George L. Gilbert' Denison University Granville. OH 43023
I
How Do I Get the ~nswer? Problem solving in chemistry
After you get into your automobile to drive to work you turn the key in the ignition and it does not start. You have many possible responses to this situation-call your local service station.. trv- to catch a bus or call a taxi.. heain . a svstematic analysis of possible causes of the failure, etc. How each of us responds depends on our knowledge of the vehicle and on the patterns we use in dealing with problem situations. The use of prohlem solving is such a pervasive activity in our lives we often fail to recognize when and how we solve the manv and varied orohlems we confront. The patterns and skills which we have developed in one area of our lives often may he carried over into another area, to become a part of our effective prohlem-solving tactics. It is my conviction that the types of problem-solving skills we develop and encourage in our students will become long term and valuable patterns for them throughout their lives. At a meeting of alumni associated with an American Chemical Society meeting in Philadelphia I encountered a student whom I had not seen for several years since his graduation. In the ensuing discussion I learned that he had ohtained a bachelor's demee in hioloev.,having taken his wneral chemistry with me, and then had gone on to receive a master's degree in the area of hiology. I asked what he was doing presently and he responded that he was working in his father's cartaee and hauling husiness. Mv resrmnse was to inauire whetKer he felt hisextensive training cn science was wasted in his current position. He responded in a verv affirmative tone that he f o k d the ability 6analyze the situations and to make observations about systems and patterns of hehavior relate specifically to prohlem-solving skills which were developed in his science courses: these habits were extremelv usefd in dealing with prohlem situations that developed in the husiness. This and other encounters with students point out the importance and enduring characteristics oi' the methods by which we solve prohlems. This oaper . . consists of three sections. The first section will present an assessment of the ways in which problem-solving skills are currently taught and will then cite difficulties students encounter as they attempt to develop these skills. The second section will discuss some of the aeneral oatterns which selected authors have developed for problem &ing, cite errors which are frequently noted in applying these techniques, describe the role of teachers in developing these techniques and comment on behavior which follows the obtaining of "the answer." The third section will propose some specific suggestions for ways to improve the quality and breadth of our teaching of problem solving. At no time do I divorce the development of problem-solving skills from the learning of subject matter, for I believe these elements must complement each other in our teaching efforts.
-.
-
How Do We Teach Problem Solving?
Conventional Methods In assessing the various methods by which prohlem solving is conventionally taught I find four patterns emerging. The first of these patterns is the teaching of prohlem solving by example. In this pattern we discuss in lecture or recitation meetings with students methods by which problems are solved and solve sample problems to demonstrate the application of these methods. Our presumption is that if students follow the
methods that we use they will he successful problem solvers in these tooical areas. A second method we use to encourage problem-solvingskill development is through the effort of students in workine homework prohlems. w e assign modest to large numbers of prohlems on the assumption that working a significant number of prohlems will lead to the recognition of certain patterns within those problems on the part of students and that these students are more likely to become more proficient and productive prohlem solvers. A third tactic is applied which includes the use of quizzes and exams to .out .oressure on students to solve nrohlems in u more limited timp frame. \Vithin this pntrern we trust that better arohlem-sol\.inr >kills will emt.ree as wpll as e.ital)lishingwhich students are better problkn solvers by their ~erformanceon such exams or quizzes. A final area where prohlem solving can be taught hut has been utilized to a verv limited extent in mv exoerience is the laboratory. Within ockrround of the prohlem solver. Whimhy feeis that the attitudeof the individual approaching the problem is an extremely critical factor in the ability to solve the problem. If an individualdoes not believe that the problem can be solved by analysis then the tartics and elfur; put into sohing the p&leni may he insuffi(ient to achieve s i r l ~ ~ t iand m the initid belief that the problem cannot be solved will he confirmed. Errors in Problem Solving
A variety of errors are made in approaching a problem, among which Polya lists the failure to include the knowns, unknowns, and conditions of the problem in a clear cut fashion. As noted earlier the omission of reference to analogous or eauivalent aroblems presents students with what appears to be a totallynew situation requiring totally new tactics and patterns. If, in developing the bridge between the givens and goals of the prohlem, students fail to use the necessary information given or to seek information from other sources and organize this material in order to transform it into the condition of the answer then they clearly will fail to solve the prohlem. One peculiar characteristic of certain problemsolving situations is the imposition of constraints which were not stated by the problem which interfere with the ability to solve that problem. These constraints may manifest themselves as an unwillingness to use previous concepts or relationships due to the compartmentalization referred to earlier. An experiment calls for samples of a metal which is available in the form of short cylinders. Each cylindrical piece must yield eight samples. How can you use a minimum number of cuts to abtain the required number of pieces?
What constraints did you impose as you considered the problem given above? Another source of serious difficulty is the lack of undernrandiny d !he h a w voncepti u hi, h are newsiary t u solve the ~ n h l e mFm . ewmple. students t.;mn
