Good luck, New York's children

With mathematics exams that will be administered starting next week, New York is jumping the Common Core gun by offering its own version of Common Core-aligned assessments for grades 3-8. Sample questions have been provided on the New York State Education Department’s web site.

Here’s a quick look at some of those questions, and our Roger Ebert-style final evaluation for each:

Grade 3

What NYSED apparently wants is for students to equate the string to a number line.  Clever diversion from rote questions.  The problem is that on a number line, a scale must be provided in the form of at least two numbers.  For example, if the left and right endpoints of the string were identified as 0 and 1, respectively, then point A might look like it’s at 1/4 on a number line, which is what we think NYSED was intending.

Missing necessary information.  Thumbs down.

Grade 3

In this question, students have to recognize the respective roles of the three numbers 54, 3 and 9, as well as the objects apples, trays, students and classes, and determine their relevance to any calculations.  The final answer can be immediately obtained by overlooking any information about trays, making the number 9 a red herring, but the inclusion of that information, which students can use in an alternate path to the solution, goes beyond the depth of the Common Core standard, which only asks students to multiply and divide within 100.

This is the level of difficulty appropriate for Grade 3 division under these standards (example taken from Common Core glossary Table 2): ``If 18 apples are arranged into 3 equal rows, how many apples will be in each row?’’

Not Common Core-aligned.  Thumbs down.

Grade 4

This problem anticipates students will write the words ``1/3 of all the points’’ as the mathematical calculation 1/3 x 108 to determine Joanne’s points (that’s what NYSED's sample solution shows).  The problem is that Common Core parses teaching 1/3 x 108 and 108 x 1/3 into two separate standards (we have no idea why), but the former, 1/3 x 108, is not taught until 5.NF.4a.

Not Common Core-aligned.  Thumbs down.

Grade 5

Although all of the points in this problem are in Quadrant I, where both x- and y-coordinates are positive, the negative numbers on the x- and y-axes will confuse students unnecessarily. Why? Because under Common Core, negative numbers aren’t introduced until Grade 6.

Not Common Core-aligned.  Thumbs down.

Grade 6

Is it possible for one word to alter the outcome of an exam?  We’ve written before about poor wording in exam questions, but the last sentence’s phrase ``closest percentage’’ even confused us.  It should read ``What is the approximate percentage of cars...’’

We also don’t like the interchangeability of three terms ``fuel efficiency’’, ``fuel efficiency level’’ and ``efficiency level’’, the last two being terms we’ve never heard before.

Finally, this problem requires converting a fraction 40/110 to a decimal, and then to a percent.  But such conversions are in Grade 7 (7.NS.2d) in Common Core.  Oops.

Obfuscating wording.  Not Common Core-aligned.  Thumbs down.

Grade 7

This question might be okay if we knew how long the group’s vacation was, but we don’t.

Missing necessary information.  Thumbs down.

Grade 8

Common Core standard 8.EE.7b simply asks students to solve equations.  It does not ask students to critique the correctness of alternate approaches.

Furthermore, while crediting only C as correct (because you cannot do arithmetic with 2x before distributing), this question supplies other answers that are also incorrect.  For example, one does not solve this algebra equation by first subtracting 2 1/3 from 7.  That assumes previous steps, such as subtracting 2 1/3 from both sides, or moving 2 1/3 from one side of the equation to the other which will result in a sign change.

Bad mathematics.  Not Common Core-aligned.  Thumbs down.

Good luck, New York's children.  You’ll need it.

(And a post-exam update.)


  1. Very nicely done, thank you.

    I assume that 1/3 x 108 vs 108 x 1/3 fits in with a more nuanced look both at multiplication and at fractions (I am searching for one of Wu's articles)... but it's not my level, and I don't pay enough attention.

    Were the math not wrong, the last example would be a great classroom extension...


    1. We opined in an earlier post http://ccssimath.blogspot.com/2012/06/concept-of-area-part-3.html that there's no need to teach these similar operations as separate concepts, and certainly not in different years.

      Wu, writing in the format of a doctoral thesis, takes 42 pages to explain to elementary school teachers how to teach fractions, so we don't consider him to be the definitive authority on the topic.

    2. Wu's newer Common Core-aligned explanation of fractions runs to 88 pages. We stand corrected.

  2. One common thread with the ELA assessments I've looked at is the same lack of attention to detail regarding alignment. There are all these odd little details that I would argue have to be regarded as important and intentional, since they are so unique. They couldn't have gotten there by accident.

