Engineering students approaching the mathematics textbook as a potential learning tool – opportunities and constraints
Doctoral thesis, Peer reviewed
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It is usually assumed that the students at tertiary level work intensively and individually with the new mathematical concepts (Wood, 2001). In this context the mathematics textbook might be an important learning tool. This thesis addresses the issue of what factors might influence the role of the mathematics textbook as a learning tool. The study is situated in the context of the basic mathematics course taken by first-year engineering students. A brief pilot study indicated that a majority of the students preferred using lecture notes rather than the textbook although in the beginning of the semester they perceived the textbook as being important when learning mathematics. This was the starting point of this research that aims to identify and explore the factors that might influence the role of the textbook proposed to first-year engineering students. The textbook is conceptualized as a cognitive learning tool embedded in the educational setting offering the basic mathematics course. The study was conducted when the students worked with the derivative concept. The process of students’ approaching the textbook is viewed from an epistemological, a cognitive and a didactical perspective. The study is an exploratory case study, and a qualitative research strategy within an interpretative paradigm was chosen. Data was gathered from a number of vantage points: students’ responses to a questionnaire, observations of lectures and task solving sessions, interviews with the teacher and the students, and informal talks with the teacher and the students. Additionally a questionnaire was sent to authors of the most used calculus textbooks with the aim of exploring their vision concerning their mathematics texts. The results of the main study confirm the observed phenomena from the pilot study. Students perceived the textbook as difficult and the lecture notes were preferred when working with the derivative concept. The textbook was used by the students mainly to read the examples and figure out possible procedures when working with the tasks. The findings of the study reveal possible opportunities and constraining factors of epistemological, cognitive and didactical nature. Students’ poor previous knowledge, their approach to learning mathematics, the cognitive demands of the textbook, and the way the textbook was used during the lectures seem to influence the role of the textbook as a learning tool. Possibilities and limitations were discussed within the given theoretical framework. This study suggests that higher awareness about the assumed and real role of the mathematics textbooks at tertiary level is necessary. Some suggestions for further research that might provide deeper insights about the issue are given.