The Alpha and Omega of Teacher Education: Organizing Mathematical Activities

The aim of this paper is to describe an introductory mathematics course for primary student teachers and to explain the philosophy behind it. The paper is structured as follows: It starts with a general plea for placing the mathematical training of any category of students into their professional context. Then the context of primary education in Germany, with its strong emphasis on the principle of learning by discovery, is sketched.

About the “Mixture” of Discourses in the Use of Mathematics in Signal TheoryÀ propos du «mélange» de discours dans l'utilisation des mathématiques en théorie du signal

An important issue for research in university mathematics education is the use of mathematics in engineering. Here we focus on praxeologies in a course on system and signal theory (SST), which represents a typical module in electrical engineering studies in the third or fourth semester. In such courses, mathematics already studied in introductory mathematics courses will be applied, but also enriched by the introduction and development of new practices, in particular the so-called Dirac-impulse. We claim that the introduction and justification of the Dirac-impulse in SST is a convenient case where basic facets of epistemological relations between mathematics and engineering sciences might be illustrated and shown to be important for a detailed description and analysis of logos blocks of praxeologies. The background for our considerations regarding logos blocks of praxeologies that concern the introduction of the Dirac-impulse is given by philosophical studies by Wahsner and Borzeszkowski (1992, 2012) and a few illuminating remarks by Dirac.Keywords: Signal Theory, Dirac impulse, Epistemology, ATD.RésuméUne question importante pour la recherche en éducation mathématique universitaire est l'utilisation des mathématiques en ingénierie. Ici, nous nous concentrons sur les praxéologies dans un cours sur la théorie du système et du signal (SST), qui représente un module typique dans les études d'ingénierie électrique au troisième ou quatrième semestre. Dans ces cours, non seulement applique-t-on les mathématiques déjà enseignées et apprises dans les cours d'introduction à la mathématique, mais on introduit et utilise aussi de nouveaux concepts mathématiques, en particulier ce que l'on appelle l'impulsion de Dirac. Nous affirmons que l'introduction et la justification de l'impulsion de Dirac dans SST est un cas pratique par lequel les facettes fondamentales des relations épistémologiques entre mathématiques et ingénierie pourraient être illustrées et démontrées importantes pour la description détaillée et l’analyse des logos blocs de praxéologies. Le contexte de nos considérations au sujet des logos blocs de praxéologies concernant l'introduction de l'impulsion de Dirac est donné par des études philosophiques de Wahsner et Borzeszkowski (1992, 2012) et quelques remarques éclairantes de Dirac.Mots-clés: Théorie du signal, impulsion de Dirac, épistémologie, TAD.

Making Mathematics Accessible to Non-Mathematics Majors

The purpose of this workshop is to present alternative strategies of instruction that will make the subjects of mathematics and statistics more accessible to students with non-mathematics backgrounds. It is not surprising that introductory mathematics and statistics courses can seem a little overwhelming and inaccessible to students with non-mathematics backgrounds. As a result, these students tend to feel distanced from the course material, or even discouraged from approaching instructors or teaching assistants (TAs) for help. The audience for this workshop includes graduate student TAs, post-doctoral fellows, instructors, lecturers, and anyone who wants to make mathematics and statistics a more engaging subject for students without the technical background. The focus of this workshop will be two-fold. First, we will examine how mathematics/statistics instructors can explain concepts to students of different backgrounds effectively via various role-play scenarios. Second, we will use the jigsaw technique to break up complex mathematical problems into pieces with the aim of encouraging collaboration and student engagement (Perkins & Saris, 2001). By attending this workshop, instructors will be able to help undergraduate students see mathematics as a more enjoyable learning experience that they can apply in their own respective fields. These two activities will help students with non-mathematical backgrounds feel more engaged with the material and become more confident when asking for help from an instructor or TA.

Using STACK to support student learning at masters level: a case study

The development of six online quizzes to support students’ study of an introductory mathematics masters module at The Open University is described and their use evaluated. The quizzes were implemented using the STACK online e-assessment system, which is powered by a computer-algebra engine. Evaluation of student feedback and an initial quantitative study of the effect of engaging with the quizzes on the final examinations marks suggest that further development of e-assessment at mathematics masters level is warranted.