Multicultural Literature as a Context for Problem Solving: Children and Parents Learning Together
Strutchens, Marilyn E., Teaching Children Mathematics
In recent years, the mathematics community has given more attention to the role that mathematics plays in our cultural society and the contributions of different cultures to mathematics (Bishop 1988; D'Ambrosio 1985; NCTM 1989; Frankenstein 1990; Joseph 1993). Teachers are encouraged to include culture in a variety of ways in the mathematics classroom. Students can be encouraged to use mathematics as a tool to examine their cultural and social environments, traditions, and artifacts. In addition, mathematics learned by students outside the classroom can be used as a bridge to learning school mathematics.
Because mathematical situations are often embedded in the social and cultural contexts provided by literature, children's multicultural literature is the perfect medium for including culture-related activities in mathematics lessons. Further, multicultural literature offers a context in which readers can celebrate their personal cultures and learn about those of others. Banks (1993) contends that education in a diverse society should affirm and help students understand their home and community cultures and free them from cultural boundaries.
Children's multicultural literature provides the context for the modules in a program titled Multicultural Literature as a Context for Mathematical Problem Solving: Children and Parents Learning Together (Literature/Mathematics Program). The Literature/Mathematics Program is a part of the parent-and-community component of a broader project called Mathematics: Application and Reasoning Skills (MARS). MARS addresses systemic reform in the elementary mathematics program of the Baltimore City Public School System (BCPSS). The project encompasses administrative policy discussions, instructional support, professional development, selection of materials, instructional supervision, curriculum, and community involvement. Most of the elementary schools in the BCPSS have predominantly African American student populations, with a few schools that are predominantly white. About 68 percent of the students are eligible for free or reduced-price lunches, and less than 1 percent of the enrolled students are classified as hav ing limited English proficiency.
The Literature/Mathematics Program is one of the MARS project's mechanisms to help parents become aware of the changes that are occurring in mathematics education. Parents and their children are invited to participate in an exciting approach to learning mathematics. Through the literature of different cultures, adult-child pairs or families solve mathematical problems. These sessions are conducted for ninety minutes once a week for six weeks. Each session is run by two teachers who have attended a professional development workshop especially for the Literature/Mathematics Program. During the workshop, the teachers receive modules designed to help them facilitate the process of the parents and children learning together.
Selecting Books for the Modules
The books chosen for the program were written by authors from various cultures or were deemed to authentically represent certain cultures on the basis of reviews in major journals of children's literature. Moreover, the books used in the program represent several ethnic or racial and socioeconomic groups and are appropriate for multiple grade levels. Further, some of the books have mathematical content naturally embedded in the text, whereas others provide avenues for creating nonroutine problems. See table 1 for the names of the books, the cultures represented, and the mathematics reinforced in the modules that focus on each book. Teachers can select to use modules on the basis of mathematical concepts, particular cultural groups, or both. Teachers are encouraged to focus on a variety of cultures throughout the six weeks to attain the goals of the program.
Components of the Program
The program has two major components: a read-aloud portion and a problem-solving portion. During the read-aloud portion of the Literature/ Mathematics Program, a book is read by one of the facilitators. As the facilitator reads, he or she asks questions related to the story to help parents and children connect with the characters, to highlight mathematical themes, and to make the story more engaging. The facilitator may prompt the families to do the mathematics embedded in the text while he or she is reading the story or ask other mathematical questions that can readily be drawn from the text.
During the problem-solving portion of the lesson, parents and children are given a series of mathematical questions that build on the context of the story. In some of the stories in which the mathematics is embedded in the text, the problem-solving portion of the session flows naturally from the read-aloud portion. If marked differences exist in the ages of the participating children, the facilitators may divide the families into groups to allow families with primary-grade children to work together and families with intermediate-grade and middle school children to work together. Near the end of the session, the families come back together to share what they have learned. Through this experience, the families learn different problem-solving strategies, such as guess and check, make a chart or table, and draw a picture. Furthermore, as the parents and children present their solutions, the facilitators ask probing questions to help them reflect on the problem-solving experience. As a consequence, parents are ex posed to the kind of questioning that they can use at home to help their children understand mathematical concepts.
