THE DIVERSITY IN SAMPLES OF STUDENT PROOFS AS A FUNCTION OF PROBLEM CHARACTERISTICS: THE 1970 STANFORD CAl LOGIC CURRICULUM

I N DOING RESEARGH on problem solving, educational psychologists face serious difficulties in obtaining detailed information on student performance in solving problems; It may be possible to observe some educational activities unobtrusively, but it is very difficult to obtain detailed records of individual problem-solving behavior in this way. In order to obtain the data necessary to investigate cognitive performance, it is necessary to record student behavior in great detail, and this is not practical in a classroom. Therefore, the systematic investigation of problem-solving behavior has generally been restricted to the laboratory (e.g., NeweIl & Simon, 1972). The advent of computer-assisted instruction (CAl) makes it possible to circumven t some of these difficulties. When a student does problems at a computer terminal, it is relatively easy to obtain a complete profile of responses (as well as the time to each response) for any problem. Since the collection of these data is automated, and therefore invisible to the student, it is possible to record problem-solving behavior over a long period of time without disrupting the process being observed. In a semester of work in mathematics done at a computer terminal, it is relatively easy to 'obtain complete profiles of individual student solutions to hundreds of problems. This implies a further advantage of using CAl for research on problem solving. In a laboratory experiment or in classroom observation, the subjects are aware that their efforts are being observed. It has been shown that, under such conditions, subjects tend to modify their behavior to fit the expectations of the experimenter (Neisser, 1967). To the extent that data collection is truly invisible, this subtle source of possible bias in the data is also eliminated. The use of a CAl curriculum as a context for research on problem solving still presents serious difficulties however. In order to exploit its full