Robert P. Bauman, Thomas Wdowiak, and Irene Loomis
It is no secret among physics instructors that most students have difficulty with many concepts of elementary physics. One popular way of attacking this problem is to apply Piaget's model of cognitive development. But Piaget worked with children from ages one through 15, so a skeptical teacher of high school juniors and seniors or of college students must surely question whether Piaget's model really applies to high school and college teaching.
Statistics show that typically 50 to 75 percent of college freshmen are not able to cope with the kinds of problems associated with the formal operational stage. Important concepts of an introductory physics course require mental operations on abstract quantities, ratio and proportion, and an awareness of one's own thought processes. The correspondence of answers given by many college students to the answers recounted by Piaget in his interviews with children reveals a striking similarity between the thought processes of the younger students classified as concrete operational, and the physically mature students enrolled in college courses.
The more important question to be asked however is: If the Piagetian model and the numerical results of current testing programs are correct, or even partially correct, what implications does this have for our classrooms? Can we do anything to effectively move students from concrete operational or transitional stages toward formal operational thinking, so that they may understand what we and our colleagues are attempting to teach?
We believe we have found one effective means of stimulating cognitive development in college students. We have heard of other programs that also offer encouragement. Following a description of our current efforts, some of the properties of these programs will be examined in an attempt to see which elements may be important for success.
Our efforts have been directed toward the specific question of whether students can be changed, and we have therefore chosen to separate this process from our conventional physics courses. More specifically, we have devoted a one-quarter, three semester-hour course entitled Mathematical Preparation for Physics to teaching logical thinking, using mathematics as the primary medium of instruction. This course, labeled PH 10, has a typical enrollment of 50 to 60 students per quarter, most of whom plan to take a physics course but who could not pass a rather simple screening examination.
Subsequently, we have also turned attention to the marginal students who would not normally take a physics course at all, but who are in need of learning logical thought processes to survive in college. We first taught a small group of