draft 1 and questions

An Analysis of Teachers’ Mathematical Judgement through the Talk of Algebra Scenario

Jill Adler

Jill.Adler@wits.ac.za

 Sitti Maesuri Patahuddin

Sitti.Patahuddin@wits.ac.za

University of the Witwatersrand

This paper arises from a larger study the Wits Maths Connect-Secondary Project (WMC-S) in which The Developing Mathematical Judgement project (DMJ) is the core project. This short paper reports on the analysis of one mathematical scenario posed to 30 secondary mathematics teachers at the beginning of the project, as a part of the base line data. This analysis informs the quality of teacher mathematical judgement and identifies determinant factors. This finding supports the notion that subject matter content knowledge is the key element of the quality of mathematical judgement. The implication of this finding to the project will be also discussed.

Several questions we must answer:

1.       What is actually mathematical judgment? Is it ability? Is it skill? Is it a specific knowledge? Is it something that can be measured easily? If it is not easy, then how do we measure it?

2.       If we want to develop teacher mathematical judgement, so we should know how to assess teacher’s mathematical judgement at a pointing time.

3.       How much Scenario 3 would enable us to measure teacher mathematical judgement?

4.       What does a good quality of mathematical judgement look like in responding Scenario 3? [If we want to assess the quality of teacher’s mathematical judgement, then at least we know what good or poor mathematical judgement looks like?

5.       What subject matter knowledge needed to be able to give a good quality mathematical judgement on Scenario 3?

6.       To what extent teacher’s subject matter knowledge leads to poor or [valid/rich] mathematical judgement on Scenario 3?

7.       What types of subject matter knowledge appears to influence teacher’s mathematical judgement on Scenario 3?

8.       Shulman etc have identified or categorised knowledge needed by teachers. Then in which domain this mathematical judgement fall into?

I am hoping that my initial analysis will help us in answering those questions.

 

This scenario productively provoked teachers to perform their mathematical judgment, which is believed to be related to the quality of mathematical judgment occurred in the process of mathematics teaching and learning in their class.