Chemical Education Today
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Teaching Science Problem Solving: An Overview of Experimental Work by Kenneth S. Lyle and William R. Robinson
Problems can be classified as exercises or true problems. An exercise is a problem that we know how to solve from the beginning. Solving one is simply a matter of writing out the solution and checking for mistakes. True problems fall into that category defined by Hayes (1), “A problem exists when a person perceives a gap between where he or she is and where he or she wants to be but doesn’t know how to cross the gap.” Problem solving is an everyday facet of chemists’ work. As a result of our years of training and practice we can handle exercises in a routine way. Our experience has also helped us to develop efficient and effective problem-solving skills and strategies that generally lead us to successful solutions for true problems. In order to assist students in obtaining these skills and strategies we need to be knowledgeable not only about our skills and strategies but also about effective instructional methods for teaching them. Problem-Solving Knowledge and Skills The combination of our knowledge base and our skills base contributes to our ability to solve a problem successfully. Our knowledge base is that collection of knowledge that allows us to recognize when a pattern or situation belongs to a category we have already learned. Our knowledge base also specifies what action is appropriate for that category. This type of knowledge base is sometimes referred to as a schema. For example, chemists have a “balancing an equation” schema; we know how to proceed when asked to balance an equation. Our skills base is harder to define. It includes obvious elements such as the ability to read, to perform mathematical manipulations, to check results, to check that no information is overlooked, and to check that the problem actually presented was solved. Other elements involve analyzing a problem, planning a possible route to a solution, and generating a representation of a given situation. Skills may be domain specific and relate to one specific schema in the knowledge base (balancing an equation, for example) or they may be more general (such as using significant figures appropriately). According to the cognitive theory of learning (2) we use our knowledge to process external information by relating it to what we already know. When presented with a problem we use our knowledge to interpret the information provided and identify the goal of the problem. Longterm memory is searched for the schemas that contain specific strategies and knowledge relevant to the problem. If the problem is familiar, a plan for solving it is created, carried out, and evaluated. True problems are more challenging and may require several cycles of interpreting, represent1162
ing, planning, execution, and evaluation. When finished with a problem we not only have a solution but we also have a new or revised knowledge base. Effective Problem-Solving Instruction Traditionally, chemistry problem solving has been taught through textbooks or lecture by providing example problems and their solutions. This instruction tends to focus on the sequence of steps used to solve the problem rather than the knowledge needed to recognize a problem and the skills (cognitive strategies) used to solve it. Students are then assigned practice problems analogous to the examples with the assumption that such practice will result in an improved performance. They work on the problems individually or in small groups, generally submitting their work for evaluation. Students having difficulty are expected to find help to assist them in solving the assigned problems. Both research and experience suggest that this method of instruction is not adequate, and that there should be more effective methods available. The characteristics of effective strategies for teaching problem-solving are addressed by Taconis, Ferguson-Hessler, and Broekkamp in their paper “Teaching Science Problem Solving: An Overview of Experimental Work” (3). As the authors point out, it is obvious that problem-solving activities need to be practiced in order for a novice to develop sufficient skill to carry out these activities fluently and without many errors. Both the structure of the skills base and its automation are strengthened by practice. However, the authors also point out that the structure of the problemsolving knowledge base is equally important, and learning tasks that focus on improving the content and structure of the knowledge base are essential. Taconis et al. attempt to identify various strategies that improve problem-solving schemas. Their paper presents the results of a meta-analysis of 40 experiments found in 22 articles published after 1980. (As described by Green (4), a meta-analysis is the statistical analysis of a large collection of results from individual studies for the purpose of integrating the findings). The aim of this meta-analysis was “to combine the results of all studies on science problem solving that estimate the effectiveness of a particular teaching method in a particular setting, and extract results that link learning effects found to characteristics of the teaching method.” The experiments studied involved teaching of problem solving in science and mathematics courses ranging from fourthgrade to college level. The analysis was limited to experiments that involved a pretest or other pretreatment comparison of treatment and control groups, followed by some form of intervention intended to improve the problem-solving skills
Journal of Chemical Education • Vol. 78 No. 9 September 2001 • JChemEd.chem.wisc.edu
Chemical Education Today
of the treatment group, and finally, a posttest. In addition, the studies were required to have a stated theoretical rationale for the choice of intervention and an interpretation of the results of the experiment. Quantitative analyses (correlation of control and experimental treatments with direct and differential effects) and qualitative analyses (contrasting effective treatments with less effective ones) were carried out. The details of the analysis of the data are beyond the scope of this article but can be found in ref 3. Taconis et al. report four main results of their work. •
They identified the variables that describe the different instructional strategies employed in the development of problem-solving skills. These variables could be useful to others wishing to conduct research in this area.
