Understanding of Inverse Proportional Reasoning in Pre-Service Teachers

Abstract

From an early age, understanding proportional reasoning is a fundamental pillar in mathematics education, and therefore, teachers should have a thorough knowledge of it. Despite its significance, there are few studies that analyse the difficulties that student teachers have in understanding proportionality, and even less so inverse proportionality. We emphasised inverse missing-value problems by analysing them according to the type of unknown and the representation used. We checked which strategies they use to solve them and related them to other generic problems of proportional reasoning. For such purposes, we used a combined quantitative and qualitative empirical study applied to how pre-service teachers solve fifteen problems. The results show that the representations used in the statements aid their understanding and help solve the problems. Similarly, it is shown here that certain problem-solving strategies complicate proportional reasoning in pre-service teachers.

Keywords

• inverse proportionality
• problem-solving strategies
• intensive quantity
• extensive quantity
• proportional reasoning
• tabular and graphic representation