From Jo Boaler’s How to Learn Math: for Students:

…we know that what separates high achievers from low achievers is not that high achievers know more math, it is that they interact with numbers flexibly and low achievers don’t.

I wonder how many times I’ve taught “the one way” to solve a problem without considering other pathways for success. Yikes!

After completing Lesson 4 from How to Learn Math: for Students, A-Sunshine, my 4th grader, asked me to solve another multiplication problem. I wondered how many ways I could show my work and demonstrate flexibility in numeracy. The urge to solve this multiplication problem in the traditional way was strong, but how many ways could I show how to multiply 44 x 18? How flexible am I when it comes to numeracy? Is the traditional method the most efficient? Are there other ways to show 44 x 18 that might demonstrate understanding?

How might offer opportunities to express flexibility? Will learners share thinking and strategies? How will we facilitate discussions where multiple ways to “be right” are discussed? What if we embrace Smith and Stein’s 5 Practices for Orchestrating Productive Mathematics Discussion to anticipate, monitor, select, sequence, and make connections between student responses?

If my solutions represent the work and thinking of five different students, in what order would we sequence student sharing, and are we prepared to help make connections between different student responses?

How is flexibility encouraged and practiced? Is it expected? Is it anticipated?

And…does it stop with numbers? I don’t think so. We want our learners of algebra to be flexible with

- the slope-intercept, point-slope, and standard forms of a line and
- the standard form, vertex form, and factored form of a parabola.

The list could go on and on.

How might we narrow *what separates high achievers from low achievers*? If number flexibility is a gateway to success, what actions are we willing to take to encourage, build confidence, and illuminate multiple pathways to success?

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We are going to start with a problem like this on the day that one of our goals is the Distributive Property. But as your work shows, it’s not the only property that should come out of the student work. Our teachers will need to think about when we want to feature the distributive property (assuming that someone in the class will use it)…I don’t think I would show it first. I think I would use what you have first with factors/commutative/associative. Thanks for calling out our need to have this discussion before we have class.

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