maria alessandra Mariotti - Profile on Academia.edu (original) (raw)

Papers by maria alessandra Mariotti

Research paper thumbnail of Doing well" in the Teaching for Robust Understanding approach revealed by the lens of the semiotic potential of tasks with the GGBot

HAL (Le Centre pour la Communication Scientifique Directe), Feb 2, 2022

In this paper we report on experiences we have provided students in a grade-3 classroom with the ... more In this paper we report on experiences we have provided students in a grade-3 classroom with the aim of introducing concepts in plane geometry through interaction with the GGBot, a drawing robot that can be programmed with SNAP! Blocks. We do this to explore the effectiveness of the use of a new theoretical approach that combines the Teaching for Robust Understanding Framework with the Theory of Semiotic Mediation. We claim that the articulation between the two frames is not only feasible but also insightful, providing an a priori analysis of two tasks, and a detailed analysis of a short excerpt from the corresponding Didactic Cycle.

Research paper thumbnail of Semiotic Mediation: from History to Mathematics Classroom

for the learning of mathematics, 1999

This article starts with a cognitive analysis of an imaginary debate -reconstructed with excerpts... more This article starts with a cognitive analysis of an imaginary debate -reconstructed with excerpts from historical sources -concerning the shape of particular sections of a right cone and a right cylinder Our analysis, based on the theory of figural concepts , suggests the following hypothesis:

Research paper thumbnail of Argumentation and proof

Developing Research in Mathematics Education, 2018

Topic Group 4 of CERME4 on "Argumentation and Proof " had 15 participants from different countrie... more Topic Group 4 of CERME4 on "Argumentation and Proof " had 15 participants from different countries across Europe. During its sessions, no formal presentations of the 9 papers were made, but every author had a chance to present her/his main ideas. The discussion was organized around three main themes that emerged from the papers prepared for the Topic Group. This report is organized likewise, in that it presents an account of the arguments and comments made in the group in terms of the three themes rather than in the order in which the discussion occurred. The three themes were • The meaning of proof in mathematics education • Comparing the teaching of proof at school • Problem solving and Conjecturing.

Research paper thumbnail of Mathematical Problem-Solving with Technology: An Overview of the Problem@Web Project

Mathematics Education in the Digital Era, 2016

This paper addresses mathematical problem solving with technologies in a beyond school web-based ... more This paper addresses mathematical problem solving with technologies in a beyond school web-based competition. We aim to disclose the ways mathematical and technological knowledge are used and combined for solving the given problems. A specific conceptual framework for accounting both these components was developed. By means of the Mathematical Problem Solving with Technology model (MPST) we report the case of Marco, aged 13, solving and expressing a geometrical problem. His ability in perceiving affordances in the tools that he chose is in line with the efficient use he made of them in the development of mathematical understanding that was crucial for finding and expressing the solution. Results suggest that digital thinking and experience have to be seen as relevant as the mathematical cognitive resources.

Research paper thumbnail of TSG 2: The Teaching and Learning of Geometry

TSG 2: The Teaching and Learning of Geometry

Proceedings of the Ninth International Congress on Mathematical Education, 2004

The discussion was organized around few short presentations which aimed to introduce different as... more The discussion was organized around few short presentations which aimed to introduce different aspects related to the theme of the Topic Study Group.

Research paper thumbnail of Proceedings of the Eight Congress of the European Society for Research in Mathematics Education

HAL (Le Centre pour la Communication Scientifique Directe), 2013

Research paper thumbnail of Creating a Synergy Between Manipulative and Virtual Artefacts to Conceputalize Axial Symmetry at Primary School

Creating a Synergy Between Manipulative and Virtual Artefacts to Conceputalize Axial Symmetry at Primary School

40th Conference of the International Group for the Psychology of Mathematics Education (PME40), 2016

Research paper thumbnail of An interactive book on axial symmetry and the synergic use with paper and pin

An interactive book on axial symmetry and the synergic use with paper and pin

This work presents results from a teaching experiment concerning the constructionconceptualizatio... more This work presents results from a teaching experiment concerning the constructionconceptualization of axial symmetry at Primary School through an interactive book, developed in a Dynamic Geometry Environment (DGE), which embeds a set of tasks to be accomplished with selected DGE tools. The tasks are part of a teaching sequence, framed by the Theory of Semiotic Mediation (TSM), whose main characteristic is the synergic use of a “duo of artefact”. The duo is made up of a digital artefact the interactive book and a manipulative artefact, constituted by paper and pin. Herein, we describe the design of the interactive book and we show how a cognitive synergy arises from its use combined with the use of the manipulative artefact within the sequence, thus leading to the conceptualization of mathematical meanings.

