This week’s post is all about the art of the question. Now with links! Gettin’ fancy all up in this blog.

A couple things worth discussing here. The first is that I keep a little box labeled “Stump the Teacher” in my classroom. Though I originally made the box as a way to let kids anonymously ask questions during sex ed the year I taught health, I decided to keep it after-the-fact because it provides a fun opportunity to engage with the kids in a different way. Once a week I collect all the little papers in the box and post responses on a whiteboard that’s exclusively dedicated to these questions.

The kids put lot of interesting things in there. This week’s submissions were, by coincidence, both animal-related. One asked, “Can spiders be obese?” The other included all kinds of statements, such as “some animals can survive space naked” and “penguins have teeth,” and I’m supposed to determine if they are true or false.

I’ve noticed 3 distinct uses for the box.

- Questions tangentially-related to the curriculum that we don’t have time to address in class (e.g. “What happens if we compose a trigonometric function within itself an infinite amount of times?” or “Is there an algorithm for rationalizing the numerator/denominator that lets us skip all the icky algebra steps?”).
- Genuine attempts to “stump” me with logic puzzles, riddles, or trivia.
- General silliness (e.g. “Can I have $20?” or “Would you rather fight one horse-sized duck, or 50 duck-sized horses?”).

So there’s that. But I also thought this would be a good time to reflect on my “How vs. Why” position. As a teacher, I’m pretty transparent about my refusal to answer most of my students’ “how?” questions. I always tell them (and remind them over and over again) that I will have a conversation with them if they can rephrase their question in the form of a “why?”

Here’s my theory. I may be totally wrong about it, but it’s just been my observation over time that “how?” questions tend to be impatient ones. “How do I…?” Insert whatever task they’re struggling with. “Can’t you just show me how?” No, no I won’t just show you how. You already know how. You might not know that you know how, but you do. It’s not my job to teach you “how.” It’s my job to set up the circumstances whereby you teach yourself “how” to do something, through observation, analysis, etc. I am a facilitator of your own learning.

I really try to make them derive as many of the algorithms on their own as possible. I know, I know… This is not an original concept, but stick with me. My precalc kids are just starting trig. On Thursday we did an activity using strings and paper plates that I’ve professionally titled, “What the Heck is a Radian?” They observed that it takes a little more than 6 (2π!) strings the length of the radius to go all the way around the outside edge of the plate. They drew conclusions about the relationship between revolutions, degrees, and radians, and completed a table with some common angles in all 3 measurement forms. Then, analyzing the pattern from the table, they developed rules for converting between each type of angle measure. *I did not need to give them the formulas for these, they came up with them on their own*. Now, it took a whole class to get there when I could’ve simply said, “To get from radians to degrees, multiply by 180/π” in a fraction (fraction, ha ha) of the time… But giving them rules they don’t understand the origin of makes me super sad. It’s no better than answering their “how?” questions. Don’t try to understand it, just do it.

So, I like their “why?” questions and I try pretty hard to make them interact with me in that way. “Why?” questions are patient, and they are rooted in a desire to understand rather than to simply get things over with. When a student asks “why?” he or she is genuinely trying to make sense out of something. For example, “Why does the government get the same revenue from a lower tax rate as from a higher tax rate?” That came up in algebra 2 while studying the Laffer Curve (and watching this clip from *Ferris Bueller’s Day Off*) in an effort to build some intuition about quadratics. I drew a couple points on the graph and looking at them, the students said, “Wait, what? Why???” Then we had a conversation.

One last thought here. I’ve been reflecting a lot about how many of my questions to them are in the form of “how?” “How did you get that?” “How do you know?” Etc. I wonder if there’s a way for me to prompt them to explain their thinking, using more “why?” questions, without sounding accusatory. “Why did you do that?” sounds a bit… harsh. I’d like to incorporate more “why?” questions from me to them, but I’m having trouble thinking of good ones. If you’ve got some ideas or any go-to ones that you like, feel free to share them with me.

Great thoughts on the difference between “How” and “Why” questions. I think it’s important to reflect the same importance in your questions to them. One of my favorite starting questions is “Why did you start by _______” to understand their initial thinking on how to solve a problem. Then, if they’re way off base, you can ask leading questions to help them realize they need to backtrack. And if they’re not, having three or four students whose initial approach was different yet arrived at the same conclusion share their thoughts with the class can lead to great discussion!

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I remember hearing once that when you ask someone, “Why did you…?” that it tends to automatically make them defensive! I think that’s where I’m getting hung up, but it’s really just probably some silly semantics. I think even just slightly rephrasing it as, “Talk to me about why you…” takes some of that edge off while preserving the intent of the question.

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Since I teach online, we have a Live room where students can go for math help, so I end up helping a lot of students who aren’t mine. One commonality I see among many differen students when working in the Live room is a student will come in and say something like, “I have a question on Algebra 1.” I will then say something like, “Great! What is your question?”

The student will then proceed to copy and paste a probelm from an assignment they are working on.

My response: “That looks like the curriculum’s question. What is YOUR question?”

I think “their” question (but pasting the whole problem) is “How do I do this?”

I never try to answer that question directly, but wonder how many other people who also work in the Live room do? Maybe they paste the question for me because that is what they do with everyone else helping in the Live room. And the other teachers just answer the, “How…” question. Sounds like a good topic for our next department meeting. Thank you for the idea!

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Ah, I totally feel you on this! I think you’re right, and that probably like 95% of the math teachers out there just go ahead and show a kid “how” to do something when he/she asks. It’s disappointing, but I also think it’s going to take a while until the community as a whole sees the value in a different type of approach. I feel similarly about just giving kids the formulas, working through examples, and then making them repeat. That’s the “traditional” method, plus it takes a ton of thoughtfulness about how to reverse-engineer what you want them to learn and give them the resources for it to play out effectively. It’s gonna take a while to get the bulk of people into a different mindset.

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Had to think a bit about your post… seems to me like part of the issue with asking the “why?” to the students is more the coupling with the “you” part, in terms of making them defensive. Because you’re asking about their work/thoughts, rather than a general mathematical principle… and “why” is somewhat synonymous with “justify” in English. All that really occurs is some sort of compromise – where. “Where might you go next?” “Where do you think things went wrong?” I don’t know, but now I have the Annie Lennox song in my head.

As to the rest, that’s a pretty neat idea with the box! Interesting how it’s origins could be adapted for mathematics or other subjects. I should try to remember that… my fear is I’d get too invested in a question and neglect to prep properly for the next day!

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Actually, I like your use of “where?” That’s something to try to work into my conversations with them, I think. I’m probably over-analyzing it, though I do work with kids who have emotional difficulties, so I try to be really careful about not provoking their anxieties and insecurities. Especially in math, which is so often focused on getting the “right” answer.

As for the box… That’s why I only do the questions once a week. I collect them on Friday and I have all weekend to decide which questions I’m going to address (if there are more than I can do all at once then I save some for a slower week). But I do need to allow myself extra time on Monday morning to get my answers up on the board. And yeah, it’s one more thing that’s a drain on my already limited time, but I do think it’s been a worthwhile use of my energy.

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