Rethinking Instruction for Lasting Understanding: An Example

By Kate Nowak

How do we help our students build mathematical understandings that endure past the unit test? If we want students to construct strong, reliable bases of mathematical knowledge, our instruction needs to do more than present explicit procedures—even when that’s done well. Providing lots of opportunities for students to reason can help. So can understanding and leveraging the progression of learning across grade levels. But what does that look like in practice? Let’s examine a single topic in grade 7: solving inequalities. 

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What I Learned Today: Scale Drawings & Maps

I asked my 15-year-old what she learned today at school. She paused for a moment and then answered,  “What did you learn at school today?”

It took me a while to think about what I had learned (which will make me more patient when I ask her again tomorrow), and then I remembered and shared with her:We are working with some teachers who are using the Illustrative Mathematics 6–8 Math curriculum. The 7th grade teachers are in Unit 1, Scale Drawings. They are working with scale drawings and maps. Today I learned to look more closely at the scale given for a map.

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