A number sentence for 5 cookies and 6 cups of whole milk?
November 1, 2013 5:12 PM Subscribe

The Washington Post reports on a ridiculous mathematics test for first graders administered under New York's Common Core standards initiative. [Common Core previously.]
posted by Westringia F. (189 comments total) 12 users marked this as a favorite

Um...Pepsi?
posted by TheWhiteSkull at 5:17 PM on November 1, 2013 [3 favorites]

That cannot possibly be a real test. It's one of those FauxNews flamebait things, right? Most of those questions do not make ANY sense.
posted by spacewrench at 5:18 PM on November 1, 2013 [3 favorites]

So that'g got to be a test that was run through an auto translator, then translated back to English, right? And then accidentally spilled some clipart on there? That's the only way that makes sense to me.
posted by Think_Long at 5:19 PM on November 1, 2013 [2 favorites]

I didn't think that test was particularly ridiculous. They were asking for the same kind of skills my kid and his class worked on last year, when he was in first grade. Is it weird to ask them whether a subtraction sentence involving one-digit numbers is true or false? Why?

The "part I know" language was unfamiliar to me, thus confusing, but it's clear from context what they're asking, and I assume this is the language in which subtraction was taught in class, which is why that's the language used on the test. Also, on question 12, I would call all four of the options addition sentences rather than subtraction sentences.
posted by escabeche at 5:22 PM on November 1, 2013 [28 favorites]

For the love of God what is the answer to question 1?!
posted by billiebee at 5:23 PM on November 1, 2013 [28 favorites]

I dunno, they kinda makes sense if the lessons were taught a certain way. Take 5 pennies out of a cup containing 6 pennies answer how many are left. Take some blocks off a stack of blocks and how many are left. Seem to be about real concrete physical examples.

Hell, what would I know, I spent most of my life in NYC public schools.
posted by Ad hominem at 5:24 PM on November 1, 2013 [3 favorites]

It's good to see that school districts are preparing kids for the bullshit that comes in a dead-end job later in life. Might as well start them early.
posted by crapmatic at 5:24 PM on November 1, 2013 [15 favorites]

If the part you know is 5 and the whole is six, then the part you don't know is 1.
posted by Elementary Penguin at 5:25 PM on November 1, 2013 [9 favorites]

Question one has a confusing picture for the overthinking sort, 12 has a typo where 'subtraction' should be 'addition'. Beyond that, it looks like they're trying to teach kids with phrases that emphasize the way we write math is a language, a form of communication. I don't think that's a bad approach.
posted by Zalzidrax at 5:25 PM on November 1, 2013 [8 favorites]

For the love of God what is the answer to question 1?!

The answer is 1. It's clear from the other questions that one of the ways they learned subtraction was to talk about the "whole", and then some "part I know" of the whole, and then consider the question of how much of the whole is "missing," i.e. not the "part I know." Seems a perfectly reasonable way to approach subtraction. If there are 10 kids on my block and I've met 4 of them, there are 6 left to meet.
posted by escabeche at 5:27 PM on November 1, 2013 [16 favorites]

Thank you Elementary Penguin.

*weeps*
posted by billiebee at 5:27 PM on November 1, 2013 [3 favorites]

Yeah, I don't have a huge problem with this test but I have to wonder how you can be expected to know the part you don't know.
posted by edd at 5:28 PM on November 1, 2013 [5 favorites]

I, uh, don't see the problem here. This all seems very straightforward if the terms utilized have also been used in the teaching of these concepts to the students (and if that's not true then I'd question the relevance of the teaching in general toward the phrasing of tests more than the specific detriments of this piece of paper). Question 12 also has a typo, which confuses things.
posted by solarion at 5:29 PM on November 1, 2013 [10 favorites]

How many math professors does it take to get a 100% on a first grade math test?
posted by Elementary Penguin at 5:29 PM on November 1, 2013 [6 favorites]

I didn't think that test was particularly ridiculous.

I agree.

There's absence of something confusing about every single one of those numbers-based problem questions. Any child with more than two-fifths of a brain should be able to arrive at a satisfactory answer with the maximum ease of usage.
posted by Atom Eyes at 5:30 PM on November 1, 2013 [9 favorites]

Elementary Penguin: "If the part you know is 5 and the whole is six, then the part you don't know is 1."

I believe this is actually a koan, and refers to the great Zen Master Donaradu Ramzferudu and his great words of wisdom:

"There are known knowns; there are things we know that we know.
There are known unknowns; that is to say, there are things that we now know we don't know.
But there are also unknown unknowns – there are things we do not know we don't know."
posted by symbioid at 5:31 PM on November 1, 2013 [39 favorites]

It is however not impossible that I am overestimating five-year-olds, which I'm happy to consider. But I have been told not to do that.
posted by solarion at 5:32 PM on November 1, 2013 [1 favorite]

For the love of God what is the answer to question 1?!

e^cosh(x)+π petri dishes
posted by Blazecock Pileon at 5:33 PM on November 1, 2013 [5 favorites]

The goal, which you may disagree with, is to introduce as few new words as possible when teaching math to children who potentially don't have great vocabularies or who might come from English Language Learner backgrounds. "Number sentence" is how you say "equation" without actually saying "equation." "Missing part" is "difference." I'm sure there are similar circumlocutions for words like "addition" and "sum."

I mean, don't most people who complain about never having learned math well because "it was taught poorly" complain about how abstract it was, how it's inhumanly difficult to make the connection between the number 6 and six of a thing, the fraction 1/2 and half of a pizza? Well, this is the language that actual teachers developed to talk about what numbers stand for and the stories people tell with numbers, while using an absolute minimum of words that kids may not know and could have trouble learning.

People asked for math instruction that uses age-appropriate language and connects math to concrete concepts. This is what that looks like.
posted by Nomyte at 5:36 PM on November 1, 2013 [50 favorites]

I looked at question 1 for several minutes and had to come here to learn that those were pennies. I kept trying to make sense of five Oreos going into a cup of whole milk, but I couldn't figure out what the six meant. For what it's worth, I have a PhD, though obviously not in mathematics.
posted by ga$money at 5:37 PM on November 1, 2013 [19 favorites]

If you choose an answer to this question at random, what is the chance you will be correct?

a) 25%
b) 50%
c) 60%
d) 25%
posted by brevator at 5:37 PM on November 1, 2013 [45 favorites]

What is the criterion of correctness? That does not make sense
posted by thelonius at 5:39 PM on November 1, 2013

Ugh. Valerie Strauss is one of the worst writers in American education. Note how that blog entry (which I realize someone else wrote - this is something she's doing a lot now) makes no reference to principles for or against the test in the mathematics pedagogy literature, just tells you someone trained in Calculus doesn't know this particular technique and that you must assume every test given in an American school is the result of some current demon (during GWB it was NCLB, now it's Common Core). I don't know that this is good, but outside some hyperventilating, I haven't been convinced its bad either.

Could you make sense of that critique? I couldn't. And I'm a PhD student in education policy.
posted by Apropos of Something at 5:39 PM on November 1, 2013 [6 favorites]

I am kind of loving this; I like that there's a lot of reading required, and the kids are encouraged to draw to think through the answer (that might have been happening before Common Core; my little one isn't even 4 yet. But the amount of sturm I'm seeing on Facebook, etc about Common Core leads me to believe this is all mostly new). And also, this seems like the kind of thing you can't really drill.
posted by shrieking violet at 5:40 PM on November 1, 2013 [1 favorite]

The thing I'm really enjoying about the test is that it's not testing your ability to do arithmetic by hand, but to connect the concept of subtraction with both equation-based and picture-based representations of what's going on. I teach a lot of College Algebra, and I have had multiple students be amazed when I showed them how to multiply two single digit integers by drawing a rectangle divided into squares. A lot of students finish high school without an intuitive understanding of what arithmetic is, which means they will have a hard time developing an intuitive understanding of algebra. You have to get them when they're young!
posted by Elementary Penguin at 5:44 PM on November 1, 2013 [10 favorites]

I have third graders. This looks fine to me. I think it's the coffee cup in question one that's throwing everybody off; I'm not sure why they used a coffee cup, but for #1 (the only iffy one here, the rest seems fine) the instruction is to "find the missing part"; the part they know is 5, the whole is 6, so the missing part is 1.

What surprises me is the number of wrong answers this child had. Perhaps it's confusing when math questions are also word problems, but that's a useful life skill.
posted by davejay at 5:47 PM on November 1, 2013 [4 favorites]

And what Elementary Penguin said.
posted by davejay at 5:47 PM on November 1, 2013

The main confusion with number 1 is that it has incompatible units. Essentially it says, "there are 6 cups of milk, if you take away 5 cookies how many are left?"

