Conceptual and representational confusion: An analysis of three foundation phase teachers’ descriptions of how they teach division

Abstract

Background: In the foundation phase, division is split along the lines of grouping (quotition) and sharing (partition). Curriculum and Assessment Policy Statements (CAPS) recommends that representations such as drawings, concrete apparatus, and symbols are used to teach all math concepts, including division.

Aim: In this article, the author investigates how three foundation phase teachers describe teaching division and the representations they would use to do this.

Setting: Grade 1 and Grade 2 teachers in one previously disadvantaged urban school were selected for this study.

Methods: Semi-structured interviews were used to gather information about how the teachers say they teach division. They were invited to use or talk about any representations such as actions, apparatus, drawings or writings that they would use during their teaching.

Results: Using a grounded theory approach, analysis of the data showed that all three teachers talked about how they would transform the mathematics in a division word problem into actions, drawings and symbols. However, none of them was able to use their representations to find the answer to the problem or to provide a division number sentence. The representations they used were relegated to end results and served no purpose in solving the mathematical problems.

Conclusion: The results show areas in which teachers need support:

• Their own mathematical knowledge – specifically division in the case of this study
• How to teach division in the foundation phase.

They lack both content knowledge and pedagogical knowledge.