    But everyone seems to have agreed to just ignore them, so... ?

  3. Also, in number 5, while it may be fairly apparent by looking at it that Dr. Logan is closest, have the students been given any tools up to this point in the standards to know this for a fact? It's a diagonal distance, presumably they aren't measuring it with plastic rulers given the online nature of CC assessment... so are we encouraging a "looks close to me" approach? The distance formula doesn't come up until 8.G.B.8, so they're 3 grades early. I was going to call the axes having negative numbers a weaker than the rest critique, but I think the stronger criticism here is that teaching mathematics as a "which one looks right" intrinsically weakens later attempts to teach formal understanding and proof, out-of-scale models, and numerically proving rather than relying on visualization. That's a pernicious question.

  4. I was going to quibble with the first question as well; the wording is misleading. "Give the fraction that represents each point on the string as compared to the whole": my answer for all POINTS is 0/1 !

    Asking what points they'd be on a number line is another way of getting at the same issue; they really want to talk about fractions of a line segment, but they're not making themselves clear.

  5. Why do we have so many of us who see the idiocy of all of this common core and Parcc and everything else, but we can't do anything about it? We need to stand up and try to be heard for our children.

  6. All this proves, as I've written about numerous times previously, is that for whatever sociopolitical/economic reasons, the Pearson tests are not adequately vetted before being given to the students. And we should be examining those politics and economics CLOSELY.

    As a side note, as a former content developer at Princeton Review (which of course does test preparation), NONE of these questions would have ever made it on to student materials in these forms--ambiguity/lack of clarity is anethema to a good test writer, and the multiple step editing process ensured that this type of wording would never make it out of the office unchanged. (The Grade 7 question presented here is particularly egregious--one cannot assume a vacation time of merely one week; in fact, one cannot assume any time at all.)

  7. Anonymous12 May, 2013

    I am baffled by two things here.
    1. What is the goal of the people who wrote these sample test questions on the NY site? Are they trying to prove the children of NY are not learning math? That the NY teachers are failing to meet the new standards? The questions are phrased in such a way as to show that most children are not meeting the new standards. Almost all children are capable of learning fractions, problem-solving, etc if taught clearly -- but very few children would be able to make sense of the sample questions you put in your post. This is especially true of children who come from homes where the main language spoken is not standard white English, not to mention children who are good at math in 3rd grade but whose reading skills might be less developed (a fairly common thing at that age).
    2. What is the math training of the people who were allowed to write the questions? The question writers lack even a basic understanding of math -- and don't seem to have a clue what math is necessary to solve their questions. Whoever wrote the question about the rope fractions and failed to provide a scale would presumably be at about a third grade math level him or herself. And the person who wrote the vacation problem but failed to say how long the vacation was ... these are such very basic errors that even an eight year old would spot them.

    This whole common core experiment seems doomed to fail if people with training in math are not being consulted.

    Also, I am wondering why such an enormous amount of money is being spent on this. Why not get rid of absurd "math" programs like Everyday Math (which anyone with any math training would have seen at a quick glance were guaranteed to fail) and replace them with Singapore workbooks? The Singapore books are clearly superior to the Common Core stuff -- and they are already written! I understand the value of having the whole country adopt uniform standards but is there any good reason they did not take a sound, already-developed set of books (like Singapore) and use those in every state which was willing to sign on to a common set of standards?

  8. Anonymous13 May, 2013

    My California school district sent out an email to parents today saying the district's "elementary school teachers are preparing to make the transition to a new curriculum that aligns with the new Common Core standards: A Story of Units. Our CCSS team of teachers and principals found that the current curriculum, Everyday Math, is not well-aligned with the rigor and coherence of teaching math as defined in the new Common Core State Standards." (They failed to say Everyday Math was not aligned with anything .... this is how they gracefully sweep under the rug their vast money-wasting experiments ... this happened before with Math Land which one could see at a very quick glance, the moment it was carried in, would have to be dragged away to wherever the failed math books with their matching manipulatives end up.)

    I'd love to hear your analysis of "A Story of Units" ... is it written by the same people who do not know you need to provide a scale in order to start putting numbers on a number line (or rope)? (I hope not!)

