The development of students' problem-solving skill from instruction emphasizing
Statement of the Problem
Successful learning of introductory college physics requires students to acquire not
only the content knowledge of physics, but the skills to solve problems using this
content knowledge. This case study will examine the development of the problem
solving ability of students in a college introductory physics class. The instructor of
the class explicitly taught a problem-solving strategy that emphasized the qualitative
analysis of a problem before the manipulation of equations.
Background and Rationale
Through many generations of experimentation and theory-building, physics has
been developed into a very powerful science. It is a science composed of well-
founded expectations of how the natural world should behave which then uses the
tools of mathematics to describe these behaviors. Students of physics should learn
both the descriptive, or conceptual side of physics, and the predictive or problem-
solving, aspects of physics.
Unfortunately, traditional instruction
in physics has not emphasized either aspect of
physics very well. Traditional instruction is typically composed of a lecture that
introduces concepts either by demonstrations or with derivations of equations
which describe the concept. The lecturer might also show the students how to solve
a few problems and occasionally suggest how to complete the mathematics cleverly.
The students are typically assigned homework that consists of reading the relevant
chapters in a textbook and completing the problems at the end of the chapter. There
might also be a laboratory associated with the course, whose instructional goals may
or may not parallel those of the lecture. Finally, the student's knowledge of physics
is tested by an exam composed of problems similar to those they have encountered
while completing their homework. Traditional instruction has been shown
repeatedly to be ineffective for the majority of students (Hestenes & Halloun, 1985;
McDermott, 1984; Sweller, 1988). Students leave traditional instruction without
gaining conceptual understanding or developing problem-solving skills.
Recently, physics educators have begun
explore how to overcome these difficulties with traditional instruction. Most
of these efforts have focused on improving students conceptual
understanding of physics (Thornton &Sokoloff, 1990; McDermott, 1984;
Laws, 1991). Another group of researchers have been trying to understand
how students solve problems and if students can be taught better approaches
to solving problems (Larkin, 1983; Chi, Feltovich, &Glaser, 1981; Reif
&Heller, 1982). While there have been laboratory experiments showing
that qualitative problem-solving techniques can be taught to students (Larkin,
1979; Larkin & Reif, 1979, Woods, 1987), there is a lack of published
research exploring if it is possible to teach such techniques in conjunction
with the traditional course content while in a classroom setting.
There are essentially only four
classroom-based instructional studies in physics
problem solving. First is Wright and Williams (1986) and their WISE strategy used
in general physics at a community college. These researchers determined that the
students who used the WISE strategy performed significantly better than those
students who did not. The second study is Van Heuvelen (1991) and Overview Case
Studies (OCS). Students in the OCS classes performed noticeably better at solving
problems on the College Board Advance Placement Test.
The next two studies are important to
this project because they used the same
problem-solving strategy used in this project. This explicit qualitative problem
solving strategy (the Minnesota Strategy) taught to the students in these studies is
based on the works of Chi et. al. (1981) and Larkin (1983) who studied the problem
solving differences between experts and novices. One of the hallmarks of the
expert-novice distinction is that experts have more and better organized subject
knowledge. Therefore, for students to progress toward the expert end of the expert-
novice continuum, they must increase their knowledge and organization of the
concepts of physics. Experts also solve problems in a more sophisticated and
intentional manner when compared to novices. Understanding this distinction, the
Minnesota Strategy was designed to develop the students' problem solving skills
from their current novice state toward the expert state. The strategy is not intended
to turn novices into experts; only to move them along the continuum.
The third study is Huffman (1994) who
used an quasi-experimental design with
suburban high school students in two groups; those taught the Minnesota Strategy
and those taught a textbook strategy. Huffman found that the students who used
the Minnesota strategy had higher quality and more complete solutions than their
peers who used the textbook strategy. However, Huffman found no difference
between the two groups on the students' conceptual understanding or organization
of their solutions. Huffman speculated that the reason only a limited effect was
seen in his study was due to (a) the limited time spent preparing the instructors to
teach using an explicit strategy (since neither instructor had used this pedagogy
before) and (b) the short duration of the study may have been too brief for the
student to embrace either problem-solving strategy. In an effort to overcome
theseshortfalls seen in Huffman's study, the project being proposed here has the
following features: (a) The instructor who taught the explicit strategy was one of the
original developers of the Minnesota Strategy and (b) data for this project was
collected for a full academic year.
In the fourth study, Heller, Keith, and
(1992) tested a version of the explicit problem solving strategy discussed in this
project in the algebra-based physics course for non-majors at the University of
Minnesota. In this setting, the Minnesota Strategy is used in conjunction with
cooperative-group learning. This study concluded that students who used the
Minnesota strategy were more expert-like problem solvers as compared to students
in a course taught without the Minnesota strategy.
The next step beyond the studies conducted by Huffman and Heller is to teach the
Minnesota strategy in a calculus-based course for scientists and engineers at the
college level, and periodically examine the students for an entire academic year.
This is a logical step since all four of the cited classroom studies were conducted in
courses designed for non-science students. Also, all four studies were looking for
student improvement after instruction instead of the development during
instruction. What has not been adequately tested is whether the Minnesota strategy
can be taught to students who have stronger math backgrounds and who have
enjoyed previous success in solving problems.
Using a population of students in the
three academic-quarter long calculus-based
physics course for scientist and engineers,
(1) In what way do students' problem-solving skills develop in a physics course
taught by an instructor who emphasizes the Minnesota Strategy?
Since there is a lack of research
examining how student's problem-solving skills and
conceptual understanding develop during any physics course, it would be difficult to
interpret the answer to this research question without knowing what actually
happens in a more traditionally taught introductory physics course. While it might
be possible to hypothesize what the student's behaviors should be by extrapolating
from the research literature, it is more convincing and satisfactory to examine a
well-taught, more traditional classroom using the same methods. Therefore, as a
supplemental question to establish a baseline for traditional instruction,
(2) In what way do student's problem-solving skills develop in a physics course
taught by an instructor who does not emphasize a problem-solving strategy?
The students used in this study were selected from regular university students
who enrolled in Physics 1251-2-3, the introductory calculus-based introductory
physics course for scientists and engineers. This course was divided up into
multiple sections with each section taught by a different lecturer with his (all
instructors were male this year) own team of teaching assistants. In one class, the
instructor (KH) emphasized the Minnesota Strategy. In another class, the
instructor (BL) did not emphasize a problem-solving strategy. Both instructors
were experienced and capable lecturers. The students used in this study were
those students who stayed with the same instructor throughout the academic
year and who completed the necessary measurement instruments. The sample
sizes cannot be controlled because the students select their instructor for the
course based upon scheduling constraints and choices typical of a large
university. From this sample of students, a matched sample will be drawn.
These students shall be matched on initial problem-solving skill; initial
attitudes; demographics; and performance on a standardized physics concept test.
I anticipate about 25 - 30 matched students from each section.
Identical data was collected from both sets of students. These data included
common test problems given throughout the quarter, demographic information,
and conceptual tests. The common test problems were written either (a) by myself
based on classroom observations of both instructors to determine what content area
would be appropriate for each question or (b) by the instructors for the purpose of a
common final exam given by all instructors. My test questions were reviewed by
each instructor and a common wording was settled upon before the problem was
given to the students. The questions for the final exam were approved by both
instructors as appropriate for their section.
The demographic and attitude information
was collected by means of a multiple-
choice questionnaire completed by all students. There were also three conceptual
tests used in this study. The first is the Force Concept Inventory (FCI), which is a
nationally administered exam which measures student understanding of force and
motion (Hestenes, Wells, & Swackhammer, 1992). The second conceptual test was a
brief multiple-choice exam designed to test students' understanding of the torque
concept. The last conceptual test was created by the instructors to test student's
understanding of electro-magnetism.
Both sections were taught at the University of Minnesota in the 1995-1996 school
year. Each section had essentially the same syllabus, assigned the same homework
from the same textbook, shared the same final exam, used the same laboratory
manual, and had the students work in cooperative-groups in the discussion sections
and the laboratory. All the teaching assistants (TAs) participated in the Physics
Department New TA Orientation which introduced the TAs to the mechanics of
using cooperative groups and other issues related to being a physics TA. The
instructors of all the sections met on a regular basis to decide on course pacing,
laboratory activities and other maintenance items. The sections were very similar
except for the instructors and instructional emphasis on problem solving.
