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It seems like Jessica had to have lots and lots of practice in order to become a “math loser.”  And yet she was just as smart as Sam and worked just as hard (or harder) at the things she really enjoyed. Imagine how much more math she could have learned, and maybe even come to like, with a focus on concepts and practice with procedure.

It’s not that practice is bad. It’s essential. It’s just that bad practice is bad, and for Jessica the sole focus on procedural understanding didn’t help. It made things worse for her.

If someone had helped Jessica develop number sense related to concepts and procedures,  she would have spent her time a lot more profitably. She’d know more math now, as an adult. And she might even feel more competent as a person.But what about number sense? Here’s a definition:

Number sense is knowing how a number can be taken apart and put back together, and then using that knowledge to solve math problems.

How many ways can you think of to “take apart” the number 8? Remember—you can use any operation and any number of numbers (positive and negative).

In truth, there are an infinite number of ways.

And how about 9? Give 6 or 7 answers!

How you put them back together depends on the problem you are trying to solve.

So let’s look at 8 times 9—which is 72.  But let’s pretend we don’t know the answer: just like many students. How do we get to the answer from things we probably do know (like 2 times 3 is 6)?  Here’s the hint:

2 x 2 x 2 x 3 x 3 … then what do you do? (Answers vary depending on what you think will make computation easier.)

It may also be important to review resources about the teaching of math to students who experience difficulty with math. In this practice guide fro the What Works Clearinghouse https://ies.ed.gov/ncee/wwc/PracticeGuide/26, they review six practices that have strong evidence for their use when teaching math. Notice how one of the recommendations is related to building fluency- but many others are related to helping students (like Jessica) develop both conceptual and procedural understanding in math.

Module: Helping Students Do Math

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