An investigation of introductory physics students’
approaches to problem solving
Laura N Walsh*, Robert G. Howard, Brian Bowe
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
• 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
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’.