provoc~tive opinion More Sample Problems with Step-by-step Solutions? Take Them Away! Beverly C. Pestel University of Wisconsin-Eau Claire, Eau Claire, Wl 54701

A recent article in this Journal1 has given me the courage to express an opinion I have harbored for years. The topic is chemistry textbooks and the issue is the increasing number of problems complete with worked-out solutions. The article I refer to addressed this issue with candor but was tempered with understanding reeardine differences in nersonal nref- erence. Taking a position that much more dogmatic, I suggest that readily available solutions are more than just an annoyance; they can a&ally generate an obstacle to learning.

Textbook reps have been coming into my office for years now with the "Boy, have I got something for you" glint in their eyes. Invariably, they begin their pitch by highlighting the presence of even more sample problems with step-by- step solutions. What a relief it is to know that those reps were wrong to imply that I am alone in objecting to the proliferation of these "teaching aids". To have this objection taken seriously, however, an explanation is required.

One of the most common complaints I hear from col- leaeues is that students either cannot or will not think. If an exam question is phrased in a different manner from sample problems performed in class, the instructors are beina unfair anrl trick>'. I t a Iatmratory exercise directs them to rneadure the aridity of usample rather thangi\.ing them step-by-step

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procedures for doing so, the inst&tct&s are imposing an unreasonable demand. What has this to do with textbooks full of worked-out solutions? Evervthine!

My objection to the step-by-stepsolu~ons is founded on a oedaeoeical basis. Students need us to give them the onnor- . - " tunity (or coerce them into the necessity) to learn instead of encouraging them to mimic. To perform, mimics require only a pattern-not any understanding of why the procedure works or how it may be applied under a different set of conditions. Mimics can arrive at answers and in that respect be successful in a course, but that success is no assurance that any learning has occurred. Learning focuses on the logic of a set of procedures and the application of those proce- dures to new problems. In fact, the process of developing thought patterns that can be applied to novel situations is what learning is all about. My contention is that too many sample problems with worked-out solutions encourage mim- icrv and discourage learning. -

Lnt'ortunntely, the criticism euprwsed earlier uf students' inability or unwillinrness t u think is often a d i d one. nut who is i t fault? In order for students to recognize a novel problem as a simple rearrangement of a previous example, they must have some experience in problem solving. Prob- lem solving is really just a euphemism for thinking, and students need practice to become effective thinkers. The ability to take ageneral direction and expand it to the appro- priate series of steps also requires experience in problem

'Carter, K. N.: Carter, E. G. J Chem. Educ. 1987, 64,310

444 Journal of Chemical Education

solving. Problems in texts can provide a means for instruc- tors to teach problem-solving ability, but only if the texts do not reduce the problems to mere exercises.

The distinction between problems and exercises is impor- tant in addressing the issue of mimicking versus learning. Problems are tasks that require the thoughtful application of previous information into a new format. Exercises are tasks that simply involve the transfer of new data into a memorized or otherwise accessible template. Problems de- mand problem-solving ability; exercises do not. An obstacle to learning can occur when all the assigned tasks at the end of the chapter can be treated as exercises. The inclusion of numerous sample problems within the chapter provide the templates that allow students to reduce problems to exer- cises. As typical a group of humans as any other, students will complete their tasks through the easiest route possible. When the textbook is full of sample problems, the route to use in doing homework is clear: thumb through the book until the appropriate example is found, replace the numbers in the example with the ones from the homework, punch the numbers into the calculator. Task complete, minimal hassle, negligible learning.

If the homework does not provide students with the op- portunity (necessity) to engage in some real problem-solving activity, how can they be expected magically to exhibit this ability on an exam or in the laboratory? Regrettably, it will not matter how many exercises we require students to per- form; exercises will not make problem solvers of them. Whether there are 10 tasks or 200 a t the end of the chapter, if the students have not nerformed these tasks bv thinkina their w3). through tua so.lution, there has been no ;eal upPo;: runits for learning to take place. In addition, it makes little diffeience how mich emphasis we place on problem solving in our teaching if every task we assign can be completed by matching it up with a worked-out solution from the text. Most students who complete assignments in this way remain unprepared to deal with novel problems on an exam regard- less of the teaching style used in class.

While it may be true that some students do learn through the extensive repetition of exercises, we need to be aware that the majority become nothing more than skilled imita- tors. These imitators can survive chemistry courses because exams generally contain only a small percentage of novel problems. As a result, these students are seduced into believ- ing they have learned chemistry when they have not. The textbooks with their worked-out solutions have subverted the instructor's ability to teach these students.

When textbook reps come tome with those texts that have been "enhanced" with numerous worked-out examples, I intend to continue to tell them "Take them away." Only now, thanks to the Carters, I will have the satisfaction of knowing that I am not alone.