The New York State Education Department clearly tried to play it safe in designing questions for the Grades 3 to 8 exams, with a lot of calculation and solve-the-equation problems, which would have been the same pre- or post-Common Core. Where NYSED gets into trouble is when it tries to be creative, particularly in word problems.

So without further ado, here’s a look at some of the released questions from the

__2013 New York State Testing Program’s Common Core Mathematics Tests__.__Grade 3__

The weakness here is one of language. The set-up question uses the word “objects” in order to cover the nouns in all the various scenarios, which include: boxes, pencils, people, buses, marbles, groups, books and shelves. Within each answer choice, the student first has to consider which “objects” are "described".

We’d be hard-pressed to apply the term “objects” to people, but it’s equally inapt for shelves and buses, so we could eliminate choice B simply because there are no “objects”. Luckily, it’s not the answer that received credit.

We’d be hard-pressed to apply the term “objects” to people, but it’s equally inapt for shelves and buses, so we could eliminate choice B simply because there are no “objects”. Luckily, it’s not the answer that received credit.

The problem with credited answer C is that while the word "objects" might apply to marbles, but not “groups”, the set-up describes neither. 24 ÷ 4 is the number of marbles

*in each group*.
The question could ask, "Which situation can be represented by 24 ÷ 4?" and the answer would be “The number of marbles in each group when 24 marbles are sorted into 4 equal groups.” That's unambiguous, grade-appropriate, and aligns with 3.OA.2. Instead, students are left to infer a question that's not explicitly asked. The task of making such a language inference is not what the Common Core standard is supposed to require here. This is a math test.

Although we understand the intent of this problem and the underlying math is sound, the problem is heavily biased against students with language weaknesses because it requires inferences and fairly advanced interpretive skills, especially for Grade 3.

__Grade 4__

Although many students would choose the correct answer by simply looking at the picture and seeing 4 bars and recognizing that each bar is ⅛ shaded, finding the answer by this shortcut avoids the real mathematics: understanding the model and what it represents, which will lead to difficulties for students applying fractions to solve problems in the future.

It’s implicit, but not made clear that each of the four bars is “a whole”. The weakness reveals itself when one does the actual calculation 4 x ⅛, because the "total shaded area" in reduced form, ½, is not visibly apparent anywhere in the model.

If the answer choices were given as fractions rather than “multiplication sentences”, and two of the four choices were ½ and 4/32, we are certain many students would choose the latter wrong answer (because 4 out of 32 rectangles are shaded), even if the problem began, “If each bar in the model represents a whole...”

__Grade 4__

The problem here is simply the phrase “wrote a pattern”. It’s not mathematical and it’s terrible English. Why not teach students good math habits from the beginning and use the correct term “sequence” (which is correctly in 4.OA.5) and phrase the question, “Rosa wrote down a sequence of numbers that contained a pattern. The pattern followed the rule: subtract 7 from each term in the sequence to get the next number in the sequence.”

__Grade 4__

The problem here again is the use of language, in particular the multiple and varying uses of the word “number” in one sentence. The “number below” and “the number represented by the digit in the thousands place” are two very different meanings of the same word. They are not referring to the same thing. Disadvantage to weak readers and ELLs.

__Grade 5__

Although NYSED purports to align this question with 5.NBT.1, this question simply does not comport with the standard, which states, “Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.”

NYSED explains, “In this case, the 3 in 3,000,000 represents 10 times what a 3 in the hundred thousands place would represent; equivalently, the 3 in 3,000,000 represents 30 hundred thousands.”

While the first part is certainly true, and 3,000,000 is ten times 300,000, the key gap in NYSED’s thinking is the magical word “equivalently”. No one says “30 hundred-thousands”, ever. What’s happening on the right side of the equation is really 30 x 100,000, which is a multiplication problem. The underlying math is sound, it just doesn’t align, and thus the question tests aptitude, not the standard.

__Grade 6__

Here is an example of bad mathematics.

While simplifying the expression in choice A leads to the correct distance, 9, one does not calculate a distance by taking absolute values and adding them. One takes the absolute value of the difference in values. Thus, the correct expression would be either | 3 – (–6) | or | (–6) – 3 |.

