TSG 28: New trends in mathematics education as
a discipline
Team Chairs
Tommy Dreyfus, Department of Science Education, School of Education, Tel
Aviv University
Address: P.O.B. 39040, Ramat Aviv , Tel Aviv 61390, Israel.
tommyd@post.tau.ac.il
Domingo Paola, Liceo Scientifico “A. Issel”,
Finale Ligure
Address: Via Canata 2-17, I-17021 Alassio (SV), Italy.
domingo.paola@tin.it
Team Members
Yves Chevallard, Group of the Didactics of Mathematics, L’IUFM, d’Aix-Marseille,
France.
y.chevallard@aix-mrs.iufm.fr
Sangsook Choi-Koh, Department of Mathematics
Education, College of Education, Dankook University, Korea.
sangch@dankook.ac.kr,
yyychoi@elim.net
Erna Yackel, Department of Mathematics, Computer
Science and Statistics, Purdue University, USA.
yackeleb@calumet.purdue.edu
Aims and Focus
The aims of TSG 28 are to portray some of the new trends in
mathematics education research and to create an environment suitable for a
meaningful discussion. The Team chose two topics which will
constitute the focus of discussion.
Topic 1. Mathematics and cognitive science, with particular attention to the theories of embodiment in mathematics education.
The theory of embodied cognition deals with questions like “what are the bodily and biological mechanisms underpinning cognition?” and, as concerns mathematics in particular, “what are the grounding metaphors used in the construction, systematization and communication of mathematical thinking?”
Topic
2. Combining quantitative and qualitative research methods in
mathematics education
The
time seems ripe to transcend the dichotomy of quantitative versus
qualitative research methods and ask which combinations of the two could
yield results that are more useful and more valid than those obtained
from either type of method separately.
Call for Papers
As regards Topic 1, generally speaking, we solicit
reports on teaching experiments, which make reference to the theoretical
background of embodied cognition. In particular, we ask for research
studies that consider how the peculiar structure of the biological brain
may be supported by new technologies to enhance mathematical thinking.
o
the relationships between the
functioning of the human brain and the formulation of mathematical ideas
o
possible connections between embodied
cognition and neuroscience research.
Practical
Information
We ask those
interested to send a three-page description of their contribution by
e-mail in .doc or .rtf or .pdf format to Domingo Paola (domingo.paola@tin.it
) by December 20th, 2003. Individuals may submit a paper
for consideration by the Organising Team of the TSG to be accepted
either for oral presentation in the TSG or as a paper presented by
distribution. The submissions will be evaluated by March 20. Only a
rather limited number of papers can be presented orally in the TSG.
Therefore, as an important component of the work of the TSG, papers
considered by the team to be of appropriate quality and relevance to the
TSG, may be accepted for presentation by distribution. Such papers will
be placed on this website and thus form part of the material produced
for the TSG. Also, authors may distribute such papers in a hard copy
version at the third session of the TSG with a label stating that this
paper has been accepted by TSG 28 of ICME 10 for presentation by
distribution.
Programme
Structure of the provisional program
July
6, 11.45-12.45 Opening session on Topic 2:
Combining
quantitative and qualitative research methods in mathematics education
(Chair:
Tommy Dreyfus)
11.45
- 12.05
Invited
Plenary. Kurt Reusser and Barbara Vetter (University of Zurich,
Switzerland): Combining
quantitative and qualitative analyses of lessons in (large scale)
mathematics video studies. Insights from research and some potentials
for teacher education
12.05
- 12.15
Questions
and discussion
12.15
- 12.35
Invited
Plenary. Jo Boaler (Stanford University): Studying
a complex practice - using multiple methods to capture the relationships
between teaching & learning
12.35
- 12.45
Questions
and discussion
July
7, 11.45-12.45 Opening session on Topic 1:
Mathematics
and cognitive science, with particular attention to the theories of embodiment in mathematics
education (Chair:
Domingo Paola)
11.45
- 12.05
Invited
Plenary. Nathalie Sinclair (Faculty
of Education, Simon Fraser University, Burnaby):
Embodied and
Evolutionary Perspectives in Mathematics Education
12.05
- 12.15
Questions
and discussion
12.15
- 12.35
Invited
Plenary. Rafael Nunez (Dept.
of Cognitive Science of the Univ. of California, San Diego): What
Embodiment for Mathematics Education? Issues and Controversies from the
perspective of Cognitive Science
12.35
- 12.45
Questions
and discussion
July
9, 11.45-12.45 Parallel sessions
Topic
1
(Chair: Yves Chevallard).
