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School of Education at the University of Wisconsin-Madison

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What's The Research On...?

Mathematics Education

WCER has long been known as the home of Cognitively Guided Instruction (CGI) for elementary students and Mathematics in Context (MiC) for middle grades students. Mathematics instruction should take as its starting point the centrality of student thinking. From that vantage point mathematics instruction becomes more effective, whether itís teaching algebraic concepts in the elementary grades or geometry in the middle grades.

Development of algebraic reasoning can be fostered in all students and should be integrated with the learning of other mathematics. WCER research has enhanced teachers' understanding of the kinds of algebraic thinking that needs to occur in elementary school mathematics. When given the opportunity, elementary students learn to adapt their thinking about arithmetic so that it provides a stronger foundation for making the often difficult transition to learning algebra.

Teaching mathematics involves uncovering and correcting information children bring with them; for example, students develop concepts about the 'equals' sign earlier than was supposed. When math teachers know more about students' thinking about space and geometry, students learn more, and this advantage is maintained over time. Promoting student contributions to classroom discussion about mathematics enhances learning, as long as teachers monitor where the discourse is going and have criteria for deciding when the class has reached the goal.

Professional development for mathematics teachers benefits student achievement when it promotes opportunities for teacher collaboration and when it supports experimentation. WCER research has evaluated summer institutes that create extended learning communities whose members participate in a wide spectrum of math and education activities. Researchers have contributed to the PBS Mathline program, which offers math teachers local professional development via collaborative learning communities. Studies found that teachers participating in the Urban Mathematics Collaborative created change in their knowledge and beliefs, in their classroom practices, and in their professional development.