Summary  of the work of the ICME 9 - Topic Study Group  No. 16 on

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(31 July - 6 August 2000 in Tokyo-Makuhari, Japan)

Chief Organizers of TSG16:
Hartwig Meissner (email:  meissne@uni-muenster.de)
Kathleen Heid     (email:  IK8@email.psu.edu)
 
The following report was sent to the organizers to be included in the ICME proceedings:
 
ICME 9 - Topic Study Group No. 16:
Creativity in Mathematics Education and the Education of Gifted Students

Chief Organizers:
Hartwig Meissner, Westf. Wilhelms-Univ. Muenster (Germany) and M. Kathleen Heid, The Pennsylvania State University (USA)
Associate Organizers:
William Higginson: Queen’s University; Kingston, Ontario (Canada), Mark Saul; Bronxville Schools; New York (USA)

Session 1 on "Creativity" (Chair Hartwig Meissner and William Higginson)
     An international team of specialists had prepared this session to give state-of-the-art reviews as well as to let the participants experience and discuss "Creative Activities." Gerald Goldin (New Jersey USA) and Norma C. Presmeg (Illinois USA) started with a survey including theoretical, psychological, social, and affective components. The emphasis on creative environments also included perspectives on representation, affect, and creativity.
     After this overview a collection of "creativity problems" was distributed to pairs of participants who selected one or two of them on which to work. Participants were focused less on correct solutions than on the creative processes that arose while solving these problems.
     On the basis of these experiences Regina Bruder, Friedhelm Kaepnick, and Marianne Nolte (all Germany) then reflected "Needs of the Learners." They concentrated on conditions necessary for creativity in pupils: it is necessary that pupils are creative, that they want to be creative, and that they are allowed to be creative. The presenters discussed individual and social components to keywords like motivation, curiosity, self-confidence, flexibility, engagement, humour, visualization, responsibility,... or fantasy, happiness, acceptance of self and others, satisfaction, success, and so on. Their case studies reported about children who can invent and modify problems, who can listen and argue, who can define goals, who can cooperate in teams, who are active, who discover and experience, who enjoy and have fun, who guess and test, and who can laugh at their own mistakes. They have analysed problem-solving processes used in characteristic problems: Often open ended, fascinating, interesting, exciting, thrilling, important, provoking, challenging, and problems with surprising contexts and results.
     William Higginson (Canada) then analysed "The Role of the Teacher". To summarize, there are different conceptions:

• Creativity as ‘novelty’ – the teacher attempts to introduce concepts in ways that are ‘different,’ ‘unusual’ or ‘innovative.’
• A "creative mathematics teacher” works hard at a ‘hands-on’ approach to learning and makes extensive use of physical materials and models.
• Creativity fits well with a ‘problem-solving’ emphasis, the use of computer software packages, modelling and Hofstadter’s idea of “Variations on a Theme." The teacher attempts to structure the learning environment so that students have maximal opportunity to follow their own interpretations.

Session 2 on “Creativity and the education of the gifted”  (Chair M. Kathleen Heid and Mark Saul)
     Invited papers presented during the second session focused on how mathematically gifted students might be engaged in creative thinking. Papers were: ”The Needs of Mathematically Gifted Learners: Raising the Challenge of Academic Tasks” by Carmel M. Diezmann, James J. Waters, and Lyn English (Queensland University of Technology, Australia); “Teaching for Mathematical Creativity” by Susan Eddins (Illinois Mathematics and Science Academy, USA), Daniel J. Heath (Minnesota Academy of Mathematics and Science, USA), and Daniel J. Teague (North Carolina School for Science and Mathematics, USA); "Environment is a Global Concept: Latvian Experience) by Liga Ramana and Agnis Andzans (The University of Latvia, Riga, Latvia) "; and “Creative Mathematics” by Tony Gardiner (United Kingdom).
     Carmel Diezmann and Lyn English presented four research-based strategies for providing gifted students with opportunities for higher order thinking. First, teachers can use the strategy of “problematising a task,” transforming routine problems so that they are problematic. Teachers can accomplish this in a variety of ways, including requiring that students’ solutions be novel applications of specific mathematical knowledge or introducing additional constraints. Second, teachers can engage students in “mathematical investigations,” problem situations in which students conduct research, collaborate with peers, explore multiple strategies, and engage in open-ended inquiry. Third, teachers can use “ends-in-view” problems with their students. In these problems, although students are clear about the desired endpoint, the existing conditions are ill-defined or poorly framed. Finally, teachers can engage students in “model-eliciting activities” (e.g., recognizing number structures, identifying rates of change, and generating notational systems).
     During session 2, Daniel Teague and Susan Eddins engaged the audience in a thought-provoking discussion of the role of the teacher in fostering or inhibiting creativity in students. In their paper, co-authored with Daniel Heath, the authors pointed out three roles that teachers need to play in order to foster the development of creative thinking in high school students. First, teachers need to create an environment that supports students taking risks and that views failures as opportunities to learn. Second, teachers need to recognize and appreciate creativity (knowing what skills and understandings the student brings to the task) and understand the advice, intervention, and coaching that will help students in the early stages of their potentially creative efforts. Third, teachers must have a deep understanding of mathematics and a store of appropriate problems. They need to know problems that can elicit creative solutions. The paper included descriptions of the programs at their own schools and the ways in which those programs address creativity.
     Liga Ramana and Agnis Andzans spoke about the Latvian experience with encouraging the development of talent in students. In their paper, they pointed out the importance of fostering the development of two kinds of creativity: the ability to apply given rules to uncommon situations and the ability to deviate form given rules. They discussed some of the ways that they created an environment for creativity within lessons:  using multi-level textbooks, supplying a great number of non-standard problems, and engaging students in problem solving in mathematics classes as well as in other disciplines. Discussing ways to foster creativity in the environment external to lessons, they described mathematical olympiad competitions, characterized by their openness at early levels, their intense competitiveness at the later levels, and their prestigious nature throughout. Opportunities exist even for students in mainly rural areas with the correspondence schools and contests. Regular courses on problem solving are offered for teachers, and degree programs are offered at The University of Latvia  in “Modern elementary mathematics.”
     As the final speaker in Session 2, Tony Gardiner provided his insights on the needs of mathematically talented students and how those needs might be addressed. He noted the necessity of providing for students at a variety of levels of talent. His paper raised and addressed the issue of the difficulty that printed materials have in conveying the problem-solving process, alluding to ways materials could be structured to help active readers produce complete solutions on their own without explicitly leading them to solutions.

Presentations by Distribution
The Topic Study Group was further enriched by "Presentations by Distribution":
Can Akkoc (Alabama School of Mathematics and Science, USA)
Shashi Prabha Arya (Maitreyi College, New Delhi India);
Mariko Giga (Department of Mathematics Nippon Medical School, Japan);
David Ginat (Tel-Aviv University Israel);
Okamori Hirokazu (Shitenouji International Buddhism University, Japan);
Ji Sung Lee (Pusan Electronic Technical High School, Korea) and Boo Yoon Kim (College of Education Pusan National University, Korea);
István Lénárt (Department of Methodology and Mathematics Instruction, Budapest, Hungary);
Keiichi Onishi (Osaka Women's Junior College, Japan), Mikiharu Terada and Hiroshi Kanaya (Seifu Senior High School, Japan), and Naoyuki Masuda (Kansaisouka Jr High School, Japan);
Assadollah Razavi (Iran);
Linda J. Sheffield (Northern Kentucky University, USA);
Daniel J. Teague and Dorothy Doyle (North Carolina School for Science and Mathematics, USA).