Maybe there's some other explanation for what the discs are supposed to be that makes more sense.
posted by justkevin at 5:49 PM on November 1, 2013 [10 favorites]

The problem is that most math is your ability to extract the question out of a jumble of lines and word-things. Real world applications don't come in easily deciphered problem sets.
posted by Elementary Penguin at 5:50 PM on November 1, 2013 [12 favorites]

I understand the value of the technique, EP, but I can't help but feel like it's a waste to use it on single digit integer equations. In my mind these should be regarded as "math facts" and memorized. I know that isn't the way it's done anymore, but I cringe when I see children reach for a calculator to answer, "What is 6 times 4?"
posted by ob1quixote at 5:51 PM on November 1, 2013 [4 favorites]

This test is consistent with the homework the students get based on my experience as a parent.
posted by humanfont at 5:51 PM on November 1, 2013 [1 favorite]

It took me a minute to understand that they were being taught to use a sentence to form the equation and to "sound it out", as it were. Once I grokked that, it became pretty obviously a test of subtraction abilities, and it was pleasantly concrete--much more so than a page of numbers stacked up.
posted by fatbird at 5:51 PM on November 1, 2013 [1 favorite]

I don't think the subject of this test IS single digit arithmetic, though. This test is supposed to be testing the translation process.
posted by Elementary Penguin at 5:52 PM on November 1, 2013 [2 favorites]

This is the kind of stuff my first grade daughter is doing, using manipulatives and word problems. Put me on the "not ridiculous" list, and add a "this is better than the way I was taught math at that age, when all I did was learn times tables" for good measure.
posted by grubby at 5:53 PM on November 1, 2013 [3 favorites]

And it kills me that my students don't know their times tables, but it also kills me that they don't know the first twenty square numbers, or double angle and half angle formulas, or a hundred other things. The fact that math education has to grapple with is that the average person has access to computers that can do literally any algorithmic mathematical process they ever learned almost instantly. When I'm doing research and I need to take an integral or multiply a bunch of polynomials together, I don't do it by hand, I let SAGE do it for me. I wish I knew the proper balance when it came to technology in the math classroom, so if anyone figures it out, let me know.
posted by Elementary Penguin at 5:57 PM on November 1, 2013 [4 favorites]

The part that screwed me up on some of the later questions was that I kept confusing the number in the box (the whole) for the question number. It's really badly laid out, and that's most of the issue.
posted by kewb at 5:58 PM on November 1, 2013 [4 favorites]

Peg me for a philosophy major, but what the fuck do 5 oreo cookies have to do with a cup of coffee with the number 6 on it.

That is just an insanely illogical visualization. "Well, we should use a cup full of coffee to represent wholeness, but because that is an absurdly difficult thing to deduce from a picture of a cup of coffee, let's put the number 6 on it. You're welcome for the drawing."
posted by phaedon at 5:58 PM on November 1, 2013 [12 favorites]

I homeschool and the math curriculum we use-- JUMP Math--teaches problems very much this. It is a very different vocabulary and approach than I learned in elementary school, which was 40 years ago. But because I've worked with my kids on this curriculum, the set-up of these problems was very comprehensible to me. I can't recall whether these specific skills were covered in first grade in our curriculum.

I wonder how the rest of the class did? It's easy to say, "This is ridiculous!" When your kid--or your friend's kid-- did poorly, but was that a typical outcome in the class? I wonder what the writer would have learned by interviewing the teacher.

I'm not necessarily in favor of early academics, I am really not in favor of graded tests in first grade, and I have not studied the Common Core well enough to have an informed opinion, but the article seems to me to represent a very uninformed opinion colored by a knee-jerk reaction shaped by prior biases.
posted by not that girl at 6:02 PM on November 1, 2013

Maybe I am wrong, but I can almost see a teacher put 6 items in an empty cup, pull 5 out and ask how many are missing. It makes perfect sense that way.
posted by Ad hominem at 6:02 PM on November 1, 2013 [2 favorites]

This whole this is kind of silly. Older people complaining about how young people just aren't learning math like I did grrr.

Now.

It-may-be that this style of math is idiotic and stupid and shouldn't be taught. But there is very little context here to make that judgement, just a bunch of "wha? I can't understand it so it must be wrong!"
posted by edgeways at 6:03 PM on November 1, 2013 [3 favorites]

This is pretty standard, yes.

However this:

So that'g got to be a test that was run through an auto translator, then translated back to English, right?

Is probably also super-true. I recently edited a math textbook that had been written in Taiwan, by non-native but English-proficient speakers. We did a fair bit of translating questions and instructions that, while technically English, were total nonsense. I imagine we caught 90-95% of these issues, but that means some slip through.

Cut school budgets, they cut their textbook expenditures. Cut textbook spending, publishers fire editors. Fire editors, you get shit textbooks full of errors. Circle of dumbness.
posted by like_a_friend at 6:03 PM on November 1, 2013 [5 favorites]

When did check marks become the common symbol for "Correct!" I kept trying to figure out why the checked questions were wrong and the circled ones were right.
posted by thorny at 6:05 PM on November 1, 2013 [3 favorites]

I wish I knew the proper balance when it came to technology in the math classroom, so if anyone figures it out, let me know.

Yeah, that's a really tricky question. The goal of "doing it by hand" is to demonstrate that the student actually has a conceptual understanding. Like, in your example with multiplying a bunch of polynomials, in a real life situation technology will save a ton of time and avoid silly arithmetic mistakes, but the person doing it ALSO needs to know that if they multiply a fifth order polynomial by a third order polynomial by a seventh order polynomial, they'd better get a fifteenth order polynomial or something went wrong. But at some point, the stuff that made sense to do by hand on a first grade subtraction exam becomes silly and irrelevant when the point of the assignment is to demonstrate your understanding of, say, Stokes' theorem.

I work with someone who simultaneously manages to be quite smart, but has zero instinct at all for realizing that "hmm, that result makes no sense, something went wrong somewhere, and maybe I should step away from the keyboard and think through the concept of what I'm trying to do". Someone will look at his numbers and say "oh, that's wrong" and he'll say "how do you knowwww?" and they'll say "because you multiplied hundreds times thousands and got 1.23*10^27, which doesn't make sense" and he comes back with more "but how do you knowwwwwwwwwww?"
posted by Blue Jello Elf at 6:11 PM on November 1, 2013 [6 favorites]

If the average 6 year old is learning 6-7 new words per day,...

They're not just teaching the average kids.
posted by goethean at 6:13 PM on November 1, 2013 [10 favorites]

Also, in regards to this section of the WaPo article:

I am amused by all of the politicians and bureaucrats who love the Common Core and see it as the salvation of our nation. I suspect they are supporting standards that they have never studied. I wonder if they have ever read the details that ask first-graders to “compose and decompose plane and solid figures” and “to determine if equations of addition or subtraction are true or false.”

I don't see what's wrong with either of those either. I guess they sound scary if you don't think about what they mean?

The first standard is basically going to result in questions like "Hey kids, here's part of a circle! select part A, B, C, or D that combines with it to complete the circle!"

And the second is just another flavor of "don't just train kids to mechanically solve addition or subtraction problems; make sure they understand what the expressions actually mean."
posted by Blue Jello Elf at 6:17 PM on November 1, 2013 [1 favorite]

>>If the average 6 year old is learning 6-7 new words per day,...

They're not just teaching the average kids.

Plus, they may be teaching above-average kids who happen live in homes where English isn't spoken, so maybe they're picking up 10 new words a day, but six of them are in %OTHER_LANGUAGE% and only four are in English.
posted by Blue Jello Elf at 6:19 PM on November 1, 2013

The jug is filled with milk. Whole milk. The six equates to a particular level of Hell. It will take me five coins to cross the River Styx, one to be placed over the dead eyes of mine enemies, two humans and a cyclops. Obviously I need one coin left to pay the ferryman. Satan's favourite drink is whole milk. Simple.
posted by urbanwhaleshark at 6:21 PM on November 1, 2013 [45 favorites]

I don't really remember much about the first grade.
posted by box at 6:24 PM on November 1, 2013 [3 favorites]

If the part you know is 5 and the whole is six, then the part you don't know is 1.

It seems to me that if the part of cookies you know is 5, and the whole of something unrelated to cookies is 6, then the part you don't know could be anything. The question depends on the picture, which could be interpreted as, 'If you have 5 cookies and some milk, what the hell are we asking you?' The correct answer would then be, 'Yes, the person who came up with these illustrations has been fired.'
posted by Sing Or Swim at 6:29 PM on November 1, 2013 [22 favorites]

This is not a Common Core math test. This is math homework. I do not have direct access to Pearson content so I don't know what specific product this is. But if this is 1st Grade, it is probably either EnVisionMATH Common Core or Investigations in Number, Data, and Space for the Common Core. You can look at them on the Pearson School website, which is a horribly incompetent piece of website design so I cannot link directly to these products.

These would be very early, nearly experimental Common Core materials, produced almost 5 years in advance of the general adoption targeted for 2015. They are only a small part of the picture, which includes "professional development" materials to help teachers deliver CC, test, and digital systems for testing and textbooks.

Disclaimer: I am a former employee of Pearson and I have nothing good to say about them. I currently work for their competitor (and occasional partner) which requests that I disclose my association with them. However, I don't think they want to be associated with me or my opinions so I will not identify them by name. Let me just say I am currently working on development of future Common Core products that directly compete with the one under discussion in this FPP, so I am a highly biased source.
posted by charlie don't surf at 6:30 PM on November 1, 2013 [20 favorites]

I'm sure it is probably because I learned math(s) in a completely different fashion, but this "part I know" and "number sentence" stuff seems ... distracting? I guess I just never saw what was so hard about solving "6 - 5 = ?"
posted by Saxon Kane at 6:34 PM on November 1, 2013 [2 favorites]

And I know people asking "one coin for the Ferryman?". That's "mate rates", and I get to sit at the bow and holla profanities into the reeking mist.
posted by urbanwhaleshark at 6:34 PM on November 1, 2013 [5 favorites]

I think cds' point here is really, really important. At best, we know from evidence provided that this test is poor, or that Pearson is poor ... but to extrapolate from that that Common Core is broken? Or be the umpteenth education article this week to idealize an ethnically homogenous and social safety net rigorous country like Finland? Much bigger leap.
posted by Apropos of Something at 6:35 PM on November 1, 2013

Use cubes to solve.