If the points were instead A(–6, 4) and B(–3,4), applying NYSED’s "method", one would get |–6|+|–3|=9, which is wrong.

__Grade 7__

The weakness in the question is the phrase “can be used” which allows the question writer to get away with (if we didn’t object) to a poorly formed task. While choice B is the only equation that will result in the correct value of

*x*, which represents the hourly charge, the equation is certainly not the initial equation we would set up to find the answer algebraically.
The term “total charge” implies that the value, $320, should sit alone on one side of the equation, and indeed, that’s the way students should be taught. Weaker students, who are nonetheless properly conversant with setting up equations, would incorrectly eliminate both choices A and B on that basis. Choice B is not the properly set up initial equation, it is an intermediate result in the solving of the initially correct equation, which would be either 320 = 5

*x*+ 70 or 5*x*+ 70 = 320.__Grade 7__

Common Core is not supposed to dictate problem solving methods. It’s supposed to allow students the freedom to choose their own method and argue on its relative merit or weakness compared to other methods. That’s one of Common Core’s alleged strengths that its authors trumpet constantly.

*See*SMP3.
Yet in this problem, students are shoehorned into selecting a method that they might ordinarily abhor, or worse, not be able to complete. And indeed, we the authors of ccssimath.blogspot.com, would never solve this equation by first dividing both sides by ⅔. It ends up looking like this awful mess...

...where NYSED conveniently glosses over what happens between steps 2 and 3.

This problem would be far better simply if it asked students to solve the equation. Then they can use any method they so choose.

__Grade 7__

This is one of the most sophisticated questions in the Grades 3-8 exams. Yet students are likely ill-prepared to take a simple relationship, such as that between the length of a square’s side and its perimeter, and represent that relationship as a linear equation.

This difficulty is compounded in NYSED’s question by its wording, particularly its abundant and overuse of the letters

*x*and*y*in different ways, which will confuse a lot of students. But most importantly, what’s missing from the problem is a critical intermediate step: an understanding that*y*, defined as the perimeter of the square, is related to*x*, defined as the side of the square, by the equation*y*=4*x*. That equation is at the core of the problem and should be an explicit part, rather than the more ambiguous wording “straight line” which appears.
To those who recognize the complexity of the mathematics of this problem, we offer a question of this sort from the Five Triangles blog, shown below, but the wording and the relationships must be made crystal clear:

__Grade 8__

Although “grasping the concept of a function and using functions to describe quantitative relationships” appears in Grade 8, functions truly make their formal debut in Common Core’s high school standards, in F-IF’s “Understand the concept of a function”. This is but one of numerous unreconciled redundancies in Common Core.

This Grade 8 question assesses students’ understanding of how to apply what is more commonly known as “the vertical line test”. It really doesn’t belong in Grade 8, since a first introduction to functions in any grade should begin with a mapping from one set to another, followed by sets of ordered pairs, followed by linear functions. Those alone would be enough for Grade 8. Choice B is particularly unsettling because it’s supposed to represent a quadratic function, which is never studied in Grade 8. How would students know that the arrows in the parabola don’t become vertical or bend back? We have no idea. It’s a bad question for the Grade 8 exam.

__Grade 8__

This question does not align with standard 8.EE.3, in which students should be able “to

express how many times as much one is than the other”. “How many” implies a whole number amount, not a fraction. Thus 4 x 10^6 is 50 times more than 8 x 10^4 would be a Common Core-aligned answer choice, but choice D is not.

__Grade 8__

Our final critique is this question, which is unnecessarily wordy. Why is it necessary to write “right circular cylinder”? It’s just a cylinder and that’s what the problem should say. “Cylinder” may have several meanings, but not in Common Core.

There are plenty of related testing issues that we're not touching on in this blog, but at the very least, questions have to be fair.

There are plenty of related testing issues that we're not touching on in this blog, but at the very least, questions have to be fair.

The key thing about all tests is that they are primarily reading tests. secondarily reasoning tests (what is the author looking for -- not what is the correct answer.

ReplyDeleteBanesh Hoffman's SAT example of a simple math question comes to mind. There are 9 blackbirds sitting on a wall. One is shot. How many remain on the wall?

