Posted by: rdkpickle | 05.05.2016

“i did it a different way.”

Are there more exciting words?

I’m at the board after some time spent in groups working on the warmup, going over a few answers and trying to clarify big ideas. They’ve stopped their work to tune in – quiet moments with eyes on me are so much rarer these days. Some kind of magic has happened in this happy, focused A block Geometry class this year. They work hard. They persist. This has so little to do with me – no one has told them they can’t be good at math, no one has told them it’s boring. So they believe they are capable, they expect to enjoy math class, and they are and they do. (I hope!) I give them good problems and explorations designed by the Geometry team and they set to work. I am so secondary to the work they do in my room.

My inexperience teaching Geometry actually feels like a gift – this combined with 3 preps at a new school (which means I can’t obsessively overplan each lesson) – means that the questions they ask sometimes surprise me; the solutions they offer often delight me.

I’m at the board, I’ve solicited an approach to a problem and written it on the board; it’s what I predicted, I’m moving on. M stops me. I can’t even remember if she raised her hand but honestly it’s better if she didn’t, let’s all just imagine she shouted at me. “Rachel, my group did it a different way.”

[“Rachel – let me share this with the class. Rachel – I know we’re all smarter than you, you tell us that all the time, let me prove it for the 30th time this week.”]

I pause (we all pause.) It’s that moment in the music where the wind players breathe before the downbeat.


3 examples of “I did it a different way” from my students from this week:

IMG_5579

IMG_5582

IMG_5581

[Note about that last one that could probably be its own post. In reflecting upon “their way” and why it felt so startling, I’ve come to the conclusion that I am deeply a product of 1) learning math through rote, procedural practice in my high school classes, and 2) of the technology that was available to me when I learned this particular concept. I had a TI-83 calculator in high school – both common and natural log were at my disposal, but I didn’t have the ability to evaluate logs of any base (without using change of base formula) – so I couldn’t type something like the example above in directly to get a decimal approximation. My students with TI-84s can. Of course the two answers are algebraically equivalent. I would never in a million years have used this approach.]

 

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Responses

  1. Nice post, Rachel! I agree: I love hearing ‘I did it a different way’ too. What I wonder is how we create the conditions for students to feel courageous enough to say this.

    There are so many situations where students watch a teacher do it one way, and don’t have the courage to volunteer their different method (particularly if they made an error that means that they don’t end up at the same answer, even if their approach was valid).

    I have some ideas but I’d love to hear what you think!

  2. Love the blog post!! That was totally me the first time I taught geometry. And I think we had better discussions because I enjoyed hearing them explain the problem to me. 🙂 in fact because of that I started incorporating “different way” problems as warm ups in all classes I taught. It opened up discussions and we had better discourse because of it.

  3. If you have never read “Mathematician’s Delight” by W W Sawyer, here is the link to a free pdf download. This is one book which got me hooked on mathematics.

    https://ia802704.us.archive.org/15/items/MathematiciansDelight/Sawyer-MathematiciansDelight.pdf


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