If schools are going to be closed and teachers fired over state tests, the tests had better be good. So I downloaded the most recent 8th grade New York State math assessment to see how it was. Out of 45 questions, I had issues with at least ten of them.
In this question, there is a pretty big inaccuracy:
The problem with this question is that ‘the Pythagorean theorem’ is used for questions where you have a right triangle and the lengths of two sides are known and you use the relationship a^2 + b^2 = c^2 to find the other side. The Pythagorean theorem, which they are instructed to use for this question, is not technically, what you do. What they mean is that there is something called the ‘converse of the Pythagorean theorem’ which says that if a^2 + b^2 equals c^2 then the triangle is a right triangle and if a^2 + b^2 does not equal c^2, then the triangle is not a right triangle. I’m not saying that they should have said ‘Using the converse of the Pythagorean theorem’ either. They should have just said to determine if this is a right triangle or not. Their ‘hint’ actually makes the question inaccurate and can confuse kids
What really bothered me is that 11 out of the 45 questions, just about 25% of the test was based on one concept in Geometry: recognizing vertical angles, complimentary angles, supplementary angles, and related angles with parallel lines. In 8th grade, apparently, students must memorize that in the configuration below in question 14 where x and y are parallel lines crossed by line z, there are 8 angles formed. Angles 1, 3, 5 and 7 are all less than 90 degrees and equal to one another while angles 2, 4, 6, and 8 are all greater than 90 degrees and equal to one another. Also, the smaller and larger angles are ‘supplementary’ meaning they have a sum of 180 degrees. So if angle 1 measures 40 degrees (as does angles 3, 5, and 7) then angle 2 (and also angles 4, 6, and 8) measures 140 degrees.
I say ‘memorize’ rather than ‘learn’ since the actual proofs of these relationships does not happen until they are in 10th grade Geometry. At this point it is merely something they they learn to recognize. The over emphasis on this concept bothers me because this isn’t really a very important concept, mathematically. It is not particularly interesting, nor does it really ‘go anywhere’ for a few years. It is the kind of mindless thing that makes students think that math is not relevant, fun, or worth learning. For the amount of value given to these questions, it would be worthwhile for an 8th grade teacher to spend 25% of the school year drilling on these mindless problems.