Rice

"Does anybody remember talking about place value? Raise your hands. What do you think of when I say place value? (Call on 2 students) [Check for understanding] "Does anyone remember talking about hundreds, tens, and ones? What do they mean?" (Call on 3 different students) [Check for understanding]

[Before the lesson:

Students will bring the board game home and share it with someone. They will explain the rules of the game as well as discuss the meaning of each place in the number.

Evaluation: