A study of first year tertiary students’ mathematical knowledge in non-mathematics majors – conceptual and procedural knowledge, logical thinking and creativity

Abstract

This study focuses on students in first year environmental science degree programs where traditionally mathematical emphasis has been much less than the strict science or math majors. The importance now placed in applied mathematics means that students need to gain more conceptual and quantitative knowledge in not only the environmental degree programs but also in most if not all sciences or non-mathematical majors. In this paper, the authors attempt to gain insights into why students fail in mathematical courses where the mathematical requirements are not as demanding as strict math majors. This is done by examining student conceptual thinking patterns and strategies as evident in student prepared scripts. A total of 133 students were requested to prepare a focus revision sheet to summarize their knowledge on topics learned, but they were also told that the focus sheets could be used in exams for notes. This motivated sheet preparation as the students prepared weekly summaries and later revised and summarized them for use in exams. Detailed examination of such sheets allowed researchers to study students' knowledge in terms procedural work, math skills, strategies and depth of conceptual knowledge. A study of linear, quadratic, and limit sections led to interesting insights not only regarding revision strategies, knowledge of content, but also conceptual and procedural knowledge base and higher order skills such as problem solving focus. Logical and creative competencies were assessed in terms of how and what student focused upon or linked to in order to facilitate application of knowledge. The results show average levels of procedural and conceptual competence but rather low levels in logical and creative competence. Almost 50% lacked competency in procedural work while around 54% lacked conceptual competency. Given the emphasis placed procedural skills by students, the levels generally were lower than expected. However, the lack of structure and deeper levels of understanding of the mathematics topics students learned was concerning. These findings have clear implications for the first year mathematics teaching teams at universities especially the non-specialist mathematical majors.