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The mathematical knowledge of secondary pre-service teachers


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Gates, Lupé Maria Theresa 1999 , 'The mathematical knowledge of secondary pre-service teachers', PhD thesis, University of Tasmania.

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The problem under investigation in this study is teachers' lack of competence to teach for
conceptual understanding of mathematics. It was assumed in this study that pre-service
teachers of mathematics go through their teacher education and training with certain
insufficiencies in their mathematical understandings and that these insufficiencies will
eventually affect the way they teach. The aim of this study, therefore, was to identify what
these insufficiencies might be by examining mathematical knowledge that secondary preservice
mathematics teachers bring with them to teacher education programs. The nature of
these mathematical knowledge insufficiencies and how these insufficiencies would affect a
person's competence to teach were of primary interest.
To explore these knowledge insufficiencies, a multiple-case study design was used. The
nineteen cases (secondary mathematics pre-service teachers) from four universities at two
Australian states were selected according to their mathematical backgrounds. It was
expected that the pre-service teacher participants (university graduates) who majored in
mathematics or in other science related areas would show less evidence of knowledge
insufficiencies than pre-service teachers who majored in other areas (e.g. economics).
Furthermore, it was expected that the participants with mathematics major backgrounds
would show more confidence to teach for conceptual understanding of mathematics than
participants with mathematics minor backgrounds.
The data collection instrument was a set of three mathematical stimulus items representing
trigonometry, logarithm, and statistics. All three items were designed to elicit responses
associated with the respondent's knowledge of the mathematics. Written and verbal
responses to these items were collected in one-to-one interviews. Skemp's (1978) model
of mathematical understanding was the instrument for data analysis.
The results of this qualitative analysis indicated four types of mathematical knowledge
deficiencies. In addition, the pre-service teachers' existing mathematical knowledge was
highly representative of instrumental understanding of mathematics. These mathematical
knowledge insufficiencies were suggested to be the outcomes of learning mathematical
content which lacked in essential knowledge aspects, rather than outcomes of rote learning.
Furthermore, these insufficiencies tended to reduce the pre-service teachers' confidence and
likewise their potential to teach for conceptual understanding of mathematics.

Item Type: Thesis - PhD
Authors/Creators:Gates, Lupé Maria Theresa
Keywords: Mathematics
Copyright Holders: The Author
Copyright Information:

Copyright 1999 the Author - The University is continuing to endeavour to trace the copyright
owner(s) and in the meantime this item has been reproduced here in good faith. We
would be pleased to hear from the copyright owner(s).

Additional Information:

Thesis (PhD)--University of Tasmania, 1999. Includes bibliographical references

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