That's Numberwang!

Have you ever had a student look at you like you're talking in a foreign language during a math lesson? It happens. Sometimes there are gaps in students' prior knowledge. Sometimes students need more time to process a new concept in order to construct and develop their understanding. Sometimes I haven't explained something clearly and I need to think of a new approach to tackle this topic. When I encounter those blank stares, I think, "That's Numberwang."

Numberwang is a skit from That Mitchell and Webb Look, a British sketch comedy show from 2006.  If you've never seen it, take a two minutes to watch a video of this skit. The premise of the skit is that while the presenter and contestants seem to understand the rules perfectly, they are completely inscrutable to the viewer. We're left scratching our heads in confusion just like our students sometimes do in class.

Delve!

So what do you do when you sense that students in your class are not getting it? I suggest that you invest some time to uncover your students' thinking. As Guildenstern implores in Tom Stoppard's play Rosencrantz and Guildenstern Are Dead, "Delve. Probe the background, establish the situation." Take the opportunity check in with students to determine their level of understanding. Here are some strategies you might use:

• Student Self-Assessment: Some teachers periodically ask students to use hand signals to express their understanding and confidence during a lesson. This strategy can let you quickly check in with a large group of students. There are numerous other strategies to get quick student feedback during or after a lesson. A strategy for a more detailed response with higher quality feedback might use a single point rubric. 
• Exit Tickets: Take the last few minutes of class to have students respond to a short question. The question might be a quick math problem or a reflection on their learning from that day. Students hand in their response on the way out the door. Andrew Crandall uses exit tickets often to plan for future lessons in response to common misconceptions.
• My Favourite No: A routine that can be used any time is called "My Favourite No" demonstrated by Leah Alcala. She asks her students to answer a single question on a note card and pass it in. She then quickly sorts the cards into two piles. One pile of correct answers and one pile of incorrect answers. She then goes through the incorrect answers and selects one as her favourite that displays a common error and then talks through the misconception and how to correct it. This strategy results in immediate feedback to students and a positive message that we all learn from our mistakes.

Reflect and Respond

Once you have a better picture of the misunderstandings and misconceptions that may be present in your class, you can plan your next steps. Was there really a misunderstanding or did you make assumptions about prior knowledge that weren't true? Were just a few students struggling or was it a commonly held misconception? Tracy Zager, in her book Becoming the Math Teacher You Wish You'd Had, writes, "If just a few students were confused, she could work with them individually. If there was a really interesting mistake, or patterns among the misunderstandings she saw, she could use those examples as her next teaching opportunity."

When I see those "Numberwang" looks I am reminded that even a well planned lesson can sometimes miss the mark. Reflecting on how a lesson went and how I can improve it helps me refine my teaching practice and be more responsive to students' needs. Don't let those "Numberwang" moments go by ignored. Matt Larson, in his August NCTM president's message, wrote "Making mistakes, getting feedback from our colleagues, and making iterative improvement are part of the natural process of continual growth. We should never forget that perseverance isn't just for students—perseverance also applies to us as professionals."

EL