What If We Changed the Book? Problem-Posing with Sixteen Cows

Overview

Featured Resources

From Theory to Practice

 

OVERVIEW

A piece of math-related children's literature, Sixteen Cows, is used to demonstrate the strategy of problem-posing. After hearing the story read aloud, students are invited to brainstorm some literary and mathematical observations to the story. With the teacher’s guidance, students then turn those observations into "what-if" mathematical extensions. These extensions become mathematical problems that students solve, both individually and as a whole class. Since this strategy highlights changing attributes of a story, it underscores for children the range of choices that authors have.

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FEATURED RESOURCES

Problem Posing with Sixteen Cows: This chart illustrates several possible math extensions for Sixteen Cows.

Good Books for Problem-Posing Extensions: This book list includes math-related children’s literature that would work well with the problem-posing strategy.

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FROM THEORY TO PRACTICE

Problem-posing involves taking a “what-if” stance toward a problem, situation, or story. It consists of describing, modifying and extending the attributes of a story. As children list these attributes, they see a world of related stories embedded within the first story (Whitin & Whitin, 2004). It has been argued that the more learners change a given story/problem, the better they understand it (Brown & Walter, 2005). As children have the opportunity to discuss their observations with peers, they are better able to write about the relationships that they see in the story (Short & Harste, 1996). Sorting through mathematical attributes supports children “to analyze situations carefully in mathematical terms and to pose problems based on situations they see” (NCTM, 2000, p. 19). In this lesson, children note the attributes of a story and use these as the basis for their own mathematical extensions.

Further Reading
Whitin, David J. & Phyllis Whitin. 2004. New Visions for Linking Literature and Mathematics. Urbana, IL: National Council of Teachers of English; and Reston, VA: National Council of Teachers of Mathematics.

National Council of Teachers of Mathematics. 2000. Overview of Standards for Grades Pre-K-12. October 2009. Web. http://illuminations.nctm.org/info/standards.asp

Brown, Stephen, and Marion Walter. 2005. The Art of Problem Posing. Hillsdale, NJ: Lawrence Erlbaum.

Short, Kathy and Jerome Harste, with Carolyn Burke. 1996. Creating Classrooms for Authors and Inquirers. Portsmouth, NH: Heinemann.

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