Language and Thought in Mathematics Staff Development: A Problem Probing Protocol

Abstract

Background/Context

The theoretical framework of the paper comes from research on problem solving, considered by many to be the essence of mathematics; research on the importance of oral language in learning mathematics; and on the importance of the teacher as the primary instrument of learning mathematics for most students. As a nation, we are not doing well enough in teaching our students mathematics, and we need to look to new perspectives about why this is happening.

Purpose

This paper looks at a promising tool for enabling students who are not skilled readers to approach problem solving tasks. But in sharing its usefulness with teachers in professional development, the instrument uncovered specific and serious gaps in teacher content knowledge. Group discussion, using the protocol, helped to clarify some of those gaps.

Setting

All three problem-probing sessions occurred during professional development activities for New York City Public School mathematics teacher leaders. The facilitator was Academic Director of a New Visions for Public Schools’ Middle School Mathematics Standards project, (MS)2, funded by NSF. The sessions were part of a variety of ongoing professional development activities, and occurred during the third year of a five year study. Therefore, the 12 to 20 participants of each session, though different from each other, all knew the facilitator.

Research Design

The research design was qualitative. Teachers were presented with a written problem and directed not to solve it. The discourse that followed flowed of its own accord, with participants speaking as they thought and responded to the facilitator and/or the other participants. Records of speakers’ words were transcribed in one case by hand, and in two other cases by audio tapes. The discourse was then analyzed by the researcher from two perspectives: what mathematical misconceptions were revealed and how the talk helped to clarify them.

Conclusions/recommendations

From preliminary explorations, the protocol seems an accessible and effective instrument for decoding and analyzing mathematics word problems by teachers who were not able to approach such tasks before. Also suggested was its potential value as an assessment instrument for teachers’ content knowledge. Further study is needed to determine what kinds of in-class supports teachers need to internalize the process and use this instrument on a regular basis with their students.

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