Title
The development of students' problem-solving skill from
instruction emphasizing
qualitative problem-solving.
Introduction |
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
to
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
Anderson
(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.
Research Questions
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?
Method |
Subjects
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.
Materials
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.
Procedures
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
student
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.
Preparation
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
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