Skip to main content

Learning and cognition in mathematics: Students´ formation of mathematical conceptions, notions, strategies, and beliefs

A307 and A308 Rooms


Organizing team composition

Proposals by


Papers and discussion documents

Team chairs:

Gaye Williams (Australia)

Deakin University

Burwood Campus, 221 Burwood Hwy, Burwood, Victoria, Australia 3125.

Research: Creative thought processes, spontaneously developing mathematical insight (novel mathematical structures), and personal characteristics, social elements, and affective factors associated with these processes.

Guershon Harel (USA)

University of California, San Diego

9500 Gilman Drive, La Jolla, California 92093-0112 USA

Research: Cognition and epistemology of mathematics and their applications in mathematics curricula and teacher education.

Team members:

JeongSuk Pang (Korea)

Korea National University of Education

Darak-ri, Gangnae-myeon, Cheongwon-gun, Chungbuk 363-791, Korea

Research: Sociomathematical processes in students' learning, mathematics classroom microculture, students' understanding and misunderstanding of mathematical constructs

Despina Potari (Greece)

University of Athens

Research: Learning of geometry, teacher professional development,methodological models of analysing mathematics teaching.

Mariana Saiz (Mexico)

Universidad Pedagógica Nacional

Carretera al Ajusco 24 Col. Héroes de Padierna. México 

Research: Primary and Secondary Teachers‚ Mathematical conceptions and knowledge.

Proposals by

- Mirela Rigo

- Therese Dooley

- Samuele Antonini

- Marita Barabash

- Matsuo Nanae

- Silfverberg Harry


Monday 13:00-14:00

Introduction and Overview

13:00-13:10 (10 Mins)

Gabriele Kaiser, Bjoern Schwarz, 13:10-13:40 (30 Mins)

“Beliefs and Professional Knowledge of Future Teachers – Qualitative Studies on Influences and Relations” (Gabriele Kaiser & Björn Schwarz)

JeongSuk Pang 13:40-13:52 (12 Mins)

“Prospective elementary teachers’ beliefs and knowledge: Division of fractions”

Reflecting 13:52-14:00:(8 Mins)

Including any papers on site linking to the day’s sessions 

Wednesday 12:00-13:30

Anna Sfard, Dani Ben-Zvi, 12:00-12:30 (30 Mins)

Topic associated with “The Learners’ Autonomy”

Gaye Williams 12:30-12:42 (12 Mins) “Optimism-building to increase problem solving capacity”

Thérèse Dooley 12:42-12:50 

(8 minutes) “How a performance glitch led to mathematical insight in a primary class

Reflecting and Connecting: 12:50-13:00 (10 Mins) Including today’s sessions, any papers from previous days linking to this, and papers on site linking to the day’s sessions.

Matuso Nanae & Harry Silfverberg 13:00-13:10 (10 minutes) “Similarities and differences between Japanese and Finnish 6th and 8th Graders’ ways to interpret and apply the definitions of geometric concepts”

Reflecting 13:10-13:20: (10 Mins)

Including papers on site linking to sessions

Preliminary Thoughts About Ways to Use Knowledge Gained 13:20-13:30: (10 Mins)

Friday 12:30-13:30

Masami Isoda 12:30-13:00 

(30 Mins) “Getting others’ perspectives through Hermeneutic Effort: A theory of understanding for planning the problem solving teaching approach.”

Despina Potari 13:00-13:12 

(12 Mins) “Prospective Primary Teachers’ Conceptions of Axial Symmetry”

Irene Biza, 13:12-13:20 (8 mins) “Models of students’ conceptions about tangent lines”

Reflecting:13:20-13:30 (10 minutes). 

Saturday 12:00-13:30

Dick Lesh 12:00-12:30 (30 Mins)

“Models & Modeling Perspectives on the Nature of Mathematical Knowledge”

Guershon Harel 12:30-12:42 (12 Mins) “Constituent Elements of Mathematical Knowledge”

Samuele Antonini 12:42-12:50 (8 minutes) “Student use of Reductio Ad Adsurdum”*

Reflecting 12:50-13:00 (10 minutes)

Plenary 13:00-13:30 (30 mins)

Developing and overview. Where to from here?

Top of page

Papers and discussion documents

Call For Papers (32.00 KB)

2 Rina Hershkowitz: Abstract (21.00 KB)

3 Terry Wood: Abstract (22.00 KB)

4 Anna Sfard: Abstract (36.00 KB)

5 Richard Lesh: Abstract (40.00 KB)

Numbering Key and Program Overview (23.00 KB)

Despina Portari P Abstract (20.00 KB)

Gaye Williams P Abstract (40.00 KB)

Guershon Harel P Abstract (52.00 KB)

JeongSuk Pang P Abstract (46.00 KB)

Information on Online Discussion (30.00 KB)

Panel_PangJ_Prospective Elementary Teachers’ Beliefs And Knowledge: Division Of Fractions (70.00 KB)

ECR_DooleyT_How A ‘performance glitch’ led to mathematical insight in a primary class (84.00 KB)


ECR_BarabashM_Characterization Of Mathematical-Cognitive Development Using Two Dimensional Model Of Insight (373.00 KB)

CFP_Mevarech & Armani_The Effects of Metacognitive Instruction on Students’ Mathematics Achievement and Regulation of Cognition (42.00 KB)

CFP_Ulep_Student Learning in Mathematical Interactions (83.00 KB)

CFP_Hagen_Raising Levels of Student Engagement through Imaginative Education – The Student Perspective (49.00 KB)

Welcome to TSG26 Online Discussion (2.00 KB)


1 Gabriele Kaiser Abstract (20.00 KB)

Discussion Almost Starting (39.00 KB)

TonyGardiner_Uk_220208_RequestInfoGayePaper (26.00 KB)

TonyGardiner220208_Optimism (1.00 KB)

GayeResponseTonyGardiner_Optimism (4.00 KB)

ECR_BizaI_Models of Students' Conceptions About the Tangent Line (96.00 KB)

CFP_White&Mitchelmore_Teaching for Abstraction: Then and Now (74.00 KB)

Discussion:PaulWhite140408 (4.00 KB)

Discussion:Dick Lesh_Response To Paul White 1404 (8.00 KB)

Changes to Expert Team Composition (25.00 KB)

ECR_RigoM_Students’ beliefs within the context of elementary school mathematics classes (80.00 KB)

6. Masami Isoda: Getting Others' Perspectives Through Hermeneutic Effort (279.00 KB)

Program Final as at 5th July 2008 (75.00 KB)

Discussion_GayeWilliams_usage_of_'Insight' (50.00 KB)

Discussion_PamelaHagen_Usage_of_'Engagement' (39.00 KB)

Panel_WilliamsG_Links Between Optimism-Building and Problem Solving Capacity (68.00 KB)