Pre-Service Mathematics Teachers’ Experience with a Dynamic Geometry Environment Whilst Reasoning in Relation to Locus Problems: A Detailed Look at Strategies

Abstract

The purpose of this study was to examine how pre-service mathematics teachers (PMTs) integrated a dynamic geometry environment (DGE) into their reasoning process while solving geometric locus problems. Task-based interviews based on the locus problems were conducted with eight PMTs working in pairs. The PMTs could use a computer with access to GeoGebra in addition to plain papers, pencils, graph paper, a ruler, and a compass in the interview environment. They were free to use any of them. The PMTs’ reasoning was analyzed by focusing on their use of DGE as they were producing mathematical arguments during problem-solving. Toulmin’s argumentation model and Hollebrands’ strategies for using DGE were combined to analyze the data. The results revealed that the PMTs used DGE reactively to make claims and proactively to test or justify their claims. Their proactive use of DGE differed depending on whether they included their warrants for this use or not.

Keywords:

• Reasoning
• argumentation
• dynamic geometry environment
• locus problems

Disclosure statement

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Notes

1 Problem Solving, Reasoning and Proof, Connections, Communication, and Representation (National Council of Teachers of Mathematics [NCTM], 2000).

2 Cabri, Geometer’s Sketchpad, and GeoGebra are all commonly used software programs in mathematics education.

3 All names used in the study are pseudonyms.

4 In a right triangle, the length of the median to the hypotenuse is equal to half the length of the hypotenuse.