Pre-Service Teachers' Mathematical Reasoning as an Imperative for Codified Conceptual Pedagogy in Algebra: A Case Study in Teacher Education

Through the use of taped interviews, the reasoning level of eleven (11) pre-service teachers relative to selected concepts in Algebra was ascertained. Yumus' (2001) levels of reasoning were applied as a guide, namely: (a) Level 1: Unable to produce any reasoning, (b) Level 2: Have awareness of the models, known facts, properties and relationships to be used but cannot produce any arguments; (c) Level 3: Able to produce some reasoning although the arguments are weak and (d) Level 4: Able to produce strong arguments to support their reasoning. Using this guide it was found that of the 121 responses given, 47.1% were at level 1, 29.8% at level 2, 16.5% at level 3 and only 6.6% were at level 4. The most difficult problem proved to be converting repeating decimals to fractions, while the easiest was on finding the value of x[superscript 0]. As a whole, the reasoning ability of the respondents, based to their average reasoning ability on the given tasks, indicate that 73% was low, 27% was moderate and that nobody had a high level of reasoning. Assessments followed as to the factors contributing to this situation and possible solutions.