This phenomenology research aims to examine prospective elementary mathematics teachers' proving and proof evaluation and their thoughts on convincing according to proof type and argument type. The participants were eight prospective teachers. The data collection tools were semi-structured group interviews, interviews video recordings and the…

Proof is central to mathematics and has drawn substantial attention from the mathematics education community. Yet, valid and reliable measures of proof comprehension remain rare. In this article, we present a study investigating proof comprehension via students' summaries of a given proof. These summaries were evaluated by expert judges making…

Two questions about certainty in mathematics are asked. First, is mathematical knowledge known with certainty? Second, why is the belief in the certainty of mathematical knowledge so widespread and where does it come from? This question is little addressed in the literature. In explaining the reasons for these beliefs, both cultural-historical and…

There is an increasing demand from employers and universities for school leavers to be able to apply their mathematical knowledge to problem solving in varied and unfamiliar contexts. These aspects are however neglected in most examinations of mathematics and, consequentially, in classroom teaching. One barrier to the inclusion of mathematical…

Formative assessment involves the gathering of information that can guide the teaching of individual or groups of children. This approach requires a sound understanding of children's thinking and learning, as well as an effective method for gaining the information. We propose that formative assessment should employ a version of clinical…

The purpose of this study was to examine pre-service teachers' teaching practice in terms of providing suitable conditions for developing students' mathematical thinking in the frame of the Advancing Children's Thinking framework. In the study, Advancing Children's Thinking framework developed by Fraivillig et al. was adopted as theoretical…