First Year Pre-service Teachers’ Mathematical Content Knowledge: Methods of Solution for a Ratio Question

Sharyn Livy, Colleen Vale


In this article, pre-service teachers' mathematics content knowledge is explored
through the analysis of two items about ratio from a Mathematical Competency,
Skills and Knowledge Test. Pre-service teachers' thinking strategies, common errors
and misconceptions in their responses are presented and discussed. Of particular
interest was the range and nature of common incorrect responses for one wholewhole
ratio question. Results suggested pre-service teachers had difficulty
interpreting a worded multi-step, ratio (scale) question, with errors relating to ratio
and/or conversion of measurement knowledge. These difficulties reveal underdevel -
oped knowledge of mathematical structure and mathematical connections as well
as an inability to deconstruct key components of a mathematical problem. Most
pre-service teachers also lacked knowledge of standard procedures and methods of


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