ment. A program that is coherent—that guides instruction from one class to the next—can be of tremendous help in managing complexity. While the findings of researchers may be relevant to practice, if they are not easily incorporated into the teacher’s instructional program, they may not be useful. Indeed, they may simply add to the complexity of an already highly complex task.

More targeted and instruction-relevant research (Hiebert et al., 2002) would be a good place to start. We can take as an example the research on the misconceptions students harbor in physics. In the course of everyday experience, people develop understandings or models of how the physical world works: as one moves closer to a heat source, temperature rises. One then draws inferences based on one’s experiences that are very often scientifically incorrect: in the summer, the earth is closer to the sun. A persuasive body of evidence suggests that the models of physical principles that students deduce incorrectly from everyday experience are powerful and resilient (National Research Council, 2000; Vosniadou and Brewer, 1989; diSessa, 1982). While students may “learn” physics in the classroom and even perform quite well on tests, outside the classroom they revert to their untrained model (see Box 1.1).

The principle at work in physics is at play in all disciplines, undermining the effectiveness of the educational process. Nu

BOX 1.1
Misconceptions About Momentum

Andrea diSessa (1982) conducted a study in which he compared the performance of college physics students at a top technological university with the performance of elementary school children on a task involving momentum. He instructed both sets of students to play a computerized game that required them to apply a force (using a job stick) to a simulated object moving across the computer screen (a dynaturtle) so that it would hit a target, and do so with minimum speed at impact. Participants were introduced to the game and given a hands-on trial that allowed them to apply a few taps with a wooden mallet to a ball on a table before they began.

DiSessa found that both groups of students failed miserably at the task. Given the momentum of the dynaturtle, students should have applied a light force very early to ensure minimum speed at impact. Despite their training, college physics majors, just like the elementary school children, applied the force when the object was just below the target, failing to take momentum into account. Further investigation with one college student revealed that she knew the relevant physical properties and formulas and would have performed well on a written exam. Yet in the context of the game, she fell back on her untrained conceptions of how the physical world works.

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