First‐year secondary school mathematics students’ conceptions of mathematical proofs and proving

Abstract

The aim of this study is to investigate students’ conceptions about proof in mathematics and mathematics teaching. A five‐point Likert‐type questionnaire was administered in order to gather data. The sample of the study included 33 first‐year secondary school mathematics students (at the same time student teachers). The data collected were analysed and interpreted using the methods of qualitative and quantitative analysis. The results have revealed that the students think that mathematical proof has an important place in mathematics and mathematics education. The students’ studying methods for exams based on imitative reasoning which can be described as a type of reasoning built on copying proof, for example, by looking at a textbook or course notes proof or through remembering a proof algorithm. Moreover, they addressed to the differences between mathematics taught in high school and university as the main cause of their difficulties in proof and proving.

Keywords:

• mathematical proof
• mathematics teaching
• students’ conceptions

Acknowledgements

The author would like to acknowledge and express appreciation to the graduate students Ozge Mantu and Hakan Cosgun for their assistance in conducting the questionnaire that was used in this study and helping with the interview transcripts.

Notes

1. By conception we mean “implicit” or “explicit models” that learners refer to, for describing, explaining and understanding an event or a situation. The term “learner” is not restricted to a student who learns in a classroom but it refers, in general, to an individual who has received (or receives) elements of knowledge. As a result, it is possible to talk about conceptions of teachers, students, a given social group or a given individual.

2. Every game has its rules and strategies. The rules and strategies of the game between the teacher and the student‐milieu system, which are specific of the knowledge taught, are called the “didactic contract”.

3. A kind of proof in which the statements (conclusions) are listed in one column, and the reasons for each statement’s truth are listed in another column.