No wonder everyone hates mathematics and considers it useless and doesn’t want to hear about creating good national standards.

I was just reading this part: **The Numbers Gap That Matters** of the article in the New York Times Blog http://roomfordebate.blogs.nytimes.com/2009/09/22/national-academic-standards-the-first-test/

In the article as an *important mathematics question* shown as an example of what our students *must know: *

From what I read: It seems that the reason our children cannot do mathematics is because such questions are not in the standards. Now I am not sure that (a) I know the correct answer to this question and (b) knowing the answer to this question does anything to improve my understanding of mathematics.

OK, I know that (d) is NOT an equation and (e) is definitely an equation, but for many (a) is a function so maybe not an equation, (b) has 2 solutions so maybe not an equation, (c) is a tautology (always true) so maybe not an equation.

Who the heck cares? And – if you do care – is x^2+3x+4=0 an equation? Oh wait, it has an equal signs. Oh no, it has no solutions. Oh wait, it has complex solutions. Oh no, we can’t graph them. Let’s go on and on about semantics instead of doing some real mathematics.

**== A REAL PROBLEM with Equations and Expressions in MATHEMATICS EDUCATION ==**

It is for sure more important that students differentiate between a problem that requires the simplification of an expression and a problem that requires the solution of an equation.

(A) to “simplify an expression” uses exactly the word “simplify” and not the word “solve” and that the answer looks like a snake (expressions connected with equal signs) and that the pupil understands that he is doing “re-organizational work” and not solving and

(B) to “solve an equation” uses exactly the word “solve” and not the word “simplify” and that the answer is a list of “expression=expression” until the student gets to a solution of the form “x=3”.

I am sick to death of students who have graduated from high school and entering an engineering program (and let us assume actually understand order of operations) that will tell me that the following is absolutely correct.

Given: **Solve 2(x+1)+x-2=6** . They will simply ** add the green** to get

** Solve 2(x+1)+x-2=6=2x+2+x-2=6=3x=6=2**

**Please – this is important.**

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BTW: Presumably - given the designers’ “definition”: *An equation is a statement that two expressions are equal.*, the “correct” answer would be: Only d is NOT an equation. See Common Core Standards Initiative