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Brescia and Bourgas. These are “professionally” prepared teams for individual and group competitions with standard time restriction of few hours and specific problems of Olympiad type. Their results were very close to the results of the Aprilov team whose preparation has not been oriented to Olympiad-like competitions. As expected, the creativity in problem posing and the creativity in problem solving are not necessarily correlated to one another, i.e. these are two different facets of creativity.
Another important conclusion we drew from the math club activities was that it is necessary to give students a longer term to manifest their capacity of creating original mathematical ideas. The opportunity to work on a specific mathematical problem (project) for a longer period is an essential step to conveying the flavor of the real research in mathematics to pupils and teachers alike.
The participating university researchers are able to help teachers and pupils in reducing the difficulties in posing real-life problems and solving them with mathematical tools. In some cases the real-life problems are only apparently similar to the mathematics problems encountered at school, and there are no simple methods to solve them. But it is not in vain that one of the definitions of the “problem solving” is:
what you do when you don’t know what to do…
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• Motivation and self reliance of students. When the focus is placed on capable pupils their motivation to work with the math subject is enforced and they get plenty of positive reactions from peers
• The teacher’s role. The teacher has to be supportive to the students in their working process, first of all by posing appropriate questions. Such questions activate the thought and reflection process. Also the students have to be supported mentally, if needed. It is an art to maintain students’ confidence, motivation and concentration when something seems unclear. But the teacher should avoid giving too many answers. The students are capable to find out the answers themselves.
Another math club admits only 8–9 graders (9th being the highest grade of the school organizing the club). As expressed by most of the club members the main reason for attending it has been to prepare better for the next academic level – the upper secondary schools. Therefore the club activities are curriculum-oriented.
Here follows an example of a questionnaire in a Danish math club that you might find useful:
• Are you good at math? How do you know?
• When do you feel you learn the most in math lessons?
• Give an example of a task, you find especially fruitful. Why do you find this task so good?
• Are you working especially well with others in your class? With whom for example?
• How often do you talk with your math teacher about difficult tasks?
• Do you think your math teacher is demanding enough of you? Or too much?
• Do you have a good advice to teachers with talented students in their class?
Concluding remarks
As it could be seen from the description of the math clubs considered above they have different target groups. The clubs in Denmark involve larger or smaller groups of high school students and the topics are closely related to the standard curriculum and to the modelling of applied problems, while in Italy the target group consists of students interested in math competitions and the topics are mainly of extracurricular character. The organization and the management of the clubs in these partner countries is quite different: the financial support of the clubs in Denmark is well organized, whereas the clubs in Italy depend heavily on the enthusiasm of university professors and high school teachers.
Even with these differences there are some common findings:
• The motivation of pupils and teachers in participating and organizing extra curricula activities can increase thanks to their experience in the club.
• New ideas of in-service teachers can emerge and then be implemented in the activities of the math clubs. Periodic meetings and courses during which teachers’
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suggestions can be discussed together with university professors in view of their realisation are of special importance.
• Participants should be encouraged to investigate and explore things on their own.
• The clubs are a very appropriate form for stimulating interest to mathematics and a joy of one’s achievements in the field.
• The students can acquire important math competences such as:
o Math thinking competence and Problem tackling competence. Regular meetings of the clubs often give a concrete math arguments and problems complementary to some points in the standard math curriculum. Some of these problems are produced by the members of the Problem posing group being formed in the Italian club in Pisa.
o Modeling competence. It has been enhanced during the regular lectures on how to formulate problems originating from real life.
o Reasoning competence. The work in math clubs helps essentially the preparation of teachers and students for solving problems requiring proofs which improves significantly this competence.
o Representing and Communicative competence. Lectures and talks at the clubs prepared by teachers and their students contribute to developing these competences.
o Aids and tools competence. The variety of tools (including IT) used in the club activities contributes to developing also this competence
Taking into account these positive effects you would hopefully be stimulated to participate in an existing math club (or even initiate a new one) so as to attract your students to studying and applying mathematics.
Before doing this you might still want to consider the following questions:
• Is there a math club you and your students might join?
• Are there appropriate conditions in your school to organize a math club?
• Are there relations with other schools interested in organizing math clubs?
• Is it possible to establish the necessary relationship with professors from universities? (Such relations are crucial for the professional orientation of the students.)
• What ways do you see for finding funds and other types of support for the club?
Math Clubs – doing math together 77 It is clear that we could extend the list of possible questions. However, to make the first step (no matter how small, e.g. organizing a club in your own school) would be a very rewarding action.
References
[1] The Math Talents in Pisa,
http://www.dm.unipi.it/~olymp/club.htm (April 25, 2013)
[2] The Unsung Hero – http://www.eroemaicantato.org/ (April 25, 2013)
[3] Ushakov, D. V. Olympics of the mind as a method to identify giftedness: Soviet and Russian experience, Learning and Individual Differences, vol. 20, 2010, pp. 337–344
[4] Cramond, B. We can trust creativity tests, Educational Leadership, 52(2), 2005, 70–71, 199
[5] Gardner, H. Seven creators of the modern era. In J. Brockman (Ed.), Creativity, New York: Simon & Schuster, 1993, pp. 28–47
[6] Paulus, P. B., Nijstad, B.A. Group creativity: Innovation through collaboration.
New York: Oxford University Press, 2003
[7] Brown, S. I., Walter, M. I. Problem posing in mathematics education. In I. Brown Stephen, I. Walter Marion (Eds.), Problem posing: Reflection and applications, Hillsdale, New Jersey: Lawrence Erlbaum Associates, 1993, pp. 16–27
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