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Topic Study Group 31:

Language and communication in mathematics education

F301 and F302 Rooms


Organizing team composition

Aims, scope, and goals

Call for papers (expired)

Detailed programme for the four sessions

Papers and discussion documents

Team chairs:

Carl Winsløw (Denmark)

Bill Barton (New Zealand)

Team members:

Beth Herbel-Eisenmann (USA)

Susan Gerofsky (Canada)

Imed Ben Kilani (Tunisia)

Aims, scope, and goals

TSG 31: Language and communication in mathematics education is a recurrent group in ICME, devoted to the discussion and diffusion of the latest research on language aspects of mathematics education in a broad sense. We strive to organise a fulfilling scientific experience for all participants, and – in consistence with the topic of the group – to maximise participants’ possibilities to communicate and discuss their results and concerns. Along this line, we also wish to point out that, while the official language of the congress is English, we are aware that this is not the native language of most of the participants, so we will do our best to ensure that non-native speakers of English can also follow and participate fully in our work.

Of course, given the breadth of the topic of the group, we face the challenge of organising the sessions in themes that will allow for focus and coherence in the discussions, and to take up issues which are of particular importance in current research. The call explains in more detail how we have chosen to do so. Please do not hesitate to contact the organisers with your concerns and questions.

We look forward to welcome you to our group in Mexico in 2008!

The organising team

Call for papers (expired)


The 11th international congress of mathematical education will held in Monterrey, Mexico, July 6-13, 2008 (see website). As in previous ICME’s, there will be a topic study on “Language and communication in mathematics education”. It will meet in four sessions during the congress (two session of an hour and two sessions of 1½ hour).

The organising team (see below) invites contributions for these sessions in the form of paper proposals pertaining to one or more of the following main themes:

A. What we write and say when teaching and learning mathematics : symbols, natural language, and other semiotic representations – what are their significance for teaching and learning?

B. Learning mathematics in another language : Challenges and approaches in teaching mathematics to students in another language than their mother tongue.

C. The way we justify, argue and prove in mathematics classrooms : Reasoning discourses in the classroom – challenges for learners, strategies for teachers.

Each of these themes will be considered according to three levels of education:

1. Primary level (learners of age about 5 to 12 years)

2. Secondary level (learners of age about 12 to 19 years)

3. Tertiary level and adult education (adults)

This leaves, in principle, the possibility of 9 different subthemes A1, A2, …, C2, C3. Depending on the proposals received, some of these may be merged, but we ask all proposals to identify with one of them as a first approximation. It may be that some papers identify with more than one of the main themes and more (or any) of the levels; still, you should indicate the one that suites best. Please send your contribution to both of the chairs (see below) with the following subject line: “TSG-31 proposal, subtheme Xn” (replace Xn by the subtheme, such as B3). Deadline is January 25, 2008 (NB: this is 10 days later than previously announced, and is due to temporary technical difficulties at this site, which has now been solved). Please notice that proposals can be up to 10 pages and that you must use the style file of PME, which can be found here . Proposals not using this style file, exceeding 10 pages, or arriving late, will be rejected without review.

Review and presentation

Papers will be reviewed by at least two referees and based on their reports, the organising theme will allot the papers to one of the following formats of presentation:

- subgroup discussion (here, the main focus will be on having focused, in-depth discussions on a group of connected papers; authors will present some questions relating to their paper that they wish the subgroup to discuss)

- paper by distribution (not presented, but may be included in subgroup discussions)

The exact planning of the four sessions is given below on this page. You can also download accepted papers below.

Detailed programme for the four sessions

The topic study group has accepted 23 papers: 17 for oral presentation and discussion in parallel sessions (P), and 6 for presentation-by-distribution (D). The accepted papers can be downloaded through the links below (in the section entitled “Papers and discussion documents”, where papers are marked “D” and “P” according to the category in which they have been accepted).

The oral presentation and discussion of papers will take place during our four sessions, as follows: each of the four sessions will have two parallel subgroups, in which a number of papers will be presented (max. 10 minutes for each paper, including if time permits short questions) and discussed (the remaining time). The papers of each subgroup are sufficiently related to enable a common discussion. Each subgroup will be chaired by a member of the organising team, who will be responsible to deliver a short report from the subgroup to the final session. Participants are encouraged to download, print and read the papers of the subgroup they attend, before the conference.

