After making the transition to Standards Based Grading a few years ago (which is awesome!), over time I realized that my class had become too skill-oriented. To fix this I first tried to create standards that were “understanding standards”, but this overwhelmed my students with too many grades.
It took me an entire semester, but I realized that what I should be doing is asking “understanding questions” on assessments instead of only skill-oriented questions.
I try to limit my assessments to three questions (sometimes a question might have multiple parts), but I now always try to include an “understanding question” as one of those three questions. I never grew up answering these on math assessments, and they’re harder to grade because there’s usually not “one right answer”, but it has helped me get a better grasp of what my students understand (or don’t).
What do these look like? Here are some examples.
Exponents: Explain why is true.
Polynomials: What does multiplying polynomials have to do with the distributive property?
Polynomials: Why can you combine some terms of a polynomial but not others? ( can be added but cannot)
Rational Expressions: Before factoring was the opposite of simplifying. What has changed and why do we factor first to simplify rational expressions?
Functions: Give an example of a function and a non-function outside of math class.
Transformations: Why does move a graph left and move a graph right? Isn’t that that the opposite of what you would expect?
Logarithms: Explain why is true.
Reflection/My Own Questions
(1) Are these “understanding questions” enough to check for understanding? Probably not by themselves. So I need to get better at assessing repeatedly over time to check for retention of understanding.
(2) Should I give students the questions beforehand? Right now I do because if they want to figure out the answers on their own, great! As long as I have enough possible questions so they’re not simply memorizing and spitting back what I say, but really understanding it. (Or should they be able to get these questions even without me providing them ahead of time?)
(3) Is there a place to get these types of questions? I primarily look in the textbook or come up with my own questions, but surely there’s a bank of these somewhere online that I haven’t found yet.
These questions are ones that get at understanding, though harder to grade (at least they take longer), are worth it. When I started these questions, I was sorely disappointed how little my Precalculus students understood (even though they have seen some things, like exponents, in Algebra II and probably even in Algebra I!). I’m really curious what people think about the three reflection questions above.
Thanks for reading!
 I’ve flip-flopped between using the vocabulary “prove” and “explain”. The former suggests there’s one right answer to students whereas the latter allows for various explanations. “Explain” also is harder to grade, but I’m very excited if I see students start to write out examples in their explanations. No, it’s not as rigorous as professional mathematicians, but it shows me that they’re starting to understand.