No abstract

It is of critical importance, in particular, for mathematics teachers who will teach future generations to understand and do mathematical proofs. It is important to determine future teachers' beliefs about and difficulties with proofs because their knowledge of this issue affects their teaching. This study aims to determine and compare the proof schemes of prospective mathematics teachers from two state universities, one in Turkey and the other in Spain. The case study was conducted within this study. The participants were 51 prospective teachers at their second year from the department of teaching mathematics education at Huelva University in Spain and 45 prospective teachers from the department of teaching mathematics education at Cumhuriyet University in Turkey. The Proof Test consisted of four questions about proofs for parallelograms. Semi-structured interviews were subsequently conducted to investigate the prospective teachers’ responses in-depth. The findings suggest that prospective teachers from Turkey and Spain indicated affinity in proving. The majority of the prospective mathematics teachers were either unable to complete the proof or completed the proof in an inaccurate way.

In mathematics the process of visualization requires the process of forming and manipulating images to explore and understand. Indeed, according to mathematicians, it is difficult to understand without visualization. There is consensus that visual proofs are important tools in mathematics education. However, there is no consensus on the effects of the visualization on proof. Therefore, this study aims to reveal the relationship between van Hiele levels of geometric thinking, spatial ability and visual proofs. In this study, relational survey method is used. The study is conducted on 85 pre-service elementary mathematics teachers studying in the Faculty of Education at a public university located in Turkey. The data is analyzed via Spearman correlation. In the study, it was seen that most of the elementary mathematics teachers were at the 3rd level of van Hiele's geometric thinking. Another result is that there is a significant relationship between van Hiele's level of geometric thinking and visual proof skills. However, there is no significant relationship between visual proof skills and spatial ability. The relationship between visual proofs skills and spatial ability can be investigated deeply with qualitative research. Moreover, experimental studies can be done to investigate the effect of training on visual proofs on the level of van Hiele geometric thinking.

There are opinions about approaching the proof in mathematics education need to change as providing students to understand the mathematical proof rather than developing formal mathematical proof skills. In this context, proofs without words described as informal proofs can be used in proof teaching. The purpose of this study was to investigate the processes of high school students to do proofs without words. This study was designed as the case study a high school in Turkey. Consequently, activities of proof without words that allow the student to take an active role in the proof process can be presented as an alternative method in proof teaching and the proof without words can be used for teaching students the stages of proof process. It is necessary for teachers to be aware of the proof process stages and guide the students.

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 preservice 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.

No abstract

No abstract

No abstract