The purpose of this qualitative study was to analyze the relationship between argumentation and proof in terms of verbal, visual, and algebraic representations of mathematical concepts. We conducted task-based interviews based on geometric locus problems with six undergraduate mathematics teachers while they were working in pairs. We identified…

In this paper, we demonstrate how atypical visual representations of a triangle, square or a parallelogram may hinder students' understanding of a median and altitude. We analyze responses and reasoning given by 16 preservice middle school teachers in a Geometry Connection class. Particularly, the data were garnered from three specific questions…

Previous research on preservice teachers' understanding of fractions and algebra has focused on one or the other. To extend this research, we examined 85 undergraduate elementary education majors and middle school mathematics education majors' solutions and solution paths (i.e., the ways or methods in which preservice teachers solve word problems)…

One aspect of professional development of mathematics teachers relates to the development of assessment skills. The aim of this study is to examine the effects of engaging prospective mathematics teachers in peer assessment, both as assessors and assessees, on the development of their assessment skills in general and assessment of geometrical…