11.45
- 11.55
Ornella Robutti (University of Torino): The
Construction of Mathematical Knowledge Through Multiple Perspectives
11.55 - 12.00 Discussion
12.00
- 12.10
Francesca Ferrara (University of Torino and TERC): Bodily
Experiments, Metaphors, Gestures and Artefacts in Grasping the Meaning
of a Motion Graph: A Case Study
12.10 - 12.15 Discussion
12.15
- 12.25
Janete Bolite Frant, Maria Cecilia Barto, Claudio Dallanese and
Antonio Mometti (Catholic University in Brazil): Reclaiming
Visualization: When Seeing does not Imply Looking
12.25
- 12.45 Discussion
Topic
2
(Chair: Sangsook Choi - Koh)
11.45
- 12.00
Mi-Kyung
Ju (Ewha Womans
University) & Oh Nam Kwon (Seoul
National University): Mixed
method: different
ways of talking about students’ views about mathematics
12.00
- 12.05
Discussion
12.05
- 12.20
Peter
Petocz and Anna Reid (Macquarie University), Leigh Wood and Geoff
Smith (University of Technology, Sydney): On
Becoming a Mathematician: an international perspective for future
professionals in the mathematical sciences
12.20
- 12.25
Discussion
12.25
- 12.45
General discussion
July 10, 11.45-13.15 Integrating closing session (Chair: Erna Yackel)
11.45 - 12.05
Invited Plenary. Jeremy
Kilpatrick (University of Georgia): Methods as Ideologies: Is Our
Research Scientific or Political?
12.05 - 12.25
Discussion
12.25 - 12.45
Invited Plenary. Marianna
Bosch (University Ramon Llull, Barcelona):
Mathematical Cognition and the Anthropological
Approach to Didactics
12.45 - 13.05
Discussion
13.05 - 13.15
Summary and conclusions
Papers
and Discussion Documents
This section will be regularly updated with others suggestions and
contributions.
Topic 1
Bosch, M. & Chevallard, Y., Ostensifs et sensibilité aux ostensifs dans l'activité mathématique, Recherches en Didactique des Mathématiques, 19/1, 77-124, 1999.
Bosch, M. & Gascon, J., Organiser l'étude. Theories & Empiries, in Dorier, J.-L. , Artaud, M., Artigue, M., Berthelot, R., Floris, R. (eds) Actes de la 11e École d’Été de Didactique des Mathématiques, 2002 - La Pensée Sauvage – Editions - Fabriqué en France.
Campbell, S. R., Enacting possible worlds: Making sense of (human) nature, In J. F. Matos, W. Blum, K. Houston, S. P. Carreira (Eds) Modelling and mathematics education: ICTMA9 Applications in science and technology, pp. 3-14, 2001, Chichester: Horwood Publishing.
Campbell, S. R., Reconnecting mind and world: Enacting a (new) way of life. In S. J. Lamon, W. A. Parker, & S. K. Houston (Eds.) Mathematical modelling: A way of life, pp. 245-253, 2003, Chichester: Horwood Publishing.
Chevallard, Y., Didactique et formation des enseignants,, Journées d’études INRP-GÉDIAPS Vingt ans de recherche en didactique de l’Éducation Physique et Sportive à l’INRP (1983-2003), 2003 Paris
Edwards D.L.Embodiment, Conceptual Linguistics and Geometry proposed and accepted paper for ICME 2004, TSG 28.
Lakoff, G. & Núñez, R.E., Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being, Basic Books, 2000 (http://perso.unifr.ch/rafael.nunez/)
Leron, U., Mathematical Thinking and Human Nature, Draft paper, new version, April 2004.