Sample Episodes from the Program
One story that is a favorite of most families is The Black Snowman, written by Phil Mendez (1989). This text can be self-affirming for African American learners and a window of insight into another culture for others. The Black Snowman focuses on an angry African American teenager named Jacob who lives with his mother and his younger brother, Peewee. Jacob's anguish stems from his belief that his poverty is a result of his being black. Fortunately, the magic of a Kente cloth brings to life a snowman made from sooty snow. This snowman is extraordinary because he can talk and he knows much about African heritage. With the help of the snowman, Jacob saves Peewee from a burning building and becomes more appreciative of his heritage and his family.
This story offers a valuable context for discussing issues of self-pride, race or ethnicity, and socioeconomic status. The book also furnishes an excellent context for mathematical problem solving through Peewee's idea of collecting cans and bottles for money to purchase a gift for his mother. One of the problems drawn from this story for the program module is as follows:
Suppose a recycling company pays $.23 per pound for under 100 pounds of cans, and Peewee and Jacob collect 60 pounds of cans. How many $.05 recyclable bottles will they need to collect if they want to raise $15.00 from the combined earnings of the cans and bottles? What percent of the earnings would come from the cans? What percent of the earnings would come from the bottles?
When discussing the percents earned from bottles and cans, parents in one session made immediate connections with their real-world experiences. For example, one parent wanted to know whether the same process would be used to determine the cost of a dress discounted by 30 percent. As a result of this discussion, the parents and children were given additional problems about percent-off sales on clothing.
To extend the problems prompted by this story about recycling bottles and cans, facilitators can also use Census Bureau data at www.census.gov to discuss the incomes of different family structures categorized by race. Students and their parents can also study the history of Kente cloth, as well as the geometry in its patterns and designs.
Sadako and the Thousand Paper Cranes by Eleanor Coerr (1993) is another book used in the program. This book has strong historical and cultural meaning for Japanese readers. It is a true story about a Japanese schoolgirl named Sadako who became ill with leukemia as a result of exposure to radiation after the bombing of Hiroshima. The book depicts the devastation caused by the bombing as Sadako, her family, and friends race against time to fold 1000 paper cranes; their belief in a Japanese legend leads them to hope that making the cranes will help Sadako become healthy again. The story also gives the participants glimpses of Japanese customs and beliefs.
As the story is read, the facilitator asks family members to compare their customs and beliefs with those of Sadako's family. Families become very involved in the story. Many of the children and parents are sad and in deep thought by the end of the book. They often state that the story reminds them of loved ones who have died of cancer. The story can also lead into a deep discussion about history and the dangers of nuclear warfare. The following question and response from a parent are from the problem-solving portion of a session focused on this story:
Question. Sadako became sick in February and died in October. By the time of her death, Sadako, her family, and friends had folded 644 cranes. What was the average [number] of cranes folded per day from the time Sadako became ill until her death?
Parent. Since I know that there are 8 months from February to October and each month has either 30 or 31 days, except for February, which has 28 days, I just estimated 30 days for each month and came up with 240 days. Then I thought if she made 1 bird a day, in 240 days, that would be 240 birds. Then if she made 2 birds a day, in 240 days, that would be 480 birds, which is not enough. Three birds a day in 240 days would be 720 birds; 720 birds are more than what she made, so my scientific answer would be two-ish.
This problem required parents and children to use mathematical reasoning skills in many ways. First they had to think about the number of days that Sadako folded the cranes. Because they were not given specific dates in February or October, the parents and children had to estimate the approximate number of days that Sadako needed to fold 644 cranes. The families were given calendars and calculators to aid them in finding a solution. Some of the families decided to estimate that each month had about 30 days. Others used the number of days in the months from a recent calendar. Thus, the families could use either 240 days, 245 days, 270 days, or 273 days, depending on whether they used 8 or 9 months as the time frame and whether they estimated or counted the number of days.
