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PROCEEDINGS of INDRUM 2016

First conference of theInternational Network for DidacticResearch in University Mathematics

March 31- April 2, 2016

Montpellier, France

Editors:Elena Nardi, Carl Winslw and Thomas Hausberger

Publisher:University of Montpellier and INDRUM

Place:Montpellier, France

Year:2016

ISSN:2496-1027 (online)

Table of contents

INDRUM 2016 Editorial

6

Plenary talk

10 Mathematics Education Research at University Level: Achievements and Chal- lenges, Artigue Michele 11

Panel28

Current interactions between mathematicians and researchers in mathematics ed- ucation, Bosch Marianna [et al.] 29

TWG1: Calculus and Analysis

32
Le r^ole de la borne superieure (ou supremum) dans l'apprentissage du systeme des nombres reels, Berge Analia 33
A model to analyse the complexity of calculus knowledge at the beginning of

University course, Bloch Isabelle [et al.]

43
Introduire la notion de convergence avec une ingenierie des annees 1980 : r^eve ou realite didactique pour l'enseignant?, Bridoux Stephanie 53
Entree des etudiants dans l'Analyse formelle de debut d'universite : Potentialite des methodes numeriques d'approximation, Ghedamsi Imene 63
Understanding irrational numbers by means of their representation as non-repeating decimals, Kidron Ivy 73

Rationality and concept of limit, Lecorre Thomas

83
Student understanding of the relation between tangent plane and the dieren- tial, Martnez-Planell Rafael [et al.] 93
1 Conceptions spontanees et perspectives de la notion de tangente pour desetudiants de debut d'universite, Montoya Delgadillo Elizabeth [et al.] 103
Concept Images of Open Sets in Metric Spaces, O'shea Ann 113
Comparaison entre l'evolution historique ayant mene aux developpements limites et leur pratique d'enseignement au debut de l'universite : Entre syntaxe et semantique, Rahim Kouki 123
Revenir a la notion de limite par certaines de ses raisons d'^etre : un chantier pour le debut de l'analyse a l'universite, Rogalski Marc 133
Densite de D, Completude de R et analyse reelle - Premiere approche, Vivier

Laurent [et al.]

143
Students' vizualisation of functions from secondary to tertiary level, Vandebrouck

Fabrice [et al.]

153
Angles, trigonometric functions, and university level Analysis, Winslw Carl 163
Comparaison de schemas de geneses didactiques de denitions, le cas de la limite d'une suite., Chorlay Renaud [et al.] 173
Didactical implications of using various methods to evaluate zeta(2)., Kondratieva Margo 175
Introduire les reels a la transition lycee universite: Questions epistemologiques et horizon didactique, Tanguay Denis [et al.] 177
TWG2: Modelling and mathematics in other disciplines 180
Relevant knowledge concerning the derivative concept for students of economics - A normative point of view and students' perspectives, Feudel Frank 181
SRP design in an Elasticity course: the role of mathematic modelling, Florensa

Ignasi [et al.]

191
Teaching Calculus in engineering courses. Dierent backgrounds, dierent per- sonal relationships?, Gonzalez-Martin Alejandro [et al.] 201
Engineering students' use of visualizations to communicate about representations and applications in a technological environment, Hogstad Ninni Marie [et al.] 211
Une approche frequentiste des probabilites et statistiques en premiere annee d'Universite au Vietnam dans un cursus non mathematique, Lagrange Jean-

Baptiste [et al.]

221
2 Quelle synergie entre mathematiques et physique au sein de l'enseignement uni- versitaire ?, Roland Michel 231
A model from signal analysis to design linear algebra activities, Vazquez Rita [et al.] 241

Using the

ipped classroom model of instruction to explore teaching and learning activities in mathematical education for engineers: An activity theory perspec- tive, Fredriksen Helge [et al.] 251
The development of the mathematical discourse of biology students working with mathematical modelling, Viirman Olov 253

TWG3: Logic, Numbers and Algebra

255
From `monumentalism' to `questioning the world': the case of Group Theory, Bosch

Marianna [et al.]

256
Approfondissement du questionnement didactique autour du concept de "borne superieure", Chellougui Faza 266
Procedural and Conceptual Understanding in Undergraduate Linear Algebra, Donevska-

Todorova Ana

276
Designation at the core of the dialectic between experimentation and proving: a study in number theory, Gardes Marie-Line [et al.] 286
A propos des praxeologies structuralistes en Algebre Abstraite, Hausberger Thomas 296
A commognitive analysis of mathematics undergraduates' responses to a commu- tativity verication Group Theory task, Ioannou Marios 306
Should university students know about formal logic: an example of nonroutine problem, Mathieu-Soucy Sarah 316
Learning Linear Transformations using models, Trigueros Maria [et al.] 326
An Inquiry-Oriented Task Sequence for Eigentheory and Diagonalization in Linear

Algebra, Wawro Megan [et al.]

