Modelling of real-world problems is often the starting point for proof

Vimolan Mudaly

doi:10.4102/pythagoras.v0i60.125

Abstract

In this paper I claim that modelling should be seen as the first stage of the proving process. I discuss an experiment conducted with grade 10 (15 year old) learners in a small suburb in South Africa. There is little emphasis placed on modelling in our schools and it is just beginning to make an appearance in our new Outcomes Based Curriculum. The research shows that as a result of the modelling process learners felt the need to know why the result was true. There is ample evidence that a lot of work on a similar topic has been done elsewhere in the world, but not much has been done in South Africa. The research was conducted using Sketchpad as a mediating tool. This in itself was a difficult task because our learners have not really been exposed to dynamic geometry environments.

Highlights

Proof is often only seen as a means of verifying the truth of mathematical statements
A survey conducted in 1984 by De Villiers (1999: 18) revealed that more than 50 % of Higher Education Diploma students in mathematics education agreed that the only function of proof was that of “making sure”, that is, the verification of the truth of the results
This is a perception that is commonly propagated in mathematics classrooms, where teachers focus on the verifying of mathematical truths that are being investigated

Summary

Introduction

Proof is often only seen as a means of verifying the truth of mathematical statements. Hodgson and Riley's argument that real-world problems could be the basis for mathematical proof stems from one step in the modelling process, namely, the testing of the solution They believe that it is essential for students to ask "why is the statement true?" after they have arrived at a solution. A further significant argument which shows this direct link between modelling and proof is made by Blum (1998) when he states that applications in mathematics (solving of real-world problems) provide contexts for what he refers to as reality-related proofs He clearly points out that: formal proofs are mostly the final stage in a genetic development – historically as well as epistemologically as well as psychologically. This study tested curriculum material that was developed (De Villiers, 1999)

Mathematical conclusions

Mathematical conclusions simulation

Findings

Conclusion