The best compliment I have ever received came from a student at the end of my first year of teaching. (Yes, my first year, when I was naive, clueless and a general mess of a human being and teacher.) I had a student named Emma. She was one of those rare students who enjoyed thinking deeply about mathematics. She was never satisfied with a procedure. She wanted to know why and how. She often stayed after class just to talk about a math problem we had done in class. At the end of our year together, she approached me in her quiet, always thoughtful manner and said, “Ms. Lee, I really liked having you as a teacher because you asked me really good questions. You asked me questions that really made me think about math.” Cue, Ms. Lee, standing still, mouth agape, speechless. She will never understand the compliment she paid me, the late nights I stayed up that first year just thinking about questions–what would I ask them, how would I ask them? If they came up with this strategy or got stuck here, what would I ask them to move them forward or connect back?
All of this is to say, I take questioning seriously. I think it’s vitally important to getting kids to reason, critique, and problem solve. Never say anything a kid can say. Ask them a question. Make them say it instead. I have two question moments to share from this school year:
- The question I’m always trying to get better at asking:
What does it mean to be proportional?
Proportionality if the central concept of 7th grade math in Minnesota. Every year I teach proportional reasoning strategies-unit rates, scale factors, scaling ratios, setting ratios equal to each other, etc-but every year I feel like students never quite get a good clear grasp of what it means for two quantities to be proportional to each other. This year, I tried to be more deliberate in my attempt to tie proportionality to fairness. I came up with a unit question, “How can proportional relationships help us make decisions about how resources should be distributed?” This helped me in planning the questions/problems I asked students to work on and helped ground the complexities of proportionality in something 7th graders are always keen to argue about, fairness. One problem that finally got them to reason, think and question fairness while using their proportional reasoning strategies came when I asked this warm-up question:Some students were hell-bent on 20/20. Other students had a gut-feeling that this wasn’t fair because there were more girls. Students who found unit rates (questions per gender) were finally able to shed some viable proof on why the 20/20 plan wasn’t fair. They were using math to construct arguments and their arguments were grounded in the concept of proportionality. My only regret, this question came at the end of the unit. I need to give them more questions like this throughout the unit that make them wrestle with fairness by using their proportional reasoning strategies.
2. The question I’m still searching for:
My friend tells me he was born on Thanksgiving Day, November 28. Instantly my noticing/wondering wheels start spinning. I wanted to know how often since then his birthday has fallen on Thanksgiving. At first, I thought maybe every 6 or 7 years, depending on leap year. The actual answer? So incredibly more fascinating than I could have ever hoped for. I’m left with more noticings and wonderings than when I started. In fact, I have so many questions now that I don’t know what exactly I would ask students.
What do I ask students?
What if he was born Nov. 27, 1990? Would his birthday repeat in the same pattern? How does the timing of Leap Year effect the pattern? What are all of the possible dates that Thanksgiving can fall on? Do they all repeat in the same pattern?
Any suggestions here would be greatly appreciated!