All this talk over #MTBoS and #iteachmath has sparked a personal motivation to start blogging again. I believe all the conversations happening on twitter in the last week indicate a difficult yet positive shift in the Math Teacher Twitter community; this is a time we will not forget. There also appears to be an increased amount of engagement within the community, so what better time to post again?
Julie Reulbach posted a weekly blogging challenge that I want to be part of as the school year begins to rev up. This week’s focus is on goals.
During my summer session of grad school, the professor drew the following diagram:
She explained most teachers believe a student’s mathematical understanding progresses the following way; teacher introduces concept A, students show proficiency in concept A, teacher moves to concept B, students show proficiency in concept B, teacher moves to concept C and so on for the remainder of the school year. If a student happens to struggling on concept C, teacher backs up and reinforces the link between the two.
Each concept is dependent upon the previous, a single broken link causes problems with all other connections. This view forces teachers to not push too far on a concept or provide challenging material due to the fear of breaking a link.
She then erased the chain of concepts and drew the following:
The image above changed me.
The professor explained this as a Web of Understanding (If this credits back to other folks, please let me know!); the missing link between concepts B and E is not a problem because through transitivity the concepts ARE linked.
Now, if a student is struggling with concept B, there are multiple links a teacher can reinforce, since multiple concepts are linked to one another. Or maybe, there is no need to backtrack and fix a link because the others may be just fine. A broken link no longer causes issues with all other concepts.
My Goal for this year is to create a classroom where students see math not as a linear topic from one concept to another, but a web of interlinked concepts connected to one another. I hope to promote equity within my classroom in providing all students with challenging content, not just the students who have solid links from one concept to another.
Quadrant Dan 
A few years back I remember analyzing math progression charts and making sure my district’s scope-and-sequence was being followed to a tee. I remember sitting in teacher observation meetings and discussing what was the lesson before and after my formal observation lesson. The administrator was looking for a specific linear sequence. I still feel as though many observe math in that way. Math is messy and there are multiple connections within the skills that are taught. It can be a powerful moment when students see the connections between the skills, instead of perceiving them as isolated silos of content. Thanks for sharing your thoughts!
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