We’re doing a lot of “speed dating” in Algebra 1, practicing our slope-finding and slope-using skills. I had created a mini crib sheet to help students develop fluency in going from two points to an equation of a line in slope-intercept form.

One of my most brilliant students is an African-American young man. Brilliant, funny, determined, respectful, stubborn, wise-cracking, mathematical, maddening, but determined. For whatever reasons, he has a low opinion of his own mathematical capabilities, even though it is clear to me that he is one of the most remarkable minds in a remarkable class and school.

But he’s stubborn. Oh so stubborn.

Here’s his pattern that I have observed: Self-doubt/self-deprecate (“I’m so stupid” is a frequent quote); ask his Asian-American or white table mates how they did something and try to defer to their methods; try on their methods and get mad at himself for not fitting into an ill-fitting set of “shoes”; self-deprecate and start the cycle over; pray for the experience to be over so he can get back to his passions.

But he is brilliant. Oh so brilliant.

So I had to try something different.

Since we had an odd number of people present in class yesterday, I had to step in as a “participant.” Speed dating requires an even number of participants. So I stepped in, chose a problem card, and traded with him. We were sitting next to each other rather than across because of some ridiculous room logistics. I used my crib card and he used his half-understood, ill-fitting method as we each worked our own problem.

He was watching me out of the corner of his eye as I worked slowly and methodically. And his eyes widened when he saw me casually flip over my problem card to confirm my answer. He burst out with, “Wait, WHAT????” He grabbed my paper (it was friendly, not aggressive), flipped his own crib card back over to reveal my template, and demanded, “OK, show me how you did that.”

Without editorializing, I showed him my three steps. He drank them in in with rapt concentration. And then he went on to do the next 15 problems quickly and quietly, without a single error or glitch. In this moment, he became one with the same model of flow I see in him out on the football field. In that moment, he connected with his own mathematical genius.

Sometimes as a teacher, the hardest thing is giving your students space and time to trust their own inherent agency — to trust that your naturally intelligent students will naturally gravitate toward the saner, more reliable practices you may be suggesting. Because they are smart, they will naturally choose to align themselves with better methods if you allow them to. If this method is better, they will arrive at that understanding out of their own innate intelligence. They have to come to their own valuing of these practices on their own. This is a matter of respecting their boundaries. Allowing space for my student to make his own choices about using — or not using — the simplest, most reliable practices allowed him to experience empowering self-knowledge in math class. I need to keep remembering that is the most important thing.

I love, love, LOVE this. So many times, I have had kids come thru my room CONVINCED they are stupid bc they see /think about math differently, and just cannot “do the math”. I love when I say, “Great! Yes. Thank you for sharing your method. Now can someone tell me ANOTHER way to look at / solve this?”

(And I have students similar to yours, so my pressing question: to write equation of line, do you use y=mx+b, solve for b and then rewrite, or do you use y-y1 = m(x-x1) and simplify to slope int form? In other words, what was on that crib sheet??)

Hi Tina,

Here you go. This is my 6-UP copy that I chop up and make freely available:

https://drive.google.com/open?id=0B8XS5HkHe5eNaWZfanJUU3hPcFU

I always tell students that the point-slope formula is basically a “Mad Lib” or a template for finding the equation of a line. It simplifies the whole “What the heck is x-sub-1” question. 😉

Thanks for commenting.

– Elizabeth

Love it! Thx!

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