Should You Pre-teach New Vocabulary?
Dr. Pam Seda asked a question on Twitter last week that got the people going:
What are your thoughts about pre-teaching math vocabulary? Should math vocabulary be introduced before a unit begins? If so, how?
You’ll find thoughtful people taking both sides of the question and I only wanted to return to some general purpose advice I offered in a recent review of research:
For explanations to be effective, teachers and students need a shared set of experiences to talk about.
When you approach a new unit, you can ask yourself, “what experiences do I and my students share that relate to that vocabulary?”
The answer is never “none.” New knowledge builds on old knowledge. Whenever your students come to know those new words, they’ll have connected them to words, images, and ideas they already had. You can make that learning (and your own job!) easier by surfacing that older knowledge in advance, helping your students remember what they already know.
When it comes to vocabulary, my favorite method for surfacing that older knowledge is asking students to work with “contrasting cases.”
This shows up in our curriculum with “Which one doesn’t belong?” screens. We show students four objects that contrast with one another in important ways and ask students to decide which one doesn’t belong and why.
Through their descriptions, students will surface the ideas they already have (symmetry, in this case) each one of which is an opportunity for you to make connections to this new, more advanced vocabulary.
I also like to put students in a position to experience the need for new vocabulary, a need that transcends the teacher’s grade or pacing guide.
Polygraph is a paired activity that combines contrasting cases with the goal of making yourself understood by a classmate.
I simply will not turn down this opportunity to cite Meyer, 2015, when I studied an early version of Polygraph for my dissertation. Check out this video for a very short summary of a very long paper.
Hanging above all of these findings and recommendations is the Truth that you aren’t going to teach anything just once—whether that’s before or during a unit. Ideas evolve and devolve. They advance and regress. Old ideas hang around past their sell-by date. Give students lots of opportunities to share the state of their ideas so you can speak directly to those ideas rather than directly from your own. This will probably work out fine.
What Else?
What We Learned About Math, Teaching, and Technology While Building Desmos. Upcoming webinar alert. The Global Math Department is one of the most amazing examples of online community and collaboration I have ever seen. For years, dozens of math educators put on webinars, sent out newsletters, and synthesized online activity—all on a volunteer basis. They’re closing shop and I’m very honored to be participating in one of their last webinars, where I and several of my Desmos colleagues will share what we learned from our work together over the last ten years.
I highly recommend the comments on my last post on “Legal and Useless Math.” You’ll see some teachers operating at the height of their craft, their math knowledge, and their relationship with their students.
Thank you for responding to my question. I posed this question on Twitter because it came up during a class I was teaching to preservice middle school math teachers. Several students thought that pre-teaching vocabulary would improve a lesson plan that we were studying. Although, I felt differently, I decided to pose the question to the larger math ed community before responding to their recommendation. There were so many thoughtful responses on Twitter that I got to share with my class. Now, I can add this one to the list. Thanks again for your thoughtful response.
Would love to hear more about how this works when students have widely varied prior knowledge. I teach 9th grade Math 1 and a problem that comes up in these lessons is that some already know the “proper” vocab and will use it in Polygraphs, but then their partners don’t have any clue what those terms mean. Do you see this as an opportunity for the original student to apply their learning and “level up” their cognition by rephrasing those formal terms in a way their classmates can understand? Many of my students with less prior knowledge then feel “dumb” or a burden to their partner because they don’t know the terms yet and their partner has to explain it to them… I definitely struggle with finding that sweet spot of front-loading juuuuust enough.