Unformatted text preview: Educating student teachers about values
in mathematics education
Alan J. Bishop
Faculty of Education
<[email protected]> 1 Mathematics educators are increasingly being
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.
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
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.
3 Whereas it is relatively easy and common in the
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.
There is a widespread misunderstanding that
mathematics is a value-free 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
concerned about, however, is that values
teaching and learning inevitably goes on in
This is because whenever teaching takes place,
choices are made, which are based on, and
therefore reveal, certain values.
However there is only a limited understanding at
present of what values are being transmitted,
and of how effectively they are being
Perhaps this is because most values appear to
be taught and learnt implicitly rather than
explicitly in mathematics classrooms.
5 Therefore there are new research questions which
can now be asked, such as:
What values are teachers of mathematics
What values are students learning from their
Are they learning more significant values from
their peers than from their teachers? 6 What values are implicitly and explicitly being
transmitted or ‘shaped’ through curricula and
To what extent can teachers be helped to teach
other values than those they currently teach?
Is it possible to develop more effective
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
the subject has developed within the particular culture.
General educational values: values associated with the
norms of the particular culture, of the particular society,
and of the particular educational institution.
Mathematics educational values: values embedded in
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
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
Ideological values: ‘rationalism’ and ‘objectism’
Sentimental values: ‘control’ and ‘progress’
Sociological values: ‘openness’ and ‘mystery’.
9 Mathematical value competences Mathematical
Valuing Rationalism means:
Valuing emphasising argument, reasoning, logical
analysis, and explanations.
Valuing Objectism means:
Valuing emphasising objectifying, concretising,
symbolising, and applying the ideas of
10 Mathematical value competencesSentimental
Valuing Control means:
emphasising the power of mathematical and
scientific knowledge through mastery of rules,
facts, procedures and established criteria.
Valuing Progress means:
emphasising the ways that mathematical and
scientific ideas grow and develop, through
alternative theories, development of new
methods and the questioning of existing ideas
11 Mathematical value competencesSociological
Valuing Openness means:
emphasising the democratisation of knowledge,
through demonstrations, proofs and individual
Valuing Mystery means:
emphasising the wonder, fascination, and
mystique of mathematical ideas.
12 Developing mathematical value
• Making the student teachers aware of
values in mathematics education.
Developing an understanding of the
history of mathematics.
Illustrating contrasts between different
Exploring cultural value differences via
13 Developing mathematical value
Identifying mathematical values in
• school and university textbooks,
• writings about mathematics
• mathematics examinations and tests
• science and engineering textbooks 14 Developing mathematical value
Using the 6 value classification to:
Create appropriate teaching materials for
Demonstrate and develop richer
Develop more appropriate assessment
15 Some other points from our
Teachers’ values in the classroom are
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
If teachers wish to emphasise values other
than those they currently emphasise, it is
possible to learn strategies from their
teaching of other subjects.
The best time to develop mathematical
value competences is during teacher
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- Winter '08
- Math, Alan J. Bishop, mathematical value