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As to narrow concepts, is being able to figure out the sign of acceleration
from knowing the directions of the velocity and whether you are slowing down
or speeding up a narrow concept? Is knowing that acceleration does not go
to zero at the top of the trajectory of a ball thrown straight up a narrow
concept? Is knowing that acceleration does not change direction (or sign)
when the velocity switches direction a narrow concept? Yet the sign and
direction misconceptions persist even after a student has taken calculus.
These are explicitly tested by the FMCE, but not by the FCI. I would think
these are fairly basic.
John M. Clement
Houston, TX