FEd December 1997 Newsletter - Student Problem Solving

December 1997



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Student Problem Solving

Alan Van Heuvelen

A recent survey (Blake, 1995) by the American Institute of Physics (AIP) asked former physics majors who are now in the workplace to identify the most important skills needed for their work. Solving problems was rated first, followed closely by the interpersonal skills needed to work effectively in groups, and by technical writing. The 864 respondents judged physics knowledge as low in importance in the workplace.

This outcome-the lack of importance of physics knowledge and the considerable importance of problem solving-may be a blessing in disguise for our physics education. We can select a reduced content of the most important principles-a less is more philosophy endorsed by the Introductory University Physics Project. Students can be given more responsibility for acquiring that knowledge-a strategy that enhances learning. Time made available by this reduced content can be used to help students develop the skills needed to address more complex problems.

The ability to work effectively in groups was also judged very important in the AIP survey. Eighty percent of our former physics majors work in a group or supervise a group. Fortunately, promoting group work in education is a win-win situation. Johnson, et al. (1981) analyzed student achievement in 51 high-quality studies comparing cooperative learning to so-called competitive lecture-based learning. They found that the cooperative groups on average scored 0.81 standard deviations (almost one grade point) higher than the lecture-based groups.

What about the recent emphasis on conceptual understanding in our college courses? This is yet another win-win situation. Research indicates that good problem solving starts with a strong conceptual foundation. Hake (1997) reports a strong correlation between student scores on a conceptual test and on a problem-solving test. Researchers at the University of Massachusetts have found that problem-solving performance improves when students use a hierarchically structured conceptual analysis strategy (Dufresne, et al., 1992) and when they integrate qualitative strategies into their problem solving (Leonard, et al., 1996). Ron Gautreau at New Jersey Institute of Technology and I have found that student problem-solving scores in university physics courses improve when concepts are introduced and used qualitatively before their use in mathematical form.

There are important reasons why a strong conceptual foundation is correlated with the ability to use with understanding the principles of physics in their mathematical form. Cognitive research indicates that the mind is essentially a symbol-processing device. The symbols in our minds are not mathematical symbols but are some special brain descriptions in a sort of internal brain language. A person makes sense of spoken language, written language, and the math symbols in an equation by a dynamic interplay between internal imagery and these external representations. If the external representations have no links to a person's internal imagery, then the person cannot construct meaning for the external representations. The symbolic language of physics is very abstract. For the symbols to make sense, they must elicit internal mental images that give meaning to the symbols.

To address this difficulty, we can integrate the mathematical descriptions of physical processes with qualitative descriptions that students learn while building their qualitative foundation-a multiple representation strategy. These representations provide links between the abstract math and the more qualitative picture-like and diagrammatic descriptions. Technology that includes intuitive diagrammatic and picture-like representations show promise in helping students visualize the quantities and concepts of physics. Familiar context also helps relate the physics to imagery in students' minds.

As students develop better understanding, they can be asked to "read" an equation and then invent a process that is consistent with the equation-I call these "Jeopardy" problems. Their description can involve words, pictures, or some other more intuitive representation. In the example below, students are to invent a process represented by the equation.

(100 kg)(9.8 m/s2)(50 m sin 37o) = («)k(50 m)2

Finally, having developed a better qualitative understanding and facility with the mathematical language, the student is ready for more complex multipart problems. To solve these latter problems, students learn to add definition to poorly-defined problems, divide complex problems in parts, access the appropriate knowledge to solve each part, choose quantities whose values must be determined in order to solve the problem, make rough estimates in order to supply missing information, interpret data tables and their graphs, and justify approximations. The problems can involve experimental apparatus, so-called "experiment problems" (Van Heuvelen, 1995), and context-rich problems (Heller, et al. 1992).

Does such a system improve learning? There is considerable evidence that strategies such as those described here enhance students' abilities to reason effectively about physical processes without using mathematics and to apply the symbolic language of physics with better understanding. There is also growing evidence that the strategies also enhance students' abilities to analyze and solve more complex problems.

Blake, G. (1995), "Skills used in the workplace: What every physics student (and professor) should know," American Institute of Physics, College Park, MD.

Dufresne, R., W. J. Gerace, P.T.Hardiman, and J.P.Mestre (1992), J. Learning Sciences 2, 307-331.

Heller, P., R. Keith, and S. Anderson (1992), Am. J. Phys. 60, 627-636.

Johnson, D. W., G. Maruyama, R. T. Johnson, D. Nelson, and L. Skon (1981), Psychological Bull. 89, 429-445.

Leonard, W. J., R.J.Dufresne, and J. P. Mestre (1996), Am. J. Phys.64, 1495-1503.

Van Heuvelen, A. (1995), Phys. Teach. 33, 176

Instructions for about 30 experiment problems can be accessed from http://physics.www.ohio-state.edu/~physedu/expros/index.cfm].

Alan Van Heuvelen is professor of physics at Ohio State University, where he does research on physics education. He conducts workshops on physics problem solving.