Le Raisonnement Géométrique, une dialectique entre les Aspects Figural et Conceptuel

Peer Reviewe

Proof in dynamic geometry environments

This article suggests that there is a range of evidence that working with dynamic geometry software affords students possibilities of access to theoretical mathematics, something that can be particularly elusive with other pedagogical tools. Yet the paper concludes that further research into the use dynamic geometry software to support the development of students’ mathematical thinking could usefully focus on the nature of the tasks students tackle, the form of teacher input, and the role of the classroom environment and culture

Reasoning By Contradiction in Dynamic Geometry

This paper addresses contributions that dynamic geometry systems (DGSs) may give in reasoning by contradiction in geometry. We present analyses of three excerpts of students’ work and use the notion of pseudo object, elaborated from previous research, to show some specificities of DGS in constructing proof by contradiction. In particular, we support the claim that a DGS can offer “guidance” in the solver’s development of an indirect argument thanks to the potential it offers of both constructing certain properties robustly, and of helping the solver perceive pseudo objects

The role of the dotted line: from 2-dimensional to 3-dimensional geometry

PID2020-117395RB-I00, AEI/10.13039/501100011033, EDU2017-84377-R, ESF Investing in your futur

Coding and Mathematical language: an educational perspective in STEM scenarios

Through the lens of the Theory of Semiotic Mediation we will introduce and discuss mathematical learning opportunities that arise from tasks involving physical and/or digital artefacts that students can interact with through coding. Exploiting didactical potentialities of coding activities pupils can be introduced to Mathematical language and its main characteristics, fostering the production and interpretation of symbolic expressions. The core of the innovative approach consists in combining physical experiences, involving moving with or watching a robot move and draw, with virtual experiences through the mediation of a graphic code. Examples of activities will be presented, showing how they can develop in the classroom. Evidences of pupils achievements will be commented focusing on the semiotic processes triggered by both planning, programming and interpreting

Semiotic mediation: from multiplication properties to arithmetical expressions

Multiplication is introduced early in primary school, but its properties are usually introduced after the rote memorization of multiplicative facts. In this paper we present a teaching experiment aimed to early introducing arithmetical properties of multiplication. It is realized through an artefact built on the rectangle model for multiplication. Children activity is designed and analyzed using Theory of Semiotic Mediation. The development of the relational meaning of arithmetical expressions is shown through the enchaining of representations from signs related to the activity with the artefact to mathematical ones. In particular, the role of the teacher in the process of semiotic mediation results as crucial. Mediazione semiotica: dalle proprietà della moltiplicazione alle espressioni aritmeticheLa moltiplicazione viene presentata presto nella scuola primaria, ma le sue proprietà sono introdotte solo dopo che le cosiddette tabelline sono state memorizzate. Nell’articolo si presenta un teaching experiment volto a introdurre precocemente le proprietà della moltiplicazione per facilitare la memorizzazione di fatti moltiplicativi. L’esperimento è centrato sull’uso di un artefatto costruito sul modello rettangolare della moltiplicazione. L’attività degli studenti è progettata e analizzata nel quadro della Teoria della Mediazione Semiotica (TMS). Lo sviluppo del significato relazionale delle espressioni aritmetiche viene mostrato attraverso la concatenazione di rappresentazioni che vanno da segni strettamente legati all’attività con l’artefatto fino a segni matematici. In particolare, si evidenzia il ruolo dell’insegnante nello sviluppo del processo di mediazione semiotica

Apprendere la matematica con gli strumenti: il ruolo di mediazione dell’insegnante.

Recognizing the relevance of the construction of knowledge by the learners, a complex educational problem concerns the movement from individual activities towards sharing and institutionalizing mathematical knowledge. Teacher’s role is crucial: how to manage the movement from a task to the evoked mathematics? We face this problem in the specific case of tasks involving digital tools; we focus our attention on the actions performed by teachers while orchestrating collective discussion, on the effects of such actions on the evolution of mathematical meaning discussed, and on the sharing of those meanings between the students. A single case study exemplifies the presented theoretical framework to show how, through the chosen lenses, we can evidence teacher’s actions during the collective discussion

Experimental Approaches to Theoretical Thinking: Artefacts and Proofs

This chapter discusses some strands of experimental mathematics from both an epistemological and a didactical point of view. We introduce some ancient and recent historical examples in Western and Eastern cultures in order to illustrate how the use of mathematical tools has driven the genesis of many abstract mathematical concepts. We show how the interaction between concrete tools and abstract ideas introduces an "experimental" dimension in mathematics and a dynamic tension between the empirical nature of the activities with the tools and the deductive nature of the discipline. We then discuss how the heavy use of the new technology in mathematics teaching gives new dynamism to this dialectic, specifically through students' proving activities in digital electronic environments. Finally, we introduce some theoretical frameworks to examine and interpret students' thoughts and actions whilst the students work in such environments to explore problematic situations, formulate conjectures and logically prove them. The chapter is followed by a response by Jonathan Borwein and Judy-anne Osborn

The CERME spirit: issues of quality and inclusion in an innovative conference style

This chapter presents findings from an analysis of data from participants in a bi-annual international mathematics education conference with regard to the practical realization of objectives relating to inclusion and quality in the conference. The chapter presents the context and objectives of the organizing Society and its interpretation of objectives in operationalizing a conference. It examines, theoretically, issues relating to inclusion of participants and quality of scientific work in the context of such a conference. It presents findings related to analysis of three sources of data – evaluation questionnaires from participants at the end of a conference, interviews with participants during a conference, and comments from group leaders written during and after a conference. Finally it synthesizes from issues raised and relates these to theoretical issues, presenting a tentative framework for creating and evaluating a conference which has principled objectives with relation to quality and inclusion