337

TWG4: Teachers' practices and institutions

339
A bridge between inquiry and transmission: The study and research paths at university level, Barquero Berta [et al.] 340
3 On the diusion of professional praxeologies at university level: the case of inves- tigation workshops., Bourgade Jean-Pierre 350
The place of computer programming in (undergraduate) mathematical practices, Bro- ley Laura 360
Envelopes in a computerized environment: the transition from 2D to 3D, Dana-

Picard Thierry [et al.]

370
Moments d'exposition des connaissances a l'universite : le cas de la notion de limite, Grenier-Boley Nicolas [et al.] 380
Addressing large cohorts of rst year mathematics students in lectures, Petropoulou

Georgia [et al.]

390
Study and research paths in online teacher professional development, Romo Ave- nilde [et al.] 400
A commognitive analysis of closed-book examination tasks and lecturers' perspec- tives, Thoma Athina [et al.] 411
A training concept for supervising self-directed problem-solving in the STEM disciplines, Bracke Martin [et al.] 421
Main challenges in teaching/learning of mathematics for cyber-security, Carriegos

Miguel [et al.]

423
Consistency, specicity, reication of pedagogical and mathematical discourses in student teacher narratives on the challenges of their school placement experi- ence, Biza Irene [et al.] 425
Stimulating and facilitating Norwegian RUME, Goodchild Simon 427
Using the interactive visualization tool SimReal+ to teach mathematics at the university level: An instrumental approach, Hadjerrouit Said [et al.] 429
The challenge of being a mathematics teacher, Martin-Molina Veronica 431

TWG5 : Students' practices

433

Anxiety and Personality Factors In

uencing the Completion Rates of Develop- mental Mathematics Students, Fuller Edgar [et al.] 434
Students' work in mathematics and resources mediation at university, Gueudet

Ghislaine [et al.]

444
4 Multiple choice questions and peer instruction as pedagogical tool to learn the mathematical language, Hoppenbrock Axel 454
Quelques dicultes d'etudiants universitaires a reconna^tre les objets "droites" et "plans" dans l'espace: une etude de cas, Nihoul Celine 464
Making sense of students' sense making: Revisiting the case of Colin through the lenses of the structural abstraction framework, Pinto Marcia [et al.] 474
Uneetude de l'autonomie en mathematiques dans la transition secondaire-superieur, Quere

Pierre-Vincent

484
Activity and performance on a student-centred undergraduate mathematics course, Ramo

Johanna [et al.]

494
Ways in which engaging in someone else's reasoning is productive, Rasmussen

Chris [et al.]

504
Comparative analysis of learning gains and students attitudes in a ipped precal- culus classroom, Voigt Matthew 514
Supporting students gifted in mathematics through an innovative STEM talent programme, Bracke Martin [et al.] 523
Diculties to teach mathematics and beliefs on mathematical modelling by prospec- tive teachers, Cabassut Richard 525
MetaMath and MathGeAr Projects: Students' perceptions of mathematics in engineering courses, Filho Pedro Lealdino [et al.] 527

Sponsors and participants

529

Author Index531

5

Editorial

Elena Nardi1, Carl Winsløw2, Thomas Hausberger3

1University of East Anglia, E.Nardi@uea.ac.uk

2University of Copenhagen, Winslow@ind.ku.dk

3University of Montpellier, thomas.hausberger@umontpellier.fr

The International Network for Didactic Research on University Mathematics (INDRUM) was founded at CERME9 (9th European Congress on Research in Mathematics Education) in Prague, February 2015. A scientific committee of 18 scholars from 12 different countries was set up to plan a first INDRUM conference in the spring of 2016; it was decided that this congress was to be held in Montpellier, France, and an organising committee with 12 members from Montpellier, Barcelona and Paris was established shortly after. At CERME9, the board of ERME (European society for Research in Mathematics Education) launched a call for proposals on

ERME Topic Conf

themes related to the work of ERME as presented in associated working groups at Working Group on University Mathematics Education, in which most of the founding members had participated in CERME9 or at the two preceding ERME conferences (CERME8, CERME7) where this TWG had convened. The proposal for the first INDRUM conference, drawn up in the months following CERME9, was accepted by the ERME Board as the second in a series of (by now, three) ERME topic conferences.quotesdbs_dbs31.pdfusesText_37

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