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:
Reflect and RespondOnce 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
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A couple of months ago, I posted a list of six exceptional math Ignite Talks. For those unfamiliar with the format, an ignite talk includes presentation slides that automatically advance every 15 seconds. Exactly 20 of these slides result in a 5 minute talk. Since I posted my first list, Suzanne Alejandre (@SuMACzanne) at the Math Forum has been busy posting videos from older Ignite sessions. These playlists are a gold mine of mathematical thought and reflection. Additionally, the Ontario Association for Mathematics Education (OAME) had their 2017 conference ignite talks. There are so many great talks posted recently that I felt the need to recommend an additional six talks. It will take just 30 minutes to watch all six... time well spent.
I've been working on my own ignite talk and have discovered how difficult it is to craft one. There is a lot of reflection and thought involved in refining what you are really passionate about as an educator, determining how to explain it clearly and figuring out how to make it entertaining. At this point, my talk is a still just an organized collection of notes, ideas and images. I don't have any plans to actually present this ignite talk, but I feel that the process of creation and reflection is very worthwhile. EL
I get so excited when my kids tell me stories of what is happening in their math classes. This is a favourite. My youngest son (age 7, grade 2) began his story as soon as I picked him up from school. "Mommy, did you know that if you wanted to buy, let's say some....fabric, you couldn't just like go the fabric store and say 'I'll have 20 pencils of fabric'" I was curious where this was heading; being a mathematics consultant, I knew what grade 2's were working on at this time of year (measurement). I didn't want to steal his thunder, so I just went with it. "Really, Michael?" I turned into teacher mode: "Can you tell me some more about that?" He went on to explain in great detail and with loads of enthusiasm about all the trouble he would run into if he wanted to measure fabric with random objects. He actually had a lot of fun naming all of the things that would be silly to use to measure fabric. He went on for a while and wrapped up the conversation telling me there was this "thing" called a "centimeter" that we could all use and understand. You would swear he discovered the metric system himself; he took such ownership of the concept. Keep in mind, I can't think of a time he has ever been in a fabric store (I am not the crafty type) and I am almost certain that before this math lesson, he would never have used the word fabric (cloth or material, maybe?). So he had no previous experience with the concept but he was still engaged? Yes. When I was at Dan Meyer's NCTM presentation (Beyond Relevance & Real World: Stronger Strategies for Student Engagement) last week, I couldn't help but think of this story from my son. I can imagine the kind of "teacher moves" my son's teacher used. She is a natural story teller, her enthusiasm is contagious and she loves to laugh. I can imagine her telling a story to the class, strategically leaving out important parts, having them experience her fabric store dilemma for themselves and brainstorming ideas with the class on how they can fix this problem! Even if he didn't really discover the metric system, he certainly thought he did. And his teacher created those conditions. And I think that's pretty cool. KZ 
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