The creation of didactic tasks on mathematics in MS EXCEL

The article studies an example of using Microsoft Excel in pre-university mathematics education. The process of creating multivariate didactic assignments, using Microsoft Excel, is described. Possible ways of formatting for the correct display of the created didactic material are also examined.

First Year Students’ Resilience to Cope with Mathematics Exercises in the University Mathematics Studies

University mathematics studies are known for high dropout especially in the freshmen year. This dropout is often traced back to the excessive demands freshmen have to face. Research aimed at identifying students’ characteristics that enable them to overcome the demands, for example through cognitive abilities, motivational constructs or self-beliefs. In this paper, we take a different perspective and suggest to include a construct that has not been considered in university mathematics education so far: mathematical resilience. Mathematical resilience is a well-established construct in school education to describe students’ attitude in handling everyday educational challenges like setbacks or frustration. We aim to transfer the construct to university mathematics education. Based on a literature review, we argue that the weekly mathematics assignments (i.e., compulsory exercises) pose a major emotional challenge for freshmen as they require advanced mathematical skills like proving, which students only scarcely learn at school. Failing at those mathematics exercises can lead to lasting frustration and, eventually, dropout. Mathematical resilience may thus be a relevant construct to consider when investigating dropout. We present a novel instrument measuring mathematical resilience against mathematics exercises. Findings of an empirical study with 424 mathematics freshmen confirm that mathematics assignments are in fact viewed as the most frustrating everyday challenge. Moreover, the data provide evidence on the validity and reliability of the novel instrument. The results show that mathematical resilience and the corresponding instrument contribute to research on academic success and failure of mathematics freshmen considering the specific conditions of university mathematics studies.

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.

The external didactic transposition of mathematics at the university level: dilemmas and challengesLa transposition didactique externe des mathématiques au niveau universitaire: dilemmes et défis

RésuméNous développons l’idée que la recherche en didactique des mathématiques au niveau universitaire devrait étudier d’une manière plus systématique la transposition didactique externe. Après avoir présenté sommairement la recherche qui semble aller dans cette direction, nous commentons pourquoi et comment cette ligne pourrait se poursuivre dans la recherche en TAD sur l’enseignement universitaire.Mots -clés : Théorie anthropologique de la didactique, Transposition didactique externe, Mathématiques au niveau universitaire.AbstractWe develop the idea that research on university mathematics education needs to more systematically address the external didactic transposition. After outlining existing research that goes more or less in this direction, we comment on the why and how this direction could be pursued by ATD research on UME.Keywords: Anthropological theory of the didactic, External didactic transposition, Mathematics at the university level.

Transition to university: contributions of a specialist mathematics school

School-university transition in mathematics is of global concern, with multiple cognitive, social and affective disjunctures evidenced. Access to, successful participation in and retention on, competitive mathematically intensive degree courses remain particular challenges in England, especially for disadvantaged young people with high mathematical aptitude. One response has been to establish mathematics specialist schools aimed at such students aged 16–18. Early cohorts have achieved encouraging progression to and through such university courses, but more qualitative and longitudinal outcomes have been less well evidenced. The reported study harnessed a student lens and documentary scrutiny to analyse the contribution to building for successful transition of the particular approaches used. Data suggest that the model adopted has initially supported transition to target degree courses well. I relate the findings to known transition challenges in the global issue of successful passage into and through university mathematics education. I argue many of those are in principle transferable to other post-16 contexts. The study therefore offers evidence suggesting broadly applicable specific strategies that can begin to address widely problematic disjunctures in transition.