Although the notion of "assumptions" is important in mathematical activity as early as the elementary school, there is limited research on how to help elementary teachers develop "mathematical knowledge for teaching" related to assumptions. In this paper, we discuss the theoretical foundation and implementation of an…

Personal epistemological beliefs are considered to play an important role for processes of learning and teaching. However, research on personal epistemology is confronted with theoretical issues as there is conflicting evidence regarding the structure, stability, and context-dependence of epistemological beliefs. We give evidence how theoretical…

The goal of this study is to identify the characteristics of pre-service primary teachers' configural reasoning, understood as the relationships between concepts and figures set to solve geometrical proof problems. Ninety-seven primary teachers were asked to solve two geometrical proof problems in which a geometrical figure was provided. The…

In this paper, 28 mathematics majors who completed a transition-to-proof course were given 10 mathematical arguments. For each argument, they were asked to judge how convincing they found the argument and whether they thought the argument constituted a mathematical proof. The key findings from this data were (a) most participants did not find the…

Current college admissions tests inadequately predict college success (Geiser & Studley, 2002) and provide insufficient information for students and teachers regarding college readiness at earlier stages of students' academic careers (Olson, 2006). This article reports on the creation and validation of a more informative test rooted in college…