TSG 12: Research and development in the teaching and learning of calculus
The final report of TSG 12 is here
Team Chairs
Johan Lithner, Department of Mathematics, UmeΠUniversity
Address: S-901 87 UmeŒ, Sweden
johan.lithner@math.umu.se
Maggy Schneider, Department of Mathematics, FUNDP
Address: 8, Rempart de la Vierge, B-5000 Namur, Belgium
maggy.schneider@fundp.ac.be
Team Members
Choe, Young Han, Mathematics Education, Korea Advanced Institute of Science and Technology, Korea
yhchoe@cais.kaist.ac.kr
Ana Isabel Sacristán Rock, Department of Mathematics Education, CINVESTAV, Mexico
asacrist@mail.cinvestav.mx
David Tall, Mathematics Education Research Centre, Institute of Education, The University of Warwick, United Kingdom
david.tall@warwick.ac.uk
Aims and Focus
Call for Papers
Practical Information
Programme
Papers and Discussion Documents
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Aims and Focus
Specific topic areas suggested for the working group included, but were not confined to, the following:
• The role and use of technology in the teaching and learning of calculus;
• The role and use of history in the teaching and learning of calculus;
• Research about cognitive process in the learning of calculus;
• From calculus to mathematical analysis (or)
• Transition between secondary school and university;
• Contextual approach;
• Graphic approach;
• Didactical engineering;
• Misconceptions, epistemological obstacles in the learning of calculus;
• Precalculus;
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Call for Papers
The Organizing Team of TSG 12 accepted papers for presentation and distribution at ICME-10. The TSG has been allocated four sessions during the conference. The first and last of these were joint sessions, and the second and third organised in smaller subgroups, if this is possible, according to the interests of participants. Papers may be proposed for three formats:
• joint session papers, of outstanding and general interest;
• subgroup session papers, related to specific topic areas (see below);
ï 'presentation-by-distributioní 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 ( click here for a template) except that the maximum length of papers is 12 pages. Authors should indicate for which format(s) the paper is proposed.
Please send submissions as electronic attachments, in Word, or in PDF format, with copies to johan.lithner@math.umu.se and maggy.schneider@fundp.ac.be.
Deadline for submission: January 1st, 2004
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Practical Information
Based on a careful refereeing process, the OT decided on whether to accept the paper in one of the indicated formats, and (if relevant) in what subgroup the paper would be presented. Notification of this decision was given by May 30, 2004. All submitting authors must affirm that their paper has not been submitted elsewhere.
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Programme
Tuesday July 6:
12.00 - 13.00 An overview of the evolution in the practices and researches about calculus teaching and learning. After a short introduction by Johan Lithner and Maggy Schneider, David Tall presented an introductory talk on the development in calculus in the 21st century after the reform movements of the 1990s, and Isabelle Bloch and Maggy Schneider considered aspects of the French approach.
Wednesday July 7:
12.00 - 12.15 Thalma Leviatan and Laure Barthel: Introducing Real Numbers: When and How?
12.15 - 12.30 Michel Helfgott: Five Guidelines in the Teaching of First-year calculus
12.30 - 12.45 Victor Giraldo and Luiz M. Carvalho: The Role of Computational Descriptions and Conflicts in the Teaching and Learning of the concept of Derivative
12.45 - 13.00 General discussion and questions
Friday July 9:
12.00 - 12.15 Erhan Bingolbali: The Calculus of Engineering and Mathematics Undergraduates
12.15 - 12.30 Yury Shestopalov and Igor Gachkov: Teaching Computational Mathematics in the Real-time Mode
12.30 - 12.45 Isabelle Bloch and ImËne Ghedamsi: The Teaching of Calculus at the Transition Between Upper Secondary School and University: Factors of Rupture. A Study Concerning the Notion of Limit
12.45 - 13.00 General discussion and questions
Saturday July 10:
12.00 - 12.15 Salahattin Arslan: Reflections on the Teaching ofDifferential Equations: What Effects of a Teaching to Algebraic Dominance?
12.15 - 12.30 Elfrida Ralha, Keith Hirst, and Olga Vaz: A Portuguese Study on Learning Concepts and Proofs: Multivariable Calculus and Mathematica
12.30 - 13.30 Panel Discussion and comments from the audience.Panel Members: Mike Thomas, De Ting Wu, David Smith.
This part of the closing session is mainly devoted to synthesis and discussion of relevant questions raised in TSG 12 and the manner in which they have been treated. The aim is to focus on future orientations in the practices and research in calculus learning and teaching. The panel members have been requested to respond to the following questions:
1) How can we differentiate the teaching of calculus or mathematical analysis according to the target public?
What means and criteria are important to realize a particular approach adapted for a specific public? How do we address the difficulty of the initial limit concept? Is it helpful to see the first approach to calculus through a blend of embodied meaning and symbolism and to postpone formalism to a study of mathematical analysis. How do we deal with the problematic transition between calculus and mathematical analysis?
2) What is the role of technology?
How can we characterize and categorize more deeply the ways of using new technologies to teach calculus and mathematical analysis? How do we take into account its use as a mathematical tool to solve problems, as a means of delivering the curriculum, and as a cognitive environment for learning?
3) What do the various didactical theories bring to structure the preceding questions?
How do we evaluate the uses of new technologies in the learning of the students?
What about the teacher's practices?Ý How can we evaluate effects of these practices?
The overheads of the three responses of the three panel members are here:
Mike Thomas, De Ting Wu, David Smith
The final report of the working group is here.
Additional papers on the website (below) are available as references in the discussions between the participants.
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