FEd December 1997 Newsletter - Problem Solving and Learning Physics

December 1997



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Problem Solving and Learning Physics

David P. Maloney

Problem solving has been an integral part of physics instruction for many years. The reason for this is the belief that when the students solve problems they really learn the physics. Certainly that is the experience most of us had. However, most of the students in our general physics courses are not physics majors and do not have anything close to our motivation to learn physics. Physics education research has made it clear that students can succeed in general physics courses, even those which require significant problem solving, without showing any growth in reasoning skills or the development of a coherent conceptual framework (McDermott, 1993). Does this mean problem solving is not a productive instructional activity?

Research on Students' Problem Solving Procedures
-One of the early studies of students' problem solving was that of Reif, et al. (1976), who pointed out students' tendency to grab an equation and plug in numbers. They tried, with limited success, to get the students to follow a more systematic problem solving strategy, although the intervention was of rather brief duration.

Larkin, et al. (1980) compared the problem solving behaviors of experts (graduate students and physics professors) with novices (students who had completed one or two semesters of general physics). In their research two computer models were developed. The knowledge development model, which worked from the given information to the goal of the problem, did a good job modeling the behavior of the experts. The means-end model, which started with the goal of the problem and worked "backwards" to the given information, better matched the novices' procedures.

In means-ends analysis the problem solver identifies the goal of the problem, determines where he/she is relative to that goal, identifies steps he/she can take to reduce the difference between the current problem state and the goal state and then applies appropriate steps. For a novice student trying to solve a textbook physics problem, the goal they will identify is finding a specific numerical value and what will look like the most reasonable and efficient way to reach that goal is to find an equation. Consequently, the characteristic "plug and chug" behavior is understandable and not unreasonable.

Sweller, et al. (1983, 1988, 1990) have proposed that novices' use of means-ends analysis on standard textbook problems is counter productive for learning the physics concepts, principles and relations that underlie problem solving with understanding. When the students focus on the goal of finding a specific numerical value that focus will direct their attention to the equations. With this focus, carrying out a qualitative analysis involving other representations seems to be of little value. In addition, applying the means-ends heuristic requires a significant part of the cognitive resources of the solver, so few resources are available to consider the concepts and principles and how they apply.

Traditional textbook problems helped us learn physics not because solving such problems is the best way to learn physics, but because we were motivated to use them to help us learn. Our success does not mean such problems will be just as useful to less motivated students. There may actually be better types of problem structures for helping the majority of our students learn the concepts, principles and relations that underlie solving physics problems with understanding. Recent work in physics education research has led to several ideas for alternative problem structures, or alternative ways to approach traditional problems; these have been shown to be more productive for focusing students' attention on the conceptual basis of problem solving.

Alternative Approaches to Problems and Problem Solving
-Two proposals for using traditional textbook problems in different ways emphasize the qualitative and conceptual aspects of the solution process. Van Heuvelen's (1991) technique, called "multiple representation problem solving," is a direct application of Larkin's sequence of representations. Students encounter a traditional word problem with a goal of finding a specific numerical value. However, the problem is at the top of a page which also contains, in sequence, a region to draw an everyday sketch of the situation, a region to draw a physics sketch (a free-body diagram, an electric field map, a lens diagram, etc.), a region to write the relevant equation, a region to work out the answer, and finally a region to make comments about what they learned from solving the problem.

An important part of this approach is that students are explicitly told that they must have all sections of the page filled in order to get full credit for solving the problem. One way to enforce this is to grade the problems by starting with the first representation in the sequence and as soon as anything is missing, the grading process stops. In other words, a student who simply writes down the answer, or the correct equation and the answer, would get a zero for the problem, since the earlier qualitative representations would not have been found. This may seem like an unfair procedure which would penalize some students who actually had the correct answer, but the whole idea is to shift the focus from the answer to the process, and if students are alerted at the outset there should be no problems.

A second way to use traditional problems, described by Leonard et al. (1996), requires students to provide a qualitative strategy for solving a problem. The strategies contain three components: (1) identification of the appropriate concepts, principles, and relations that apply to the problem; (2) a reasonable and appropriate explanation of why they apply; and (3) a description of how they apply. Students in the section where the strategy writing was employed were found to be better at problem classification tasks and at recall of major ideas from the course when tested several months after the end of the course.

Other approaches proposed for problem solving employ different problem structures from the traditional items. In one approach D'Alessandris (1995) has developed problems which do not ask the students to find any specific numerical value. Instead the students must thoroughly analyze the given situation, determine exactly what is happening and essentially find all major values associated with the situation. With the focus of finding a specific numerical value removed, the students cannot simply look for an equation into which to plug numbers. Before deciding what values to find, and what equations to use, the students must figure out what is happening in the situation and what physically important quantities are relevant.

D'Alessandris has developed this alternative format as a part of an entirely different way to run the introductory course. The problem format is an integral part of his "Spiral Physics" approach. However, the idea of modifying the format of the problems to make students thoroughly analyze physical situations is certainly one that can be adopted by other instructors. There are actually several ways to produce problems of this type. One way is to present a traditional problem without the identification of a specific value to find and instead ask the students, "What can you assert about this situation?" They then have to determine, and calculate, all of the major quantities they can from the given values.

-Research in physics education has shown that having students solve traditional textbook problems is of limited usefulness in helping them learn the concepts, principles and relations. One possible explanation for why these problems are less productive than expected is that the students' use of means-ends analysis in trying to solve the problems leads them to plug and chug procedures which ignore the qualitative analysis that is involved in problem solving with understanding. In employing plug and chug approaches the students do not work with the other representations, such as physics diagrams, which is where the links are to the appropriate conceptual knowledge. Modifying how traditional problems are done, or modifying the problem format has been shown, in certain cases, can produce better outcomes for conceptual understanding. A fuller review of the physics education research relating to problem solving can be found in Maloney (1994).

D'Alessandris, P., "Assessment of a Research-Based Introductory Physics Curriculum" AAPT Announcer 25 (4), 77 (1995)

Larkin, J.H., McDermott, J., Simon, D.P., and Simon, H.A. "Expert and Novice Performance in Solving Physics Problems" Science 208, 1335-1342 (1980); also, "Models of Competence in Solving Physics Problems," Cognitive Science 4, 317-345 (1980).

Leonard, W.J., Dufresne, R.J. and Mestre, J.P. "Using Qualitative Problem-solving Strategies to Highlight the Role of Conceptual Knowledge in Solving Problems," Am. J. Phys. 64, 1495-1503 (1996)

Maloney, D.P., "Research on Problem Solving: Physics" in Handbook of Research on Science Teaching and Learning D. Gabel (Ed.), MacMillan Publishing Co., New York (1994).

McDermott, L. C., "How We Teach and How students Learn-A Mismatch?" Am. J. Phys. 61, 295-298 (1993).

Reif, F., Larkin, J.H. and G.C. Brackett "Teaching General Learning and Problem-Solving Skills" Am. J. Phys. 44, 212-217 (1976)

Sweller, J., Mawer, R.F. and M.R. Ward "Development of Expertise in Mathematical Problem Solving,"J.Exp. Psych.: General 112, 639-661 (1983)

Sweller, J. "Cognitive Load During Problem Solving: Effects on Learning" Cognitive Science 12, 251-285 (1988)

Van Heuvelen, A. "Overview, Case Study Physics" American J. Phys., 59, 898-906 (1991)

Ward, M. and J. Sweller "Structuring Effective Worked Examples" Cognition and Instruction 7, 1-39 (1990)

David Maloney is professor of physics at Indiana University-Purdue University, Fort Wayne.