First of all, let me say, “yikes!” I went ahead with my plan and recorded the audio of one my calculus class. It was…. enlightening and a bit terrifying. I have tried to type in all the questions I asked during the 44 minute time I was recording.

After having typed these up I realized that often times my questions are a bit confusing. I use “it” and “this” and “that” far too often. Sometimes the meaning is clear in context, but other times I am sure my students are a bit confused. I was also surprised by how many questions I asked during that time. I’m asking more than a question a minute. Considering some of the questions require some amount of thinking and wait time, I may be moving too fast. On the other hand, many of these questions weren’t meant for deep thinking, but just to monitor the class or help the class monitor their progress through a problem.

The questions below are in order, but because of the lack of context they don’t make much sense. You will see I ask a lot of “how many agree with this?” kind of questions. I also ask if there are any questions from students pretty often. I call these monitoring questions. Of all the questions I asked, I think I’m most proud of the ones that I have labeled “exploring student thinking.” **This is what questioning is really all about, in my mind: figuring out what students are thinking.**

- Anybody have any questions for me on that? [Monitoring]
- On a scale from 1-5 how comfortable did you feel about the assignment overall? [Monitoring]
- Student A, can I see whatchya got? [Not really a question…. 🙂 ]
- How many agree with Student A’s graph on the left? [Monitoring]
- Student A, why did you do what you did in that graph? [
**Exploring student thinking**] - What is the purpose of those lines you drew in? [
**Exploring student thinking**] - And the “derivative” meaning? [Clarifying vocabulary]
- And you are trying to match that slope? [Clarifying]
- Does that seem reasonable to everyone else? [Monitoring]
- How many of you had something vaguely parabolic looking? [Monitoring]
- How many of you had something different? [Monitoring]…. <I don’t know why I asked this, since it should be the “rest” of the students from the previous question.>
- Student B, what does your “part B” look like? [Not really a question]
- What kind of graph is that? [Concept check]
- How many of you agree with her graph on the right? [monitoring]
- How did you get the points that you got? [
**Exploring student thinking**] - What do you mean? [Clarifying]
- For the graph of which thing? [Clarifying]
- The graph of f? [Clarifying]
- And Student B is using them as the y-values? [Clarifying/exploring student thinking]
- What obvious connections should we look at when comparing the f graph and the f ‘ graph?
**[Exploring student thinking**]. <I wish I didn’t use the word “obvious” here.> - Why do those points “match up?” [
**Exploring student thinking**] - How would you describe the f’ graph when x<0? [Concept check] <I actually included wait time!!>
- Is it always increasing? [clarifying]
- Is there any other way we can describe f’ when x<0? [Concept check] <
**I wish I included this type of question even when I can’t think of another way to describe things. I think I make it too obvious when students don’t give me the answer I want to hear.**> - Would you describe it as positive or negative? [Concept check] <Turn and talk to your neighbor. Followed up with a vote. I should do this more often. “Think, pair, share” really does help improve class responses.>
- Student B, can you point to the portion of the line in the third quadrant? Those of you who said it was positive, why did you say it was positive? [They answer that the slope of the line is positive.] <
**By the way, who was supposed to answer this question? I hate questions that ask for a choral response when I haven’t made it clear that is what I’m looking for.**> - But isn’t the graph itself negative? Aren’t the y-values negative? [Rhetorical]
**Should I even ask questions like this?** - Anybody else? [Monitoring]
- When x>0 would you agree with me that f’ is positive? [Rhetorical]
**Like anyone would disagree with the teacher.** - How does f'<0 in this region tie in with the behavior of f on the same interval? [Concept check]
- Should’t we be able to say that the derivative is negative on this interval just because the slope of f is negative? [Rhetorical]
- Student C, why did you settle on x^2 as your function? [
**Exploring student thinking**] - x^2 graph is going to be a parabola? Correct? [Rhetorical]
- What else is left for this part of the problem? [Monitoring]
- Well, what did you get? [Redirected question] <Directed at a student who asked me what the answer should be.>
- What was your reason again? [
**Exploring student thinking**] - Student D, what was your function equation? [Clarifying]
- Student C, do you agree that your line is not y = 2x? [Clarifying/rhetorical]
- What’s the equation of this line? [Concept check]
- Did we match up with the values we were given? [Problem Monitoring]
- Anybody else? [Class Monitoring]
- What is a modified conjecture that is a better guess? [Concept check] <Turn and talk to a neighbor.>
- Anybody want to make a conjecture? [Monitoring] <Drawing the class back together.>
- If I plug -2 into here, what am I going to get? [Concept check]
- Does it seem reasonable? [Problem Monitoring]
- Does it go through (-2,1)? [Problem Monitoring]
- Does it have a slope of -2? [Problem Monitoring]
- What does the y-value of the derivative mean? [Concept check]
- Any other questions? [Class Monitoring]
- Is that the end of Problem 1? [Problem Monitoring]
- How many of you guys agree with the answer of Student E? [Class Monitoring]
- Anybody else? [Class Monitoring]
- What does Part B even ask? [Problem Monitoring]
- Will you type that into my calculator? [A “request”]
- Student F, you have a question? [Monitoring]
- So, Student G, looking at the graph on screen, for what x-values negative? [Concept check]
- Do you guys know what I mean by that? [Monitoring]
- Does that match up with our parabola graph? [Problem Monitoring]
- Student H, can I see your work for part C? [A “request”]
- Here I think we are just using another function and finding the derivative? [Is this even a question?… I guess it is rhetorical]
- How many of you agree with that answer? [Monitoring]
- Looking at h, and h’. Do the coefficients in h play any role in h’? Anything that you notice? [
**Exploring student thinking**] - 5 is twice as big as? [Clarifying]
- What about the negative 4? [Clarifying]
- What happened to the 12? [Clarifying]
- What happened to the -1? [Clarifying]
- What happened to the -2? [Clarifying]

**Best question from a student**: “What does the intersection of a derivative function and the original function mean?” Unfortunately I fielded this question. I wish I had allowed students to discuss it and grapple with its meaning, but I was feeling short on time.

I have found it very helpful to list out my questions and really think about what I was trying to accomplish with each one. I definitely plan on continuing to record and review my classes. It has given me a lot to think about. However, I will try not to bore you all with the details in the future.

{Cross posted at andysunknownquantity.blogspot.com}