- 8 (one was shot off the wall)

- none ( one shot fell off the wall, and the others flew away)

- 1 (the dead one - it's a wide wall)

- 9 (the dead one and the others remained on the perch)

- 9 (shooter missed)

- 0 (shooter missed and all flew away)

etc.

Raising the grade-level expectations for students is, in my opinion, a very good thing. However, these example questions point to the type of semantic fine tuning that needs to happen for the CCSS test to be effective.

ReplyDeleteSo, in all the caterwauling about the test, we need to separate out these two things...the merit of the increased expectations itself and how the test actually measures these increased expectations.

I am assuming that New York became an early adopter of the test to give their teachers a jumpstart in implementing the CCSS. This leading edge preview, became a "bleeding" edge as NY is now a victim of the questions not being shaken out adequately.

Don't throw the baby out with the bathwater...fix the questions!

Here's an idea. Pearson and the NY State Dept. of Ed should do the "semantic fine tuning" before subjecting tens of thousands school children to questions such as these. Regarding how "the test actually measures these increased expectations", the NY State DOE has not produced one shred of empirical evidence that the tests measure anything at all, including "college and career readiness". Regarding NY giving "their teachers a jumpstart implementing the CCSS", the DOE failed to supply materials or curriculum to teachers before the test was given. The kids were tested on material that neither they nor their teachers had seen. The bathwater to which you refer is toxic.

DeleteFirst, I hope the publisher of this site doesn't get in trouble. I was under the understanding that all the new tests were under lock and key and "secure" indefinitely. But the reasoning behind this "security" is clear. They do not want the open, transparent discussions that are going to arise when people see the kinds of questions that are being asked. They wish to tell us only to "improve" without knowing exactly what it is we need to improve. It would be akin to a building inspector telling a contractor that the plumbing was wrong in the house, without explaining exactly how it was wrong. "Just fix the plumbing" is what the state is telling us without us knowing what is exactly wrong with the plumbing. And on top of that, because the tests are all scored in a mystical, statistical process, we might improve next year; but if neighboring schools improve more than us, it makes us look like we didn't improve at all because of the relativistic nature of the tests. It's not about what the students know. It's about how much better they did than the neighboring schools. The state effectively is choosing what percent of students it wants to fail every year using statistics. Horrible. Just horrible.

ReplyDeleteNYS released them earlier this week. http://www.engageny.org/resource/new-york-state-common-core-sample-questions

Deletethese have got to be the most idiotic questions I have ever seen - this is what they are teaching to? No wonder why these kids can't think or read. I feel bad for our children.

ReplyDeleteI'm so glad I went to school in the 50s and 60s this has my head hurting ...God help these kids

ReplyDeleteI believe this way of thinking will greatly increase the math ability of our youth. Sorry. We have an epic disaster on our hands now, perhaps caused by people who don't really "get" math designing things. Trained as an engineer, I can tell you this will help kids actually understand how things work, instead of the memorization we all grew up with. I believe people don't like this because they don't like math. I am not an educator, but a business owner, saddened by the lack of ability to understand how to use numbers in the people I employ. It allows them to make financial mistakes, etc., and is a real life problem. If you are not good at manipulating numbers and math concepts, please don't chime in about how this is not good; it's not helpful.

ReplyDeleteI am a student taking these tests. There's so much stress on me and school-mates during this time of year just because of these tests. It's difficult and honestly... stupid. I believe that the state should just use the normal "old-fashioned" teaching. The type of educational system my parents received at my age. Even with english, it saddens me when I see people at my age or older than me who can't spell. When our school was taking the test I saw a page of another student who had spelled it "hapend". But anyway, the tests are ridiculously hard and should be saved for high school where it is traditionally taught. The math just puts so much stress on everyone, including myself I'm afraid of not being promoted. If only the state could just look inside the average N.Y classroom...

ReplyDeleteThey're asking the little pre-kindergarteners to explain their thinking in words, they cant even write their names!

ReplyDeleteI hate these tests their just so stressful its just a waste of time with these tests even my teacher is stressed out

ReplyDelete