Unformatted text preview: Educating student teachers about values
Educating
in mathematics education
in
Alan J. Bishop
Alan
Faculty of Education
Faculty
Monash University
Melbourne
Australia
<[email protected]> 1 Mathematics educators are increasingly being
Mathematics
challenged about the goals to which mathematics
education should aim: technology, societal demands,
scientific development, economic growth….
To a large degree these goals are all about the values
we should be inculcating in our students.
we
Therefore we need to think about what mathematical
values teaching we are doing with our student teachers.
values 2 Values are the deep affective qualities
Values
which education aims to foster through the
teaching of mathematics.
Values are not the same as beliefs,
although the two constructs are related,
and there is much research on beliefs in
mathematics education but little on values.
mathematics
3 Whereas it is relatively easy and common in the
Whereas
teaching of humanities, arts subjects and
perhaps also the sciences to discuss the
development of values, this is not the case at
present in mathematics teaching.
present
There is a widespread misunderstanding that
There
mathematics is a valuefree subject, and many
policy developers (as well as some educators)
might initially be concerned about explicit values
education in mathematics.
4 What policy developers and others should be
What
concerned about, however, is that values
teaching and learning inevitably goes on in
mathematics classrooms.
mathematics
This is because whenever teaching takes place,
This
choices are made, which are based on, and
therefore reveal, certain values.
therefore
However there is only a limited understanding at
However
present of what values are being transmitted,
and of how effectively they are being
transmitted.
transmitted.
Perhaps this is because most values appear to
Perhaps
be taught and learnt implicitly rather than
explicitly in mathematics classrooms.
5 Therefore there are new research questions which
Therefore
can now be asked, such as:
What values are teachers of mathematics
teaching?
teaching?
What values are students learning from their
What
teachers?
teachers?
Are they learning more significant values from
Are
their peers than from their teachers? 6 What values are implicitly and explicitly being
What
transmitted or ‘shaped’ through curricula and
textbooks?
textbooks?
To what extent can teachers be helped to teach
To
other values than those they currently teach?
other
Is it possible to develop more effective
Is
mathematics teaching through the values
education of student teachers?
7 Values in mathematics education are of three basic kinds:
Mathematical values: values which have developed as
Mathematical
the subject has developed within the particular culture.
the
General educational values: values associated with the
General
norms of the particular culture, of the particular society,
and of the particular educational institution.
and
Mathematics educational values: values embedded in
Mathematics
the curriculum, textbooks, classroom practices, etc. as a
result of the other sets of values. 8 My research approach to these issues has been to focus
My
on mathematical values, and on the actions and choices
concerning them – mathematical value competences
mathematical I have used White’s (1959) three component analysis and
have
terminology:
terminology:
Ideological values: ‘rationalism’ and ‘objectism’
Sentimental values: ‘control’ and ‘progress’
Sociological values: ‘openness’ and ‘mystery’.
Sociological
9 Mathematical value competences Mathematical
Ideological
Ideological
Valuing Rationalism means:
Valuing emphasising argument, reasoning, logical
analysis, and explanations.
Valuing Objectism means:
Valuing emphasising objectifying, concretising,
emphasising
symbolising, and applying the ideas of
mathematics.
mathematics.
10 Mathematical value competencesSentimental
Valuing Control means:
emphasising the power of mathematical and
emphasising
scientific knowledge through mastery of rules,
facts, procedures and established criteria.
Valuing Progress means:
Valuing
emphasising the ways that mathematical and
scientific ideas grow and develop, through
alternative theories, development of new
methods and the questioning of existing ideas
methods
11 Mathematical value competencesSociological
Valuing Openness means:
emphasising the democratisation of knowledge,
through demonstrations, proofs and individual
explanations.
Valuing Mystery means:
Valuing
emphasising the wonder, fascination, and
mystique of mathematical ideas.
12 Developing mathematical value
Developing
competences 1.
competences
•
•
•
• Making the student teachers aware of
Making
values in mathematics education.
Developing an understanding of the
Developing
history of mathematics.
history
Illustrating contrasts between different
Illustrating
mathematical histories.
mathematical
Exploring cultural value differences via
Exploring
ethnomathematics.
ethnomathematics.
13 Developing mathematical value
Developing
competences 2.
competences
Identifying mathematical values in
• school and university textbooks,
• writings about mathematics
• mathematics examinations and tests
• science and engineering textbooks 14 Developing mathematical value
Developing
competences 3.
competences
Using the 6 value classification to:
Create appropriate teaching materials for
Create
classroom use.
classroom
Demonstrate and develop richer
Demonstrate
pedagogical repertoires.
pedagogical
Develop more appropriate assessment
Develop
instruments.
15 Some other points from our
Some
research
research
Teachers’ values in the classroom are
Teachers’
shaped to some extent by the values
embedded in each subject.
This implies that changing teachers’
values and understandings of the subject
being taught may well change the values
they can emphasise in class. 16 Some other points from our
Some
research
research
If teachers wish to emphasise values other
If
than those they currently emphasise, it is
possible to learn strategies from their
teaching of other subjects.
teaching
The best time to develop mathematical
The
value competences is during teacher
training.
training.
17 ...
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 Winter '08
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 Math, Alan J. Bishop, mathematical value

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