Zambian University Student Teachers’ Conceptions of Algebraic Proofs

Abstract

This paper reports on a case study that aimed to evaluate the perceptions of 73 student teachers at Mukuba University on the nature and purpose of mathematical proof. They were presented with a mathematical reasoning and proof arguments assessment tool followed by a 10-member focus group interview. Algebraic tasks presented to them involved (i) proof construction on simple number and set theory, (ii) assessment of given mathematical statements and arguments to validate them, and (iii) validating formally structured inductive proofs. More than 75% of the student teachers had limited understanding of the nature and purpose of mathematical proofs and they believed that proof construction and validation entailed inspection of a few examples and the testing of single extreme cases. Concrete examples of empirical forms of mathematical arguments which student teachers perceived as valid were found but these demonstrated limited forms of mathematical reasoning and comprehension. It is proposed that paying attention to analytical and deductive mathematical arguments in school based assessment will alleviate mathematical learning problems and improve the quality of mathematics education.

Keywords: student teachers, algebraic proof, conceptions of proof, mathematical reasoning, school based assessment.