Development and evolution of instrumented schemes: a case study of learning programming for mathematical investigations

Gueudet, Ghislaine; Buteau, Chantal; Müller, E.; Mgombelo, Joyce; Sacristán, Ana Isabel; Rodríguez, Marisol Santacruz

doi:10.1007/s10649-021-10133-1

Cited by 6 publications

(8 citation statements)

References 21 publications

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“…In this paper, we discuss results that are related to the first research question and that were recently presented at the International Network for Didactic Research in University Mathematics (INDRUM) 2020 conference (Buteau et al, 2020;Gueudet et al, 2020). At the conference, we were interested in investigating a more precise sub-question:…”

Section: School Curricula Are Getting In the Game: Universities Prepa...mentioning

confidence: 99%

“…It also has a limitation: we do not directly observe participants' project engagement. We mitigate this limitation by triangulating all the data available on each participant (Gueudet et al, 2020).…”

Section: How We Are Researching "It"mentioning

confidence: 99%

“…Investigate the mathematical concept (search on the internet, take notes); search for a representation; search for a pattern Concepts-in-action Representation; pattern Theorems-in-action Understanding related concepts helps to formulate a conjecture; an appropriate representation is helpful to find a pattern; I can learn mathematics by exploration Table 1 -Jim's scheme for formulating a mathematical conjecture (Gueudet et al, 2020)…”

Section: Rules-of-actionmentioning

confidence: 99%

“…Code nested loops articulating the nested process; code them incrementally Concepts-in-action Nested system; nested loops; loop Theorems-in-action A nested system can be processed by programming technology as nested loops; incremental coding helps to properly structure the nested loops Table 2 -Jim's scheme for articulating a nested process in a programming language (Gueudet et al, 2020)…”

Section: Rules-of-actionmentioning

confidence: 99%

“…Organize the mathematical process as a nested system; decompose the nested system in individual processes before programming; code individual processes; start by "translating" in the programming language how I would do it by hand Concepts-in-action Mathematics and programming as nested systems; solving-by-hand method; decomposition of a system; individual process Theorems-in-action A mathematical process can be seen as a nested system (i.e., made of many parts); to program a nested mathematics process, one can break it down and individually code the smaller parts; a programming language can work in a similar manner as one works in mathematics by hand; programming and mathematics as systems have embedded layers Table 3 -Jim's scheme of articulating a mathematical process in the programming language (Gueudet et al, 2020) In the above three examples, we illustrate three schemes in the context of Jim's first project, but we also observed these schemes in Jim's later investigation projects. Sometimes the schemes were stable (i.e., we observed the same rules-in-action, theorems-in-action, and concepts-in-action), and other times the schemes evolved (i.e., we observed new or modified rules-in-action, theoremsin-action, or concepts-in-action), depending on the task that Jim faced.…”

Section: Rules-of-actionmentioning

confidence: 99%

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Students using programming for pure and applied mathematics investigations

et al. 2023

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In this paper, we recount our research on undergraduate mathematics students learning to use programming for mathematics investigation projects. More precisely, we focus on how a particular theoretical perspective (the Instrumental Approach) helps us better understand this student activity. Pulling data from students' and instructors' experiences in a sequence of courses (offered since 2001), our results expose, at the micro and macro levels, how the student activity is organized (through stable 'ways of doing'), and highlights the complexity of this activity (as an intertwined web of 'ways of doing' involving a combination of both mathematics and programming competencies). We end with concrete recommendations to instructors. Dans cet article, nous présentons notre recherche sur les étudiants de premier cycle en mathématiques apprenant à utiliser la programmation pour des projets d'investigation en mathématiques. Plus précisément, nous nous concentrons sur la façon dont une certaine perspective théorique (l'Approche instrumentale) nous aide à mieux comprendre cette activité de l’étudiant. S’appuyant sur des données des expériences d’étudiants et d’instructeurs dans une séquence de cours (offerts depuis 2001), nos résultats décrivent comment l'activité de l’étudiant est organisée (par le biais de «façons de faire» stables), et met en évidence la complexité de cette activité (comme un réseau entrelacé de « manières de faire » impliquant une combinaison de compétences en mathématiques et en programmation). Nous terminons par quelques recommandations concrètes pour les instructeurs.

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Section: School Curricula Are Getting In the Game: Universities Prepa...mentioning

confidence: 99%

Section: How We Are Researching "It"mentioning

confidence: 99%

Section: Rules-of-actionmentioning

confidence: 99%

Section: Rules-of-actionmentioning

confidence: 99%

Section: Rules-of-actionmentioning

confidence: 99%

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Students using programming for pure and applied mathematics investigations

et al. 2023

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Evolution of teachers’ professional learning when using a technological resource: a case study of a Tunisian primary school teacher

Khalloufi-Mouha

2024

Educ Stud Math

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Differences in Students’ Computational Thinking Activities when Designing an Algorithm for Drawing Plane Figures

Büscher

2024

Int J of Sci and Math Educ

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Computational thinking (CT) is becoming increasingly important as a learning content. Subject-integrated approaches aim to develop CT within other subjects like mathematics. The question is how exactly CT can be integrated and learned in mathematics classrooms. In a case study involving 12 sixth-grade learners, CT activities were explored that learners engage in when drawing geometric figures with a visual programming language. The empirical findings indicate differences not only across various CT activities but also within a single CT activity. Subcategories were developed to describe these differences. Implications for further research and classroom practice are discussed.

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Development and evolution of instrumented schemes: a case study of learning programming for mathematical investigations

Cited by 6 publications

References 21 publications

Students using programming for pure and applied mathematics investigations

Students using programming for pure and applied mathematics investigations

Evolution of teachers’ professional learning when using a technological resource: a case study of a Tunisian primary school teacher

Differences in Students’ Computational Thinking Activities when Designing an Algorithm for Drawing Plane Figures

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