A description of entry level tertiary students' mathematical achievement: Towards an analysis of student texts
Jacobs, Mark Solomon
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A DESCRIPTION OF ENTRY LEVEL TERTIARY STUDENTS' MATHEMATICAL ACHIEVEMENT (Towards an analysis of student texts) M.S. Jacobs PhD Thesis, School of Mathematics and Science Education, University of the Western Cape. This research provides insights into the mathematical achievement of a cohort of tertiary mathematics students. The context for the study is an entry level mathematics course, set in an engineering programme at a tertiary institution, the Cape Peninsula University of Technology (CPUT). The participant members are first year, first semester students. The materials for the inquiry are student produced test scores and examination scripts taken from their entry level course. The characteristics of the mathematical achievement of the cohort concern the understanding of procedural and conceptual knowledge and problem solving abilities in mathematics. The facility with mathematics is another central concern of this study as it forms the dominant aspect of mathematical achievement which is accessible to research in the materials employed for the study. This research also develops a mathematical achievement profile for individual members of the cohort. The methodology makes use of content - and textual analytic methods for profiling the students. When viewed across the different kinds of profiling techniques adopted, this study suggests that these techniques complement one another: the profiles developed provide a cohesive and complementary overview of the achievement of the cohort. 111 This study challenges perceptions that responses to constructed response questions offer little information about the mathematical knowledge of students. This study investigates the possibilities of providing a bridge between the assessment of students by means of tests scores and a taxonomy of mathematical objectives, on the one hand, and the critical analysis of student produced texts, on the other. Findings suggest that diagnostic uses of paper and pencil tests can be revealing about the achievement of students. The wide range of responses to test items revealed a distribution of incompleteness in terms of employing algorithmic techniques. This research revealed that even in cases of wrong solutions, participant members' responses were reasonable, meaningful, clear and logical. The participants responded in many ways as predicted by the research literature. Evidence could be found for the use of child methods; poor use of reflective abstraction for coordination; accessing the wrong cognitive frames; not seeing the underlying structure of the mathematics and treating letters as objects. Findings suggest that the use of a textual analytic method, which led to the creation of critical indicators as a way of sign-posting events, enhanced the achievement profile of the students.