Feb 10 2012

New York State Tests: 7th grade math 2010

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.

Here’s another ‘mass’ question.  So easy to confuse with ‘volume.’  Why is this worth two questions out of 38 altogether?  Answer is B.

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.

So the first part of this questions seems pretty contrived, 189 = 9 * 21 = 3 * 3 * 3 * 7 = 3^3 * 7.

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.

16 Responses

  1. I’m a college gradate with a successful career at an esteemed university, and this sample test just about undid me. Sorta like the standardized tests I used to take in high school, when I was able to manage the pressure, frustration and feeling of helplessness. But now tests like these are given to the littles? It’s perverse. It is, it’s sick. And totally irrelevant to real life as a grown up. It’s why I’m opting my daughter out. Thanks for this. Look forward to failing another round.

    • attila

      Should You prefer Chinese immigrants taking the job your daughter ought to have ? I guess your answer…….
      Allow your child work hard through early ages in school to have an enjoyable life.

  2. New Teacher

    The issue I have with #26 is that a fish tank (as opposed to a fish bowl) sounds much larger than any scale that a student would encounter. It would be much easier to measure the volume and convert to mass using the density of water, simple in SI units.

  3. Jenna

    Good stuff! I’m eager to immerse myself in anything anti-standardized test. I’m trying to keep as informed as possible, so that I can formulate and articulate my thoughts (and offer alternatives) to those around me. Can you point me to any articles or essays that can help me deepen my thoughts and slowly start to add to the conversation? Thanks!

  4. attila

    I think it is a good idea to get children ready for real life. This exam helps them to get prepared for real life.

  5. scott

    oh yeah, i’m definitely going to find the prime factorization of my deck and i’m definitely going to have to determine if a random triangle put in front of me is a right triangle…probably on a weekly basis..maybe even daily! If I can’t, I certainly won’t be prepared for real life! These tests are ways for the government to blame all educational shortcomings on the teachers and the teachers to blame these shortcomings on society… now that’s real life.

  6. JMS

    I think what is also telling is that now teachers will be evaluated on the performance of their students on these tests. I teach in a fairly well-off district. The children took a practice test as a HW assignment. There was a question about a dinner bill being 15.20. The tip is 15%. They are asked to estimate the tip and are given choices of 1, 2, 3, 4 dollars. To do this without a calculator, the children are supposed to take 10% and then half of that. They come up with about 2.28 and the correct test answer is $2.00. HOWEVER, many of my children have been taught that when you tip a waitress you would always round up. They said their parents would never leave $2…they would leave $3. On another questions, there were some animals in a rectangular pen. It was an area question. An ESL student called me over and had drawn a picture of a writing pen….she knew what was expected of her, but was confused about the idea of the animal pen. Can you blame her??

  7. MegB

    Ummm… I can tell it is not a right triangle because there is no right angle?

  8. Peter

    For #36 which of the two dimensions is the width? I don’t think that is clear. If we choose 3×63 as the dimensions then we could say the width is 63 and the length is 3, satisfying the requirements of the problem! In fact, any pair of factors would work since one of them will always be greater than 6!

  9. Harold G. Diamond

    Number 5 is indeed hard, but not as hard as the given solution suggests.
    The better way to proceed is to note
    that there are 6×5/2 = 15 ways to choose two red pens out of 6 and 10×9/2 = 45 ways to choose 2 pens out of 10. The ratio is 1/3.

    • Mary Rose O'Leary

      Interesting, Harold. How do you explain to 11 year-olds WHY you calculate it this way?

    • mpledger

      We used to do these things as tree diagrams (always horizontally) in school (hopefully, the diagram works)

      -+-
      / \
      First roll R / \ B
      6/10 / \ 4/10
      * *
      Second R / \ B R /\ B
      Roll 5/9 | | 4/9 6/9 | | 3/9
      | | | |
      Outcome 30/90 24/90 24/90 12/90

      (by multiplication down the chain)
      and choose the path you want i.e.
      P(RR) = 30/90 = 1/3

      We didn’t learn any formulae or even the name etc. We just knew if the outcome we wanted was part of a chain of events then use a tree diagram.

      Hopefully, kids would have enough understanding to eliminate C and D (too many Red pens) and then it would be 50/50 guess on A or B. (which is actually worse in a way if your teaching job comes down to a student’s flip of a coin).

      • mpledger

        I’ll try this to see if the diagram comes out right (and then stop wasting any more space)

        -+-
        / \
        First roll R / \ B
        6/10 / \ 4/10
        * *
        Second R / \ B R /\ B
        Roll 5/9 | | 4/9 6/9 | | 3/9
        | | | |
        Outcome 30/90 24/90 24/90 12/90

        • mpledger

          Agggggghhhhh!

  10. Mary Rose O'Leary

    Arne Duncan should take this test and publicize his results. Better yet, how about everyone who’s pushing for standardized tests as the be-all-and-end-all for schools, teachers and principals?

    The phrasing of math word problems on standardized tests is often painful to witness. I find that my more creative kids have difficulty because they think outside the box — not a welcome skill in standardized tests. Teachers find themselves in the idiotic position of warning kids not to “over-think” questions. Can you imagine? “Think hard, but not too hard.”

    It’s even worse with “Language Arts” tests. Try these, for example, given to 10-14 year-olds to test their grammar skills:

    1. Worried, and frayed, the old man paced the floor waiting for his daughter. (Correct/Incorrect)

    Now, if you’re like me, you’d say it’s incorrect because there shouldn’t be a comma after “worried”. But, no — it’s incorrect because “frayed” should be “afraid”. Really? If nerves can be frayed, can’t the old man whose nerves they are also be frayed?

    OR

    2. Fortunately, Jim’s name was (accepted, excepted) from the roster of those who would have to clean bathrooms because he was supposed to go downtown to (accept, except) a reward for the German Club.

    I’m 56 years old and can maybe count on one finger the times in my life I’ve heard “excepted” used as a verb. How many times do you s’pose 10-14 year-olds have heard it?

    I teach 6th grade in Los Angeles and have just been teaching my students the probability of dependent events (#5). A very difficult concept for 11 year-olds to grasp. And, dare I admit that, after nine years teaching this same standard, I have to refresh my memory every year on exactly how it’s done? And I’m pretty good at 6th grade math!

    I suggest we measure the “sadist quotient” of those writing the test questions. They often seem much more interested in tricking kids into choosing the wrong answer than in measuring what kids actually know.

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By a somewhat frustrated 1991 alum

Region
Houston
Grade
High School
Subject
Math

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