Forum Outposts

The Geometry Forum Newsletter

Spring 1995, page 2

Learning & Mathematics Discussions:
Research in Math Education

The Geometry Forum offers the only newsgroup of this kind, where research summaries are prepared for purposes of discussion by a wide community of educators, many of whom are not familiar with the literature summarized. The Learning and Mathematics Discussions provide readers with an opportunity to raise questions, share insights, and 'test the waters'. Each discussion consists of a summary of work by math researchers or educational psychologists followed by an open discussion among readers. A new summary is posted every two weeks, although some discussions last well beyond this time frame.

Much of the work in the area of the NCTM Standards indicates that the 'traditional' classroom needs to be changed if more effective learning (learning that is more conceptual and less formulaic) is to take place. The summaries of articles posted to the group include implications for classroom practice.

Following is a sampling of responses to the posting of some ideas of Magdalene Lampert of the Institute for Research on Teaching at Michigan State University. Lampert advocates incorporating students' intuitive knowledge about mathematics into classroom lessons and encourages putting new concepts into familiar contexts so that students may more readily relate to the problems being investigated. She believes that the teacher's role in the classroom is to help students make explicit their ideas about analyzing and solving problems, to act as referee in arguments about the reasonableness of competing ideas, and to sanction students' intuitive use of mathematical principles.

• Lampert's article is an outstanding contribution to mathematics education because it blows up the long-standing "procedural knowledge (computational/symbolic) vs. conceptual knowledge (understanding)" debate. Instead, Lampert argues, students need to learn both for mathematical development (though, consistent with her theory of building upon intuitive understanding, she does advocate a delay in the introduction of symbolic knowledge). Lampert's work addresses positively, for a change, the relation between intuitive understanding and knowledge of symbolic procedures, and it provides us with some concrete examples of this integrated understanding in the form of her lessons. -- Maria Ong Wenbourne, U.C. Berkeley

• ... most teachers know that students gain a better understanding of a subject if the student is given the opportunity to verbalize or make sense of the information him or herselfÉ this technique is often neglected in the realm of mathematics. -- Hilary Gehlbach, Swarthmore College

Problem of the Week - March 13-17, 1995

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