Number Sense – Who Has It?

A few tangents tonight. This great post from Number Loving Beagle got me thinking, in particular this piece:

I hear occasionally from teachers that we need to teach kids “responsibility” and we can’t force them to learn if they don’t want to.  This line of thinking bothers me a great deal as places the burden of being eager to learn on the student.  Some kids place “learning at school” very low on their priority list.  We must acknowledge that rather than disregard it with “he/she never came and asked a question.”  If we are being honest with ourselves, we know exactly which kids need the help but won’t outwardly seek it.  We know which kids won’t ask questions when they have them, and which ones won’t make an effort to turn in assignments that they’ve missed.   It’s not that they are incapable of seeking help, asking questions, and turning in assignments.  But by stating that “help was offered but not taken” we do not absolve ourselves from the responsibility to reach these students.

I’ve been guilty of this. It perpetuates the haves/have nots divide in students — those who are invested in school, see the positive effects of their hard work, and continue to work hard for their education; and those who struggle to get invested and are continually discouraged by negative feedback and internalize that they are out of control of their learning. That’s one big issue, and one I care a lot about, as I think my biggest failures this year have been in a few students I’ve struggled to give reasons to engage in my class.

This got me thinking about number sense as well. We talk about number sense in these same terms — either students have it or they don’t, and especially in upper middle school we give little thought to teaching number sense. When we do “teach” number sense, it’s often asking students if their answer makes sense, or showing students a  shortcut, or giving students worksheets of “basic skills” (decimal and fraction operations).

But students who have number sense gained it by making sense of math problems — by constantly checking their thought process and their answers against a mental image of the problem and solution space, by using multiple representations to understand a concept, by estimating quickly and strategically. Asking students who struggle with these skills to do them without support is asking them to fail and revert to their answer-getting ways that have got them this far.

So what does a lesson look like that supports all students, no matter where their number sense is? I have no idea. Number talks are all I have right now, but I’m looking.

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