I’ve finally settled on the problem domain used for this project, which will be vectors in physics. This is actually a bigger area than I first thought, and although the concept of vectors is relatively straightforward, there is a bit of notation to get acclimated to, as well as a lot of different applications for it.
After looking through a lot of curriculum materials for teaching vectors, I’ve decided that it’s best to start with sort of a “proof of concept” rather than try to come up with the complete package from the outset.
Here are some potential problem domains dealing with vectors:
- Vector arithmetic. Add and subtract vectors. Use scalars and apply commutative, associative & distributive laws of vector multiplication.
- Vector analysis. Find the unit vector, given a vector (what’s known as normalizing the vector). Resolve a vector into its X, Y and Z components. Determine vector equality.
- Vector word problems. Calculate relative velocity (given a plane at a particular velocity with a head/tailwind, what is the relative velocity of the plane?). “Riverboat” problems (given a boat that needs to get from one side of a river to another, at what direction must the boat go at a particular velocity, in order to reach the other side given a current?).
I have to say that obviously, the 3rd option seems to most worthwhile. I think the solutions for the first 2 domains will be very straightforward, but the challenge will lie in user input and manipulation issues. For the word problems, there are 2 well-defined problems with non-trivial solutions that put vectors into a realistic and somewhat interesting domain.
January 28, 2007 at 2:27 pm
[...] The topic of instruction… I’m going to take an instructional unit out high school/college physics. Specifically, the unit will deal with vectors, and the current plan is to implement vector word problems, such as relative velocity problems and riverboat problems. [...]