Sunday, March 17, 2013

My Notes from Taking a (Shortened) NECAP Math #takethetestpsu

I jotted some notes down in a corner of my scrap paper and smuggled it out of the testing site.

I had one moment of panic which I think reflects the kind of thing a lot of kids would go through on the test on a question that I thought was very emblematic of the exam. We had to analyze a sequence of fractions, which was tricky mostly because the second fraction had been reduced to lowest terms, which disguised the pattern. This was enough to convince my table neighbor, the Chair of the Providence City Council Education Committee, that there was an error in the test.

But also, the list was formatted oddly -- I'm not 100% sure that it was this way in the original NECAP -- with the commas separating the fractions floating just below the bar in the fraction, so it looked like the denominators might actually be 5', as in "five to the apostrophe," some notation I'd never heard of. For a few seconds I just froze and thought "5-apostrophe?!? This must be some new math we never covered in class!" Then I calmed down and decided it was just bad formatting. A lot of already rattled kids wouldn't make that recovery. If you actually talk to kids in city schools about these tests, they get hung up on that kind of thing all the time.

I eventually figured out that to find the answer you could go through the four choices of expressions for finding the 20th item in the sequence and see which one would correctly match the third or fourth fraction shown. I think I got it right, and it took some reasoning, but it whether or not that was math is an open question.

Another question I thought was typical showed two spinners that would give you random numbers from 1 to four. It wanted to know the probability that the sum of the two would be a prime number. I drew a complete blank, until I realized I could easily write out all 16 combinations and just circle the ones that resulted in a prime number. That more clearly took mathematical reasoning, problem solving and content knowledge.

I like the question, and I like the direction it should push math curriculum. But I'm also aware that if even if kids have been taught probability, if they haven't been taught it in a way that encourages flexible and resourceful problem solving -- rather than pulling numbers out of stereotypical word problems and following procedures -- they will be completely screwed.

On the whole, the NECAP math pushes for deep conceptual understanding, which is great, unless you don't have it and you need to pass the test to graduate. For a math test, I thought it required very little knowledge of terminology. In the sequence question I mentioned above, you needed to know the prime numbers between 2 and 8. There was one that required knowing the definition of sine and tangent (I guessed). Those were the exceptions though. It was about applying math in what seemed like odd abstract contexts. A lot of them, particularly the multiple choice but even some of the short answers, seemed solvable by what seemed like brute force approaches if you understood the concepts well enough to narrow down the possibilities quickly.

I have no idea if there are textbooks that are made up of questions like these. If there are, I didn't get the impression from the students running the event that PPSD uses them.

I didn't leave thinking that the NECAP was a bad test, but it is completely different from a test you would design from scratch as a graduation requirement.

Thanks to the Providence Student Union for putting this together.


Mike said...

Thanks for posting this. Did they compile multiple years of NECAP released items?

Tom Hoffman said...

Yeah. I'll tell you, one hour of that is enough. Hard to say if they picked the more difficult problems though.