Yesterday I was working with a student on some very sophisticated geometry problems that require a lot of synthesis and creativity. She had come to me with the questions she hadn’t been able to figure out from her summer geometry homework assignment.
For a second I thought she meant she hadn’t known how to start on the problem, but while I was putting the diagram up on the whiteboard for us to refer to together, she said, referring to her preparation, “I was just doing this big thing, and I don’t even know if it’s right.”
I was like, awesome! I was so happy that my student dove in and explored, even though she wasn’t sure if she had done the right thing.
When math becomes more demanding, it frequently requires two completely different skills: really internalizing everything you’re learning so much that it’s completely automatic, (like writing your name or eating with a fork); and THEN, being able to creatively combine those ideas, concepts, and strategies in ways you’ve never done before when you’re faced with something mathematically completely unfamiliar.
I told this student how proud I was of her that she had tried to solve the problem so extensively even though she wasn’t sure what to do – instead of just giving up or waiting.
I explained, “It just means that you’re in the exploration and experimentation zone, instead of the repeating and recycling zone.” We go through the process of internalization in order to flourish when faced with the unfamiliar.
And then, we train ourselves to be comfortable – even lighthearted and jubilational – when faced with something we’ve never seen before. To be comfortable with being uncomfortable, and to ask ourselves questions like:
What could I try here?
What concepts do I recognize in this problem – even if I’ve never seen anything quite like this before?
How could I get started?
Is there anything I could fill in on the diagram?
OK, if that didn’t work, what could I try instead?
So, is it OK to not be totally sure? Absolutely! In fact, it is an extremely important space to become acquainted with, and to befriend: “the not-totally-sure-if-it’s-right space.”
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Sending you love,