Unpacking First Year University Students’ Mathematical Content Knowledge Through Problem Solving

Abstract

Current calls for reform of education include suggested changes in the mathematics content courses required for university education programs. One suggestion is the inclusion of more complex problem solving activities. The context of this study was a homogeneous group of first year college students majoring in engineering. The researchers investigated the use of problem solving as a vehicle for these students’ to: unpack previously learned mathematics; assess understanding; reconstruct understandings; and connect mathematical concepts for deeper understanding. The researchers considered what students bring with them to the college mathematics content classroom based on their national examination grades (SPM). They found that the students have an instrumental understanding rather than a relational understanding (Skemp, 1976), where they were not able to unpack their mathematical content knowledge and apply it to new contextual situations. The study adds to the accumulation of evidence regarding the nature of students’ understanding of basic mathematical concepts and some critical factors to be taken into account in facilitating their development. Secondly, the grades obtained in the national examination of Sijil Pelajaran Malaysia (SPM) for mathematics did not indicate their mathematical knowledge in problem solving. This study also indicates that there was no difference in about 50% of the test items performance between “A Math students” and “Non A Math Student” on the problem solving test. In summary, this study seems to indicate that that majority of this college freshmen have learnt how to do numerical computation at the expense of learning how to think and to unpack their mathematical content knowledge.