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# 6 x __ = 240

You can’t say that the kid is incapable of understanding what the box means here. Still, in the space of one line, it slipped through her fingers.

Is this connected to the way kids inconsistently treat exponents? I’m struggling to articulate a general principle, but it goes something like “Operations defined in terms of others are strongly associated with their parent operation, to the point that students often perform the parent in place of the derivative operation. As a result, students should always be introduced to a new operation in its own context, not in terms of other operations, whenever possible.”

Thoughts?

## 2 replies on “6 x __ = 240”

kmorrowleongsays:

I was thinking that this is an equal sign issue. ( http://www.sciencedaily.com/releases/2010/08/100810122200.htm ) Consider this equation 5 + 12 = ___ + 9 One like it has yielded unexpected answers in a NAEP assessment. Students routinely answer with 17 or 26. 8 is not as common as we might expect. Student who do this have an operational view of the equal sign: they see it as a operator of sorts, instead of as a symbol setting two expressions equal to each other.
Maybe when the fact is a memorized fact, it does not require reasoning and the operator decision is not required. However, if any reasoning is required, the placement of the box makes the equal sign appear as an operator.
OR, I have no idea and the child had a lapse of vision…

icarlysays:

6 x 40=240