Ok.
posted by tylerkaraszewski at 6:36 PM on November 1, 2013 [2 favorites]

New math. It's so simple, so very simple, that only a child can do it. The more things change...

Put me in the not ridiculous camp as well here. The cup in the first question is annoying. But other than that? No problem at all.
posted by Francis at 6:36 PM on November 1, 2013 [1 favorite]

Re: the best statistics question ever...

Any reason why C is 60% and not 75%?
posted by Saxon Kane at 6:38 PM on November 1, 2013

It took me a long time to figure out question 1 -- I basically had to go through the whole test and figure out the vocabulary they were using and then go back and solve it, but it seems like if the kids are being taught using those words, it probably makes a lot more sense to them than it does to me.

It actually reminds me a bit of an experience I had when I went to Brazil as an exchange student. We had these little tests every few weeks that covered a variety of subjects. I could generally parse the STEM subjects well enough to answer the questions, could barely even read the questions in subjects like Lit and Geography, but I fully expected to ace the English (as a second language) questions.

I fully expected it, right up until the very first question on the very first test was "Classify morphologically the underlined words in the following sentence." Fortunately it was multiple choice, so I figured out what they wanted based on the available answers, but as a native English speaker, the word 'morphologically' had certainly not ever been a part of my English language education. I could have written a 500 word essay on the themes in Merchant of Venice, but a question aimed at ESL students was potentially out of my reach because of an accident of vocabulary. The other students in my class had no issues with the question, because they'd also been in the class however many years before when classifying things morphologically had first been taught to them so they knew what the question was asking.
posted by jacquilynne at 6:41 PM on November 1, 2013 [2 favorites]

I'm not prepared to say this alleged test is poor, until I see it in context. There are many intermediate steps in teaching common core that do not seem logical until you consider that they are intended to develop analytic skills, they are not necessarily representative of the capabilities of students at this grade level. Here are the basic objectives of the Common Core Math program.

Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
posted by charlie don't surf at 6:42 PM on November 1, 2013 [1 favorite]

It looks like it is a test included in the instructor's supplement that needs some proof reading, but that is what first editions are for, nowadays.
posted by Elementary Penguin at 6:46 PM on November 1, 2013

Also, what are question 3's cubes?

They are actual cubes; at this grade students use various types of objects to represent number sets in problems. The ones I see most often are actually kind of like big legos, they connect into sets of 10 and can then be broken into smaller sets.
posted by like_a_friend at 6:47 PM on November 1, 2013

Rephrasing my question: what IF answer C were 75% (or 0%) instead of 60%?
posted by Saxon Kane at 6:49 PM on November 1, 2013

It made sense to me right away, because my daughter had this exact same work last year. Unless the teacher is incompetent, the kids have been taught these concepts before being handed this work.

What's throwing me now is 5th grade math. It's so different from how I learned it, a long time ago and in another country, that there are evenings when I just have to say "I'm sorry, you're going to have to ask your teacher" when my son asks me for help.
posted by The corpse in the library at 6:51 PM on November 1, 2013

> Also, what are question 3's cubes?

Snap Cubes. The kids use them at school for counting, and when they're younger for working on making patterns.
posted by The corpse in the library at 6:53 PM on November 1, 2013

Rephrasing my question: what IF answer C were 75% (or 0%) instead of 60%?

The C would still be wrong, I think. If it were right, there would be a 25% chance of getting the question right at random, not a 0% chance.
posted by Elementary Penguin at 6:53 PM on November 1, 2013

I call bullshit on this.

I did similar things in first grade in New York decades ago. Yes the graphics for the first question are stupid, yes to understand some of the questions you need to understand obscure jargon that was probably created specifically for the standard. No that doesn't mean the test is unfair if you've been given proper instruction.
posted by ethansr at 6:53 PM on November 1, 2013

Also, can I just say that this:

Why are some kids crying when they do homework these days? Here’s why. . .

made FLAMES! on the SIDES OF MY FACE!

As if no child ever, in the history of homework, was ever frustrated until the Common Core came to destroy America forever.

For that sentence alone that blogger should be fired and possibly blacklisted from the internet forever.
posted by like_a_friend at 6:57 PM on November 1, 2013 [9 favorites]

I like 'use cubes to solve'. I think it evokes a zen-like state of No Mind, and would be a marvelous phrase to introduce, out of any context, into other kinds of problem-solving, later in life. What will you do with your bachelor's degree? How many jobs must you have in order to earn enough to sleep indoors? Use cubes to solve.
posted by Sing Or Swim at 6:57 PM on November 1, 2013 [16 favorites]

It's good to see that school districts are preparing kids for the bullshit that comes in a dead-end job later in life. Might as well start them early.

It's funny, I'm just working on going back to school to finish my degree. Admissions came back and told me I needed to take a placement test to see which math I needed. This inadvertently started a two-month odyssey where I had to do things like sit through an unskippable 8 hour "orientation" slideshow online with quizzes throughout to make damn sure I paid attention to where the library was on a campus I'd never even heard of, among other things, but then when I finished, I had to print out a PDF certificate and bring it in because of course they couldn't just update their records through the system I was using to take the test.

Likewise I had to take half a day off to go talk to an advisor to find out what test I needed to take even though I already knew what test I needed to take and had a letter from that very college stating it, but I went through the whole process and he said, "Oh, you have to take the math placement test" and I said "I know, that's why I'm here" and everyone acted like I was being an asshole.

But it's way less annoying this time around because I've been in the working world and the academic level of pointless bullshit just can't compete. It's good prep for those other poor bastards but I want to warn them they haven't seen anything yet.
posted by Ghostride The Whip at 6:58 PM on November 1, 2013 [3 favorites]

> As if no child ever, in the history of homework, was ever frustrated until the Common Core came to destroy America forever

And that's not what the homework looks like, anyway, at least not in my daughter's experience with Common Core math. She did those handouts in class, where the teacher (or a volunteer, like me) was there to talk about it.
posted by The corpse in the library at 7:02 PM on November 1, 2013

No that doesn't mean the test is unfair if you've been given proper instruction.

Doesn't that mean they're being taught more to take tests than the subject of the test?

BTW, make sure to read charlie don't surf's comment, above. This isn't a test, it's homework, and it's not in widespread use at the moment.
posted by JHarris at 7:04 PM on November 1, 2013

I agree with what others are suggesting about the silliness of the language used here; there's nothing intuitive or immediate about "number sentence". Learning what that is and how to write one requires just as much tutelage as saying "equation". So why not simply state it in that manner, especially when the child will ostensibly learn the word "equation" in a couple of years when they advance in grade? This is complicated by the fact that the language utilized is "number sentence" in some areas, but specifically "subtraction sentence" in others, even, as in question 12, when the operation being performed is addition.

What I definitely do dig, though, are the pictures. Maybe they could be a little better done and more consistent, but it's definitely a bonus to have an immediate visual method of performing math to reinforce the words.
posted by Room 101 at 7:27 PM on November 1, 2013 [2 favorites]

I'm one of the parents of a homework-crying kid. And I'll tell you it's not coming from the instruction the teachers are giving, it's coming from the fact that I have no fucking clue how to help him with the homework.

I can't tell you how many fights I've had over "here's how to make ten, son" vs "no, the teacher told us do to it THIS way". I've had homework sent back with comments letting me know as much. How the hell can I help him when I have no idea what they're trying to do? Yeah yeah, I know, this is the "OMG New Math" gripe of every parent.

And this was before Common Core, when we've spent the last two years struggling through UCSMP Everyday Math (fuck you, UChicago. And I'm a local). Even the teachers here now admit (off the record, of course) that Everyday Math was a bad way to go.

Now I've been informed that the third graders are spending 5-10 minutes a trying to catch up to Common Core because, in those last two years of heuristics and strategies and elaborate definitions for common mathematical terms, they forgot to teach them their fucking addition and subtraction tables.
posted by JoeZydeco at 7:35 PM on November 1, 2013 [13 favorites]

All the awkward and strained phrasing around "part I don't know" and "missing part" seems designed to make 'x the unknown' less of a shock when kids get to algebra.

The idea of a symbol for an unknown quantity in an expression with numbers is apparently just too much for many people; many people I know, in fact.

It's very ordinary to us, but it sure took a long time to show up historically.
posted by jamjam at 7:37 PM on November 1, 2013 [2 favorites]

All the awkward and strained phrasing around "part I don't know" and "missing part" seems designed to make 'x the unknown' less of a shock when kids get to algebra.

The idea of a symbol for an unknown quantity in an expression with numbers is apparently just too much for many people; many people I know, in fact.

This is exactly the rationale as I have heard it.
posted by like_a_friend at 7:47 PM on November 1, 2013 [1 favorite]

I suppose it's a little late to ask this, but perhaps somebody will explain #2 to me: I get the part about 8 jars, of which 6 have jelly and the rest have peanut butter. Yum! But why is the picture that goes along with this 6 cubes? Why does 8 go in the big box over a line of length 1? Why does the correct answer include two squiggles that look like sixes in the question-mark side of the box, next to the other 6 cubes?

If you have to have pictures, why not pictures of jars? Even the kid who answered this test, drew circles for the 7 balloons in problem 11. (Apparently he miscounted the number that were not red, after drawing "R"s in the two that are red, but whatever. At least he's aware that some balloons are round.)
posted by spacewrench at 7:50 PM on November 1, 2013

There are eight jars in total, so the 8 goes over the line that encompasses all of them. (Nothing about it having length one.) Among that total are six jars of jelly (shown as cubes for some reason) and a question mark for the unknown number of peanut butter jars. The child has drawn in those jars as circles.

