Mathematics education undergraduates’ personal definitions of the notion of angle of contiguity in Kinematics

The concept of a mathematical definition causes severe difficulties among students during problem solving and proving activities. Students’ difficulties with the use of mathematical definitions often arise from the fact that students are often given those definitions instead of constructing them. With the aim of developing an understanding of the kinds of student teachers evoked concept images of the notion of angle of contiguity, a qualitative case study was conducted at one state university in Zimbabwe. Purposive sampling was used to select 28 mathematics undergraduate student teachers who responded to a test item. Qualitative data analysis was guided by ideas drawn from the theoretical framework of Abstraction in Context and idea of imperative features of a mathematical definition. Student teachers written responses revealed that student teachers personal concept definitions consisted of ambiguous and irrelevant formulations that did not capture the essence of the idea of the angle of contiguity. In some cases their responses were not consistent with the definition of the angle of contiguity. Although there were a few instances of adequate descriptions of the concept, (8 out of 32) these and the inadequate descriptors elicited can contribute significantly towards efforts intended to improve mathematics instruction. Improved mathematics instruction will lead to enhanced conceptualizations of mathematics concepts.

Backward Reasoning and Epistemic Actions in Discovering Processes of Strategic Games Problems

The paper focuses on the cognitive and epistemic characterization of backward reasoning in strategy games resolution. It explores the use of abstraction in context (AiC) theory as a tool for the analysis of the epistemic actions involved in these processes. We follow a qualitative methodology based on design experiments, focusing on a study carried out with mathematics and engineering students. The analysis allowed us to combine the two models derived from the epistemology of mathematical backward reasoning and AiC theory in a unified framework that allowed us to focus both short-term and long-term processes in mathematical activities. Recurring patterns of epistemic actions were identified.

,Abstraction in Context‘ zur Optimierung einer Lernumgebung zum präformalen Beweisen mit digitalen Medien in der Primarstufe

Das Projekt ‚Prim-E-Proof‘ verfolgt das Ziel, Lernumgebungen mit digitalen Medien (Open Source Applets auf Tablet PCs) zur Unterstützung von Argumentations- und Beweisfähigkeiten in der Primarstufe zu generieren. Der Fokus des Projektes liegt darauf, klassische Lehr- und Lernprozesse mit Lernumgebungen, in denen – falls sinnvoll – digitale Medien Anwendung finden, zu unterstützen. In diesem Beitrag werden Schlussfolgerungen für die Weiterentwicklung der ersten Version der Lernumgebung auf Grund von Ergebnissen einer empirischen Untersuchung gezogen.