Questions used early in the investigation. In each case, students were asked to draw velocity vectors and to indicate the approximate direction of the acceleration for various points in the motion.
Questions used to examine the relation between vector skills and conceptual understanding: (a) 1D pretest on collision of two carts, (b) 1D matched pretests on manipulation of vectors, and (c) 2D post-test on manipulation of vectors.
Examples of pretests administered to large numbers of students. Students were asked to draw velocity and acceleration vectors at various points during each motion. (a) 1D pretest on ball moving up and down a ramp. (b) 2D pretest on object moving at constant speed along a closed, horizontal track. Some students were also asked about the case that the object speeds up from rest.
Examples of 1D post-tests. (a) Two pucks collide on a frictionless table. Students were asked to give the directions of the accelerations and the relative magnitudes. (b) Two blocks of different mass move on a frictionless incline. Students were asked to indicate the direction of the acceleration of block B at the earlier instant and to draw the change in velocity vector for block A.
Example of 2D post-test. Students were asked to sketch velocity and acceleration vectors at the labeled points for the case that the object moves at constant speed and to draw acceleration vectors for the case that the object moves with increasing speed.
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