I don't know if I'm just younger than everyone else here or what, but this doesn't seem that far off from what I remember of first grade math. We used Unifix cubes, and I recall the phrase "number sentence" going around. I has the advantage of being analyzable by first graders. I had not the grammatical sophistication at that age to connect "equation" with "equals", but I could figure out that a "number sentence" had something to do with numbers. I even had some idea what a "sentence" was.
posted by eruonna at 7:59 PM on November 1, 2013

People asked for math instruction that uses age-appropriate language and connects math to concrete concepts. This is what that looks like.

Yeah, like

┌───┐
│ 9 │
└───┘

is a 'concrete concept' which is seen in many other aspects of five-year-old life. I'm pretty sure it doesn't mean anything in the rest of mathematics, too.

Why not

There should be nine pennies.

[picture]

Draw the missing part.
Write the numbers.

And then instead of 'part I know', maybe 'part I can see.' Because 'know' makes no sense.

All the awkward and strained phrasing around "part I don't know" and "missing part" seems designed to make 'x the unknown' less of a shock when kids get to algebra.

This is exactly the rationale as I have heard it.

Yeah, five-year-olds aren't exactly starting algebra the next year.
posted by Quilford at 8:01 PM on November 1, 2013

Also, what are question 3's cubes?

In later grades, "cubes" can also mean "six-sided number cubes," which in turn stand for the dreaded D word that textbooks for children aren't allowed to mention.

No, yes, of course, this is terrible graphic design, the visual metaphors are used in haphazard and confusing ways, and the resulting visual "aids" in fact conceal or misrepresent more information than they actually communicate.

And yes, there is no reason to believe that if children can learn the word "sentence," that they then cannot learn a small number of other school-related words like "equation."

I completely agree that making up new, "easier" words for children to use is pretty much uncleftish beholding.

Also, the production of test preparation materials for schoolchildren is a nightmarish gauntlet of bullshit that I have repeatedly written about on MeFi.

All that being said, these materials didn't fall out of the sky. They are examples of exactly the kind of materials that the public asked for, that columnists promoted, that parents praised, and so on.

You want more unsupported, long-debunked, entirely unscientific stuff for "visual learners" and "tactile learners"? Fine, here's a bunch of pictures and cubes and other crap! You think children can't think abstractly because Piaget said so 70 years ago? Sure, let's express every problem in terms of physical objects and people. You think words used in math are confusing and unnecessary? Let's replace them with heretofore meaningless strings of other common English words!

Everything on this test addresses something the lay public has been complaining about in regard to how math is taught to children. This is the better, more intuitive, more hands-on, more practical, more sensible, more reading-intensive, more reasoning-based math you wanted.
posted by Nomyte at 8:06 PM on November 1, 2013 [8 favorites]

The "part I know" language was unfamiliar to me, thus confusing, but it's clear from context what they're asking, and I assume this is the language in which subtraction was taught in class, which is why that's the language used on the test.

I bet people making comments like these did not read the article, in which the blogger specifically states that the test is not the main problem, but the teaching itself. i.e. This should not be the language subtraction is taught in in class. It's stupidly complicated.
posted by Quilford at 8:11 PM on November 1, 2013

In later grades, "cubes" can also mean "six-sided number cubes," which in turn stand for the dreaded D word that textbooks for children aren't allowed to mention.

Is the word 'dice' now slang for 'fuck' or something now?
posted by el io at 8:11 PM on November 1, 2013 [1 favorite]

They can't say dice? This sounds like the kind of thing that would appeal to the crafts people who think that it's a big deal that everyone say "chenille stem", not "pipe cleaner". Walk into a craft store this weekend and ask for pipe cleaners, see what happens.

In the early 70's, our elementary math worksheets had problems like 9 - _ = 7, which is as much a preparation for algebra as is anything I see here.

As long as instruction in math is done by fetishizing particular methods for basic arithmetic, kids are not going to really going to understand anything except mechanically applying that method, I fear. Maybe this stuff is helpful for some kids, who knows. Someone, I hope....
posted by thelonius at 8:24 PM on November 1, 2013 [4 favorites]

Every ten years or so, someone writes the exact same article when some parent realizes their child is doing math with different vocabulary then they used as a child and panic ensues. This test is really straight forward, and one of the things these adults should have learned about math (but apparently haven't) is that the core concepts of math are independent of the vocabulary you use to express them.
posted by zanni at 8:27 PM on November 1, 2013 [8 favorites]

I can only assume that they've done the studies, but it does seem surprising that small children find this more understandable than the "If Bob has five apples and John takes two how many apples is Bob left with" language that most of us are presumably used to.
posted by markr at 8:28 PM on November 1, 2013 [1 favorite]

This test is really straight forward, and one of the things these adults should have learned about math (but apparently haven't) is that the core concepts of math are independent of the vocabulary you use to express them.

The test is really not straightforward, and while the core concepts of mathematics are independent of the vocabulary used to express them, some vocabularies are easier to comprehend than others and mathematics really depends on a strict, coherent vocabulary and setting out to make your meaning clear and also to ensure you don't make mistakes. These are abstract concepts, so you need precise language to articulate them.
posted by Quilford at 8:33 PM on November 1, 2013 [4 favorites]

"Would you like fries with that?"
"Yes please."
"OK, let me just make a quick number sentence so I can work out the missing part. You have no fries. You want some fries. The part I know is some fries, so the whole is...no, wait, you have no fries, so the difference...wait, I'll get it..."
posted by obiwanwasabi at 8:33 PM on November 1, 2013 [3 favorites]

Is the word 'dice' now slang for 'fuck' or something now?

There are large states that make very large textbook purchases from the major textbook publishers. Those states drive decisions about what's allowed into children's textbooks by the publishers and the instructional design companies they subcontract work to.

I guess a parent in Texas thought that "dice" is synonymous with "gambling," so the word is never used in textbooks. Also, cartoon animals in textbook pictures don't have genitals, and so on. As previously mentioned, modern textbook publishing is a vortex of bullshit.

If you google for "six-sided number cube," you will find lots of children asking for homework solutions on Yahoo Answers.
posted by Nomyte at 8:37 PM on November 1, 2013 [10 favorites]

"dice" is synonymous with "gambling"

..or with D&D. Satan is tireless and he will try to get in via the math homework, dontcha know.
posted by thelonius at 8:44 PM on November 1, 2013 [5 favorites]

My kid is in first grade, learning math using Math Expressions, which is a curriculum that teaches to Common Core. Her homework is better written than this, but otherwise looks very similar. She has zero problem with it and races right through it, stopping only when her hand gets tired.

As an extra bonus, I showed her some simple algebra the other day (x+4=9, that kind of thing) and said that the x stood for the part you don't know, and she just grabbed the pencil, rewrote the equation as 9-4=x, and then looked at me and said "X is five." I gave her no other explanation, it just made perfect sense to her. Sure, it's different than how I learned math, but from my sample size of one, it seems to be doing a great job.
posted by KathrynT at 8:49 PM on November 1, 2013 [12 favorites]

These are abstract concepts, so you need precise language to articulate them.

This is one of the most important aspects of Common Core. As I quoted previously from the CC standards:

Construct viable arguments and critique the reasoning of others.

One of my colleagues is always insisting that you can know all the math in the world, but if you can't communicate it to anyone with precision, your knowledge is useless. So at the upper levels, there is a huge emphasis on being able to write logical arguments in the form of proofs. Without the ability to write logical proofs, you can't even construct an argument that will convince yourself.
posted by charlie don't surf at 8:58 PM on November 1, 2013 [2 favorites]

I was always bad at math in school and these questions make perfect sense to me. Apparently I was born too soon.
posted by interplanetjanet at 9:08 PM on November 1, 2013 [1 favorite]

Sure, it's different than how I learned math, but from my sample size of one, it seems to be doing a great job.

It does seem to me to boil down to "this is different and therefore it is bad." Well, the way you learned math as a kid? A lot of kids never really learned much math at all, eventually got passed through high school barely able too add and subtract, never had a lot of career options that required better math skills. The way we all did it as kids was not perfectly adequate, so something not resembling what we did as kids is probably a requirement for finding a way of teaching it that actually works.
posted by Sequence at 9:13 PM on November 1, 2013 [1 favorite]

Yeah, five-year-olds aren't exactly starting algebra the next year.

I can't tell from the context of your comment whether this is sarcasm or actually meant to say, "Yeah, 5 year olds aren't ready to learn the word and concept of 'variable' as such."

In case it was sarcasm, though, I can tell you that the use of x, y, z in place of the unknown quantity appears as early as Grade 3 in some books. The term "variable" is taught at least at Grade 5, possibly Grade 4.

Many other countries' math standards start with algebraic concepts much, much earlier than we generally do in the U.S. There is really no reason not to lay a groundwork for "unknown quantity" in first grade.
posted by like_a_friend at 9:20 PM on November 1, 2013 [2 favorites]

Yeah, five-year-olds aren't exactly starting algebra the next year.

I can't tell from the context of your comment whether this is sarcasm or actually meant to say, "Yeah, 5 year olds aren't ready to learn the word and concept of 'variable' as such."

It's more like 'why don't we start five-year-olds off with the most easy, understandable language possible and gradually phase them in to concepts like unknowns as necessary?'

