First, we replicated a number of previous findings of student difficulties in the arrow format and discovered several additional difficulties, including the finding that different relative arrow orientations can prompt different solution paths and different kinds of mistakes, which suggests that students need to practice with a variety of relative orientations. Most importantly, we found that average performance in theijk format was typically excellent and often much better than performance in the arrow format in either the generic or physics contexts.
My question is, is this the result of an inherent conceptional problem in the arrow representation, or simply a matter of correcting some of the ways we teach vectors to students?
Zz.
Well, the i,j,k approach and knowing the vector product rules for the i,j,k vectors does let you do a nice explanation of where the "determinant" approach to cross products comes from. Pictorial representations with arrows can be helpful for visualization, but unclear drawings may do more harm than good.
ReplyDeleteI wonder if someone has done a similar study about "phasor" graphical approaches to RLC circuits vs. complex notation.
Clever idea, Douglas. I would imagine that the confusion is even deeper, as there is no "physical" vector to picture, as is the case with velocity and acceleration vectors.
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