Wednesday, May 28, 2014

If You Could See My Expression, You'd Know It Has No Equal

I've started reviewing for the new New York Common Core Algebra Regents Exam which will be given next week. My students are worried. They should be. No one really knows what it will look like, and the prep material is all over the place. I've given them sample tests, and tried to cover both new material and the basics.

I need to work on the basics.

I gave a quiz last week, with 10 multiple choice questions. Many of them had questions about the correlations and the correlation coefficient. Those didn't surprise me. What did surprise me what the question asking "Which of these is an example of an algebraic expression?" Most of the class picked choice 1) y = mx + b.

I had to ask them today about expressions and equations, and they seemed to know the difference. So I wrote y = mx + b on the board and asked what that was. They looked at me oddly, as if it were a trick question. Testing jitters? I don't know.

At least, no one picked the inequality, and no one picked the Pythagorean Theorem. But too few people picked the expression.

For those playing along at home, an expression doesn't have an equal sign and can't be "solved". It can only be "evaluated" if you know the values of all the variables. (Moreover, it doesn't actually have to have any variables or parentheses or operators. "6" is an expression.)

As for my students, their expressions were "puzzled" and "bewildered". Mine was more "disappointed".

We're working on it.


William Ricker said...

I'm not surprised the syntactic distinction between expression and equation is hard on students. Do they have a foundation in Grammars, did they do Diagramming Sentences is English? Didn't think so. And most "expressions" are in a Context where some (in)equality is implied and understood by the surrounding English of the Story Problem, even if though stated in mathematical = syntax. If a bare 6 is an expression grammatically, it's also the value of a elided variable, except in the unnatural context-free context this quiz question.

(x, why?) said...

In the beginning of the school year (which I, unfortunately, didn't have with these kids) I stress and overemphasize the difference between expression and equation (which has two expressions and an equal sign), along with the difference between the words "solve" and "evaluate".

That said, after solving quadratic equations for a couple of weeks in all sorts of forms and varieties, if you give them a polynomial to "factor completely", they will add a mysterious "=0" and attempt to solve for x.