Measured Formal Thought and That Required to Understand Formal Concepts in Secondary School Biology

Students (N=22) enrolled in secondary school biology were evaluated for their abilities to use: combinatorial logic; correlational reasoning; separation and control of variables; exclusion of irrelevant variables; proportional reasoning; and probabilistic reasoning. Each student responded individually to six Piagetian tasks designed to measure their levels of function on the six variables. Students were then asked two questions. The first question (which tested understanding of the concept "Plant growth is not affected by chemicals.") required correlational reasoning, combinatorial logic, separation and control of variables, and exclusion reasoning. Although the 22 students could have shown formal thought 88 times, only 24 such instances were found. The second question (which tested understanding of the concept "Heredity and environment interact in the expression of traits.") required combinatorial, probabilistic reasoning, proportional reasoning, and separation of variables. Again, although it was possible to demonstrate formal thought 88 times, only 25 instances were found. These and other findings indicate that using specific formal operations with which students demonstrate they can function, is not a good predictor of success on a question whose satisfactory response requires those specific formal operation. Thus, the exact formal operations necessary to understand a formal concept need not be isolated. (Author/JN)