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Instructional methods that both enhance the quality of the knowledge base of the students and demonstrate the use of the knowledge base in problemsolving were found to be of the greatest benefits to students. Methods that involve the students in explaining examples to each other, making diagrams of their schema using concept maps, sorting the elements of knowledge in problem situations, and constructing problems appeared to be most effective. Methods identified as having a minimal or negative effect on the development of problem-solving skills include the use of solved examples with attention focused only on the step-by-step solution followed by numerous practice problems, strategy training followed by worksheets designed to support students in the use of the strategy, and focusing on a strategy alone without giving attention to the knowledge base behind the strategy.
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Learning conditions that have an influence on the overall effectiveness of an instructional method were identified. Favorable conditions include the use of immediate feedback, providing students with external guidelines and criteria, and giving attention to the different types of knowledge and/or construction of task-related schema. It is probable that these factors trigger or facilitate cognitive processes that enhance the knowledge bases. The solving of complex chemistry problems at the level of first-year university courses is one of this group of “successful” experimental treatments (6). It appears that working in small groups improves problem-solving performance only when the group
is provided with well-chosen study material, guidelines, and feedback. Working in groups without specific structure tends to have no effect, and in one case a negative effect, on the development of problem solving skills. Successful group work has been observed with chemistry students solving stoichiometry problems at the high school (7 ) and university chemistry (6 ) levels.
Another interesting finding of this work is that the instructional method used to develop problem-solving skills does not need to focus directly on the goal of solving a problem. Working with the concepts involved in the solution of the problem is also effective. For example, studying solved problems with emphasis on the concepts involved, possibly including the construction of concept maps as part of the analysis, can contribute to improved problem-solving skills. The authors attribute the effect to the fact that the development of both the knowledge base and thinking skills are stimulated. In summary, with appropriate instructional strategies it is possible for individual instructors more effectively to assist their students in developing problem-solving skills. Instructional strategies incorporating cognitive activities that involve both the knowledge and skills bases are effective, especially when external guidelines, feedback, and attention to schema are included as part of the instruction. Working in groups without external guidelines and structure does not enhance the ability to solve problems. Literature Cited 1. Hayes, J. R. The Complete Problem Solver; Franklin Institute Press: Philadelphia, 1981. 2. Newell, A.; Simon, H. A. Human Problem Solving; Prentice Hall: Englewood Cliffs, NJ, 1972. 3. Taconis, R.; Ferguson-Hessler, M. G. M.; Broekkamp, H. J. Res. Sci. Teach. 2001, 38, 442–468. 4. Glass, G. V. Educ. Res. 1976, 5 (10), 3–8. 5. Bunce, D. M.; Heikkinen, H. J. Res. Sci. Teach. 1986, 23, 11–20. 6. Niaz, M. J. Res. Sci. Teach. 1995, 32, 959–970. 7. Tingle, J. B.; Good, R. J. Res. Sci. Teach. 1990, 27, 671– 683.
Kenneth S. Lyle, a graduate student in the Chemistry Education Program, and William R. Robinson, his research supervisor, are in the Department of Chemistry, Purdue University, West Lafayette, IN 47907;
[email protected].
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