ADAPT Program (Accent on Developing Abstract Processes of Thought)
Date of this Version
October 1982
Abstract
Usually in the beginning courses I teach there are several students who never seem to understand what is really going on. These students are neither lazy nor dumb. Some even work very hard in math and do quite well in their other courses. Yet there seems to be something about their work in mathematics which produces frustration instead of understanding. I recall experiencing that kind of "learning" in high school geometry. I and many of my friends got fairly good grades in that course by memorizing without much understanding. As a high school sophomore I was just not ready for deductive reasoning, proofs, axioms, etc. There were some essential mental skills which I had not yet developed.
As all college teachers know, the lack of certain specific mental skills is not restricted to high school students. Recent research can document that fact quite well, (Kohlberg and Gilligan, 1971; Lawson and Renner, 1974). To be more specific about mathematics consider the following examples of reasoning from freshmen.