Regents Recap — January 2018: Isn’t this Algebra?

What constitutes an algebraic solution? Let’s find out.

Here’s number 37 from the January, 2018 Common Core Algebra Regents exam. Only the final part of this six-point question is presented: Determine algebraically the number of cats and the number of dogs Bea initially had in her pet shop.

The key phrase here, apparently, is determine algebraically. If you don’t determine the answer algebraically, you can’t receive full credit. Here’s an example from the official Model Response Set in which the student loses a point for using “a method other than algebraic to solve the problem”.

In this solution, the student manipulates multiple equations, proportions, and equivalencies, determines the values of the variables that made the equations simultaneously true, and then applies substitution to verify their correct answer. That sure sounds like an algebraic solution to me.

Apparently it wasn’t the algebraic solution the test makers were looking for. But so what? We should be rewarding students for applying tools and techniques flexibly, not penalizing them for failing to adhere to a narrow, and secret, definition of what mathematics is.

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