Research paper thumbnail of Images and Concepts in Geometrical Reasoning

Images and Concepts in Geometrical Reasoning

Exploiting Mental Imagery with Computers in Mathematics Education, 1995

Geometry is a school subject, but also and primarily geometry is a mathematical domain. As mathem... more Geometry is a school subject, but also and primarily geometry is a mathematical domain. As mathematics educators we are interested in geometry from both points of view. That is the reason why a first discussion is devoted to highlighting some characteristics of geometry as a mathematical domain. Une premiere caracteristique de la geometrie reside dans les liens complexes qu'elle entretient avec l'espace physique qui nous entoure.(Laborde [17], p. 341).

Research paper thumbnail of Geometry: dynamic intuition and theory

Research paper thumbnail of Conceptualising the regular pentagon in collaborative argumentation

This case study examines a group of Hungarian mathematics pre-service teachers solving an open pr... more This case study examines a group of Hungarian mathematics pre-service teachers solving an open problem collaboratively, where they must determine whether a folded shape is a regular pentagon. The study looks at how different factors, such as using perceptual evidence, ostensive arguments, and mathematical arguments, impact proof development. The study draws from theories such as Cognitive unity and the van Hiele model to analyse the students' argumentation. The video recording of the session was used to collect data. The results showed that students' argumentation had a strong dynamic between perceptual and mathematical character; moreover, the conceptualisation of the regular pentagon evolved as they advanced in the construction of their proof.

Research paper thumbnail of From paper and pencil-to computer-based assessment: Some issues raised in the comparison

HAL (Le Centre pour la Communication Scientifique Directe), Feb 1, 2017

Comparative studies on pen-and-paper and computer-based test principally focus on statistical ana... more Comparative studies on pen-and-paper and computer-based test principally focus on statistical analysis of students' performances. In educational assessment, comparing students' performance (in terms of right or wrong results) does not imply a comparison between the solving processes followed by students. In this paper we present an example of task analysis that allows to highlight how students' solving processes could change in switching from paper to computer format and how these changes could be affected by the use of one environment rather than another. The aim of our study lies in identifying possible consequences that specific changes in task formulation have, in terms of students' solution processes.

Figure 1: "Walking" paper version, administered in PISA 2003 survey First of all, there is a difference in the editing of the text. In the paper version the task is presented in a compact way: sef-up and information components are given in the same text and the question is presented under this text. In the digital format, the task is divided into two main sections. On the right there are the set-up and information components: they consist of an image and a description of the situation, both in words and algebraic formulas. On the left there is the question. The difference in editing seems to complicate the task; in the digital format, the text is presented in two separate columns. Therefore, the change of the question position could create variances in solution processes: the solver has_to coordinate the interpretations of the different parts in which the text is divided. In other cases this change could affect the solver’s comprehension. For instance, Thevenot et al. (2007) show that putting the question before a word problem (rather than classically presenting it at the end) conditions problem solution in young students and in particular it facilitates students in engaging a correct solution process. In Fig 2, the question is presented in the bottom-left of the screen; in this case the solver probably reads the question before reading the set-up and information components.

Research paper thumbnail of A computer-based environment for argumenting and proving in geometry

HAL (Le Centre pour la Communication Scientifique Directe), Feb 6, 2019

In this paper, we face the issue of argument and proving in geometry. Overcoming difficulties enc... more In this paper, we face the issue of argument and proving in geometry. Overcoming difficulties encountered by the students when moving from argumentation to proof may require suitable didactical interventions. Our contribution to research concerns the design of a specific computerbased didactic environment. We report how 14-15 years old students from high school conjecture and prove within the designed environment and we discuss the preliminary findings.

Research paper thumbnail of Constructing validity in classroom conversations

CERME9 - Ninth Congress of the European Society for Research in Mathematics Education, Feb 4, 2015

We account for different strategies used by a group of students to talk about and assess the vali... more We account for different strategies used by a group of students to talk about and assess the validity of mathematical models while working in a problem-solving task. Two main competing strategies are described, one centred in ritualized uses of well-known mathematical constructs as a means to cope with perceived didactical expectations and a second strategy centred in the assessment of the representativeness of mathematical models when accounting for the proposed empirical situation. The interactions analyzed exemplify the difficulties students and teachers experience when dealing with epistemological aspects of knowledge being constructed in classroom conversations. Our findings point to the need for research to focus on epistemological aspects of the mathematical culture of the classroom.

