pected to understand a range of concepts and laws organized around such domains as force and motion, electricity and magnetism, waves and optics, etc. Typically, understanding was demonstrated by the solution of problem types using quantitative methods that minimally demanded algebra. However, over the past several decades, research on student understanding has called into question whether the goals of instruction were being achieved.

The Route: Progression of Understanding

Historically, the implicit assumption in physics instruction has been that novice students could come to understand physics by receiving classroom presentations of what physics experts know. Research, however, has uncovered problems with that assumption. Students’ naïve ideas and conceptions about the physical world are not easily changed and in fact often remain substantially unaffected by typical classroom instruction. In the 1970s and 1980s, research conducted by John Clement (1982), Andrea diSessa (1982), Lillian McDermott (1984), and others revealed that even those students who can recall physics laws and use them to solve textbook problems may not understand much about the implications of these ideas in the world around them. For example, in diSessa’s research, college physics students performed no better than elementary students when asked to strike a moving object so that it will hit a target with minimum force at impact. Students relied on their untrained ideas in this task, ignoring the role of momentum, even when they could precisely reproduce the relevant laws of momentum on a test. Similarly, a study of student solutions to a problem with simple electrical circuits confirmed that students can reproduce scientific knowledge for a test, but revert to everyday ways of thinking when that knowledge is tapped outside the classroom (see Box 4.1).

Additional work over many years has led to the conclusion that students bring to physics a substantial set of persistent conceptions that are significantly different from those needed to understand aspects of the physics curriculum. By far, the largest amount of work on student conceptions has been in the area of Newtonian mechanics (McDermott and Redish, 1999). Both before and after passing high school and even college physics courses, students often behave as if their conceptual under-

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