# Improving multiplicative reasoning in a context of low performance

## Abstract

In this paper we analyze the outcomes of a design experiment that sought to improve the multiplicative reasoning of 12–13 year-old learners across two schools in a South African context of low performance. Using a hybrid theoretical base in Realistic Mathematics Education, variation theory and analogical reasoning, a short-term intervention consisting of four lessons, designed with attunement to classroom culture and levels of learning, was implemented. Outcomes based on pre- and post-testing pointed to substantial gains in both schools, leading to interest in understanding the nature and extent of changes in models and calculation approaches in high performance and high gain item clusters. Increases in appropriate setting up of symbolic models of multiplicative situations and in more efficient calculation are discussed.

## Keywords

Multiplicative reasoning South Africa Low attainment Design experiment RME## Notes

### Acknowledgements

This study is located within the South African Numeracy Chair project at the University of the Witwatersrand. It is generously supported by the FirstRand Foundation (with the RMB), Anglo American Chairman’s fund, the Department of Science and Technology and the National Research Foundation.

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