KH used, but did not require that his
always use, an explicit problem solving strategy (Minnesota Strategy) that
emphasized a complete, qualitative understanding of the problem before the
problem could be solved mathematically. In this section, students were
graded both for the content of their solutions to the problems and how they
communicated their solutions to the problems. BL's course was taught more
traditionally (as described earlier) and the grading emphasized the correctness
of a solution. A total of 26 problems were given to all the students in both
sections, with 8 of those problems occurring on mid-quarter examinations
and the remaining 18 from the 3 final examinations.
The demographic information was
collected at the start and the end of the academic
year. The FCI was administered during the first week of the first quarter and again
as part of the first-quarter final exam. The second conceptual test was administered
as part of the second-quarter final. The last conceptual test was part of the third-
quarter final exam.
Design and Analysis
The design of this study is a developmental case study. The case-study method is
used since the focus of the study is on a single case, specifically the matched sample
of students in KH's class who enrolled in his course each quarter for the academic
year. As a study of this unique case, the results of this study will need to be
interpreted accordingly, and will have limited generaliziabilty (Stake, 1994). This
study is developmental: The focus is on how problem-solving skills of students
develop when the Minnesota Strategy is taught.
The test problems given to the students
will be judged for difficulty using a scale
developed by the Physics Education Research and Development Group at the
University of Minnesota (PERDUM). This judging is necessary so that the relative
ease or difficulty of each will problem will not confound the results. Student
solutions from the exam problems will then be coded for problem-solving skill.
The coding rubric used was also developed by the PERDUM. This coding scheme is
based on the expert-novice research and will be used for both samples of students.
Since Huffman (1994) reports that there is no significant difference between his
treatment groups after six weeks of instruction, the first two problems given to the
students will be used to determine the initial problem-solving ability for each
student. The analysis of the student solutions will be conducted identically on both
samples of students. Once it is understood what the baseline for traditional
instruction is, the results of this study can be interpreted.
I have the background to complete this study. I have a Master's degree in Physics
and I am familiar on both theoretical grounds and with actual experience with the
Minnesota problem-solving strategy. My job as Mentor TA in the physics
department makes me acquainted with all aspects of both course sections in this
study. I have also completed a diverse complement of qualitative and quantitative
Chi, M. T. H., Feltovich, P. S., & Glaser, R. (1981). Categorization and
representation of physics problems by experts and novices. Cognitive Science, 5,
Halloun, I. A., & Hestenes, D. (1985). The initial knowledge state of college
physics students. American Journal of Physics, 53(11), 1043-1055.
Heller, P., Keith R., & Anderson, S. (1992). Teaching problem solving through
cooperative grouping. Part 1: Group versus individual problem solving. American
Journal of Physics, 60(7), 627-636.
Hestenes, D., Wells, M., & Swackhammer, G. (1992). Force concept inventory. The
Physics Teacher, 30, March, 141-153.
Huffman, D. W. (1994). The effect of explicit problem solving instruction on
students conceptual understanding of Newton's laws. Unpublished doctoral
dissertation, University of Minnesota, Minneapolis.
Larkin, J. H. & Reif, F. (1979). Understanding and teaching problem solving in
physics. European Journal of Science Education, 1(2), 191-203.
Larkin, J. H. (1979). Processing information for effective problem-solving.
Engineering Education, 285-288.
Larkin, J. H., (1983). The role of problem representation in physics. In D. Gentner
& A. L. Stevens (Eds.), Mental Models (pp. 75-98). Hillsdale, NJ: Lawrence Erlbaum.
Laws, P. (1991). Calculus-based physics without lectures. Physics Today, 44(12),
McDermott, L. C., (1984). Research on conceptual understanding in mechanics.
Physics Today, July, 24-32.
Reif, F., & Heller, J. I. (1982). Knowledge structure and problem solving in physics.
Educational Psychologist, 17(2), 102-127.
Stake, R. E. (1994). Case Studies. In N. K. Denzin & Y. S. Lincoln (Eds.),
Handbook of Qualitative Research (pp.236 -247). Thousand Oaks, CA: SAGE
Sweller, J. (1988). Cognitive load during problem solving: Effects on learning.
Cognitive Science, 12, 257-285.
Thornton, R. K., & Sokoloff, D. R., (1990). Learning motion concepts using real-time
microcomputer-based laboratory tools. American Journal of Physics 58, 858-867.