Tuesday, March 24, 2015

When it matters whether 1 is prime

As I write this post, my home schooled daughter is over at a neighbor’s house spending one school day on what her public school peers have had to devote a week or more of their school year to. That is, she is taking a standardized test. To satisfy Pennsylvania’s home school law, she had to do this once in 4th grade, and once (now) in 8th grade. And since we can pick whichever standardized test we want, we pick the best one: the tried and true Iowa Test of Basic Skills (ITBS). And since anyone can apply to be a certified ITBS administrator, we walk a few blocks to the nearest neighbor who has, a fellow homeschooling mom.

As a tried and true standardized test (I took it several times several decades ago), and one with straight forward, well-written questions, the ITBS will give us results that are actually useful. In other words, it isn't anything like the new Common Core-based tests.

Nonetheless, in some ways I would rather my daughter could forgo testing altogether. Useful as a good standardized test is for diagnosing her weaknesses, not to mention for preparing her for other standardized tests, there are probably better things we could do with our time--both right now, and during the couple of hours we spent preparing for this test. Even the best of multiple choice tests risk occasionally testing knowledge of labels rather than knowledge of concepts, and therefore, so that she wouldn’t feel stumped for stupid reasons, I found myself drilling her on things I really couldn’t care less about. Things like:

Is 1 a prime number?

Is 0 a natural number?

What is the “median” vs. the “mode”?

What does the expression |X| mean?

What is scientific notation?

But, as far as the Labels as Concepts Fallacy goes, the ITBS is much better than its Common Core counterparts.  So I didn’t find it necessary to drill her on the meanings of “kite” and “number sentence” and “rate of change” and “Cavelieri’s Principle”, not to mention “dilation,” “reflection,” and “translation.”   It could have been a lot worse—and for so many kids and their parents, it is.

Anonymous said...

I hate remembering whether 1 is a prime number or 0 is a natural number, and I always forget right away.

On the other hand, I know what dilation, reflection, translation, rate of change, number sentence are. I didn't know what "kite" was mathematically or Cavelieri's principle, but I think I know those things now, and that I won't forget.

So, for me, anecdotally, two of these labels are harder than the others. (mode, median, absolute value -- assuming that's what your symbol is, something similar is also used for determinants of matrices, and scientific notation are also unforgettable in my mind).

bj

Anonymous said...

Fortunately, the ITBS doesn't test that sort of thing.

Anonymous said...

The reason 1 is not a prime number is because if it was it would break unique factorization (each natural number can be *uniquely* factored into a product of primes). I think that's a pretty theoretical concern for 8th grade (in my opinion). I probably wouldn't bother testing it if I was teaching.