One of the classes I teach is a non – AP Calculus class. Many of my students are showing a reasonably firm grasp of the ideas of Calculus that we are studying, but they are plagued by algebraic struggles and fears at times. I was thinking about the following two ways that I could ask them the same question:
I asked this class today how they would feel about these two forms of the question. Most of them quickly agreed that they would feel more comfortable answering question B than question A. I followed up by asking whether success on question A might feel more like success and a handful agreed that this probably was true. I am not sure what to make of this informal poll and I am bouncing this idea around in my head. I’d love to hear what you think and push back with some questions about my motivations/hopes in (possibly) restructuring my assessment in this direction.
P.S.
I have been urging them to have GeoGebra open nearby when they do their work so that they can look at graphs and ask for derivatives to verify their own work.
Hi Jim!
I would have Power Rule/Chain Rule questions of 3-4 levels of difficulty including your √ question without providing the answer. I don’t recommend the “Show that the derivative is…” type IF you’re testing skill. Of course there will always be an issue of the FORM of their answer.
Giving the derivative is ideal for concept/graph questions:
Given f(x)=√(25-x²), f'(x)= -x/√(25-x²)
(a) Find f'(4) .
(b) Explain relationship between answer to (a) and the graph of f(x).
Note: This is difficult for non-AP students but I’m sure you would only ask it if they experienced many of these.
Students will always opt for “EASIER”!