Assessing for conceptual understanding can be challenging. My students in Prob/Stat are used to explaining their thinking or interpreting their results. They get good at writing sentences to justify their answers. After seeing students struggle on today's Calculus quiz, I know that I need to do a better job getting my calculus students to show they have a conceptual understanding of the first and second derivative as it relates to a specific function. In addition, they need to learn how to verbalize their understanding. (Note: I haven't actually graded the quizzes yet, but my perception was that they were struggling. Stay tuned when I blog more about this topic tomorrow.)
Here is one of the quiz questions from today.
Here are some predictions relative to this question.
1) Students will say that there is no maximum, only a minimum at x = 0. They are correct that the derivative has a minimum at x = 0, but that doesn't mean that the original function has a minimum at x = 0.
2) Students will explain that at x = -1 and x = 1, the derivative is 0. However, they won't be able to explain how the graph of the derivative is related to the sign of the derivative.
3) There will be some other wacky stuff. Not sure what, but based on some of the questions students tried to ask me during the quiz, I am confident that there is some other wacky stuff that students wrote about.
I hope you'll return to this blog tomorrow to see how the students did and what I think I need to do to get my students to improve in this area.