Abstract
Recently, studies have been carried out on alternative proof methods due to the change in the perspective of teaching proof and the difficulties of learners in proof. In this context, proof without words, which are presented as an alternative to proof teaching, defined by diagrams or visual representations and require the student to explain how proof is, are discussed in this study. The aim of this study is to examine pre-service mathematics teachers' explanations of proof without words about the sum of consecutive numbers from 1 to n. The data were collected by the proof of the sum of consecutive integers. 27 pre-service teachers from a university in the Middle Anatolia region participated in this study, which was conducted using a basic qualitative research design. At the end of the study, it was seen that most of the pre-service teachers were unable to explain the proof without words of the sum of integers from 1 to n. One of the reason for this may be related to the spatial thinking skills of pre-service teachers. However, there are pre-service teachers who can interpret the visual given in the proof correctly, use the necessary mathematical knowledge, but cannot generalize using the given visual. The reasons why the pre-service teachers could not express the general situation are considered as the lack of algebraic thinking.
Highlights
Proof plays an important role in the development of mathematical thinking skills
Heinze and Reiss (2004) state that formal proof can be done by experts, and this will not happen in school mathematics
The purpose of this study is to examine the explanation of pre-service secondary mathematics teachers the proof without words which is related to the sum of consecutive numbers from 1 to n
Summary
Proof plays an important role in the development of mathematical thinking skills. For this reason, it has been an important part of mathematics education at all grade levels. Finding a new proof is not possible at all levels. The proof is a ritual without understanding (Ball, Hoyles, Jahnke, & Movshovitz-Hadar, 2002). In this context, the perception towards proof has begun to change especially in recent years. How students' deeper understanding of mathematical proof is seen as a difficult research area (Marrades & Gutierrez, 2000)
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