This test makes it look like five-year-olds are being angled towards algebra before they even have a basic understanding of arithmetic. If the kid is having trouble with 4 + 6 (question 7), what the crap are we doing trying to subtly introduce things like unknown and known parts?
posted by Quilford at 9:27 PM on November 1, 2013

I guess a parent in Texas thought that "dice" is synonymous with "gambling,"

s/parent/member of the State Board of Education/

You will never find a more wretched hive of scum and dumbfuckery.
posted by ROU_Xenophobe at 9:28 PM on November 1, 2013 [1 favorite]

The thing is, teaching kids weird terminology will do them no favors when they enter a system that doesn't use that terminology -- which could be as soon as middle school.

My armchair layabout opinion is, simply, instead of offering problems like "2 + 3 = (blank)", just present them like "2 + 3 = X" Then when it comes time for Algebra, OMG, that 'X' they put all along, it can come somewhere other than the end MIND BLOWN.
posted by JHarris at 9:35 PM on November 1, 2013 [6 favorites]

Everything on this test addresses something the lay public has been complaining about in regard to how math is taught to children. This is the better, more intuitive, more hands-on, more practical, more sensible, more reading-intensive, more reasoning-based math you wanted.

The problem is that not all of us are the lay public, but all of our children must learn this bullshit, even if they are in fucking private school. And count me in as another parent who tried teaching my kid some math for her homework and was told "no, mom, the teacher really does want me to solve these problems by making boxes of squares rather than actually doing the math."

Also, the idea that not all children are average thus they all have to learn "number sentence" instead of equation is just pandering to the lowest common denominator. Or, sorry, the "tiniest get-along buddies" or whatever they happen to be calling that now.
posted by corb at 9:49 PM on November 1, 2013 [5 favorites]

I should disclaimer that I live in New York and so this is personal for me, having a school age child.
posted by corb at 9:49 PM on November 1, 2013 [1 favorite]

Use cubes to solve.

I think Analysis Services is probably beyond most primary school kids.
posted by pompomtom at 9:58 PM on November 1, 2013 [1 favorite]

Use cubes to solve. Choose the number sentence that shows the story. Faiza has 3 purses. She gives 2 away as gifts. How many purses does Faiza have left?

3 - 2 = x

3 = x + 2

3x^2 + x - 1 = x^3 + 2x^2 + x - 1

x^3 - x^2 + x - 1 = x - 1

Now that we have our number sentence in cubic form, for any number sentence ax^3 + bx^2 + cx + d = 0, we have three roots:

x1 = -b/(3*a) + cbrt(-2*b^3+9*a*b*c-27*a^2*d + sqrt[4*(-b^2+3*a*c)^3+(-2*b^3+9*a*b*c-27*a^2*d)^2])/(3*cbrt[2]*a) + cbrt(-2*b^3+9*a*b*c-27*a^2*d-sqrt[4*(-b^2+3*a*c)^3+(-2*b^3+9*a*b*c-27*a^2*d)^2])/(3*cbrt[2]*a)

x2 = -b/(3*a) +(-1+i*sqrt[3])/2*cbrt(-2*b^3+9*a*b*c-27*a^2*d+sqrt[4*(-b^2+3*a*c)^3+(-2*b^3+9*a*b*c-27*a^2*d)^2])/(3*cbrt[2]*a) +(-1-i*sqrt[3])/2*cbrt(-2*b^3+9*a*b*c-27*a^2*d-sqrt[4*(-b^2+3*a*c)^3+(-2*b^3+9*a*b*c-27*a^2*d)^2])/(3*cbrt[2]*a)

x3 = -b/(3*a) +(-1-i*sqrt[3])/2*cbrt(-2*b^3+9*a*b*c-27*a^2*d+ sqrt[4*(-b^2+3*a*c)^3+(-2*b^3+9*a*b*c-27*a^2*d)^2])/(3*cbrt[2]*a) +(-1+i*sqrt[3])/2*cbrt(-2*b^3+9*a*b*c-27*a^2*d-sqrt[4*(-b^2+3*a*c)^3+(-2*b^3+9*a*b*c-27*a^2*d)^2])/(3*cbrt[2]*a)

However, note that our cubic number sentence is not quite of the desired form (x-1 on the rhs instead of 0). However, once we solve for lhs=0, we may manually seek the solution from the set such that it also satisfies rhs=0. After a few elementary number sentence stories, it can be shown using cubes that our final number sentence is that Faiza has (-1/2 + i*sqrt(3)/2)^3 purses remaining, which sounds very glamorous indeed.
posted by chortly at 10:22 PM on November 1, 2013 [26 favorites]

Show off.
posted by JHarris at 10:24 PM on November 1, 2013

At this rate, we'll be getting to basic Galois theory in no time.
posted by Nomyte at 10:46 PM on November 1, 2013 [3 favorites]

If the kid is having trouble with 4 + 6 (question 7), what the crap are we doing trying to subtly introduce things like unknown and known parts?

I don't follow. Every unsolved equation involves known and unknown parts. All this structure is doing is articulating what the kid is mentally tallying no matter how the kid solves the problem: what do you know (I have four of a thing and six of a thing), what do you need to know (how many things do I have)?

The terminology isn't some weird jargony mathspeak, it's actually telling students what an arithmetic problem is made of and what it is trying to accomplish, in plain English. Which apparently strikes many adults as totally fucking ridiculous, but I think that might be mostly because we have had decades to internalize this concept.
posted by like_a_friend at 10:47 PM on November 1, 2013 [9 favorites]

If you google for "six-sided number cube," you will find lots of children asking for homework solutions on Yahoo Answers.

Okay, this I really don't understand. When I was a kid, there were ten numbers. Why isn't it a pentagonal trapezohedron?
posted by RobotHero at 11:10 PM on November 1, 2013 [1 favorite]

AskMetafilter: Use cubes to solve.
posted by salishsea at 11:21 PM on November 1, 2013 [1 favorite]

Why isn't it a pentagonal trapezohedron?

I think maybe children in elementary school are a bit too young to learn about shining trapezohedrons and unknowable geometry.
posted by Pyry at 11:28 PM on November 1, 2013

If the kid is having trouble with 4 + 6 (question 7), what the crap are we doing trying to subtly introduce things like unknown and known parts?

I don't follow. Every unsolved equation involves known and unknown parts. All this structure is doing is articulating what the kid is mentally tallying no matter how the kid solves the problem: what do you know (I have four of a thing and six of a thing), what do you need to know (how many things do I have)?

Forget that sentence.

The emphasis should be on basic arithmetic, counting and the number system. Not on algebra. Instead of using terms like 'known part' and etc., questions should spell out what they're asking clearly and carefully so that these crucial foundations in arithmetic and counting can be laid. There's no point even considering algebra before then.
posted by Quilford at 11:30 PM on November 1, 2013 [1 favorite]

I don't get the hatred for "number sentence". Equations are sentences that (usually) involve numbers. Many of my students struggle with scientific writing because they don't get that equations are sentences. I would love it if students learned early that equations aren't this weird thing dropped on them from otter space, but just another way of using language. It seems reasonable to introduce the concept of an equation using words the kids likely already know. Is it really that hard for a parent to figure out what a number sentence is?

It also seems great to me that students start learning in first grade that math is about ways of representing knowledge (unknown part, representing numbers with squares to have a visual representation of arithmetic) instead of just algorithmic operations with numbers. This could help me avoid situations like the nightmarish conversation I had with a student who complained that the content of my college course "isn't really math" because "math is about numbers" but in class "everything on the board is letters".
posted by medusa at 11:33 PM on November 1, 2013 [5 favorites]

What we have here is a failure to communicate.
posted by St. Alia of the Bunnies at 11:47 PM on November 1, 2013 [5 favorites]

It's pretty odd to see how many people who in all other contexts will complain about how boring and useless their maths education was become fervent defenders of the status quo when confronted with anything different.
posted by Proofs and Refutations at 12:21 AM on November 2, 2013 [2 favorites]

Back in the "good" old days when I was in first grade, arithmetic was taught with a ruler to the hand or a slap to the head. Crying over homework earned a spanking. Didn't learn much math but learned not to show any emotion about it.
posted by a humble nudibranch at 1:26 AM on November 2, 2013

The word for the entity is 'equation'. 'Dumbing it down" doesn't help anyone.
posted by mikelieman at 1:37 AM on November 2, 2013 [1 favorite]

Can you say 'equation', boys and girls? I knew you could!
posted by mikelieman at 1:38 AM on November 2, 2013 [2 favorites]

And the salient point of all this is, "If a child cannot multiply, nor read, why bother continuing to teach them more content **dependent** upon those two critical, lacking skills."

Take any 4th grade class, give them a blank sheet of paper, and have them write out the times tables from 1 x 1 = 1 to 12 x 12. See how far they get in five minutes ( they *should* complete it without pause) , then go crawl into bed with a bottle of bourbon and cry...

The kids don't get the skills in third grade.

The 3rd Grade assessments don't catch the deficiency.

The 4th Grade teachers do catch the lack of skills, but...

They're too overloaded implementing the new content, they can't do the needed remedial work.
posted by mikelieman at 1:43 AM on November 2, 2013 [4 favorites]

The issue isn't that the kids aren't doing worksheets in class with this material. This issue is that if a kid is daydreaming while they should be doing the worksheet, the teachers are too busy with the next worksheet that they can't diagnose the deficiency at the time of occurrence, and if the kid is even remotely facile at 'gaming the system', then they'll be able to 'fake it' sufficiently for them to 'pass' the 'assessment tests'.

While being unable to multiply two single digit numbers without issue.

I suspect this 'falling through the cracks' and 'gaming the system' were things which only precocious children had to worry about in the past -- until the teachers got so overloaded... Now the cracks are so large it seems that ALL the kids are falling through them.
posted by mikelieman at 2:05 AM on November 2, 2013 [1 favorite]

I guess a parent in Texas thought that "dice" is synonymous with "gambling," so the word is never used in textbooks.

