Archived Information

State of the Art: Mathematics - July 1993

image omitted Teachers need to listen to students and to incorporate into their instruction what they learn from listening.

The first several years of teaching I really was into "This is the section of the book that we're doing today, and here's the practice problems, and now we'll go over homework, and then I'll teach you how to do it, then you'll practice, and then you'll have some to try before you go home," and that kind of thing. I teach very differently now. 
                             (Middle school teacher Becky Wickham 
                            as quoted in Philipp et al. 1992, p. 30)
Teachers who listen to students, and who plan instruction based on what they learn from listening, transform student learning. For example, two children may arrive at the same solution of a problem but with different strategies. These strategies may reflect different levels of understanding and suggest different follow-up activities. Moreover, teachers who listen carefully to students' mathematical explanations often find that their students know a great deal of mathematics at an informal level. By building upon this informal knowledge, teachers can help their students construct more sophisticated concepts.

Effective teachers listen carefully to how students go about solving problems. They know their students' mathematical strengths and weaknesses and they can develop a teaching strategy based on this understanding. Research shows that when teachers act upon their knowledge of student thinking, their beliefs about learning and instruction, their classroom practices and, most importantly, their students' learning and beliefs can be affected profoundly.
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[All students can and must learn mathematics, which should serve as a "pump," not a "filter."] [Table of Contents] [Students learn mathematics best when they construct their own mathematical understanding.]

This page was last updated January 4, 2002 (jca)