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An investigation of introductory physics students’ approaches to problem solving

Author - Laura N Walsh*, Robert G. Howard, Brian Bowe

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Theoretical background

A large body of research in physics education has reiterated research from cognitive psychology, indicating that for students to develop an understanding of the conceptual nature of physics, education must first start with their prior conceptions (Roth 1990: Redish et al. 1998; Redish 2003). These prior conceptions, which are internally inconsistent, are remarkably resistant to change and conventional instruction can make almost no difference to a student’s conceptual beliefs (Halloun and Hestenes 1985). According to these researchers, the teaching approach must allow for students to restructure their own understanding by first seeing where, when and why their conceptions fail. Only after this can students start to build up a new and correct understanding. Research into student understanding in physics indicates that certain ‘misconceptions’ about the physical world are common among students entering third-level education (Clement 1982; McDermott 1991; Hake 1998; Knight 2002) and this is particularly true for many mechanics concepts (Trowbridge and McDermott 1981).

    While a large amount of physics education research has been carried out on conceptual difficulties experienced by students, fewer studies have focused on students’ ability to solve quantitative problems (Heron and Meltzer 2005). This is surprising, as one of the principles goals of a physics course is to produce adept problem solvers who can transfer their knowledge and understanding to real world situations. An issue which has been raised by a number of physics education researchers recently is whether the community is placing too much emphasis on gains in conceptual understanding, while ‘sacrificing problem solving skill development’ (Hoellwarth et al. 2005 p. 459). Many studies have shown that although students can learn to solve quantitative problems by simply plugging values into formulae and obtaining a correct answer, they may not be developing the skills necessary to transfer their understanding and solve more complex problems (Leonard et al. 1996; Mazur 1992; Mazur 1997; Thacker et al. 1994; Tuminaro and Redish 2005; Van Heuvlen 1991). A common view throughout most of this literature is that instruction should encourage students to ‘think like a physicist’ or result in a shift from ‘a novice problem solver’ to ‘an expert problem solver’. Reif and Heller (1982) pioneered the view of student problem solvers by comparing and contrasting the problem-solving abilities of novices and experts. Their findings show that the principle difference between the two was how they organise and use their knowledge in the context of solving a problem. Experts rapidly re-describe the problem and often use qualitative arguments to plan solutions before elaborating on them in greater mathematical detail. Novices rush into the solution by stringing together miscellaneous mathematical equations and very quickly encounter difficulties. Physicists organise their knowledge in a very structured way and therefore can call on this knowledge when and in the order that it is needed. However novice physics students do not necessarily have this knowledge structure, as ‘their understanding consists of random facts and equations that have little conceptual meaning’ (Van Heuvelen 1991: 893).

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