What makes my classroom uniquely mine? Well, my students would probably say my occasional rapping and our many choral response ditties.

But when I think about what I do that I am most proud of, I think about the questions I pose to them and how I listen to their ideas… (btw, these are all a work in progress):

— Really listening to student ideas and learning from them! I try to follow their train of thought, and I try to be open to allowing them to adjust my thinking. This reminds me of something interesting that happened a couple of weeks ago. I gave the students a MARS performance task where they had to create an equation for a situation. The graph of the situation was a horizontal line (constant > 0) that at a given point increased linearly. The rubric expected the students to create an equation for the linearly increasing piece only. So when one of my students said he had created an equation for the entire graph, I listened although I was, inside, skeptical, that it would work. As a class we tested his equation, and amazingly it works. The equation included an expression in absolute value, and it was really brilliant. I am so glad I listened.

— Asking open-ended questions for the students to think about. When they respond to a question, I try to ask clarifying follow-up questions. It’s exhausting sometimes, but worth it.

— Lately I’ve been trying to get the class to answer each others questions more. I’m trying to follow the advice: A teacher should never answer a student question that another student in the class can answer.

— Each week, as part of their homework for the week, my students write about a reflection topic that I give them. These are topics where they either synthesize information we’ve gone over recently or think more critically or creatively about a topic. Some examples are:

- What’s the difference between 0/x and x/0? Is there a way to prove why they evaluate to differently?
- Create a math story for the equation 3(x+2) + 5 = 23 . What is x in your story? Solve equation. Does the solution make sense for your story?
- Summarize the conditions for when you would get a compound inequality, a single inequality, no solution , or all real numbers as the solution for an absolute value inequalities.

I love these. I think it gives students a chance to use the math vocabulary in their own words, to organize their thoughts, and to respond creatively in order to make more sense of a topic. A little time consuming to grade, but many of these response put a smile on my face. Math teachers don’t get to see original written work like this enough.

I think that “never answer a student question that another student in the class can answer” is such a powerful tool in the classroom. I’m still struggling to do this sometimes, but I think I’m getting there – it goes hand-in-hand with answering a question with your own question that guides them to their answer