Here is the plan for the four sessions (papers are indicated by author name, see complete title and link to paper below); a more detailed plan, with room numbers for subgroups and so on, will be announced at the first session of the topic study group. Notice that the time slots for TSG’s were recently changed; if they are (again) different in the final congress programme, we will of course have our sessions at the times indicated in that programme, and the times below will have to be read accordingly.

SESSION 1 – TUESDAY JULY 8, 12.00-13.00


Welcome, introduction to the group (B. Barton, C. Winsløw)


Subgroup 1x: Theme C, Argumentation and proof (J. Hunter, D. Won Kim; Chair: I. Ben Kali)

Subgroup 1y: Theme A, Gesture (M. Cestari et al., S. Gerofsky; Chair: B. Herbel-Eisenmann)

SESSION 2 – WEDNESDAY JULY 9, 12.00-13.30

Subgroup 2x: Theme B, Second language (M. NiRiordain, M. Civil, K. Garegae; Chair: B. Barton)

Subgroup 2y: Theme A, Semiotics and representations (R. Rubenstein, N. Hardy, G. Foley; Chair: C. Winsløw)

SESSION 3 – FRIDAY JULY 11, 12.30-13.30

Subgroup 3x: Theme A, Writing and genres (R. de Oliveira, T. Meaney et al.; Chair: S. Gerofsky)

Subgroup 3y: Theme A, Role of teachers and language (F.-J. Hsieh, L. Ejersbo; Chair: B. Herbel-Eisenmann)

SESSION 4 – SATURDAY JULY 12, 12.00-13.30


Subgroup 4x: Theme B, Second language (R. Hunter; Chair: S. Gerofsky)

Subgroup 4y: Theme A, Semiotics and representations (F. Roubicek; Chair: I. Ben Kali)


Reports from subgroups by chairs (2½ minutes per paper, including questions)

Closing (B. Barton, C. Winsløw)

Papers and discussion documents

P-J.Hunter: Developing students' use of justification strategies (3.00 MB)

P-Kim: The process of negotiation of proofs acceptable in a mathematics classroom (59.00 KB)

P-Bjuland&Cestari&Borgersen: Gestures and discourse as communicative strategies in presenting a mathematical task: A case study (146.00 KB)

P-Gerowski: Gesture studies as an emergent area in the language of mathematics education (44.00 KB)

P-NiRiordain: Challenges faced by Gaeilgeoirí in the transition to English medium second level maths education (167.00 KB)

P-Civil: When the home language is different from the school language: Implications for equity in mathematics education (83.00 KB)

P-Garaegae: Language in Mathematics Education: A Double Jeopardy for Second Language Learners (161.00 KB)

P-Hardy: A subtle interplay of ordinary, algebraic and analytic registers in college level Calculus courses as a source of students' difficulties (442.00 KB)

P-Foley: The Multi-Semiotic Nature of Mathematical Language and Its Secondary School Classroom Implications (26.00 KB)

P-de Oliveira: Reading and Writing in Mathematics Classes at the Upper Secondary Level (50.00 KB)

P-Meaney&Fairhall&Trinick: Genres in the mathematical writing of Mäori-immersion students (1.00 MB)

P-Hsieh&Wang&Wu: Understanding the teachers' use of sentences in a mathematics classroom (236.00 KB)

P-Ejersbo: Research based Teaching (112.00 KB)

P-R.Hunter: Do they know what to say and why? Developing the discourse of inquiry and argumentation with Maori and Pasifika students (78.00 KB)

P-Roubicek: Conventional and inventional representations in pupils´ communication. (47.00 KB)

D-Leung&Lai: An exploratory study into Chinese and English Speaking Children’s Visual Perception (30.00 KB)

D-Singer: Language and Mathematics—Distant Relatives? (68.00 KB)

D-Azrou: Let’s teach alive mathematics (22.00 KB)

D-Hesselbart: Physical World metaphors for the abstract mathemical world – the case of The verbal description stage within proof understanding (43.00 KB)

D-van Eerde: Teachers' designs of language sensitive math lessons (80.00 KB)


P-Rubenstein: Mathematical Symbolisation: Challenges across levels (123.00 KB)

L. Maurice: Reflexions on Teaching Methods of Proof to College Students and Students' Difficulties (English) (101.00 KB)

L. Maurice: Reflexions on Teaching Methods of Proof to College Students and Students' Difficulties (Spanish) (38.00 KB)

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