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.
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 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."
High school exams in Nova Scotia (grade 10-12) typically run in the second to last week in June. This is the time that grade 9 students are writing some exams as well. The week prior to exams is often set aside by teachers for a cumulative review. This is a time to revisit the curriculum outcomes, consolidate learning and make final connections. What teachers do with this review time can vary greatly from class to class. Many teachers create a booklet of review questions that cover the main topics from the course. This can be a helpful resource for some students but not all that engaging.
Here are some additional ideas for reviewing outcomes that might increase student engagement and allow for some differentiation.
No matter how you decide to review for the exam, by the time you get to exams, "the hay is in the barn". Here is a note from Alberta Education... "The best way to prepare students for writing the achievement test is to teach the curriculum well and to ensure that students know what is expected. Many of the skills and attitudes that support test writing are, in fact, good skills and strategies for approaching all kinds of learning tasks."