Variation in First Year College Students’ Understanding on Their Conceptions of and Approaches to Solving Mathematical Problems

A primary goal of mathematics learning and teaching in secondary school is to develop student’s ability to solve a wide variety of complex mathematical problems as a preparatory stage for college. In view of this, the objective of this paper is to investigate the mastery of content level that first year college students bring with them to the mathematics classroom with reference to their national examination grades (Sijil Pelajaran Malaysia). The study investigated the conceptions of 127 student and their heuristic actions in mathematical problem solving. Among these students 98.5% had obtained an A grade in the national examination for mathematics. Both quantitative and qualitative approaches, namely written assessment (five mathematical problems) and interviews were utilized in assessing student’s relational understanding of mathematical concepts in problem solving. The percentage of correct responses from these students, who can be considered as the cream of the crop of the nation, for the five items in the written test were 74.8%, 72.4%, 67.7%, 52.8% and 18.9 %.The data indicates that the grades obtained in the national examination did not reflect their mathematical knowledge in mathematical problem solving. The study concludes that capable mathematics students (the ones who obtained an A grade in the national examination) when placed in the context of non-routine problems have difficulty solving what may be considered elementary mathematics for their level of task achievement. This evidence seemingly indicates that many students from high schools are not acquiring the mathematical skills expected of college level mathematics