The purpose of this chapter is to reflect on the influence of the adoption of a combination of research paradigms on the design, implementation, and outcomes of a research exercise. The research question for the study was: How may students' approaches to learning (engineering) mathematics be characterized? The aim of the exercise was to characterize students' approaches to learning mathematics on an Engineering Mathematics course, based on evidence from student interviewees' transcripts. The individual student learning approach characterizations were undertaken through the adoption of an integrated framework comprising the “approaches to learning” theoretical framework and goal theory, with secondary data analysis, based on the “three worlds of mathematics” framework. The research paradigm employed was essentially interpretivist/constructivist. The neo-positivist paradigm, inductive mode, was also referenced. Qualitative research methods were employed with integration of multiple theoretical frameworks for the design, data collection and analyses, and interpretation of the results of the study.
TopChapter Overview
The purpose of this chapter is to reflect on the influence of the adoption of a combination of research paradigms on the design, implementation, and outcomes of a research exercise. The research question for the focal case study was: How may students’ approaches to learning (engineering) mathematics be characterized? The aim of the research was to characterize or interpret a student’s approach, at the course level, to learning mathematics on an Engineering Mathematics course at a British university, based on evidence from student interviewees’ transcripts. Mathematics is a disciplinary field of inquiry that students have historically found challenging as Sawyer (1943) observed: “Very many students feel that they will never be able to understand mathematics, but that they may learn enough to fool examiners into thinking they do” (p. 7). Empirical characterizations on how students approach mathematics learning may make a valuable contribution to addressing this.
To undertake these characterizations, I utilized Marton and Saljo’s (1976a) approaches to learning theory (ALT) framework (see also Case & Marshall, 2004; Biggs, 1999; Entwistle & Ramsden, 1983; Skemp, 1976). To provide alternative views of student learning approach characterizations, I also employed goal theory (e.g., Pintrich, Conley, & Kempler, 2003) and, for secondary data analysis, the three worlds of mathematics framework (Tall, 2008). The research goal was to characterize individual interviewees as to whether they exhibited a procedural surface, procedural deep, and/or conceptual deep approach to learning (engineering) mathematics.
Student Learning Approaches
It is now recognized that student approaches to learning are heavily influenced by the context, hence the approaches that students adopt in different disciplines may vary due to the often different requirements (e.g., Drew, Bailey, & Shreeve, 2002; Ramsden, 1988, 1992). It is also now recognized that it is possible for students to change their learning approach in moving from one course context to another, i.e., a student may adopt a surface approach in one course context, and then “switch” to a largely deep approach in another course (e.g., Barnett, 1990; Entwistle & Ramsden, 1983; Meyer, 2000; etc.). Hence, student approach to learning is sometimes construed as a response to the perceived course context (e.g., Case, 2000; Case & Marshall, 2004; Hazel, Prosser, & Trigwell, 1999). A distinction has also been made between the type of approach that students adopt at the task level, and that which they employ at a whole course level (e.g., Booth, 1992; Case & Marshall, 2004; Drew et al., 2002).
In mathematics, research also suggests that there is a correlation between student perceptions of mathematics and the type of learning approach adopted. For example, Crawford, Gordon, Nicholas and Prosser (1994, 1998) indicate that students who have a “cohesive” conception of mathematics, i.e., see mathematics holistically as a template for the creation of knowledge in the form of mathematical thinking, are more likely to adopt deep learning strategies (also see Drew, 2001). In contrast, students who have a “fragmented” conception of mathematics, i.e., see mathematics more or less as an elevation of arithmetic or a combination of formulae to use in answering questions, are more likely to adopt surface approaches to learning.