    The district email mentions that "educational experts from across the country studied the differences between how math is taught in U.S. classrooms and compared it to teaching in "A+ countries". I am still puzzled by why they feel they must hire non-mathematicians to come up with a brand new math curriculum rather than make use of the curriculum used in one of the A+ countries. If something works, why not use it? I know there is more to success than just good textbooks -- but it is a start. On the other hand, using really poor math books can make it much more difficult for parents to provide support at home or help out in the classroom so it's a handicap right from day one.

    Also, if a program like Singapore math does not perfectly match the common core standards, could it not be adapted much more easily than having "experts" dream up problems with bits of rope which then have to be recalled and fixed and replaced with problems that will have a scale but are missing the rope? When education experts dabble in math, no good ever comes of it. Surely the last 40 years have taught us that!

    1. I have read about a number of school districts with "buyers remorse" about Everyday Math, which the curriculum that is being tossed in your school district.

      Can you tell me what curriculum has been chosen to replace Everyday Math. Is it Singapore Math? Thanks.

    2. Anonymous23 July, 2013

      The replacement, from what I could tell from the district's email, will be "A Story of Units" -- not Singapore. It might be a rough transition if the district chose Singapore math for our district (Berkeley) because the level of math training of the teachers is not high enough for them to be able to solve many of the 4 - 6th grade Singapore math problems, let alone explain them. I remember reading a few years ago of some schools trying to switch to Singapore but the teachers could not pass the Singapore unit tests (I think it was 5th or 6th grade) so the schools had to go with a "softer" math program. I did Singapore for a few years with my own kids but when the first one started high school in Berkeley, many of his classmates had not yet mastered column addition, finding averages, making bar graphs ... yet somehow they had made it through Everyday Math.
      For a rigorous program like Singapore Math to work in Berkeley, the elementary teachers would need to be taught the curriculum first (or the district would need to hire outside math people to come in and teach). One difference between Everyday Math and Singapore is that you simply can't fake an understanding of math and solve the Singapore problems. With Everyday Math, kids can move along from year to year, stuck (like many of my son's classmates) at about a second grade level) but with Singapore, if a child could not perform basic operations with fractions (for example) at the grade that is covered, they would not be able to do the work. I would describe Everyday Math as "dabblers' math" ... you can dip into things and talk about them a little and the leave them behind, with no real accountability. When one of my children had Everyday Math in his classroom, his teacher proudly told me "with Everyday Math you feel like you never really understand anything because it is a spiral approach". That was thought to be a plus! The actual content was things my son had easily picked up when he was five or six (working in Singapore books for a few minutes a day).
      Better than Everyday Math would be to give each child the Singapore books and just let them do their best, even if the teachers could not solve the problems or were trying to figure them out alongside the kids. This would be far from ideal -- but certainly superior to EM.

    3. Singapore Math is obviously the more sensible program. No wonder they're selling oodles of books to parents desperate to under the intellectual damage caused by rubbish like Everyday Math. --New York City Eye

  9. Anonymous29 May, 2013

    Seriously, I do not see major issues with the tests. With the exception of running out of time, the questions are mostly on par with what I have experienced living in Europe. It will be a difficult process, but it is needed for the US education system to catch up with the top tier nations of the world.

    1. I agree with your point. It is not the standards, per se, but the radical change that is the sticking point.

      The real problem, IMO, will be in the transition years when Johnny or Sara's parents are going to be very surprised to hear that their child is not-proficient when their grades and tests in previous years have been satisfactory or better.

    2. I found a counterargument to every one of the author's complaints here with a 2 minute perusal of the actual CC standards. The much-ballyhooed first question says "as a fraction of the whole" which implies a scale of 0 to 1. The whole point of a graphical representation with equal scales is to be able to eyeball data and estimate. Subtracting 2 1/3 from 7 is the same as subtracting from both sides -- and one can answer that question WITHOUT actually doing any equation solving as the incorrect answer involves subtracting something outside the parenthesis from something inside the parentheses when, even if using something like PEMDAS, you know you can't do. Students are introduced to the cartesian plane as "distance" and "direction" from the origin in 4th grade, so the negative axis should not confuse. Whether the student does 1/3 x 108 or 108 x 1/3 doesn't matter for this question so it is CC appropriate, etc. etc. etc.

  10. For question 8 the answer C is flat out wrong. One would subtract 1/2 x from 4/3 x.

  11. Looks like you've attracted the attention of the Libertarian International Organization at their SMILE twitter on Lib friendly/unfriendly trends today: https://twitter.com/LIBIntOrg

  12. Tried to Subscribe to your blog but I got this error message:
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    --New York City Eye