You’re lecturing to your introductory college astronomy class about Newton’s law of gravitation. You’ve carefully explained that the gravitational force depends on the product of the two masses involved and on the inverse square of the distance between them. You’ve shown a few examples or perhaps videos and animations to help your students connect the abstraction of an equation to the real physical world. You may assign thoughtful homework problems, and you encourage the students to ask questions if they don’t understand, either in class or during your office hours. You’re known as a good lecturer, and your students always rate you highly at the end of the term. Yet when you give your exam, you’re dismayed to see how many of them can’t answer straightforward questions of the type you covered in class and assigned as homework. So why does the same thing happen to instructors all over the...

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