Despite our best efforts to actively engage our students in mathematical thinking, there are times when all you see is a sea of blank stares and the sound of crickets. In Fall 2022, I used an ICTM Travel Grant to attend the NCTM Annual Meeting & Exposition in Los Angeles, California in search for some guidance to increase student engagement. Throughout the conference, I listened to speakers share ideas on how to consistently garner students’ attention - every period. What I learned is not new, but perhaps assembled in a new way for me. I will share some of the highlights.
Iowa State University Professor Ji-Yeong I adeptly points out that students work best when they are competing and content is delivered hands-on. Their engagement is more natural and curious when the setting doesn’t seem to be a math task. For instance, the launch to one of her Algebra 2 geometric sequence lessons was asking groups of students to fold chart paper as many times as possible. They made predictions about how many times they could fold it and how small they could get the paper. I can visualize just how excited my own students would be to engage in this activity and have tangible results to build mathematical ideas on. Their enthusiasm would get them invested in the task and they would be able to connect the things they were doing in class with mathematical concepts.
Robert Kaplinsky shared the hallmarks of unforgettable lessons. One such characteristic was problems with unexpected results cause us to shift our thinking, and hence, making the lesson more memorable. Making mathematical ideas “stick” came from Chip Heath and Dan Heath’s book, Made to Stick: Why Some Ideas Survive and Others Die… I imagine that in the lesson described above about folding chart paper in half, students are surprised by their limitations and it assists in the memory of the experience.
As a teacher of many emerging English learners, I appreciated Iowa State University Professor Ji-Yeong I’s guidance on providing 5-Act Tasks. This is a take on Dan Meyer’s 3-Act Tasks, but in addition to Acts 1, 2, and 3, there was a new Act 0 where vocabulary is intentionally discussed or missing prerequisite skills are demonstrated just-in-time for the learning. There is also an Act 4 where students debrief what was learned and spend more time formalizing notes on vocabulary or the mathematics used. I wholeheartedly believe that all students would benefit from this practice and will make plans to incorporate the additional acts into my lessons in the future.
Finally, Dan Meyer enlightened teachers on his critique of calling errors “mistakes,” when in many cases they were unlearned knowledge about a subject. Especially when students are new to a concept, many of their errors were not mistakes. (Mistakes were defined as not answering the questions in which students were asked to solve.) In many cases, they had oversimplified the problem and weren’t even aware of characteristics or conventions that make some problems unique. He illustrated many examples and used them to explain why students think they are “so bad at math,” when in fact, math education has created a culture where natural inquiry, curiosity, and trials are not prioritized. Students feel a need to be perfectionists because that’s what we have lead them to believe, even though that is not the way we approach science, language arts, or social sciences where questioning, drafts, and experimentation are regularly used and valued. The lesson here is that we don’t want to undo all of the good work we are doing by labeling undeveloped thinking as mistakes.
Finally, I appreciate the efforts of ICTM for getting math teachers to conferences to be life-long learners to hone a craft that is never going to be perfect, but can be perfected every year and every lesson along the way.
Mathematics Department Chair and Mathematics Teacher
Ottumwa High School