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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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Research findings

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.

 

Scientific approach

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.

(Student 3)

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.

Plug-and-chug

Structured manner

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.

(Student 2)

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

Unstructured manner

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.

(Student 14)

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.


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