University students' conceptions of mathematical symbols and expressions

Abstract

Undergraduate mathematics instructors often report that students make careless errors or have not previously learned key mathematical ideas and strategies. The purpose of this study is to explore evidence of an alternative explanation that at least some of these "errors" may result from students' application of conceptions developed in the narrower contexts of their earlier learning. Analysis of formal printed lecture notes, student work and questionnaire responses is performed. Data collected from two Australia Universities' first year mathematics students are reported in this paper that explores respondents' conceptions related to symbolic mathematical expressions in different contexts by using the survey research design. The data were analysed through two lenses in order to both identify likely supportive and problematic conceptions and also distill the aspects of symbolic expressions contributing to this classification. The findings show that students' errors patterns are associated to problematic conceptions that might arise from contexts previously encountered by students. More than 50% of the recorded errors related to-1() by University 1 students are linked to problematic conceptions. This study is significant because it shows that it is important to explicitly address such potentially problematic conceptions in order to help students bridge the transition between contexts and this may be done through lecture notes.