One development at my school this year that I’m excited about is increasing informal observation. Several teachers in different disciplines visited my class during the fall, and I’ve had a chance to observe a number of other teachers as well.

I have really enjoyed the sense of professional collaboration that comes with this observation, and I learn a great deal from my colleagues. But if I talk with another teacher about their class after an observation, I often struggle to give effective feedback. I’ve come back to two questions that I’ve found essential in productive conversations about teaching: “What were your goals?”, and “Do you think you reached them?”.

In conversations about teaching, it’s easy to feel like a colleague and I are talking past one another if we don’t understand the other’s goals. I have received some pretty frustrating feedback, at many points in my career, where I felt like an observer didn’t understand what I was trying to do.

One example: I was teaching a lesson on functions and function notation, and presented students with a task that was too hard. They spun their wheels for a bit, I tried to give them some hints to move their thinking in a productive direction, was unsuccessful, and decided to bring the task to a quick resolution and move on. A piece of feedback I received on that lesson was that I didn’t reach “deep understanding”. That feedback was absolutely true — but deep understanding wasn’t my goal in that lesson. The class had been struggling with function notation and getting tripped up on more challenging tasks because of that notation. My goal was to provide some focused practice with function notation to build a foundation for future work. Because of that misunderstanding, I felt resentful of the feedback and there was less opportunity for productive conversation after the lesson.

I’ve found that one of the most important things I can do to improve the quality of my lesson planning is to improve my focus on learning goals, and drill down on exactly how I will reach them. It’s easy to get trapped in a cycle of “oh, there’s this cool activity…”, or “I’m teaching polynomials and umm I’ll start with this…” instead of ensuring my lessons help students reach worthwhile mathematical and social goals that lead to the big ideas of my course. And hopefully creating some more conversations around goals will help me improve my thinking and planning and get a little better at teaching, and maybe help some others along the way.

howardat58“The class had been struggling with function notation and getting tripped up on more challenging tasks because of that notation.”

Let me have a look at various examples.

Also, can you have a look at a function not using the notation, even not using the “x”.