Understanding the meaning of average and thinking about an appropriate strategy to solve the problem were difficult for most families. At one site, the facilitators gave a minilesson on finding the average of a set of data: 15, 10, 20, and 30. Working with this data set prompted a discussion about remainders. Without using a calculator, one student found the mean as 18, with a remainder of 3, and a parent used a calculator to find 18.75. As a result of these responses, a parent asked how the relationship between remainders and decimals is taught in the different grade levels in school. After showing the parents the connection between the two responses and introducing another possible response, 18 3/4, the facilitators stated that as the grade levels increase, the students learn more relationships between numbers and different ways of representing the same quantities. This discussion shows the potential of the program for helping parents learn about the mathematical connections that their children make in sch ool.
Another activity related to the story is making paper cranes. As family members make paper cranes, the facilitators ask the parents and their children questions about the geometric terms associated with making the shapes. The geometric ideas discussed include lines of symmetry, diagonal lines, properties of a square, vertices, and other properties of polygons. Even though parents and children find the task of folding cranes to be difficult, they are excited when they see the final product. Further, parents refresh their knowledge of geometry, and students reinforce what they are learning in school. A good reference for folding the peace crane is Origami Magic (Temko 1993).
The Rajah's Rice (Barry 1994), a mathematical folktale from India, is well liked by both parents and children. This book focuses on a clever girl named Chandra who loves elephants and numbers. She is the rajah's elephant bather, and when the elephants become sick, she cures them. The rajah offers her the reward of her choice for curing the elephants. Chandra asks for the amount of rice that the rajah would need if he were to place two grains of rice on the first square of his chessboard, four grains on the second square, eight on the next, and so on, doubling each pile of rice until the last square is reached. If the rajah had been able to complete the task, he would have needed enough rice to fill Mount Kilimanjaro. This story helps parents and children see the power of mathematical thinking and exponential growth.
Unifix cubes can be used to simulate doubling the grains of rice during the reading of the story to help younger children understand what is happening. Following the reading and discussion of the story, parents and their children are given additional problems related to finding patterns.
Another favorite book of the families is The Girl Who Loved Wild Horses by Paul Goble (1978), a dramatic tale of a Plains Indian girl who "understood horses in a special way" and preferred to live among them. One of the questions asked during the problem-solving portion of the session is "Across the village, the girl saw 3 people and 4 horses. How many legs were there?"
Family members answer this question in a variety of ways. Primary-age children are given counters to help solve the problem. One student made piles of counters to represent people and horses. The student made three piles of two to represent the people and four piles of four to represent the horses, then counted the pieces in her piles. Another student drew stick people and stick horses to determine the number of legs. A grandmother said that she knew that three people have six legs because 3 x 2 = 6, and four horses have sixteen legs because 4 x 4 = 16; her total, then, was 6 + 16, or 22, legs. A more difficult question was posed to the families as a follow-up:
She also counted the number of people and the number of horses in the village by the number of legs and heads. If there were 17 heads and 50 legs, how many horses were there?
Many of the family members attempted to answer this question using some of the same strategies. One parent said that she used an educated guess. She started out by guessing that ten people were in the village. Then 10 x 2 gave 20 human legs, and 7 x 4 gave 28 horse legs. Because the total number of legs that she found did not match the total in the problem, she changed the number of people to 9. Then 9 x 2 gave 18 human legs, and 8 x 4 gave 32 horse legs; the total was 50 legs, which matched the number of legs in the problem.
Other Features of the Program
Even though the teachers receive modules about the different books to guide their interactions with families, they are encouraged to individualize their programs. Many facilitators begin each session with a warmup activity to give all the families time to arrive and help them begin to focus on their purpose for attending the sessions.
The facilitators are also encouraged to give families homework and to help parents see the connections between the Literature/Mathematics Program and students' everyday mathematics experiences. The homework ranges from reminding parents to ask their children mathematical questions related to everyday situations to asking parents and children to do follow-up assignments for sessions of the program. In one interesting long-term assignment, each family in a program was asked to develop a mathematics story by the end of the six weeks. One of the more creative books focused on a shopping trip to the mall. The story is about three children who go shopping with $25 to spend. They stop at different stores to make purchases, and every time that they make a purchase, the reader is encouraged to figure out how much money they spent and how much they had left. Figure 1 is a sample of one of the problems from this story.
