Two crazy good Do Nows

Recently, I’ve been trying to be super duper conscientious of every part of my lesson. For example, I wrote out comprehensive solutions to some calculus homework, paired my kids up, handed each pair a single solution set, and had them discuss their own work/the places they got stuck/the solutions. I actually had made enough copies for each person, but I very intentionally gave each pair a single solution set. It got kids talking. (Afterwards, I told them I actually had copies for each of them.) That’s what I’m talking about — the craft of teaching. I don’t always think this deeply about my actions, but when I do, the classes always go so much better.

In that vein, of super thoughtful intentional stuffs, I wanted to share two crazy good “do nows” from last week. Not because they’re deep, but because they were so thought-out.

For one calculus class, I needed my kids to remember how to solve 5\ln(x)+1=0 (that equation was going to pop up later in the lesson and they were going to have to know how to solve it). I also know my kids are terrified of logs, but they actually do know how to solve them.

I threw the slide below up, I gave them 2 minutes, and by the end, all my kids knew how to solve it. I didn’t say a word to them. Most didn’t say a word to anyone else.

How I got them to remember how to solve that in 120 seconds, without any talking, when they are terrified of logarithms and haven’t seen them in a looong while?

I can’t quite articulate it, but I’m more proud of this single slide than a lot of other things I’ve made as a teacher. (Which is pretty much everything.)  Not deep, I know. It’s not teaching logs or getting at the underlying concept, I know. But for what I intended to do, recall prior knowledge, this was utter perfection. The flow from each problem to the next… it’s subtle. To me, anyway, it was a thing of perfection and beauty.

The second slide is below, and I threw it up before we started talking about absolute maximums/minimum in calculus.

As you can imagine, we had some good conversations. We talked about (again) whether 0.9999999… is equal to 1 or not (it is). We talked about a property of the real numbers that between any two numbers you can always find another number (dense!). I even mentioned the idea of nonstandard analysis and hyperreal numbers.

So I know it isn’t anything “special” but I was proud of these and wanted to share.



  1. I like this piece, it reminds me of my teaching strategy ; monkey see, monkey do.

    I show my algebra 2 procedure examples on the board, in this case writing logs in expo form without saying a word. Then, my students copy the problems, without saying a word, to anyone. Once that is finished , I ask clarifying questions . If they don’t ask, I make sure that I ask probing questions. I continue the process with a few more problems until they are able to answer my questions.
    The final piece of the puzzle is for them to work together or individually on similar problems and have them write it on the board for the class to review and copy.

  2. I appreciated your thoughts on the “craft of teaching.” I have been doing a collaboration with credential students this past month and sometimes (well, most times really) I get the feeling they think I am OCD when it comes to planning. We’ll come up with something decent, then a day later I’ll decide it needs revision, then we revise and I decide it needs to be revised again, then we use it in class and I revise it again before my next class. The type of attention to detail you mention is what makes teaching so fascinating to me…the smallest changes can make such an enormous impact.

  3. Thanks for calling us out on attention to detail and intentional design. Your examples are wonderful, and I appreciate the impact that your reflective teaching is having on a future generation of mathematicians from Brooklyn… and around the globe.

    The hard part of all this is that it takes so much time to be so intentional, and overtaxed teachers lead to burned out teachers: we’ve all been there. I suppose that’s where the blogosphere is helping… now I just have to figure out how to spend less time scanning blogs in search of good ideas!

  4. It’s true – it can lead to burn out. But I’ve been feeling burned out, and I decided to just start from scratch and redo/heavily revise many things — and even though I’m working until 9pm or 10pm, I am feeling so much better about myself/my teaching. I know it comes in waves — so I’ll be feeling burned out and bad soon enough.

    As for scanning blogs… I keep my virtual filing cabinet (link at top of page). I haven’t updated it in a few months, but when I do, it’ll expand a lot. It’s great inspiration to me when I want to rethink/teach somethign in a different way. To mix things up.

  5. I like how you gave them the problems and just had them do it. To often, as teachers, we want to hold their hands throughout every process we do. But, this Constructivist approach works wonders, especially with our better math students. It allows them the opportunity to make their own connections, memories and meanings. It’s amazing how much you can teach with a well-placed question.

    1. That’s THE key, isn’t it; the well constructed question. I have become so convinced over the years that questions are way more important than answers/explanations.

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