I guess I'm a bad parent. I taught my eight-year-olds to play penny-ante poker, first with my money and then with their allowances. We play stud variations and two kinds of hold 'em, and they love it, as do I.

My two favorite outcomes:

- When my son went bust and lost 5 cents of his own money, for the first time. He got very upset with himself, and said "I can't believe I wasted all that money for nothing!" A lesson much more cheaply learned now than later.

- When my daughter, who never folds -- a fact that I'd pointed out more than once -- was staring at an all-in call, knew she had a bad hand, paused, sighed deeply, announced resignedly "well, I am The Girl Who Never Folds", went all-in...and took the whole pot.
posted by davejay at 2:31 AM on November 2, 2013 [20 favorites]

- When my daughter, who never folds -- a fact that I'd pointed out more than once -- was staring at an all-in call, knew she had a bad hand, paused, sighed deeply, announced resignedly "well, I am The Girl Who Never Folds", went all-in...and took the whole pot.

Now that is a kid who was raised right.
posted by Elementary Penguin at 3:21 AM on November 2, 2013 [1 favorite]

First grader Me would have gotten really pissy about the lack of space allotted for 9) Write a subtraction story for... It probably would have made me cry and give up.
posted by jwhite1979 at 5:35 AM on November 2, 2013

I'm going to start referring to actual sentences as "word equations".
posted by Lentrohamsanin at 6:13 AM on November 2, 2013 [6 favorites]

An equation is a kind of sentence, a special kind that asserts that one quantity is equal to another. Making this fact explicit isn't "dumbing down," it's putting weight on an important mathematical point that students often miss.
posted by escabeche at 6:24 AM on November 2, 2013 [8 favorites]

And this stuff about addition and subtraction and multiplication tables? Unless the public school in question is radically different from my kid's public school, they are teaching those too! My son has worksheets that look a lot like his, and he also has to do speed tests for addition and subtraction within 20; he has to get them all right within 3 seconds each in order to move on. There are obviously big controversies about curriculum but the people who design them are not idiots and they understand that computational fluency is a critical skill. Here, you can even look at the relevant section of the Common Core standards for 1st grade, it's right there, as well as pre-algebra skills like "Determine the unknown whole number in an addition or subtraction equation involving three whole numbers." which are tested on the worksheet in the link.
posted by escabeche at 6:32 AM on November 2, 2013 [3 favorites]

An equation is no more a sentence than a computer program is, or a genetic sequence. The word "sentence" in English refers exclusively to sequences of words with grammatical structure and it is doing these kids a disservice to use it in this nonstandard way for no good reason.
posted by enn at 6:36 AM on November 2, 2013 [5 favorites]

I don't want to make this whole thing about this one nomenclatural question, but are you saying that

"One plus two is equal to three"

is a sentence but

1+2=3

is not, even though they are pronounced exactly the same? Or are you saying that "One plus two is equal to three" isn't a sentence, even though it's a sequence of words that makes an assertion?
posted by escabeche at 6:43 AM on November 2, 2013 [5 favorites]

It is using it in a nonstandard way to emphasize the fact that the equation "4(x-3) = 2x+5" means the exact same thing as "Four times the difference of an unknown quantity and three is the same total as five more than two times that same unknown quantity," just written compactly.

Or what escabeche said.
posted by Elementary Penguin at 6:45 AM on November 2, 2013

I don't think there's anything wrong with pointing out that 'equations' in math class are analogous to 'sentences' in english class since there both -- in theory -- atomic entities of coherent thought.

But I don't think it serves the children to rebrand all the content under a 'new' cognitive framework while missing basic skills.

Drills are IMPORTANT. All this theory is useless if you need to STOP WHAT YOU'RE DOING when doing more complicated math, and work out 6 x 7 on a piece of scrap paper, simply because you never actually tested if it was committed to memory...
posted by mikelieman at 7:38 AM on November 2, 2013 [3 favorites]

> Yeah, five-year-olds aren't exactly starting algebra the next year

Mine did, playing Dragon Box.
posted by The corpse in the library at 7:43 AM on November 2, 2013 [3 favorites]

> Drills are IMPORTANT. All this theory is useless if you need to STOP WHAT YOU'RE DOING when doing more complicated math, and work out 6 x 7 on a piece of scrap paper, simply because you never actually tested if it was committed to memory...

My daughter's school uses these Pearson work sheets, and they also spend time doing drills. They call it "math facts" but that's what it is. She isn't up to 6 x 7 yet, but she's only in 2nd grade; I don't remember learning multiplication tables (which we learned by chanting them as a class) until I was 10 or so, so I'm okay with that.
posted by The corpse in the library at 7:45 AM on November 2, 2013 [1 favorite]

this is one of the the actual common core standards that a 1st grader should meet.

CCSS.Math.Content.1.OA.A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.1

And that's what that assignment seems to be testing for. Not at all confusing.

Nor does that seem to be an actual common core test since the organizations that are tasked with developing them are using computer adaptive models that aren't even meant to be released until the 2014-15 school year.

Valerie Strauss is indeed not a great blogger.
posted by brookeb at 7:50 AM on November 2, 2013 [3 favorites]

Great. Elementary math tests written by the people who brought you impossible literacy tests. My favorite part is question 12, where none of the "subtraction sentence" answers actually contain subtraction.
posted by workerant at 8:48 AM on November 2, 2013 [1 favorite]

I don't get the hatred for "number sentence".

This is different from my vague, garbled recollections of how I was taught 20/30/40-odd years ago, therefore it is stupid. Also I never really learned math, not down to my bones, so anything presented in a slightly different way confuses the hell out of me, but my reaction is not that maybe kids these days should use a method that's been tested to actually teach math better, but should do things in the way that didn't actually teach me math because that way I don't feel confused and embarrassed.
posted by ROU_Xenophobe at 8:51 AM on November 2, 2013 [3 favorites]

I don't want to make this whole thing about this one nomenclatural question, but are you saying that "One plus two is equal to three" is a sentence but 1+2=3 is not, even though they are pronounced exactly the same?

I don't pronounce them the same. I can think of several different "pronunciations" for your trivial example; for something even moderately more complex, I could come up with dozens or hundreds of variant "pronunciations." But that doesn't matter anyway. I could come up with a contrived "pronunciation" of a line of C code that happens to also be an English sentence. That doesn't make it a sentence.

A language is defined by its community of speakers, not semantic arguments about what you think a word should mean. It's very clear from this thread that many English speakers find the phrase "number sentence" nonsensical and self-contradictory.
posted by enn at 9:01 AM on November 2, 2013 [1 favorite]

Two six-sided-number-cubes are "dice".

One six-sided-number-cube is a "die".

I'll bet that's the forbidden word.
posted by Cookiebastard at 9:04 AM on November 2, 2013 [1 favorite]

What exactly is self-contradictory about "number sentence?" Can sentences not be about numbers?

They can, but sentences are not generally described with their topics used as adjectives directly modify the word "sentence." The phrase "*dog sentences" is just as silly. There are sentences about dogs, and that is exactly what people call them: "sentences about dogs." Nobody calls them "*dog sentences."

Can numbers not be expressed as a sentence??

No, numbers cannot be expressed as a sentence. That's the purpose of having numbers, to express things that cannot be expressed well or at all in words. What would that even mean? What sentence is π, or the set of positive integers?

Who wins if the US continues to teach math poorly?

I don't give a fuck how they teach math. I do care that they they teach the actual language as it is spoken. The long history of children being forced to learn idealized, "more logical" forms of languages that don't correspond to the living language has been very destructive.
posted by enn at 9:24 AM on November 2, 2013 [5 favorites]

The object representing the whole six items in question 1 is obviously a measuring cup (to me:-P), which will be a perhaps useful visual metaphor for proportionality and fractions when sudents completing the assignment in the FPP get to these concepts in a year or two. It's not the image I would have used in that particular question, but, [shrug], it doesn't seem horrible to me either.

The more interesting question to me is, particularly given the number of math educators in this thread, can we diagnose some potential or likely sources of confusion or conceptual misunderstandings that would lead to this particular student's set of answers to the questions?
posted by eviemath at 9:28 AM on November 2, 2013

I attended first grade in 1981. We used the phrase "number sentence". For those that find this sort of thing difficult, that means this terminology was in use 32 years ago.* I remember sometime around, I don't know, third or fourth grade, encountering the word "equation" for the first time. "What's an equation?" "It's a number sentence." OK, that took two seconds. Like, I don't feel as though having the phrase "number sentence" in my brain took up such significant cognitive real estate that I was unable to immediately grasp the terminology "equation" and switch to it when we began using it.

FWIW I found the test, while ugly, completely straightforward and easy. Don't really get all the keening and wailing going on about it. (But I understand the "number sentence" debate even less.)

*While I consider my education to have been pretty bog-standard public schooling, I was actually in the Department of Defense Dependents Schools system, so maybe we were actually unknowingly some kind of DARPA project and that's why the civilian populace is only now reaping the rewards of the number sentence.
posted by Hal Mumkin at 9:55 AM on November 2, 2013 [5 favorites]

No, numbers cannot be expressed as a sentence. That's the purpose of having numbers, to express things that cannot be expressed well or at all in words. What would that even mean? What sentence is π, or the set of positive integers?

That's right! And this is why I am so excited, as a working teacher of mathematics, that kids are being exposed to the idea of "number sentence" early.

