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Rethinking Instruction for Lasting Understanding: An Example

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...

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When is a number line not a number line?

When is a number line not a number line?

By William McCallum The number line is a seemingly simple object: a straight line with two points marked 0 and 1. Those two points are the seeds of great complexity, however. Whole numbers are located at positions marked off by iterating the interval. Fractions are...

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The Art of Reflection

The Art of Reflection

“In times of stress, the best thing we can do for each other is to listen with our ears and our hearts and to be assured that our questions are just as important as our answers.” —Mr. (Fred) Rogers By Kaneka Turner We are never more “on” than when we are teaching a...

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Ratio Tables are not Elementary

Ratio Tables are not Elementary

By William McCallum In grade 3, as students start to learn about multiplication, they think about products like 6 x 7 in terms of equal groups. 6 x 7 is the number of things when you have 6 groups with 7 things in each group. They might start out calculating that...

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The 5 Practices: Looking at Differentiation Through a New Lens

The 5 Practices: Looking at Differentiation Through a New Lens

By Catherine Castillo Our district had seen a downhill trend in standardized test scores in mathematics. This forced us, as educators, to take an intentional look at our teaching practices. The past few years have been an exciting time in math instruction. Research on...

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Learning through Teaching

Learning through Teaching

By William McCallum I was in New Orleans a couple of weeks ago visiting a school using IM 6–8 Math and was inspired by the efforts the school was making to implement problem-based instruction. I saw teachers at different stages on a learning curve with the...

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Using Instructional Routines to Inspire Deep Thinking

Using Instructional Routines to Inspire Deep Thinking

We want students to think about math deeply. Creatively. Analytically. Instead, what often happens is that students race towards quick solutions. So what can we do to support this other kind of thinking in class—the slow, deep kind? By Jenna Laib One way is through...

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