The role of mathematical competitions and other challenging contexts in the teaching and learning of mathematics

Following ICME-10 an ICMI Study titled “Challenging Mathematics in and beyond the classroom” was conducted and the study volume is in progress. The title of DG19 at ICME-11 reflects the tendency to widen the sphere of interest of the group to include not only mathematical competitions but other activities and opportunities of a challenging nature.

Can it be claimed that in mathematical competitions – and in challenging mathematical contexts in general – what is commonly known as elementary mathematics both continues to thrive and inspires young minds? To what extent do problems set in mathematical competitions adequately reflect the variety and richness of mathematical activity in problem solving?

Are there mathematics and mathematical problems apt for challenging all students? How can competitions and other challenging mathematical contexts motivate and foster mathematical creativity with students at large?

Organizing team composition

Breakdown of DG-19 Sessions at ICME-11

Papers and discussion documents

Maria Falk de Losada (Colombia)

Bill Richardson (United Kingdom)

Radmila Bulajich (Mexico)

Romualdas Kasuba (Lithuania)

romualdas.kasuba@maf.vu.lt

Since ICME-10 an ICMI Study titled “Challenging Mathematics in and beyond the classroom” has been conducted and the study volume is in progress. The title of DG19 at ICME-11 reflects the tendency to widen the sphere of interest of the group to include not only mathematical competitions but other activities and opportunities of a challenging nature. Furthermore, questions of interest have been honed and horizons expanded.

DG19 will focus its discussion on the following questions:

1) Do mathematical challenges better reflect the nature, the beauty and other characteristics of the corpus of elementary mathematics, as well as the experience of doing mathematics, than does ordinary school mathematics? Does this make the mathematics involved more likely to engage the learner?

2) Does the widespread use of calculators and computers – marvelous tools that they are – imply that mathematics education can only justify itself (aside: in as much as it prepares the learner to use a calculator or computer in an intelligent fashion, or) in as much as it is challenging, non-routine and cannot trivially be done on a calculator or computer, that is, in as much as it provides opportunities for all learners to be engaged in challenging mathematics?

3) How does this last question apply to in-service and future teachers? What are the needs and characteristics of teacher education with regard to challenging mathematics?

4) What are the implications for more challenging assessment in mathematics – both in and beyond the classroom?

On each of these points, besides analyzing programs, projects and experiences, the questions of what research has been done and of what research is needed in the future will be examined.

The primary goal of this Discussion Group is to provide an opportunity for an international group of interested mathematics educators to examine the contexts in which more challenging and demanding mathematics can and should be offered to students at all levels of mathematical studies.

Following the long and fruitful tradition of mathematical competitions providing challenge through engagement in problem creation and solving, as well as new points of interest brought forward by ICMI Study 16, the group will address the following areas, both by analyzing programs, projects and experiences and examining relevant research:

1) Challenge and mathematics

2) Challenge and the student

3 Challenge and the teacher

4) Challenge and assessment

The organizing team for this discussion group has formulated four principal questions to stimulate contributions and discussion which are included in the description of the group seen above.

Those wishing to participate in DG 19 are encouraged to submit a one-page description of their interest and/or research related to these questions or more generally on the topic of the role of competitions and other challenging contexts in mathematics teaching and learning. This should be received by each of the five members of the committee no later than December 10, 2007 and should specify the question or questions that will be addressed.

No later than January 10, 2008, participants who have been accepted by the organizing team should submit, via e-mail attachment, a paper of 1000 to 2000 word in extent, to each member of the Organizing Team.

The organizing team expects to make its selection of participants no later than January 22, 2008. It is understood that a necessary condition for participation in the group and posting of any material is that the participant be a registered delegate to ICME 11.

No later than April 15, 2008, the organizing group will circulate an agenda for the four sessions of the study group and indicate how certain participants might contribute to its work.

The set of questions included here seeks to provide a stimulus for papers. They are not intended to limit the areas of discussion. Those wishing to participate in the discussion group are encouraged to e-mail other possible areas of discussion to the group chairs for inclusion in the draft program even if not supported by a discussion paper.

Breakdown of DG-19 Sessions at ICME-11

Three slots have been scheduled for meetings:

On the panel for question 1 and related issues: Petar Kenderov, Alexander Soifer, Ana Rechtman, Agnis Andzans and Ilza France, Chair: Romualdas Kasuba. Secretary: Yahya Tabesh or Maria de Losada

On the panel for question 2 and related issues: Sergei Pozdnyakov, Romualdas Kasuba, Chair: Bill Richardson, Secretary: Yahya Tabesh or Maria de Losada

On the panel for question 3 and related issues: Andy Liu, Josef Molnar and Jaroslav Svrcek, Bill Richardson. Chair: Radmila Bulajich. Secretary: Yahya Tabesh or Maria de Losada

Depending on the number of people registered for DG-19 and attending the session, we will break into small groups for discussion of question 4. Each group will have one member of the Organizing Team in it who will act as secretary and record the proceedings of the group.

16:30 – 17:00 Each member of the discussion group introduces him/herself.

17:00 – 18:30 Panel for question 1 and related issues

17:00 – 18:00 Panel for question 2 and related issues

18:00 – 19:00 Panel for question 3 and related issues

15:00 – 16:00 Small group discussion of question 4 and related issues

16:00 – 16:30 Organizing team discusses final report.

Papers and discussion documents

Discussion document 1. Agnis Andzans and Ilza France (87.00 KB)

Discussion document 3. Romualdas Kasuba (127.00 KB)

Discussion document 5. Posov, Pozdnyakov and Stepulenok (244.00 KB)

Discussion document 6. Rechtman (56.00 KB)

Discussion document 7. Soifer (97.00 KB)

Discussion document 7. Soifer (97.00 KB)

Discussion document 4. Andy Liu (38.00 KB)

Discussion document 8. - Yahya Tabesh (184.00 KB)

Discussion document 9. - Molnar and Svrcek (121.00 KB)

Discussion document 2. Petar Kenderov (79.00 KB)