Discussion group 3:
Mathematics education: for what and why?
Don Victor Gómez Garza and C103, C201, C202, C203,C204,C205,C206 - FACPYA
  • - What is mathematics education for?
  • - What are the most productive ways of characterizing “mathematical literacy”?
  • - Should school mathematics education be dominated by the discipline of mathematics, rather than reflecting the diversity of mathematical practices?
  • - Can a balance be achieved between a homogeneous, monolithic, globalized curriculum and the diversity of people and forms of knowledge construction and use?
  • - How should mathematics education prepare people for technology?
  • Claude Gaulin (Canada)
    claude.gaulin@fse.ulaval.ca
  • Brian Greer (USA)
    brian1060ne@yahoo.com
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Team members:
  • John Volmink (South Africa)
    johnv@cornerstone.org.za
  • Roza Leikin (Israel)
    rozal@construct.haifa.ac.il
  • Ole Skovsmose (Denmark)
    osk@learning.aau.dk
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Aims and focus

The overarching question for this Discussion Group is: What is mathematics education for? There is no single answer to this question. The aspects listed below all have validity, and the relative weights given will depend on the life experience, intellectual and educational history, and values of any individual:

  1. The nurturing of the next generation of mathematicians and those who will use mathematics in their work.
  2. Teaching how to think rationally, dispassionately, objectively.
  3. Providing skills for dealing with situations in everyday life.
  4. The training of a workforce equipped to compete successfully in the global economy of the information age.
  5. Intellectual enrichment, acknowledging mathematics as equally a part of humankind’s cultural and aesthetic heritage as literature or music.
  6. Making accessible powerful tools to analyse, critique, and act upon, social and political issues.
  7. Building critical skills for understanding how mathematical ideas influence social and political issues that impact our lives.

Against this background, we propose to discuss the following issues:

• Mathematical literacy

“Mathematical literacy” has become a popular term to refer, roughly speaking, to the mathematical disposition and proficiency desirable in a citizen. As such it represents a step towards a more widespread access to powerful mathematics, particularly in relation to the practicalities of personal, social, and economic life. However, the term is interpreted in so many different ways that its meaning has lost definition. For example, there is a stark contrasts between an interpretation that focuses on “basic skills” or “numeracy” as preparation for the workforce and one that focuses on development of critical tools for the analysis of social and political issues.

What are the most productive ways of characterizing “mathematical literacy”?

• Diversity of mathematical practices and school mathematics education

Developments in mathematics education, such as the field of ethnomathematics founded by Ubiratan D’Ambrosio, reactions against the Eurocentric narrative of the history of mathematics, the acknowledgment of mathematics as a human activity, and a parallel shift in cognitive psychology to theories of situated cognition, mean that the dominance of mathematics-as-school-subject by mathematics-as-discipline can no longer be taken for granted. Mathematics educators and others express concern that school mathematics has scant relevance to the personal and collective lives of the students or the adults they will become.

Should school mathematics education be dominated by the discipline of academic mathematics, rather than reflecting the diversity of mathematical practices?

• Implications of globalization for mathematics education

There are tensions within mathematics education resulting from globalization. Should homogenization of curriculum be resisted, as with the disappearance of languages under the dominance of English? Is there an imposition of a single view of humankind, and the associated European construction of rationality? Is it possible to reconcile honoring the mathematics of a culture and planning mathematics education for economic progress – in a post-colonial country, for example?

Can a balance be achieved between a homogeneous globalized curriculum and the diversity of people and forms of knowledge construction and use?

• Mathematics education for living with technology

Mathematics influences and controls our lives in ways that, for most people and most of the time, are not recognized. Complementary to such mathematization is “demathematization” whereby mathematical models become hidden within black-box devices. Should a major aim of mathematics education be to prepare people to critically examine such phenomena and react appropriately? Rather than training in routine expertise and simplistic thinking, should we aim to nurture adaptive expertise and the ability to recognize, and ideally have some grasp of, complex situations modeled through mathematics? Is a major aspect of such a goal to provide students with better analytical tools to evaluate the exponentially increasing information made accessible through technology?

How should mathematics education prepare people for technology?

CORE PAPERS TO FOCUS DISCUSSION

The key questions just presented are phrased in rather general terms, so further information to frame the discussions has been presented in the form of “core papers” selected by the Organizing Team for DG3. These are posted below. Participants are expected to have read, and be prepared to discuss, this set of papers in advance of the meeting. Experience shows that participants in Discussion Groups generally do not read a lot of papers ahead of time! Accordingly, there is a relatively small number of core papers, and they are short.

PLANNED STRUCTURE FOR THE THREE SESSIONS

In keeping with the spirit of Discussion Groups at ICME, there will be no formal presentations. Rather, time is intended for focused discussion, with emphasis on every participant having a voice.

First session (plenary, 2 hours): After a brief introduction, participants will be allowed a short time (depending on the number who attend) in which to comment, depending on their interest, on one or more of the issues related to the questions formulated above and addressed in the core papers. (Note that given the likely number of participants, our original plan to allow all participants to comment during the first session is unlikely to be possible). For this arrangement to work effectively, it is essential that all participants:
(a) read all the core papers.
(b) direct their comments to the questions formulated above or raised in the core papers.
Any time left at the end will be devoted to general discussion, and to the organization of subgroups for the second session.

Second session (subgroups, 2 hours): Division into subgroups will enable all participants to have a voice, given that numbers may prevent this happening in the plenary sessions. One subgroup will be devoted to each of the issues listed above and the core papers related to them. In addition, it is envisaged that there will be a Spanish-speaking subgroup. The sixth subgroup will address the example of South African approaches to actualizing a vision of mathematical literacy. Each subgroup will be led by a moderator. Recorders will be selected for each group, who will provide a written summary ahead of the third session.

Third session (plenary, 1 hour): A designated reporter from each subgroup will summarize the discussions of the subgroup. If time allows, there will then be a general discussion.

Preparation of report: After the meeting, reporters from the subgroups will revise the written record of their discussions as necessary and give these final reports to the Organizing Group. The co-chairs will prepare a report on the working of the DG, based on the subgroup reports, and on documentation of the first and third sessions (recorders will be selected for these sessions). A draft of our report will be circulated to the other members of the OG, and to all participants, for comment and reaction.

GUIDELINES FOR WRITTEN CONTRIBUTIONS

The deadline for submission of new papers has now passed.

It is suggested that, if you have submitted a paper, you also prepare it in the form of a poster. The conference organizers have confirmed that any poster submitted will almost certainly be accepted and they will issue documents acknowledging that you have made a presentation at the conference, which for some participants may be necessary to secure funding from their institutions. The poster does not have to be elaborate, and could simply be an adaptation of your written contribution. Please consult the ICME11 Website for details on size, etc.

Looking ahead, the Organizing Team is considering a publication, in the form of a journal issue or book, based on the work of the group. Such a publication would include the core papers and a selection of the written contributions. One idea would be invite longer versions of these papers. The publication would also include summaries of the discussions during the conference.

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