Abstract
This case study research was carried out with eight pre-service teachers enrolled in a non-thesis Masters degree program at the university where the author works after having earned undergraduate degrees in mathematics from different universities in Turkey. The study is part of a large-scale study. The main part of the study aimed to identify the conceptions of participants about proof and proving in a period of ten weeks. The present study contains the preliminary findings regarding the participants' opinions about the meaning of proof and proving and the purposes of proof. Three groups of data were used in this article. The first group involves the essay writing of pre-service teachers; the second group involves whole group discussions; and the last group contains individual semi-structured interviews. The results demonstrate that the pre-service teachers often prefer using formal discourse to define proof but have certain difficulties in making sense of these definitions. The general opinion of the participants about the purposes of proof concentrates on verification and explanation. Another problem examined in the study was concerned with whether the pre-service teachers' opinions about the meaning and purposes of proof can change. The results showed that their opinions may change regarding both. However, the changes involved expansion of their previous opinions by adding new dimensions, without moving in another direction.
Highlights
Proofs are among the key instruments in the development of mathematics even to the present day
The definitions of pre-service teachers are more or less similar, and from the common points in all of their responses, we could obtain the following primitive definition: “Proof is the verification of a mathematical statement”
It is seen in the table that out of eight individuals, seven used the term ‘verification’ in their definitions, which gives a general idea about what the pre-service teachers think of the purposes of proof
Summary
Proofs are among the key instruments in the development of mathematics even to the present day. What proof is has long been a subject of debate among mathematicians, philosophers and educators (LEE, 2002; HEALY; HOYLES, 2000; HANNA, 2000) These debates originated both from the fact that proof is complex in itself - an activity that can be performed on the basis of a series of mental and logical processes in a variety of different ways and from the rich diversity of its functions. The curriculum designates proof as a sub-learning domain within the domain of logic learning included among the first subjects of grade 9, and uses a scheme with regard to the methods of proving Following these observations about the mathematics curriculum, it could be concluded that the new curriculum attaches relatively greater importance to proof. Today’s teachers are mainly expected to gain insight into the notional changes about teaching proof within the framework of reform movements, and to educate themselves and later their students in line with this notion
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