Students know that WolframAlpha and other software/computational resources exist and will make use of them as they see fit. Is there anything we can change about the way we teach calculus (in particular, for this thread) to make use of these tools? Ideally, we would like to simultaneously:
- Prevent students from committing academic dishonesty (however it be defined in your context) and, hopefully, discover when it occurs
- Show students the immediate benefits of using such resources: save time in computation, visualize a graph, check our work
- Show students the long-range benefits of using such resources: explore similar problems (e.g. sensitivity to initial conditions for diff eqs), experimenting with problems to identify patterns, getting a "solution" to discover a method that would yield such an answer
I'm interested in examples where you have made use of WolframAlpha (or others) in class or on an assignment, and whether the students seemed to gain anything from it. Did you address some of the points I listed above? Are there other potential positive/negative aspects that you noticed?
I'm also somewhat interested in how you address questions like, "Why do I need to learn this when WolframAlpha can do it for us?", but I'd prefer if the thread didn't devolve into only discussing this topic. Instead, have you addressed such a query by showing students the benefits of bringing mathematical knowledge and intuition to a problem so as to make it tractable for software?
Assume all of this is in the context of a college calculus course.