Núñez, R.E, Mathematical idea analysis: what embodied cognitive science can say about the human nature of mathematics, in Nakahara & Masataka (editors), Proceeding of the 24th Conference of PME, v 1, 1-23, 2000.
Radford, L. (forthcoming). Rescuing Perception: Diagrams in Peirce’s theory of cognitive activity. In Lafayette de Moraes and Joao Queiroz (Eds.), C.S. Peirce's Diagrammatic Logic. Catholic University of Sao Paulo, Brazil.
Schiralli, M. & Sinclair, N, A constructive response to "Where mathematics come from", Educational Studies in Mathematics, 52(1), 79-91, 2003 ( http://www.math.msu.edu/~nathsinc/papers/Response_to_WMCF.pdf )
The followings four papers are availables, in pdf, format at the "David Tall Academic Page": http://www.warwick.ac.uk/staff/David.Tall/
Tall,
D. (2000), Biological Brain, Mathematical Mind & Computational
Computers (how the computer can support mathematical thinking and
learning). In Wei-Chi Yang, Sung-Chi Chu, Jen-Chung Chuan (Eds), Proceedings
of the Fifth Asian Technology Conference in Mathematics, Chiang Mai,
Thailand (pp. 3–20). ATCM Inc, Blackwood VA. ISBN 974-657-362-4.
(2000h)
Tall, D. & Watson, A., (2002). Embodied action, effect, and symbol in mathematical growth. In Anne D. Cockburn & Elena Nardi (Eds), Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education, 4, 369–376. Norwich: UK. (2002j)
Tall, D., Using
Technology to Support an Embodied Approach to Learning Concepts in
Mathematics, First Coloquio de Historia e Tecnologia no Ensino de
Matemática, at Universidade do Estado do Rio De Janiero, February
21-3, 2002. (to appear) (2003~)
Watson, A.,
Spirou, P., Tall, D. O. (2003). The Relationship between Physical
Embodiment and Mathematical Symbolism: The Concept of Vector. The
Mediterranean Journal of Mathematics Education. (in press). (2003a)
We also
suggest to visit the web
site of the proget of Jim Kaput, Jeremy Roschelle and Ricardo
Nemirovsky, (http://www.simcalc.umassd.edu/
) and the web site of Math in motion (Ricardo Nemirovsky, Tracy Noble,
Cara DiMattia, Djalita Oliveira-Ramos, http://www.terc.edu/mathofchange/MathinMotion/home.html)
Topic 2
AAVV, Highlights From the TIMSS 1999 Video Study of Eighth-Grade Mathematics Teaching, NCES (National Center for Education Statistics), 2003.
AAVV, Teaching Mathematics in Seven Countries - Results from the TIMSS 1999 Video Study, NCES (National Center for Education Statistics), 2003
Boaler, J. King’s College, London, Open and Closed Mathematics Approaches: Student Experiences and Understandings, Journal for Research in Mathematics Education. 1998. 29 (1) 41-62.
Boaler,
J., When
Learning no Longer Matters - standardized testing and the creation of
inequality,
Phi
Delta Kappan, 2003,
March, 84 (7), 502-506.
Kilpatrick, J., Where's
the Evidence? , Journal for Research in Mathematics Education 2001,
V. 32, Issue 4, 421 - 427.
Petko, D, Reusser, K. & Noetzli, C, Collaborative video analysis in a virtual learning environment, ICNEE Conference 2003
Reusser, K., Pauli,C., Grob, U., Waldis, M., Hugener, I. & Krammer,K: Integrating insider's (participant's) and outsider's (researcher's) perspectives on teaching and learning: the case of adaptive instruction (Paper presented at the Invited Symposium "From cultural context to classroom practice: Video-based, crosscultural studies on the quality of teaching and schooling", 9th European Conference of EARLI, August 31- 2001 in Fribourg, Switzerland)
Reusser, K, Bridging Instruction to Learning‘ -Where we come from and where we need to go. A research strategy and its implementation in a crosscultural video survey in Switzerland, 9th EARLI Conference Fribourg/CH, September 1, 2001