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Maybe I should have said "build intuition" rather than "target misconception". Because in many cases, my students come in with no sense of the subject at all. They have no misconceptions about momentum, energy, charge, electric fields, vectors...for all of those things, they are a clear slate, ready for only those misconceptions that I give them :)
But they most certainly do believe that objects prefer to be at rest. And they believe that objects retain a memory of forces that no longer act. The FCI tests both of these notions multiple times. Those particular misconceptions must be attacked.