1 | 2022

This special guest-edited first issue is co-edited by Nicolas Grenier-Boley, Hussein Sabra, Louise Nyssen and Avenilde Romo-Vázquez.

1. Meeting the challenges of teaching mathematics in higher education today

Nicolas Grenier-Boley ; Hussein Sabra.
Editorial to the first issue of ÉpiDEMES.Among the research in Mathematics Education devoted to higher education, two types of initiativescan be distinguished: those promoting the development of research results and those promotingreflections on mathematics teaching. In both cases, mathematics educators and Mathematicsresearchers have played – sometimes jointly – a leading role. The creation of the journalÉpiDEMES (Epijournal de Didactique et Epistémologie des Mathématiques pour l'EnseignementSupérieur in French) is positioned in the continuity of these efforts.

2. Challenges related to the teaching of mathematics in higher education today

Nicolas Grenier-Boley ; Hussein Sabra ; Louise Nyssen ; Avenilde Romo-Vázquez ; Viviane Durand-Guerrier.
Parmi les recherches en didactique des mathématiques consacrées à l’enseignement supérieur, ondistingue deux types d’initiatives : celles qui favorisent le développement des résultats de rechercheet celles qui promeuvent les réflexions sur l’enseignement des mathématiques. Dans les deux cas, desdidacticien.ne.s des mathématiques et des chercheur.e.s en mathématiques ont joué un rôle moteur,et parfois conjoint. En retraçant quelques éléments liés à l’histoire de ces initiatives, nous verronscomment la création de la revue EpiDEMES (Épijournal de Didactique et Epistémologie desMathématiques pour l’Enseignement Supérieur) se positionne dans la continuité des efforts entrepris.

3. Transition secondaire-supérieur: Ce que nous apprend la recherche en didactique des mathématiques

Ghislaine Gueudet ; Fabrice Vandebrouck.
This article presents a synthesis of international research in mathematics education about the secondarytertiary transition, with a specific interest in the most recent works. These studies may concern students' difficulties, and investigate different factors causing these difficulties: notions become more abstract, expected practices refer to those of mathematicians, the institutional culture changes. Some studies analyze more broadly the practices of teachers and students at the end of high school or at the beginning of post-secondary level. Research in mathematics education provides keys to understanding current practices and their consequences, whether in ordinary courses or in teaching device specially designed to improve the transition from secondary to tertiary education. In some cases, it also proposes innovative courses fostering active student involvement, and highlights the benefits of these courses. The development of initial and in-service training for university teachers could help extend such teaching beyond experimental contexts.

4. The development of mathematics support: teaching and learning practices, scholarship and communities

Duncan Lawson ; Michael Grove ; Tony Croft.
Mathematics support for students is an innovation in the teaching and learning of mathematics which now plays a vital role in their learning experience and which is provided by most universities in the United Kingdom, and increasingly in other parts of the world. This paper describes and reviews research into the development of this provision over the last 30 years or so, providing a rationale for its establishment in terms of student under-preparedness for the mathematical demands of university study, widening participation in higher education and the increasing importance of mathematical and statistical skills to a very wide range of disciplines. The most common model used to provide mathematics support is a 'drop-in' centre which offers one-to-one support to students who attend to see an

5. Research situations for accessing mathematical concepts at university entrance

Isabelle Bloch ; Patrick Gibel.
This article presents a device which is organised in the University of Pau and aims to help first year students to overcome their difficulties and adapt themselves to mathematics of this level. They are invited to become involved in the research of mathematical problems. We present two of these situations and analyse students' productions. These productions show clearly that they have reasoning difficulties and do not master the specific concepts of Calculus in this transition Secondary/University. The device helps students to question the meaning of concepts and then, to fit into the logic of University mathematics.

6. The need for reconstruction: students’ learning of the calculus of bivariate functions

Maria Trigueros Gaisman ; Rafael Martínez-Planell.
This article presents a review of our research on students’ understanding of the calculus of bivariatefunctions. It summarizes findings from studies conducted during 15 years of research on the topic with the aim ofdisseminating our overall results in an accessible format. The results discussed underscore the new challenges thatstudents face when dealing with this new type of function and suggest that the belief that students can easily generalizefrom their knowledge of one-variable functions is not sustained by research, so the different foundational notionsnecessary for the context of bivariate functions need to be considered explicitly during instruction. We include researchbased suggestions that have practical value for teaching these functions, and update the state of research in thisimportant area of the didactics of mathematics, which makes the need for further research apparent.

7. Quelques pistes pour améliorer les usages de l'implication mathématique en début d'université

Viviane Durand-Guerrier ; Zoé Mesnil.
Fresh university students face from the very beginning the need to study and develop by themselves more and more complex reasoning and proofs, which they had little opportunity to make in their secondary studies, including in the scientific tracks. In this article, we focus on the notion of implication. We first come back to the main known difficulties; then we present theoretical tools allowing to foresee and analyze these difficulties. Based on our practice as teachers in undergraduate mathematics and by research in didactics of mathematics, we consider that for the teaching of notions of logic it is necessary to find a balance between a formal approach, which is known to be not effective, and an approach that would eliminate the formal aspects which is also known to be not effective. Then, we will propose activities aiming explicitly to work on aspects related to the notion of implication, while mentioning opportunities for reinvest the knowledge developed during these activities in the teaching and learning of other concepts.

8. The evolution of a study and research path in Statistics

Kristina Markulin ; Marianna Bosch ; Ignasi Florensa ; Cristina Montañola.
We present the organisation of a first course in statistics for Business Administration degree students, which includes a study and research path (SRP) as an inquiry-based teaching proposal. The paper aims to summarise the course’s evolution, design, and reflections on its various components separately and together as a complete unit. The analysis considers three perspectives on the course: those of the students, the lecturer, and the researcher to provide a critical perspective. The discussion includes the joint evolution of the course and the SRP. Under the Anthropological Theory of the Didactic framework, we show that the design and management of the SRP cannot be detached from the course as a whole. We also see how the course components nourish the SRP and how this, in turn, drives the evolution of the course content and adapts it to the students’ professional needs. This inquiry proposal requires a multidimensional approach in both its planning and the dissemination of its outcomes in the research and professional literature. Therefore, our study can contribute to didactics research on SRPs and serve as a starting point for newcomers to inquiry-based teaching, and as a reflection to foster collaborations between researchers in didactics and lecturers.

9. Making UME research accessible and meaningful to the Mathematics community: A Special Issue commentary

Artigue Michèle ; Elena Nardi.
Commentary to the ÉpiDEMES Special Issue aims to offer accessible accounts of University MathematicsEducation (UME) research to the Mathematics community