There is much written about differentiation in the math classroom. But at the core of it all, there seems to be a central idea: a student-centered classroom managed by a teacher who knows the varying learning needs of his or her students and addresses those needs appropriately.

Easy, right? Well, as Mark Twain said, “If talking were teaching, we would all be smarter than we could stand.”

We kept this in mind when developing Singapore Math®, which uses a problem-solving approach and incorporates opportunities for multiple representations—both of which provide the context for differentiation. Let’s consider this adding with regrouping problem:

Can you find one way? Can you find more than one way? How many ways are there, and why? Think about this problem with your students. Which students would you ask for one way? More than one way? How many ways?

With Singapore Math®, differentiation often becomes about what questions to ask students rather than developing different tasks. Perhaps your struggling students find one way, while your on-level students find more than one way, and the higher-achievers for this lesson find how many ways and why. Students must learn how to break concepts down and, just as important, how to build them up. Differentiation is as important for advanced learners as it is for struggling learners.

An opportunity for multiple representations helps students conceptualize the math while also helping to develop number sense. Let’s consider subtraction. If students are simply taught to put the “larger number on top and the lower number on the bottom” to subtract, it will likely lead to subsequent issues. Students may end up incorrectly subtracting decimals (not to mention integers) like this—after all, the larger number is on top:

Through the use of multiple representations—including concrete manipulatives, pictorial representations, and abstract symbols—students can begin to visualize the math (in this subtraction problem, place value) and develop strategies which lead to them developing number sense, persistence, and confidence in math class.

*The views expressed in this article are those of the author and do not necessarily represent those of HMH.*

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*Interested in learning more about Singapore Math®, which aims to facilitate differentiation in the math classroom? Register here for our webinar, “Differentiating and Small Group Instruction in Singapore Math®,” presented by Terry Goldfischer and Christopher Coyne on Sept. 19 at 4 to 5 p.m. ET.*

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