Research paper thumbnail of La scienza in 4D

Research paper thumbnail of The French Didactic Tradition in Mathematics

European Traditions in Didactics of Mathematics, 2019

This chapter presents the French didactic tradition. It first describes the emergence and develop... more This chapter presents the French didactic tradition. It first describes the emergence and development of this tradition according to four key features (role of mathematics and mathematicians, role of theories, role of design of teaching and learning environments, and role of empirical research), and illustrates it through M. Artigue

Research paper thumbnail of Exploiting the Feedback of the Aplusix CAS to Mediate the Equivalence between Algebraic Expressions

Exploiting the Feedback of the Aplusix CAS to Mediate the Equivalence between Algebraic Expressions

abstract. This paper stems from the ReMath European project1 that focuses on the role of represen... more abstract. This paper stems from the ReMath European project1 that focuses on the role of representations in dynamic digital artefacts (DDAs), and on the role of theoretical frameworks with respect to their use in educational contexts. Framed within the Theory of Semiotic Mediation, the paper presents some results concerning how the potentialities of the Aplusix DDA, and in particular of the feedback component, can be exploited by the teacher in relation with the notion of equivalence between algebraic expressions. Through a semiotic analysis of excerpts from a classroom discussion, evidence of the semiotic process triggered by the teacher’s interventions is provided

Research paper thumbnail of Figural and conceptual aspects in a defining process

Figural and conceptual aspects in a defining process

In the reference frame of the theory of figural concepts (Fischbein 1993) we planned a teaching e... more In the reference frame of the theory of figural concepts (Fischbein 1993) we planned a teaching experiments at 6th grade. the paper discusses some aspects concerning the defining process in a geometrical context, as it emerges in a collective discussion

Research paper thumbnail of L'Algebrista: un manipolatore simbolico elementare

Research paper thumbnail of Indirect proof: an interpreting model

Starting from a general discussion on mathematical proof, a structural analysis was carried out, ... more Starting from a general discussion on mathematical proof, a structural analysis was carried out, leading to the construction of a model within which indirect proofs can be described. The model shows itself a good interpreting tool to identify and explain cognitive and didactic issues, as well to precisely formulate research hypotheses concerning students' difficulties with indirect proofs.

Research paper thumbnail of Doing well" in the Teaching for Robust Understanding approach revealed by the lens of the semiotic potential of tasks with the GGBot

HAL (Le Centre pour la Communication Scientifique Directe), Feb 2, 2022

In this paper we report on experiences we have provided students in a grade-3 classroom with the ... more In this paper we report on experiences we have provided students in a grade-3 classroom with the aim of introducing concepts in plane geometry through interaction with the GGBot, a drawing robot that can be programmed with SNAP! Blocks. We do this to explore the effectiveness of the use of a new theoretical approach that combines the Teaching for Robust Understanding Framework with the Theory of Semiotic Mediation. We claim that the articulation between the two frames is not only feasible but also insightful, providing an a priori analysis of two tasks, and a detailed analysis of a short excerpt from the corresponding Didactic Cycle.

Research paper thumbnail of Semiotic Mediation: from History to Mathematics Classroom

for the learning of mathematics, 1999

This article starts with a cognitive analysis of an imaginary debate -reconstructed with excerpts... more This article starts with a cognitive analysis of an imaginary debate -reconstructed with excerpts from historical sources -concerning the shape of particular sections of a right cone and a right cylinder Our analysis, based on the theory of figural concepts , suggests the following hypothesis:

Research paper thumbnail of Argumentation and proof

Developing Research in Mathematics Education, 2018

Topic Group 4 of CERME4 on "Argumentation and Proof " had 15 participants from different countrie... more Topic Group 4 of CERME4 on "Argumentation and Proof " had 15 participants from different countries across Europe. During its sessions, no formal presentations of the 9 papers were made, but every author had a chance to present her/his main ideas. The discussion was organized around three main themes that emerged from the papers prepared for the Topic Group. This report is organized likewise, in that it presents an account of the arguments and comments made in the group in terms of the three themes rather than in the order in which the discussion occurred. The three themes were • The meaning of proof in mathematics education • Comparing the teaching of proof at school • Problem solving and Conjecturing.

