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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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Individual interviews

Although many possible sources of information can reveal a person’s understanding or conception of a particular phenomenon, the method of discovery is usually an individual interview. For this study semi-structured interviews were used in which specific questions were prepared but any unexpected lines of reasoning were also followed. One aim of the interviews was to investigate each student’s conceptual understanding of a small number of concepts. However the most important aim of the individual interviews was to examine the various ways in which the students approach quantitative physics problems. The interviews provided data to answer the following research questions:

What are the students’ perceptions of certain mechanics conceptions, such as motion and force?
• How do students in introductory physics courses approach various levels of quantitative problems?
• Can students who do not have a full understanding of certain basic physical concepts correctly solve quantitative problems?

    The interviews consisted of six physics problems, with the first two being typical end-of-chapter linear motion problems. The remaining problems were adapted from context-rich questions developed by the physics education research group at the University of Minnesota (UMPERD 2006). The interviews lasted approximately 45 minutes each and were all videotaped. The interviewer read each question aloud to the student and then asked him/her to state their first thoughts on what they thought the problem involved. The student was then asked to describe, qualitatively, how they were going to go about solving the problem, and after this the student was encouraged to ‘talk aloud’ as they solved the problem on paper. Once the student had solved, or attempted to solve, the problem, the student was asked how confident they were in their answer and asked to explain this level of confidence. In this way each interviewee was encouraged to qualitatively analyse their solution.

Interview participants

Twenty-two participants were selected from four programmes in a Higher Education institution in Ireland; two were four-year Honours Degree (Level 8, National Qualifications Authority of Ireland 2006) physics programmes delivered through problem-based learning (Bowe 2005; Bowe and Cowan 2004), one was a Level 8 medical science programme and one was a three-year Ordinary Degree (Level 7, NQAI 2006) general science programme. Both of the latter were delivered in a predominantly traditional manner, although each was delivered by a different lecturer. The participants were all in their first year of study and the sample comprised of 12 male and 10 female students, ranging in age from 18 to 24. The participants in the study had completed the Irish Leaving Certificate (Department of Education and Science 2006), which typically consists of six subjects taken at either higher (honours) or ordinary (pass) level. Ten of the participants had studied physics as a subject for the Leaving Certificate, either at higher (honours) or ordinary (pass) level. This two-year course of study is a broad introduction to physics and covers the general areas of mechanics, optics, heat and temperature, sound, electricity and modern physics. The participants for the interviews were chosen based on the results of a diagnostic tool, the Force and Motion Conceptual Evaluation (Thornton and Sokoloff 1998), in order to obtain a cohort with a cross-section of abilities. The FMCE is a 47-item research-based, multiple-choice assessment that was designed to ‘probe conceptual understanding of Newtonian mechanics’ (Thornton and Sokoloff 1998: 338). The interviews were carried out over a two-week period following six weeks of formal instruction in mechanics.

Method of analysis

The interviews were transcribed verbatim from the videotapes and, in analysing the data, qualitatively distinct categories were identified that described the students’ approaches to problem solving. Transcripts of the students’ interviews were examined independently by three members of the research group, looking for both similarities and differences among them, selecting significant statements and comparing these statements in order to find cases of variation or agreement and thus grouping them accordingly. Through this process initial categories were developed that described students’ approaches to problem solving, with the initial categories developed using only a sample of the interview transcripts. Once this initial categorisation was complete, the researchers met to discuss their categories and their interpretation of the answers. The categories were then revised until the researchers reached a consensus about the final set of categories.

    An outcome space was developed that included the minimum of categories, which explained all the variations in the data. With these categories in mind the interview transcripts were re-examined, to determine if the categories were sufficiently descriptive and indicative of the data. This iterative data analysis procedure is consistent with the phenomenographic approach (Sharma et al. 2005), as Marton (1986: 43) states ‘definition for categories are tested against the data, adjusted, retested, and adjusted again’.

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