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Summary of Reference

Author:
Lampert, Magdalene

Title:
Choosing and Using Mathematical Tools in Classroom Discourse

Bibliographic data:
Lampert, M. (1989). Choosing and using mathematical tools in classroom discourse. Advances in Research on Teaching, 1, 223-64.

Summary: 
Children learn new mathematical content at schools through learning to do new things and learning a new language, in part involving new symbols. Students may be guided by their teacher in the process of constructing meaning for the operations and symbols so that what is learnt is related to the central concepts of the discipline.

The paper sets a number of questions relating to mathematical pedagogy, directed towards understanding what it takes to teach students about doing mathematics at school.

All of the conceptual frameworks - mathematical, psychological and philosophical - require the teacher to reflect on the mathematical principles and the mathematical forms of reasoning that underlie the competence desired for the student. Successful instruction also depends on an assessment of what the student could find difficult about those principles and on the appropriate methods that could be useful to confront the difficulties successfully.

The paper explains in some detail the processes used by Lampert as she decided what to teach a fifth grade class for a unit on decimals and how to teach it. She used three representational tools (money, the number line and pieces of a circle) rather than numerical symbols and the words of English as they were more meaningful to the students. The lessons described then move to teaching students how to use representational tools and then teaching them to choose to use those tools to reason about comparisons among numbers written as decimals.

The kind of mathematics teaching described in the paper could result in students becoming independent and confident users of mathematics. There are, however, significant problems involved in making this sort of teaching practical and widespread in schools. They include:

  • the social structure of the classroom and the extent to which it can be altered to accommodate the students and teacher arguing about mathematical assertions
  • determining what teachers need to know to do this kind of teaching and how to educate them to do it.