I was hesitant to put up this problem. There was part of me that didn’t want to admit I was stuck. That I didn’t know the *why* of the answer.

I’m a teacher. I’m supposed to be the “expert”. How could I publicly admit that I didn’t know how to do something? I thought about putting the “*Here’s an interesting problem. How would you solve it*?” spin on it for a moment. I couldn’t do that though. Instead of asking for help here, I thought about asking one of my coworkers.

In the end, I chose to admit that I was stuck and to ask for help. I chose to let all of you know that I didn’t know something (*probably not that shocking, I know*). Yet it took me a while to come to this decision. I ended up asking myself, what would I want my students to do?

So I published the question. John responded. I now understand what I was missing, which was my goal. Yet I am still intrigued by my initial responses at reading the solution. “I feel stupid. I should have known that.”, “I wonder what the math teacher readers who are reading this think of me?”, “I can’t believe I didn’t know that.” I’m not sure *why* I think this way. I *am sure* I don’t want my students to think this when they don’t know. This was a good reminder to me to continually work at creating an environment where students feel safe asking questions.

It is okay not to know. It is what we do with the not knowing that matters.

**Clarification**: I do **not** believe it is okay for a teacher to not know (or know well) the material he or she is teaching. Which is why I began working out these problems weeks before I gave them to my team. I’m also a little looser with math team than I am with my classes. At math team practice, I have no problem saying “I don’t know, let’s find out.” I just don’t want it to happen *too* often.

Image: Introspection via flickr by cc-sa-2.0

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I actually have a very different take on it. I almost never have examples (except the most complicated ones) worked out ahead of time in class. I just did two days of review before the second miterm in my multivariable calculus class, winging my way through problem after problem in the areas my students feel nervous about.

Yes, I make mistakes. But I recover, and the students see that if your first guess of how to approach a problem isn’t right you haven’t lost. You can back up and try again. I also think it’s valuable to see that even the experts don’t know all the answers the first time they look at a problem. You should know (well) the material you’re teaching, but the examples are not the material.

Besides all that, you’re talking about a math team question, which is about as far from “material” as you can get. If you see the trick the problem falls open, and if you don’t you’re probably not going to get it. There’s precious little mathematics in it because it’s all sleight-of-hand and no

problem solving.Frankly, I’d take your situation and run the other way with it. Sit down with the students and walk through ideas of how to attack the problem. Do your experiments with and . Find the right answer, and make clear that even though we have an answer we still haven’t really explained the pattern, so there’s still something interesting to work on. Then they might see that mathematics isn’t a list of tricks and pat answers. It’s the

processthat’s important.But then again, maybe that’s why I’m not a high-school math teacher.

Interesting. As it’s my first year, I wonder how this will change. Not that I work out every example before class now – if it’s something I know well, I’m comfortable “winging it”.

However, if it’s something I haven’t done in a while, I do brush up before class. We’re starting trig proofs. I haven’t done these in almost 20 years, so I’m playing with them now. Will I do the same next year? I don’t know.

Thanks again for you thoughts John. You’ve got me thinking,

again.