Here's the thing I try to convince my students of, that they have had trained out of them at an early age...

What you write down, when you write your work doing a problem, is *not* some random collection of jottings. It should be communication, just like if you were writing a paragraph! Everything you write down should be pronounceable, in English (or your language of choice). This means, in particular, that your mathematical sentences should have verbs!

And the main verb? An equals sign.

Students insist on writing chains of equalities without the equals sign, just in consecutive rows or (worse!) just randomly next to each other, I presume because no one taught them that they should be reading what they write to themselves in their heads! But it gets in the way of actually understanding why they're writing down what they're writing.

Think about the sentence "the integral from 1 to 4 of x-squared integrated with respect to x is equal to the function one-third x-cubed evaluated from x = 1 to x = 4, which is equal to one-third of 4-cubed minus one-third of 1 which is equal to 63/3, which is equal to 21".

Ok, it's a bit of a run-on sentence, but the point is that the reason we use numbers and symbols in mathematics is *not* because there's some mystical thing we're doing with numbers that cannot be communicated with language, it's just that it's more compact notation. But the words should still be there in your mathematical strings of equations!

Taking a scenario like
"Ilana has 5 pieces of candy and Matilda has 7 pieces of candy. How much candy do both girls have together"

and being able to translate it into the number sentence

5 + 7 = 12

which is read "five plus seven is equal to twelve"---note the verb!

is a super-useful skill! It foreshadows the development of algebra: it's easy to transition into
"Ilana has 5 pieces of candy. How many pieces of candy does Matilda have if both girls have a total of 12 pieces of candy?"

which then turns into 5 + M = 12

Which then students are able to do (albeit with blanks, instead of named variables) in first or second grade! So you now have students engaging with really quite sophisticated mathematical concepts---functional notation! basic algebra!---in very early grades. Mathematics is *not* arithmetic. Drilling on basic arithmetic facts is not thinking mathematically. But what I am so excited about in many of these new curricula for early grades (Everyday Math, what I've seen of the Common Core materials) is that they *do* encourage actual mathematical thinking, even as they are teaching the basic arithmetic skills.
posted by leahwrenn at 9:59 AM on November 2, 2013 [10 favorites]

"2 + 2 = 5" or "3 and 5 hugged 11" are number sentences and given the meaning of the words "number" and "sentence" would appear to me to be just as valid as "I tripped and fell up into the sky".

They are not however equations, and it might be nice to not confuse children by using simple words incorrectly.
posted by crayz at 10:16 AM on November 2, 2013 [1 favorite]

Well, shit, 3 + 5 > 7 is also not an equation, but I think it counts as valid.
posted by Hal Mumkin at 10:18 AM on November 2, 2013 [3 favorites]

Notwithstanding my previous comments, I'm actually quite sympathetic to the "number sentence" locution, for similar reasons to those already mentioned here: it avoids combining a new and perhaps scary notation with a new and (perhaps already, by some pre-existing familiarity) scary term. More importantly, it does stress that this string of symbols can just be read out like a string of words can, and that this is an important step in learning how to read, understand, and manipulate such things. "Number sentence" might not be the best locution for the job, but it's a decent one, irrespective of whether the string of words produced is officially a grammatical sentence.

What drove this point home for me was when I was teaching an introductory math class for graduate students. Often one does stuff on the board then asks what the answer is, or students have a question about some specific mathematical issue. Either way, the student needs to be able to verbally communicate things like: (2+x^2)^3/3 or 3sin(x^2+1)/n dx. Even though most of them had had math through calculus, they hadn't learned how to actually speak these sorts of things, and doing so I think helped all of us not just to communicate, but to think better mathematically.
posted by chortly at 10:32 AM on November 2, 2013 [1 favorite]

The long history of children being forced to learn idealized, "more logical" forms of languages that don't correspond to the living language has been very destructive.

This is not OK. Like Jim Crow "literacy" tests, this seems like it is more designed to distinguish between an in group and an out group than evaluate real knowledge. If your first grader didn't go to the trendy school where they use neologism jargon like "number sentence," he fails.

So, there are two issues here.

First: is an equation a sentence? (No, a number in and of itself, like pi or three, is a word, not a whole sentence. It is better to go back to the original framing and compare equations and sentences. Or what leahwrenn said, on preview.) If I knew Russian and wanted to write down "I am happy" in Russian (apologies, I do not speak Russian myself), would it not be a sentence if I wrote it in the Cyrilic alphabet versus if I wrote it in (some transliteration to) the Latin alphabet? What if I translated to a language that is (or has in the past been) commonly written in a non-alphabetic script, eg. either a consonant-based alphabet, a syllable-based one, or something even further from a "true alphabet" that is phoneme-based? Mathematical notation is just another script. It's not a phoneme-based alphabet; the symbols stand for full concepts much like more complex syllable-based alphabets. But mathematical notation is just a shorthand for (certain, technical) things that can be expressed in any full language used for everyday communication. Every mathematical symbol has a name that we can say aloud as a word, which has a meaning, and there are grammatical rules for how we string these words together. Mathematical notation was developed in part out of laziness - it's shorter and quicker to write 2 + 3 = 5 than two plus three equals five, and quicker to read if you are familiar with standard mathematical notation. In some cases this brevity obscures the meaning, and in some cases it can help clarify meaning, eg. by organizing the information presented in a long and complicated word problem. But yes, an equation is a sentence.

And one of the major causes of student frustration and difficulty as they get farther along in math that those of us who teach math see is students not understanding this connection very well. Some students will pick up on this idea implicitly, no matter how they've been taught basic arithmetic. But this is far from universal, and it's more helpful to teach people to think of mathematical notation in this way, as a parallel language, initially, because unlearning incorrect concepts is way harder than learning new concepts. So when students don't learn to make the sort of conceptual connections between things expressed in mathematical terminology and things expressed in their everyday language of communication (English, in the case of the FPP link) when they are first learning arithmetic, and instead take arithmetic statements and equations as disconnected facts to memorize that don't have any underlying structure or reason behind them, they form certain habits or approaches to learning math that are very counterproductive yet hard to unlearn and change later on.

"2 + 2 = 5" or "3 and 5 hugged 11" are number sentences and given the meaning of the words "number" and "sentence" would appear to me to be just as valid as "I tripped and fell up into the sky".

They are not however equations, and it might be nice to not confuse children by using simple words incorrectly.

Technically, 2+2=5 is an equation. It satisfies mathematical grammar rules, and asserts that one algebraic expression is equal to another. It happens to be a false equation, under any standard set of arithmetic axioms, and thus just as valid an equation as "I tripped and fell up into the sky" is as a sentence. But it is an equation, just as "I tripped and fell up into the sky" is a sentence.

Second, is using the term "number sentence" any more or less obscure than using the term "equation"?

The argument seems to be that students will somehow naturally learn and understand precise technical terminology from the area of mathematics, or that the meaning of "equation" is not also something that students need to be taught, just as they would need to be taught the meaning of "number sentence"? Certainly "equation" is a more precise, technical term. This sort of precision in the terminology used to describe mathematical concepts is important farther along, when students get to subjects like calculus and beyond, or when they get far enough along in developing their mathematical (abstract/quantitative/logical) reasoning and argumentation (i.e. proof) skills that they need to worry about mathematical rigor. But describing the technical terminology of mathematics as less logical, more of a living language, as part of an all-encompassing knowledge base that won't distinguish between in- and out-groups, as avoiding jargon... while this point of view excites and pleases me somewhat as a mathematician, these are not the usual complaints levied against technical mathematical terminology. Students would have to learn a definition of equation just as they would have to learn a definition of number sentence. This seems equivalent to me.

Additionally, throughout mathematics education, we refine and add to the initial definitions of mathematical terminology and concepts that students are taught. (And there are some good reasons for this: empirically at least, when educators have attempted teaching mathematics carefully and rigorously from first principles, eg. the Bourbaki books, it hasn't been a particularly effective pedagogy.) So introducing the concept of equations as number sentences, then later adding the terminology "equation", is a quite minor addition to the amount of refinement that students will already experience.

Given that what an equation is has to be defined and taught to students, and involves telling students the requirement that the verb involved be "equals" (or any of it's variants, like "is"), adding a similar requirement to the definition of "number sentence" to exclude examples like "3 and 5 hugged 11" doesn't seem any more involved to me.
posted by eviemath at 10:35 AM on November 2, 2013 [7 favorites]

As my tenth grade math teacher would say: I'm bad with numbers but great at math.
posted by (Arsenio) Hall and (Warren) Oates at 10:43 AM on November 2, 2013

Sounds like being taught about "number sentences" will prepare the youth of today for the jargon of tomorrow. Who knows what kind if impactful leaning in they might achieve.
posted by Lesser Shrew at 10:57 AM on November 2, 2013 [2 favorites]

Math always involves jargon and neologism. "Quotient" is jargon. The goal is to choose useful jargon–useful in a pedagogical sense. People seem to be objecting to it here because it confuses them, reading it now. But learning it in these terms for the first time would be no more confusing than whatever other words might be used, and at the end, students will be less likely to think that a mathematical equation is somehow not exactly isomorphic to a declarative sentence. Sorry, but I think that's a fundamental misunderstanding of what mathematics is, and a lot more worrying than not knowing the multiplication tables.

I teach physics. A major predictor for success is familiarity and comfort with math as a language for expressing ideas. It is amazing how many students who see themselves as "bad at math" suddenly excel at physics once they realize that equations are just another way of writing down an idea. That understanding is what the "number sentence" construct is designed to instill.
posted by Pre-Taped Call In Show at 11:41 AM on November 2, 2013 [10 favorites]

Why isn't it a pentagonal trapezohedron?

