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 Though I originally made the box as a way to let kids anonymously ask questions during sex ed the year I taught health, I decided to keep it after-the-fact because it provides a fun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.