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					Implicit and explicit philosophy in secondary school curriculum of mathematics.

                                      Karen François
                                CLWF Free University Brussels

During my research into the curriculum of mathematics, I discovered that there is small scope
for an explicit philosophy of mathematics. Nevertheless there are some initial concepts
formulated in the general objectives which tended to a more absolutist view of mathematics.
However, in formulating the new curriculum, there was some attention paid to the inclusion
of humanistic values.
The mainstream of the implicit philosophy of mathematics is still a rather absolutist one,
viewing mathematical truth as absolute and certain, connected with some humanistic values.

There is a large gap between general and vocational education.
On the one hand, we can say that mathematics in vocational education is completely
embedded in a modular system, and attention is paid to core skills. On the other hand we must
say that pupils are prepared for specific occupations, for personal and social functioning, to
survive in our society. Access to higher education is theoretically possible but unlikely for the
Mathematics in general education is a separate course. General education provides a strong
base for higher education.

In the words of Alan J. Bishop who makes a difference between the small m and the large M
of mathematics, where the small m stands for mathematical basic competence (such as:
counting, designing, explaining, locating, measuring and playing) and the large M stands for
mathematics as the Western scientific discipline, we can say that pupils in vocational
mathematics are taught the small m and pupils in general education are taught the large M.
The more general the education, the larger the M, and the higher the respect in society.
In this presentation I want to:
    - Set out some arguments for the absolutist and the humanistic values
    - Explain the gap between general and vocational education
    - Search for the role of ethnomathematics in western school curricula.

Arguments for the absolutist, I want to refer to:
   - The fact that there is no room to discuss the status of mathematics
   - The status is clear and rather static
   - There is no philosophy in vocational education
   - The larger the M, the higher the respect in society
   - The appreciation for mathematics that pupils are encouraged to gain is seen as the
     highest form of motivation,
   - Experience-based learning is only used to hold the interest and to motivate
     disinterested pupils, to help them to gain an appreciation for mathematics with the
     large M.

Arguments for the connection with some humanistic values:
   - The limited space for philosophy in general education
   - The limited attention given to the possibilities and the limitations of mathematics
   - The attention given to the application of mathematics
   - The limited attention to cultural and historical components (where most of the space is
     filled with art).

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