Most of the families do the homework assignments and look forward to discussing them in class. Further, the homework gives the parents more opportunities to interact with their children about mathematics. One assignment that facilitators are highly encouraged to give asks parents to talk to their children's teachers to find out what the children are learning in mathematics and what they should be learning at their grade levels. This assignment helps parents start communicating with their children's teachers about mathematics if they are not already doing so.
The Literature/Mathematics Program is an exciting effort to inform parents about innovations in mathematics education and to invite parents to become partners in the mathematics education of their children. Both parents and children have responded positively to the program and often want the program to be extended beyond the original six weeks. Moreover, the facilitators enjoy working with the families.
The benefits of the program are many. First, as parents work collaboratively with their children to solve nonroutine problems, they learn problem-solving strategies that they may not have thought to use at home. For example, in one session, a parent commented that during the previous week, her child had mathematics homework that required him to complete a challenging number pattern that she could not do. That very night at the Literature/Mathematics Program, she learned how to solve the problem!
Second, parents and children are introduced to a variety of cultures while learning mathematical problem-solving skills. This introduction enables parents to think about how they can discuss mathematics with their children on a daily basis in ways that extend beyond helping them with their homework. Parents and their children see that mathematics is a multicultural venture.
Third, parents begin to understand that rote memorization is not the only way to learn mathematics. They learn the importance of helping students understand mathematics conceptually and using good questions to help students think about what is required in a given problem situation. Often, the facilitators teach parents basic operation strategies, such as recognizing near doubles and counting on, along with other useful tips, to help their children at home.
Fourth, the lines of communication about students' mathematics education are opened for parents and teachers. Even though the facilitators may not be the students' regular mathematics teachers, they help parents see the need to talk to their children's teachers about mathematics learning. A facilitator at one school commented that one of her colleagues thanked her for running the program because she had seen an improvement in some of her students' mathematics participation and learning.
Finally, one of the biggest benefits of the program is that parents and children become excited about doing mathematics together. For some of the parents, the program is a reawakening. They begin thinking about mathematics in a completely different way and are excited about their newfound confidence. Children enjoy watching their parents' enthusiasm and are eager to show their parents what they know and can do mathematically.
The Literature/Mathematics Program's use of multicultural literature as a context for mathematical problem solving creates a cultural environment that fosters excitement about mathematics that is contagious and rewarding. One of the program participants put it this way:
What a beautiful and eye-opening experience this has been. Our math and literature sessions were a tremendous success. The families enjoyed the wide variety of literary selections, the interactive tasks, and manipulatives utilized in each session.... Thanks for the opportunity to participate in such a rewarding and worthwhile experience.
[Figure 1 omitted]
TABLE 1 Books used in the Literature/Mathematics Program Title Author The Rajah's Rice David Barry (1994) Fly Away Home Eve Bunting (1991) Sadako and the Thousand Paper Eleanor Coerr (1993) Cranes Two Ways to Count to Ten: Ruby Dee (1988) A Liberian Folktale One Grain of Rice Demi (1997) The Patchwork Quilt Valerie Flournoy (1985) The Girl Who Loved Paul Goble (1978) Wild Horses The Village of Round and Ann Grifalconi (1986) Square Houses The Doorbell Rang Pat Hutchins (1986) A Million Fish ... More Patricia C. McKissack (1992) or Less The Hundered Penny Box Sharon Bell Mathis (1975) The Black Snowman Phil Mendez (1989) Grandfather Tang's Story Ann Tompert (1990) Title Cultural Emphasis The Rajah's Rice Indian mathematical folktale Fly Away Home White, homeless populations Sadako and the Thousand Paper Japanese Cranes Two Ways to Count to Ten: Liberian folktale A Liberian Folktale One Grain of Rice Indian mathematical folktale The Patchwork Quilt African American The Girl Who Loved Plains Indian Wild Horses The Village of Round and African Square Houses The Doorbell Rang Multicultural A Million Fish ... More Cajun and African American or Less The Hundered Penny Box African American The Black Snowman African American Grandfather Tang's Story Chinese Mathematics Emphasized in Title the Module The Rajah's Rice Expontential growth, doubling, patterns Fly Away Home Money, addition, subtraction, multiplication Sadako and the Thousand Paper Origami, averages, addition, Cranes subtraction, geometry Two Ways to Count to Ten: Counting to ten, skip A Liberian Folktale counting, multiplication, prime and composite numbers One Grain of Rice Exponential growth, doubling, patterns The Patchwork Quilt Multiplication, fractions The Girl Who Loved Counting, basic operations, Wild Horses algebra The Village of Round and Geometric solids, volume, Square Houses area, polygons The Doorbell Rang Equal sharing, partitive division, multiplication, fractions A Million Fish ... More Place value up to a million, or Less addition, subtraction The Hundered Penny Box Addition, subtraction, money, counting to one hundered The Black Snowman Addition, subtraction, money, percents Grandfather Tang's Story Polygons, spatial sense, fractions
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Barry, David. The Rajah's Rice. New York: W. H. Freeman & Co., 1994.
