Pre-service Secondary Mathematics Teachers’ Behaviors in the Proving Process

Abstract

Pre-service secondary mathematics teachers' (PSMTs) understanding and ability of constructing a proof is not only important for their own learning process, but also important for these PSMTs to help their future students learn how to do proofs. Therefore, this study is focused on and explains PSMTs' behaviors that they revealed throughout the proving process of a proposition. In this qualitative case study, the participants were fifteen volunteer PSMTs from a public university in Turkey. The participants were given a proposition which they were asked to think aloud and prove it on the blackboard. The findings of this study show that PSMTs' behaviors and thoughts regarding the given proposition were limited. In detail, PSMTs had difficulties in application of mathematical language and notations, understanding the meaning of the given proposition, knowing where to get started on a proof, using examples efficiently, using appropriate and efficient methods to construct the proof, and defining logical structures of the proposition to construct the proof.

What should be the object of research with respect to the notion of mathematical proof?

“…Fourth, Ug ǔrel's [20] study on pe-service secondary teachers' behaviors in the proving process is examined. The major goal of the study was to generate insights about the kinds of proof behaviours revealed by pre-service teachers when they proved a given proposition.…”

“…The major goal of the study was to generate insights about the kinds of proof behaviours revealed by pre-service teachers when they proved a given proposition. Ug ǔrel [20] studied 15 volunteer pre-service teachers of whom 5 were male and 10 were female. To solicit data each pre-service teacher was asked to prove a given proposition on the chalkboard by thinking aloud as the student teacher presented the proof.…”

“…However, with Ug ǔrel [20] data collection was a one day event which made it impossible for the study to derive benefits associated with prolonged engagement in the research setting that would have allowed Ug ǔrel [20] to uncover less visible aspects about students' proof behaviour difficult to unravel in a single day as asserted by Maxwell [21]. Further, collecting data on a single day is likely to cause conversational fatigue on the part of participants and even the researchers themselves.…”

An Innovative Approach to Linear Algebra Course: Using Manga Comics

“…One of the main objectives of mathematics teaching is for students to like mathematics, enjoy mathematics and have confidence in their mathematical abilities (Cantürk, 2006). Since attitude is a tendency formed in the previous step before a behavior is exhibited, attitudes developed negatively towards mathematics turn into behaviors by being influenced by other reasons one step later and they constitute an obstacle in achieving success in mathematics teaching (Uğurel & Moralı, 2006). Attitude towards linear algebra course can be expressed as all feelings such as whether they like linear algebra course or not, their self-confidence towards the course, their enjoyment of linear work and their confidence in their abilities.…”

Towards a Comprehensive Conception of Mathematical Proof

“…al. [5]. Hence, if undergraduate mathematics education students do not master the concept of mathematical proof adequately they are less likely to develop it in their own learners in a persuasive manner.…”