You asked…

Posted on May 22, 2017

7


From twitter:

Seeing this everywhere across all grades. Anyone have ideas? radical349root

The replay speaks volumes — seems that person didn’t catch the mistake, either.

I remember going through this tendency, and while I’m not a typical learner, it’s reasonable to presume that others might make the mistake.

The square root operation is even more abstract than other operations.   When we add, subtract, multiply, or divide, or raise to a power — we include the number doing the operation.  Square root?  Nope.   I know I tended to keep rooting things — even without adding the confusion of having x squared under the radical.

It took me a while to drill into my brain that the square root of x squared was x, in the same way that dividing and multiply undid each other.  That connection wasn’t facilitated.   When I teach it I talk more about that.

Quick suggestions before I get off to work:

Put up the big ol’ pictures of powers from mathequalslove and point to ’em often.  One side of that square is the “square root.” That works well for visual learners (not me ;)) . http://mathequalslove.blogspot.com/2016/07/posters-of-perfect-squares-and-perfect.html

Put the “two” in the radical where you’d put a 3 if it were a cube root.  What’s with these math people?  It’s okay to say “if its’ not there it’s one” because the one *is* a tad redundant but … this isn’t redundant, this is “secret code you have to know…”

For me, turning it verbal was necessary.   I’d tell myself that “the square root of four is two,” and visualize the two being a “regular” two, without its little radical, and acting just like a normal number instead of having that funny hat.

… I’ll ponder ways to do conceptual frontloading on this one… this is exactly the kind of predictable error that lends itself to that…

 

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