Voices in Urban Education

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Extending Learning
VUE Number 16, Summer 2007

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EXCERPT:
Understanding and Supporting Children's Mathematical Learning Lives

By Sophia Cohen and Dennie Palmer Wolf

Sophia Cohen is a consultant in mathematics education and mathematics education research.
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Dennie Palmer Wolf is director of opportunity and accountability at the Annenberg Institute for School Reform.
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A documentation of students’ “learning lives” reveals an untapped opportunity to connect mathematical learning in and out of school.

Children build a foundation for logical and mathematical thinking from their actions and reflections. Logical and mathematical thinking further evolves as children engage in social interactions, games, commercial transactions, and discussions with others. As students they encounter conventional representations and reasoning practices that will affect the course and even the nature of their mathematical thought. A theoretical account of mathematical reasoning requires uniting the findings of developmental psychology, everyday mathematics, and mathematical learning in schools. It will also require a careful analysis of the structure and semiotics of mathematics itself.
—Analucia Schliemann and David Carraher, “The Evolution of Mathematical Reasoning”

Schliemann and Carraher (2002) remind us that children create their mathematical understanding not only in mathematics class, but also in a variety of other activities. For example, children experiment in science with race cars on ramps, engage in the quick, implicit calculations of catching a fly ball, or watch in amazement as a grandmother does her neighbor’s taxes without ever reaching for a calculator. This lived quality of children’s mathematics — and its implications for their learning — is our focus in this article.

Using data on mathematics teaching and learning in an urban district, we explore three main points:

• Young people’s mathematical thinking develops across many contexts, both in school and out of school. For instance, what a student learns in mathematics class may shed new light on a fence the student helps build at home; and what that student learns while building the fence may provide a sharper understanding of topics explored in mathematics class, like measurement or shape.
  
  
• We need to understand the particular “genius” of each of these different mathematics contexts in order to figure out how each one might support children’s engagement with and understanding of mathematics.
  
  
• We need to consider how best to connect these multiple resources into comprehensive learning systems for mathematics that make use of the many contexts in which children develop their mathematical thinking.

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