Research paper thumbnail of Mathematical Problem-Solving with Technology: An Overview of the Problem@Web Project

Mathematics Education in the Digital Era, 2016

This paper addresses mathematical problem solving with technologies in a beyond school web-based ... more This paper addresses mathematical problem solving with technologies in a beyond school web-based competition. We aim to disclose the ways mathematical and technological knowledge are used and combined for solving the given problems. A specific conceptual framework for accounting both these components was developed. By means of the Mathematical Problem Solving with Technology model (MPST) we report the case of Marco, aged 13, solving and expressing a geometrical problem. His ability in perceiving affordances in the tools that he chose is in line with the efficient use he made of them in the development of mathematical understanding that was crucial for finding and expressing the solution. Results suggest that digital thinking and experience have to be seen as relevant as the mathematical cognitive resources.

Research paper thumbnail of TSG 2: The Teaching and Learning of Geometry

TSG 2: The Teaching and Learning of Geometry

Proceedings of the Ninth International Congress on Mathematical Education, 2004

The discussion was organized around few short presentations which aimed to introduce different as... more The discussion was organized around few short presentations which aimed to introduce different aspects related to the theme of the Topic Study Group.

Research paper thumbnail of Proceedings of the Eight Congress of the European Society for Research in Mathematics Education

HAL (Le Centre pour la Communication Scientifique Directe), 2013

Research paper thumbnail of Creating a Synergy Between Manipulative and Virtual Artefacts to Conceputalize Axial Symmetry at Primary School

Creating a Synergy Between Manipulative and Virtual Artefacts to Conceputalize Axial Symmetry at Primary School

40th Conference of the International Group for the Psychology of Mathematics Education (PME40), 2016

Research paper thumbnail of An interactive book on axial symmetry and the synergic use with paper and pin

An interactive book on axial symmetry and the synergic use with paper and pin

This work presents results from a teaching experiment concerning the constructionconceptualizatio... more This work presents results from a teaching experiment concerning the constructionconceptualization of axial symmetry at Primary School through an interactive book, developed in a Dynamic Geometry Environment (DGE), which embeds a set of tasks to be accomplished with selected DGE tools. The tasks are part of a teaching sequence, framed by the Theory of Semiotic Mediation (TSM), whose main characteristic is the synergic use of a “duo of artefact”. The duo is made up of a digital artefact the interactive book and a manipulative artefact, constituted by paper and pin. Herein, we describe the design of the interactive book and we show how a cognitive synergy arises from its use combined with the use of the manipulative artefact within the sequence, thus leading to the conceptualization of mathematical meanings.

Research paper thumbnail of Images and Concepts in Geometrical Reasoning

Images and Concepts in Geometrical Reasoning

Exploiting Mental Imagery with Computers in Mathematics Education, 1995

Geometry is a school subject, but also and primarily geometry is a mathematical domain. As mathem... more Geometry is a school subject, but also and primarily geometry is a mathematical domain. As mathematics educators we are interested in geometry from both points of view. That is the reason why a first discussion is devoted to highlighting some characteristics of geometry as a mathematical domain. Une premiere caracteristique de la geometrie reside dans les liens complexes qu'elle entretient avec l'espace physique qui nous entoure.(Laborde [17], p. 341).

Research paper thumbnail of Geometry: dynamic intuition and theory

Research paper thumbnail of Conceptualising the regular pentagon in collaborative argumentation

This case study examines a group of Hungarian mathematics pre-service teachers solving an open pr... more This case study examines a group of Hungarian mathematics pre-service teachers solving an open problem collaboratively, where they must determine whether a folded shape is a regular pentagon. The study looks at how different factors, such as using perceptual evidence, ostensive arguments, and mathematical arguments, impact proof development. The study draws from theories such as Cognitive unity and the van Hiele model to analyse the students' argumentation. The video recording of the session was used to collect data. The results showed that students' argumentation had a strong dynamic between perceptual and mathematical character; moreover, the conceptualisation of the regular pentagon evolved as they advanced in the construction of their proof.

Research paper thumbnail of From paper and pencil-to computer-based assessment: Some issues raised in the comparison

HAL (Le Centre pour la Communication Scientifique Directe), Feb 1, 2017

Comparative studies on pen-and-paper and computer-based test principally focus on statistical ana... more Comparative studies on pen-and-paper and computer-based test principally focus on statistical analysis of students' performances. In educational assessment, comparing students' performance (in terms of right or wrong results) does not imply a comparison between the solving processes followed by students. In this paper we present an example of task analysis that allows to highlight how students' solving processes could change in switching from paper to computer format and how these changes could be affected by the use of one environment rather than another. The aim of our study lies in identifying possible consequences that specific changes in task formulation have, in terms of students' solution processes.

