I'm teaching a math course which covers several mathematics topics including differential equations (DE). In a recent exam I asked the students a question in which they are given a DE and are asked to solve it using at least two of the different solution techniques they learned in class. My intention was that asking for different solution techniques reflects fundamentally different skills than a single solution. Do you think this is true?
In other words, are there fundamental differences in the learning outcomes measured between the following two questions:
- Solve the differential equation dy/dx = y/x
- Solve the differential equation dy/dx = y/x using at least two different solution techniques.
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