I’m increasingly grateful that my first two years of teaching were spent using Connected Math in 6th grade and then after that Common Core launched and I spent the next two years in professional learning teams at Math for America unpacking and making sense of the progressions. Most math teachers don’t get to experience that level of progressional development that leads to internalization of the connections within the subject. I spend a significant amount of my time as an instructional coach helping teachers understand the important connections and how to plan for students to see those connections. I agree that a strong curriculum should really surface those for teachers (and I currently use IM and agree that it does attempt to!), but I still think there is a missing piece around teacher development and collaboration. Math for America has been a great model for this but was never broadly adopted.
Shout out IMP. Best years of my teaching career. Part (c) was the most difficult part for teachers. Starting with knee-jerk reactions to the perceived lack of deliberate practice, and ending with too much proceduralizing.
Well, I only just formulated them, but I think all the curricula I mentioned have done some combination. And, full disclosure, I am a cofounder of Illustrative Mathematics, which is why I left it off the list, but I do think it is an attempt at all three layers. The mention of the different forms of a straight line was really a call out to what we tried to do there.
I love this. I have been having an ongoing debate (verging on argument) with one young teacher this year about guided discovery and explicit instruction. I'm trying to get him to see that it's not an either/or -- that IM, which he is supposed to be following (in NYC) does both. He insists on explicit procedures, disconnected from context and from the next procedure. Sure, the Regents exam, which determines whether or not kids graduate from high school, focuses on procedure, but I'm struggling to help him see that procedure and depth of understanding can go hand-in-hand. I may send him this article.
Yay! You emphasize that it is super important to keep mathematics in math teaching. Dr Valeriy Manokhin (https://valeman.medium.com/how-many-children-learned-mathematics-from-kiselevs-textbooks-ff4efceade0d) makes the same point about A.P. Kiselev’s arithmetic book used from the 1880s to the 1970s in Russia and the Soviet Union.
Thanks for that pointer! Looks like a fascinating article, I'll give it a read.
Clearly you don't have to be a cognitive psychologist to show which ways the connections should be growing. Nice!
I’m increasingly grateful that my first two years of teaching were spent using Connected Math in 6th grade and then after that Common Core launched and I spent the next two years in professional learning teams at Math for America unpacking and making sense of the progressions. Most math teachers don’t get to experience that level of progressional development that leads to internalization of the connections within the subject. I spend a significant amount of my time as an instructional coach helping teachers understand the important connections and how to plan for students to see those connections. I agree that a strong curriculum should really surface those for teachers (and I currently use IM and agree that it does attempt to!), but I still think there is a missing piece around teacher development and collaboration. Math for America has been a great model for this but was never broadly adopted.
Shout out IMP. Best years of my teaching career. Part (c) was the most difficult part for teachers. Starting with knee-jerk reactions to the perceived lack of deliberate practice, and ending with too much proceduralizing.
Is anybody using the three layers for a high school algebra curriculum?
If not, is there a specific reason why it's not being attempted given the foundational position of algebra?
Well, I only just formulated them, but I think all the curricula I mentioned have done some combination. And, full disclosure, I am a cofounder of Illustrative Mathematics, which is why I left it off the list, but I do think it is an attempt at all three layers. The mention of the different forms of a straight line was really a call out to what we tried to do there.
thank you
I love this. I have been having an ongoing debate (verging on argument) with one young teacher this year about guided discovery and explicit instruction. I'm trying to get him to see that it's not an either/or -- that IM, which he is supposed to be following (in NYC) does both. He insists on explicit procedures, disconnected from context and from the next procedure. Sure, the Regents exam, which determines whether or not kids graduate from high school, focuses on procedure, but I'm struggling to help him see that procedure and depth of understanding can go hand-in-hand. I may send him this article.