Here's where I find it ironic that they are stumped. I have to ask them what the graph of position looks like. It doesn't take much to get them to see it is an upside down parabola. But then I ask them where in the graph is reaches it's highest point and how they can find it without using Calculus. I tell them they have more than one way that they knew when they started the year in the class. It takes awhile for the wheels to churn and spit out things like midpoint value of the x-intercepts, or complete the square, or -b/2a. Much discussion happens over these ideas. Then, and only then, we get to the calculus option of finding the derivative. But getting all the other ideas back in their brain and to a level of it making sense is a challenge. I marvel at how little students remember. When we discuss the -b/2a option, I ask them if they have seen that anywhere else. Someone inevitably says "quadratic formula" and I ask if we should sing. Several do. I say isn't that great, but you aren't even aware that what that formula does is generate the x-intercepts equidistant from the midpoint (and proceed to split the formula apart). They are amazed as though I just performed a magic trick. I re-emphasize the importance of graphs to help them see what is happening.
Wish graphical approach was used a lot more in the earlier classes. Seems like we teach a lot of "just memorize this formula" without the pictures to help it make sense. If we taught reading that way (no pictures), do you suppose kids would come to high school not being able to read all that well? Wonder why kids prefer "the movie" over "the book" when its available? Do you suppose we are more picture driven in our brains? I do. I tell the kids "I love pictures". I know they help. Getting them "back to basics" takes some time. It makes me sad that they have had it "beaten out of them".
I just need to find some more Stats video games!