An investigation of introductory physics students’
approaches to problem solving
Laura N Walsh*, Robert G. Howard, Brian Bowe
Approaches to problem solving
The analysis of the interview transcripts revealed the hierarchical
set of categories that describe the interview participants’
approaches to solving quantitative physics problems (see Table 1).
Most students could be described by only one category. There were
some cases, however, when a student would change their approach
on different problems; this will be discussed later in the paper.
Table 1 outlines the categories, the key characteristics of each
category, and the number of students in each category, Table 1.
Students who follow the scientific approach initially approach
a problem in a qualitative manner as they first describe the situation
qualitatively, based on their knowledge of the physical world. These
students identify the concept/s that would be involved in solving
the problem and discuss, in a coherent manner, the way in which
those concepts relate to the problem.
Based on the principle of gravity, like gravity is a constant force
acting always downwards, knowing this we have a constant acceleration
in a single direction, making it a form of linear motion.
These students outline a plan for solving the problem and then
correctly identify the variables that will be used to find an answer.
Within this small group, the students are familiar with the equations
that they require to solve the problem (they do not need to refer
to the equation sheet). The students use the information they have
to solve the problem but they may not always get the correct answer
due to either a mathematical mistake or a conceptual problem. These
students do, however, evaluate their solutions either qualitatively
or by defending/dismissing the numerical value they have obtained
based on what they believe the solution should be.
This group consists of students who do – at some stage –
identify the concepts that are involved, but who instead of qualitatively
evaluating the problem begin by identifying the variables given
in the problem and immediately seek an appropriate formula. Thus
they identify the variables that are not given, but are needed for
a solution to be found. Students in this category are often able
to coherently link their physics knowledge to approach and solve
the problem. One such student made the following statement as he
prepared to solve Problem 2, in which the student was required to
find out how long it would take an object to reach the ground after
being thrown upwards at a certain velocity.
Well you’re given a distance and initial velocity so if you
work that out, using em, you’re asked to find its time, you
know its acceleration is going to be … its going to have to
fight against negative acceleration, in the form of gravity pushing
against it, so if you use the formula and let 9.8 equal a minus
value, you should be able to find t.
These students often come across obstacles, because even though
they are using a problem-solving strategy, it is based primarily
on the variables they are using rather than on a solid analysis
of the physical situation
Students in this group tend to concentrate solely on the variables
that are given in the problem. When asked their first thoughts on
the problem they often replied by stating the variables that were
known or that linear motion equations were involved. These students
often identify the variables and equations correctly but may not
notice that the manner in which they are solving the problem is
incorrect or does not in fact answer the question. These students
have difficulty when it is necessary to manipulate a formula or
to combine a number of concepts to solve a problem. Another obvious
trait amongst these students is that their use of physics knowledge
is sometimes rather incoherent. In the following statement the student
has been asked his first thoughts on Problem 1, which entails dropping
a watermelon from a certain height and finding its velocity as it
reaches the ground. The mass of the watermelon is given in the question
but it is not needed in order to find the final velocity.
You drop the watermelon and it’s accelerating at -9.8, speed
of gravity. And you want to know how fast it is going before it
hits the ground, so its final velocity. And we have three things,
well we have its weight and we have acceleration due to gravity,
its initial velocity and distance. So we can get the final velocity.
Students in this category often choose an appropriate formula,
that could in theory produce a correct answer, but many do not actually
find a correct answer. This is mainly due to the incoherency in
the structure of their solution.