Figure 1: "Walking" paper version, administered in PISA 2003 survey First of all, there is a difference in the editing of the text. In the paper version the task is presented in a compact way: sef-up and information components are given in the same text and the question is presented under this text. In the digital format, the task is divided into two main sections. On the right there are the set-up and information components: they consist of an image and a description of the situation, both in words and algebraic formulas. On the left there is the question. The difference in editing seems to complicate the task; in the digital format, the text is presented in two separate columns. Therefore, the change of the question position could create variances in solution processes: the solver has_to coordinate the interpretations of the different parts in which the text is divided. In other cases this change could affect the solver’s comprehension. For instance, Thevenot et al. (2007) show that putting the question before a word problem (rather than classically presenting it at the end) conditions problem solution in young students and in particular it facilitates students in engaging a correct solution process. In Fig 2, the question is presented in the bottom-left of the screen; in this case the solver probably reads the question before reading the set-up and information components.

Research paper thumbnail of A computer-based environment for argumenting and proving in geometry

HAL (Le Centre pour la Communication Scientifique Directe), Feb 6, 2019

In this paper, we face the issue of argument and proving in geometry. Overcoming difficulties enc... more In this paper, we face the issue of argument and proving in geometry. Overcoming difficulties encountered by the students when moving from argumentation to proof may require suitable didactical interventions. Our contribution to research concerns the design of a specific computerbased didactic environment. We report how 14-15 years old students from high school conjecture and prove within the designed environment and we discuss the preliminary findings.

Research paper thumbnail of Constructing validity in classroom conversations

CERME9 - Ninth Congress of the European Society for Research in Mathematics Education, Feb 4, 2015

We account for different strategies used by a group of students to talk about and assess the vali... more We account for different strategies used by a group of students to talk about and assess the validity of mathematical models while working in a problem-solving task. Two main competing strategies are described, one centred in ritualized uses of well-known mathematical constructs as a means to cope with perceived didactical expectations and a second strategy centred in the assessment of the representativeness of mathematical models when accounting for the proposed empirical situation. The interactions analyzed exemplify the difficulties students and teachers experience when dealing with epistemological aspects of knowledge being constructed in classroom conversations. Our findings point to the need for research to focus on epistemological aspects of the mathematical culture of the classroom.

Research paper thumbnail of La scienza in 4D

Research paper thumbnail of The French Didactic Tradition in Mathematics

European Traditions in Didactics of Mathematics, 2019

This chapter presents the French didactic tradition. It first describes the emergence and develop... more This chapter presents the French didactic tradition. It first describes the emergence and development of this tradition according to four key features (role of mathematics and mathematicians, role of theories, role of design of teaching and learning environments, and role of empirical research), and illustrates it through M. Artigue

Research paper thumbnail of Exploiting the Feedback of the Aplusix CAS to Mediate the Equivalence between Algebraic Expressions

Exploiting the Feedback of the Aplusix CAS to Mediate the Equivalence between Algebraic Expressions

abstract. This paper stems from the ReMath European project1 that focuses on the role of represen... more abstract. This paper stems from the ReMath European project1 that focuses on the role of representations in dynamic digital artefacts (DDAs), and on the role of theoretical frameworks with respect to their use in educational contexts. Framed within the Theory of Semiotic Mediation, the paper presents some results concerning how the potentialities of the Aplusix DDA, and in particular of the feedback component, can be exploited by the teacher in relation with the notion of equivalence between algebraic expressions. Through a semiotic analysis of excerpts from a classroom discussion, evidence of the semiotic process triggered by the teacher’s interventions is provided

Research paper thumbnail of Figural and conceptual aspects in a defining process

Figural and conceptual aspects in a defining process

In the reference frame of the theory of figural concepts (Fischbein 1993) we planned a teaching e... more In the reference frame of the theory of figural concepts (Fischbein 1993) we planned a teaching experiments at 6th grade. the paper discusses some aspects concerning the defining process in a geometrical context, as it emerges in a collective discussion

Research paper thumbnail of L'Algebrista: un manipolatore simbolico elementare

Research paper thumbnail of Indirect proof: an interpreting model

Starting from a general discussion on mathematical proof, a structural analysis was carried out, ... more Starting from a general discussion on mathematical proof, a structural analysis was carried out, leading to the construction of a model within which indirect proofs can be described. The model shows itself a good interpreting tool to identify and explain cognitive and didactic issues, as well to precisely formulate research hypotheses concerning students' difficulties with indirect proofs.