Topic Study Group 20:
Visualization in the teaching and learning of mathematics
Roberto Casas Auditorium (FACPYA) and A201, A202, A203, A204, A205 and A206 Rooms
  • Abraham Arcavi (Israel)
    abraham.arcavi@weizmann.ac.il
  • Norma Presmeg (USA)
    npresmeg@ilstu.edu
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Team members:
  • Fatimah Saleh (Malaysia)
    sfatimah@usm.my
  • Patricia Salinas (Mexico)
    npsalinas@itesm.mx
  • Athanasios Gagatsis (Cyprus)
    gagatsis@ucy.ac.cy
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WELCOME!

TSG 20 is designed to promote scholarship on the topic of visualization in the teaching and learning of mathematics. This topic has been gaining increasing attention in the mathematics education community over the last few decades. A broad range of related topic areas fall under this general heading. These may include the roles of external and internal representations (sometimes designated inscriptions and mental imagery respectively), metaphor, metonymy, and gesture, dynamic computer programs, and other aspects of visualization in the teaching and learning of mathematics. Both theoretical papers and reports of empirical research in these and related areas will be considered for inclusion in the program.

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CALL FOR PROPOSALS

The Organizing team of TSG 20 is accepting papers for presentation and distribution at ICME-11. The TSG has been allocated four sessions during the conference. The first and last of these will be joint sessions, and the second and third will be organized in smaller subgroups according to the interests of participants. The last session will allow time for general discussion. Papers will be assigned to one of three formats:

joint session papers, of outstanding and general interest;

subgroup session papers, related to specific topic areas (see below);

‘presentation-by-distribution’ in the TSG and on its website (no oral presentation).

For any of the formats, manuscripts must conform to the formal standards of PME research reports (see the link “TSG20 Template” at the end of the web page) except that the maximum length of papers is 12 pages. Authors should indicate that the paper submitted to TSG 20 has not been submitted to another TSG.

Deadline for submission: November 20, 2007.

Based on a careful refereeing process, the Organizing Team will decide on whether to accept the paper in one of the indicated formats, and (if relevant) in what subgroup the paper is to be presented. Notification of this decision will be given by January, 2008.

Specific topic areas may include, but are not confined to, the following:

 The strengths and difficulties associated with visualization in mathematics.

 Pedagogy and classroom cultures that promote visualization in learning mathematics.

 The roles of metaphor, metonymy, and gesture in mathematical visualization.

 Promoting connections amongst registers that include visualization in mathematics.

 The roles of computer technologies in promoting mathematical visualization.

 Components of a theoretical model of visualization in mathematics education.

For preliminary enquiries, contact any of the members of the Organizing Team. Submission of papers should be directed to one of the co-chairs.

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TSG20 Template

Please make use of the Template below in preparing your proposal

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Program

Monday, July 7 (1 hour) Introduction and 2 plenary papers. Chair: Abraham Arcavi

1. Norma Presmeg: An overarching theory for research in visualization in mathematics education.

2. Fernando Hitt, Alejandro S. González-Martin, & Christian Morasse: Visualization and students’ functional representations in the construction of mathematical concepts. An example: The concept of co-variation as a prelude to the concept of function.

Wednesday, July 9 (1.5 hours) 3 parallel threads, A, B, and C

A. Visual representations and conversions. Chair: Athanasios Gagatsis

1. Athanasios Gagatsis, Areti Panaoura, Iliada Elia, Nicolaos Stamboulidis, & Panayiotis Spyrou: The axis of reflective symmetry as representation in mathematics learning.

2. Flor Rodriguez, Gisela Montiel Espinosa, Ricardo Cantoral Uriza: Visualization in iterative processes.

3. Allen van Blerk, Iben Maj Christiansen, & Trevor Anderson: Learner’s visual recognition of geometry theorems.

4. Orlando Monsalve Posada: Monstrations as a complementary concept for visual thinking: Implications in the teaching and learning of geometry.

B. Aspects of visualization, including technology issues. Chair: Patricia Salinas

1. Patricia Salinas & Angeles Dominguez: Simcalc mathworlds as a tool to support visualization in a calculus course.

2. Thiago Maciel de Oliveira, Rafael Garcia Barbastefano, & Luiz Carlos Guimarães: A discussion about the role of the computer in representation and understanding of 3D objects’ mathematical properties.

3.Eleni Deliyianni, Iliada Elia, Areti Panaoura, & Athanasios Gagatsis: The role of representations in the understanding of fractions in elementary and secondary education.

4. Ricardo Pulido & Patricia Salinas: A visual approach to the graph of a two variable function and to the idea of partial derivative.

C. Issues of teaching involving visualization. Chair: Fatimah Saleh

1. Gonzalo Zubieta & Rafael Meza: Visualization in the teaching/learning of mathematics.

2. Patricia Marchand: Visualization: From sports’ training experiences to school teaching’s practices.

3. Sofia Anastasiadou: Representations and learning in statistics: A comparative study between Greek primary school students and immigrants.

4. Vimolan Mudaly: Visual literacy in mathematics education.

Friday, July 11 (1 hour) 3 parallel threads, A, B, and C

A. Visual representations and conversions. Chair: Athanasios Gagatsis

5. Annita Monoyiou & Athanasios Gagatsis: A coordination of different representations in function problem solving.

6. Jorge Soto-Andrade: Mathematics as the art of seeing the invisible…

B. Aspects of visualization, including technology issues. Chair: Patricia Salinas

5. Sofia Agathangelou, Veronika Papakosta, & Athanasios Gagatsis: The impact of iconic representations in solving mathematical one-step problems of the additive structure by primary second grade pupils.

6. Claudia Acuña Soto & Victor Larios Osorio: Prototypes and learning of geometry: A reflection on its pertinence and its causes.

C. Issues of teaching involving visualization. Chair: Fatimah Saleh

5. Vassiliki Farmaki & Petros Verikios: Function representations as problem solving strategies: The case of inequality.

6. Hui-Yu Hsu: Learning opportunities of reasoning: The interplay between gestures and diagram properties.

Saturday, July 12 (1.5 hours) Chairs: Abraham Arcavi & Norma Presmeg

Discussion in theme groups, chaired by committee members:

Visualization and representations.

Roles of icons, pictures, simulations.

Visual reasoning, visual operations.

Visual literacy.

Visualization and geometry.

Status of visualization.

Creativity.

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