Bishop, Alan. "Mathematics Education in Its Cultural Context." Educational Studies in Mathematics 19 (May 1988): 179-91.
Bunting, Eve. Fly Away Home. New York: Clarion Books, 1991.
Coerr, Eleanor. Sadako and the Thousand Paper Cranes. New York: Dell Yearling, 1993.
D'Ambrosio, Ubiratan. "Ethnomathematics and Its Place in the History and Pedagogy of Mathematics." For the Learning of Mathematics 5 (February 1985): 44-48.
Dee, Ruby, reteller. Two Ways to Count to Ten: A Liberian Folktale. New York: Henry Halt & Co., 1988.
Demi. One Grain of Rice. New York: Scholastic Press, 1997.
Flournoy, Valerie. The Patchwork Quilt. New York: Dial Books, 1985.
Frankenstein, Marilyn. "Incorporating Race, Class, and Gender Issues into a Critical Mathematical Literacy Curriculum." Journal of Negro Education 59 (summer 1990): 336-47.
Goble, Paul. The Girl Who Loved Wild Horses. New York: Aladdin Books, 1978.
Grifalconi, Ann. The Village of Round and Square Houses. New York: Little, Brown & Co., 1986.
Hutchins, Pat. The Doorbell Rang. New York: Greenwillow Books, 1986.
Joseph, George G. "A Rationale for a Multicultural Approach to Mathematics." In Multicultural Mathematics. Teaching Mathematics from a Global Perspective, edited by David Nelson, George G. Joseph, and Julian Williams, pp. 1-24. New York: Oxford University Press, 1993.
McKissack, Patricia C. A Million Fish ... More or Less. New York: Dragonfly Books, 1992.
Mathis, Sharon. B. The Hundred Penny Box. New York: Puffin Books, 1975.
Mendez, Phil. The Black Snowman. New York: Scholastic, 1989.
National Council of Teachers of Mathematics (NCTM). Curriculum and Evaluation Standards for School Mathematics. Reston, Va.: NCTM, 1989.
Temko, Florence. Origami Magic. New York: Scholastic, 1993.
Tompert, Ann. Grandfather Tang's Story. New York: Crown Publishers, 1990.
U.S. Bureau of the Census. Statistical Abstract of the United States: 1992. 112th ed. Washington, D.C.: U.S. Government Printing Office, 1992. www.census.gov.
Marilyn Strutchens, firstname.lastname@example.org, teaches at Auburn University, Auburn, AL 36849-5212. She is interested in African American students' mathematics achievement, equity issues in mathematics education, and parental involvement in education.…
Questia, a part of Gale, Cengage Learning. www.questia.com
Publication information: Article title: Multicultural Literature as a Context for Problem Solving: Children and Parents Learning Together. Contributors: Strutchens, Marilyn E. - Author. Magazine title: Teaching Children Mathematics. Volume: 8. Issue: 8 Publication date: April 2002. Page number: 448+. © 1999 National Council of Teachers of Mathematics, Inc. COPYRIGHT 2002 Gale Group.