Numerous writers have claimed that a distressingly large percentage of students entering college--and especially those entering community colleges--are ill equipped to meet the kinds of intellectual challenges that their college experience will, or should, present to them. More particularly, it is claimed that many students who have completed secondary school are unable to engage in abstract or, in Piagetian terms, formal operational thinking ( Carpenter, 1980; Chiapetta, 1976; Karplus, 1974; Kolodiy, 1975; Lawson & Renner, 1974; McKinnon, 1971; McKinnon & Renner, 1971; Renner & Lawson, 1983; Tomlinson-Keasey, 1972; Towler & Wheatley, 1971). These students appear to be stuck at the concrete-operations stage of cognitive development.
Concern about this problem has motivated the development of several programs designed to teach formal operational thinking to entering college students who appear to need such training. Many of these programs have a strong Piagetian orientation and make use of the "Learning Cycle" approach to instruction developed by Karplus ( 1974; also Campbell, Fuller, Thornton, Petr, Peterson, Carpenter, & Narveson, 1980; Fuller, 1980).
The "Learning Cycle" distinguishes three phases of learning process: (1) a relatively unguided exploration phase, (2) an invention phase, and (3) an application phase. The Piagetian flavor of the approach is seen in the care that is taken to introduce students to concrete concepts before confronting them with abstract relationships. During the exploration phase of the learning cycle, students engage in exploratory activities involving concrete experiences in a fairly open-ended and non-directed way. During the invention phase, they are encouraged to generalize concrete experiences