The question "What are the three forms of a number?" came home on a worksheet in my son's homework. I have a math degree and work with real math in my daily life. I can think of lots of different forms a number can take, but was unable to come up with the trinity of number forms on my own.

I have a mind like a steel sieve, so I thought maybe I'd learned this but had forgotten. So I Googled it.

Google was no help. The only Google hit for "three forms of a number" is an oblique reference to a Powerpoint presentation for teachers.

And so I consulted a Prentice Hall book entitled *Preparing for the New York State 6th Grade Math Test* which my son had brought home from school, and in that book, there is an answer to this question.

Am I to conclude that the idea that there are "three forms of a number" is an invention either of the authors of the New York State 6th grade math test, or of text book writers? Or is there out there in the world, some other provenance for this coinage?

Help me out here. I want to know. Are they teaching to the test? Or what?

I am unsettled by the idea that a reason that it is necessary to teach to the test is that the *test authors are making up new mathematical coinages of their own* that students are responsible for regurgitating.

UPDATE 9/24: So I had a meeting with the teacher yesterday. In summary, the phrase I reacted to comes from the Everyday Math curriculum that was in use in the elementary school when Peter was there, and so there was an expectation that students would recognize it in that form. Other answers differing from the Everyday Mathematics formulation would have been acceptable and were accepted with full credit. (The district has since replaced the U. of Chicago's Everyday Mathematics with a different curriculum, at least for my daughter's first grade class.) Peter's teacher is not using that curriculum (thank God!) at this point. The use of NY State practice tests was as a tool to assess what gaps in knowledge were there to be addressed, but the day-to-day classroom curriculum is not particularly oriented toward the test except as necessary to meet state standards.

I'd say I over-reacted to the assignments given by the middle-school teacher based on experience with the attitudes of the more testing-oriented elementary school teachers. Based on our conference, I'd say that preliminarily, I think the situation with the math class is going to be at least fine, if not better.

So my reaction was not baseless, but my experience as a Chappaqua elementary school parent left me with enough post-traumatic stress that I can be a bit quick on the trigger to judge the middle school which is, in the words of a local pediatric psychiatrist, a good bit more "touchy feely" in its academic stances than our elementary school.