I love mathematics. I love teaching and learning it, and exploring maths’ beauty and creativity through relationship building and the sharing of ideas. Thinking, problem-solving, and connecting around mathematical concepts are the joy of my existence. Unfortunately, there are times when I encounter other maths educators who (often unintentionally) close the gates to our beautiful, creative, fun and empowering community. Lately, I’ve been pondering how to bring this situation to light, and open up opportunities for more people to see themselves as mathematicians.
At the 2018 National Middle School Math Conference, I got to watch Dan Meyer attend to the whole child on stage as he taught middle schoolers about mapping events on the coordinate plane using Graphing Stories. The lesson was excellent and if you haven’t read Dan’s blog about it, do yourself a favor and do so now. What most impressed me was the gentleness and care with which he handled each student’s math identity. Precisely and intentionally, in some instances with great effort, he worked to find a way to authentically say, “Yes, you’re right about x, now let’s get more correct with y.”, or “I see what you’re thinking, that makes sense because…”.
My favorite moment was when the kids figured out they were graphing position/speed to time, instead of waist-height from the ground. Dan’s questioning sequence (something to the effect of “What does it MEAN to have a height of zero? You ARE graphing a body part, but it’s not his waist? What part are YOU graphing?”) led to the “Aha!” moment for kids that they were mapping the height of his feet over time, much to their entertainment. Some of them actually giggled! It made my heart sing to see children smile at discovering their own mistake in their thinking and be glad to have discovered this treasure. ALL of them went straight to work to be more right than their first drafts. It was incredible to watch.
Returning to the daily grind of teaching, I was hyperaware of how many times we miss these opportunities in class because of a pacing guide, standardized test, report cards, parent expectations, etc. How often do we (again, more often than not, unintentionally) make kids feel like their answers are wholly incorrect, when in actuality we are imposing our fully-formed conceptions onto their learning journey? What effect(s) do our impositions have on their budding identities as capable, creative mathematicians?
While in the classroom, I devoted the first two weeks or so to building a growth mindset culture of respect in the room, and made sure to pay attention to the need for “maintenance lessons” throughout the year. Despite the fact that this is my fourth year out of the classroom, I still teach relatively often. I decided to try the aforementioned rough draft language during an intervention day with a random group of kids (meaning they were 6th & 7th graders from several different teachers’ classrooms and included a variety of backgrounds and “labels”). Having someone else’s everyday students, it was even more important to carefully consider my words. We did a clothesline/number talk combo and I was amazed at how simply referring to the first double number line we built (manipulating numbers only, not algebraic expressions) as our “rough draft” lowered the floor and successfully invited all but 1 child to play math with us. [As an aside, she later let the Drama teacher know that she understood that I was trying to make math fun, but, “It was not working out!”. Oh well, can’t win them all in single lesson, I guess. She has no idea the fire she’s started in my heart to change her mind, though.] I tweeted the aftermath of their good work at the play table. If you open your heart and mind, you can feel the laughter and happiness in the room from the pictures.
In the end, accepting a math teaching position means I necessarily accept the responsibility of treating each child’s math self-concept with care. Failure, as with anything, comes with the territory of a learning environment, but we can always apologize for any harm done and try to do better next time. How do you ensure that you are empowering students’ mathematical identities? What instructional decisions/routines/strategies help your students see the mathematician in the mirror? I’d love to get better at this with you.