[Teacher Tune Up] How Do You Teach the Ideas Students Just Have to Remember?
And how do you know those ideas when you see them?
If my time in education has taught me anything it is that I can’t learn an idea for you and there are some ideas you can’t learn without me. But it’s often hard for me to know one kind of idea from the other, especially in the fog of teaching, and especially what to do with the “can’t learn without me” ideas when they arise.
Ideas I can’t learn for you.
Something the lesson I Saw the Signs from Amplify and Desmos Classroom does very well is help students develop the connection between the written, algebraic, and number line form of an inequality. It does that through the connected representations, one of the distinctive tastes of a Desmos lesson.
I’m convinced that thirty students took thirty different routes to make that connection, though. You can watch one of those routes in this video here.
The students start at a card sort, get into a dispute with themselves, then head back several screens to harden their connection, and then return.
Direct instruction, in these circumstances, especially whole class direct instruction, often fails to account for the knowledge those students already have, pulling them off of their learning path (familiar, full of cognitive resources) and onto mine (resources of a different, less familiar sort).
Ideas you can’t learn without me.
At a certain point, it became clear to me that the class’s understanding of how the ≤ and ≥ signs translate to English language was wobbly, heavily dependent on access to the Desmos interactives, and in need of solidifying.
I think this is an idea the students actually can’t learn without me, or without some knowledgeable other person. But I thought I was in the “ideas I can’t learn for you” category. So I asked students “how do you remember what the symbols mean?” which led to students sharing all kinds of mnemonics that were each of variable reliability and didn’t really cohere as a set.
So I’m looking for some help tuning up my teaching:
How do you know when you’re dealing with ideas that you just need to teach students through direct instruction?
How would you have dealt with this moment specifically? How could I have helped students solidify their understanding of this mathematical idea?
What Else?
Here is an Amazon customer complaint that’s worth, at minimum, five minutes of discussion during your area unit. (via @ECR_Maths)
If you enjoy watching people expand their mathematical universe in realtime, I highly recommend the quote tweets on Howie Hua’s recent video explaining how it’s possible to subtract from left to right.
Nice thread from Ed Southall highlighting the value of textbooks and the challenges teachers face when asked to construct their own curriculum as well as teach it.
Who’s headed to NCTM later this month? Any talks you’re excited to see? I’m involved in a pile of fun events which I swear I’ll remember to share shortly.
The conference proceedings are live from the math modeling conference hosted by MSRI in 2019. I’m pretty happy with the talk I gave there (title: “All Learning is Modeling”) and the conversation it kicked off. You can read Evelyn Lamb’s thoughtful summary of my presentation on page 23.
Thank you for sharing I loved hearing the student thinking as they made sense and accessed their resources to evaluate how they were matching cards. Your questions made me wonder if direct instruction was necessary or rather a facilitation to stamp co-constructing understanding based on their experience with the cards. Something like posting a symbol on the board and have students "list all the things they are expecting to see in a graph/statement of that symbol". Quickly generate from the students a list in an anchor chart/notes or a place for reference. I used to do summaries in my secondary math classrooms using this method.
Regarding remembering the symbols for inequalities, I like to encourage students to "read" the comparison like a sentence - left to right. It seems like an easier way to connect the schema of the alligator that they may have been taught early on to the vocabulary of inequalities; the open side of the symbol is "bigger" or greater than the vertex, hence the left value is greater than the right value in the inequality statement and vice versa.
I'd love some other ideas too!
PS - Thanks for sharing the Amazon review. We'll be discussing this real world situation tomorrow!