Looking over the 7th grade math test, I try to view it through someone else’s eyes — anyone’s eyes who is not a professional math teacher, and when I do, I think, “I forgot almost all this stuff.” When you learn something in English class, like the definition of the word ‘satire,’ that knowledge generally stays with you for life since you learned something meaningful. When it comes to textbook math, you were lucky to keep it in your head long enough to get it right on the test, and then again, possibly, on the end of the year assessment. Examining these tests causes me to examine, again, what the math curriculum has devolved into. Getting an excellent score on this test, in my opinion, does not mean that a student really ‘knows’ math or that the student will live a fuller, more prosperous, life than another student who bombed this test.
I invite everyone reading this to attempt the eight questions I want to highlight in this analysis of the 2010 New York State 7th grade math assessment.
This question is quite a difficult question for a seventh grader. I teach at Stuyvesant High School which is one of the top schools in the country, and we teach this topic to our 10th graders (who are all a year ahead and taking 11th grade math — Algebra II / Trigonometry). It is an example of something called conditional probability where you determine the probability of two things happening by multiplying the probability of the first thing happening by the probability of the second thing happening once the first thing already happened. This is why the answer is A. Cory has a 6/10 chance of picking a red pen while Todd, because Cory has already taken one of the red pens, only has a 5/9 chance of picking one. 6/10 * 5/9 = 30/90 = 1/3. Many students would write B since that would be the answer if Cory was to put the first pen back. Then the probability would be 6/10 * 6/10 = 36/100 = 9/25. This is one of the problems with multiple choice tests. I think a student would deserve partial credit for writing B, but the scoring (as is the Value-Added metric that it is based on) is unforgiving.
In this question, I just object to the contrived nature of finding a way to turn the question -50 * 5 into a word problem. In what card game would the value of a card be -50? It makes no sense. For those playing at home, the answer is A since a negative times a positive is a negative.
This question hearkens back to a science class where we learned that ‘mass’ is not the same thing as ‘weight’. On the moon, your weight would be different while your mass would be the same. The answer is ‘A’ but I could see someone writing ‘C.’
Because of the poor wording of this question, I believe that there are two correct answers. What the answer key will say is C since 56 days is the amount of time that they will ‘next’ walk the dogs on the same day. But D is accurate also, and since it doesn’t say when is the soonest time, just ‘in how many more days,’ a good argument is made for D. Even if they did say ‘when is the next time,’ I feel a student would deserve at least partial credit for D since 8 * 14 = 112 which is an important fact related to the actual solution. Also we should call the ASPCA for animal negligence on these two boys.
I’m not trying to be annoying, but I truly think that I can make an argument for every one of these choices. A: The vegetarians would be the most knowledgeable about whether mushrooms or some other vegetable would be best. B: The students at the pizza parlor are experts at pizza so they would have a relevant opinion. C: Students who bring lunch from home might choose, instead, to get pizza from the cafeteria if it has a topping they like. Actual answer, I guess, is D.
What is ironic about this question is that almost the same question is on the 8th grade test that I analyzed, but in that test they gave a hint of how to do this question (a hint which I found misleading). So why is it that 7th graders don’t get a hint while 8th graders do? Answer: It is not a right triangle because the sum of the squares of the smaller two sides, 7^2+6^2=49+36=85 does not equal the square of the larger side, 10^2=100.
Then the second part reveals why we did that. It says ‘using your result from above’ which implies that the two answers are 7 by 27 and 9 by 21. But that means that if a student writes something like 8 by 23 5/8, which is a correct answer too, it would not be accepted since it is not something that would follow directly from ‘your result from above.’ They should have said that the numbers needed to be whole numbers to prevent someone from losing credit for something that I would consider correct.
I plan to continue this series, working my way back to the 3rd grade test.