I think maybe children in elementary school are a bit too young to learn about shining trapezohedrons and unknowable geometry.

If they don't deal with bleak unfathomable realms in school, they'll be completely unprepared for the workforce.
posted by RobotHero at 11:44 AM on November 2, 2013 [3 favorites]

Regarding the "Jim Crow" comment. The point is not to check their understanding of the phrase "number sentence". You are thinking about it backwards. The point of the phrase "number sentence" is to frame math instruction in a way that helps students understand what they are actually *doing* when they are doing arithmetic.
posted by Pre-Taped Call In Show at 12:00 PM on November 2, 2013 [1 favorite]

This is not OK. Like Jim Crow "literacy" tests, this seems like it is more designed to distinguish between an in group and an out group than evaluate real knowledge. If your first grader didn't go to the trendy school where they use neologism jargon like "number sentence," he fails.

1) this is a national curriculum that will soon be taught in all schools, private or public. So...sorry, theories about trendy schools hiding all the secret math code words don't apply here.

2) What Pre-Taped Call-In Show said, and also to repeat for like the 24th time that this is homework, not a test. Students working on this worksheet have been taught the things that are on it. The WaPo blogger calls it a test because the word "test" gets everyone immediately and irrevocably blindly furious and because she's a blogger trying to get hate-clicks.
posted by like_a_friend at 12:20 PM on November 2, 2013 [3 favorites]

"Jim Crow" is the education version of Godwining.
posted by Apropos of Something at 12:49 PM on November 2, 2013 [1 favorite]

The long history of children being forced to learn idealized, "more logical" forms of languages that don't correspond to the living language has been very destructive.

I never thought of all this core-curriculum math as 'Math Esperanto", but in that context the gymnastics involved does make quite a lot of sense..
posted by mikelieman at 1:05 PM on November 2, 2013

See how far they get in five minutes ( they *should* complete it without pause)

Um... according to who? I agree that having a basic understanding of math provides many benefits later in life, as mental apparatus for understanding day-to-day things, understanding current events, etc. But how much of that is really necessary is debatable.

You don't actually need to have that much practice with basic arithmetic, in this age of computers, to do higher math, which is more about how values relate and change than 7 + 4 = ?.
posted by JHarris at 1:19 PM on November 2, 2013

According to me. My point is that if you have to stop what you're doing to work out trivial 'math facts' when they're embedded n-levels deep in the problem you're working on, no-one did you any favors by letting you skip doing the actual difficult work of memorizing them. The 'context switch' from real problem solving to trivial arithmetic has a cost, too. And that cost adds up every time the context switch occurs.
posted by mikelieman at 2:37 PM on November 2, 2013 [2 favorites]

> If your first grader didn't go to the trendy school where they use neologism jargon like "number sentence," he fails

Heh. My daughter's Title 1 public school definitely isn't "trendy."
posted by The corpse in the library at 2:38 PM on November 2, 2013 [1 favorite]

I don't think 30 seconds to write down each in the series : 1x1 = 1 .. 12 x 12 = 144 is really too much of a challenge... That's two seconds per equation just about...
posted by mikelieman at 2:39 PM on November 2, 2013

The point of the phrase "number sentence" is to frame math instruction in a way that helps students understand what they are actually *doing* when they are doing arithmetic.

How does that help? As others have pointed out, you have to define what a "number sentence" is anyway so it's not like you're avoiding explaining the concept. And at some point you're going to have to teach the students that a "number sentence" is an "equation" so you're just adding an extra step later on.

Is there actual evidence that students perform better when you call equations "number sentences"? Not sarcasm; have they actually tested this or is it just another theory which will be tested in the field, except the field is every classroom in the USA?
posted by Justinian at 3:30 PM on November 2, 2013 [2 favorites]

have they actually tested this or is it just another theory which will be tested in the field, except the field is every classroom in the USA?

For anybody doing curriculum development, there's no winning here. Test too few places, and people wonder why it hasn't been tested more. Test too many, and people wonder why it hasn't been piloted yet. Test in too many disadvantaged schools, and people argue this untested idea's being forced on the poor. Test in too few disadvantaged schools, and people argue the solution is too one-size-fits-all.

During the sequester, we argued (rightly) that access to trials of experimental drugs for cancer patients should be inalienable. It's a shame we don't feel the same way about new educational techniques.
posted by Apropos of Something at 4:13 PM on November 2, 2013 [1 favorite]

Can't you test it in whatever the equivalent of a clinical setting is? Take 200 students, teach 100 with the new method and 100 with the old method and compare test results after instruction? I suppose it would be hard to control for teacher skill with only 1 teacher per sample...
posted by Justinian at 5:07 PM on November 2, 2013

Can't you test it in whatever the equivalent of a clinical setting is?

Do you have any idea of what a complicated, contentious, and downright acrimonious subject educational experimentation can be? It turns out that parents and community leaders are extremely averse to letting children act as experimental subjects. Everyone wants "proven," "scientific" teaching methods, but no one wants to be the guinea pig. And so we get educational psychology that works with very small samples, compromised designs, and sometimes tries to understand things from first principles by appealing to the writing of leading figures from the early part of the last century.

Seriously, it's a lot easier to pay participants to join a clinical trial than it is to test an experimental curriculum. To do the latter, you need entire classrooms, you need multiple classrooms to abstract away the individual teacher's unique contribution, you need the cooperation of the school system, you need parental consent… it's a nightmare.
posted by Nomyte at 5:35 PM on November 2, 2013 [5 favorites]

mikelieman: According to me.

Fair enough, and well said!

My point is that if you have to stop what you're doing to work out trivial 'math facts' when they're embedded n-levels deep in the problem you're working on, no-one did you any favors by letting you skip doing the actual difficult work of memorizing them.

Well, I'm not sure. I do some amount of computer programming, and it is true that having some things memorized has helped me out a lot (128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536). But I have also noted that, as my brain has become more bloated with miscellaneous information, that my recall of any specific part of it has slowed. That is purely anecdotal, of course, but it fits in with the nature of hashing functions, which (I presume) is basically what your brain uses to look up information. (It explains why you sometimes think of the wrong thing when you try to remember sometimes - there was a hash collision.) Well, anyway, it is true that basic arithmetic isn't a particularly bad thing to teach kids, although instant recollection seems overboard. To me.

People sometimes ask of what use is math in day-to-day life, in their seeking to state why it's not important that they, personally, don't know this stuff. I am not one of these people. But I do think that the basics of algebra are more useful, in day to day life, than the traditional mechanisms of manual calculation. Not that times tables aren't useful, but I can count the number of times I've had to do multiplication or division on paper in the past decade on my ~~twelve~~ ten fingers.
posted by JHarris at 5:56 PM on November 2, 2013

Part you want: Three-day Time Cube
Part you have: Educated stupid
posted by thelonius at 8:04 PM on November 2, 2013 [1 favorite]

have they actually tested this or is it just another theory which will be tested in the field, except the field is every classroom in the USA?

I've been to math ed talks on similar topics, though not this exact topic. My guess would be that there's probably been several studies, maybe more given that the term "number sentence" has been around for 20 or 30 years according to some of the other comments in this thread, though probably not ideal clinical model studies with test groups and control groups and giant sample sizes and double-blind collection and analysis of results and all that, for the reasons that Apropos of Something mentioned, as well as for the reason that there's not as much grant money available for funding educational research as there is for research that is likely to have direct commercial or defense applications. We could check this by, eg. going to scholar.google.com and doing a search on number sentences, which returns a list of mostly relevant research articles, whose abstracts should all be publicly available for perusal.
posted by eviemath at 8:37 PM on November 2, 2013 [1 favorite]

I'm going to start referring to actual sentences as "word equations".

And if you were thinking about the actual concepts, you'd realize not all word sentences are equations - we have a lot of different verbs. Actually, not all math sentences have to be equations either - you can have greater-than and less-than statements. (What are those usually called? Expressions?) I don't think there's anything confusing about saying number sentence. Maybe it will help some kids who just memorized and then forgot things actually grasp what's going on.
posted by mdn at 6:59 AM on November 3, 2013 [1 favorite]

"Backmapping" college-ready skills to first grade brains, without consulting early education specialists? Gott im Himmel. I understand some of what they're going for here, but this is mostly asinine.

It's as if they're rolling education back into the era before we were able to test separately for verbal skills versus math skills. Many of those questions are poorly communicated - somebody with an already shaky verbal skill set is also going to flunk the math test!
posted by Sticherbeast at 8:46 AM on November 3, 2013 [1 favorite]

Even with resources, we haven't mentioned how insanely difficult it is to do random assignment in American schools. Kids are never assigned randomly to classes, no matter what districts say: principals and administrators and teachers all weigh in on where kids go. Then, there's no hope of blindness: it's pretty clear to everybody what the treatment is and what the control is. From there, teachers naturally talk, and kids in the control will get some percentage of the treatment, and you're totally screwed up.

What ed researchers are more likely to do as a result is use propensity score matching, a technique which tries to identify schools which are very similar to each other to function as treatment and control. Which works relatively well ... except, of course, it can only match on things we can and do measure systematically. For the reasons Nomyte identifies, you're also unlikely to push your treatment school into being guinea pigs as much as you look for a school with a high propensity score match that has already implemented the curriculum you're interested in. And in those environments, of course, level of participation in the treatment is all over the map.

So, long story short, we get close to experiments: but not without intrinsic ethical issues, enormous budgets we don't routinely have, and the caveats that tend to always accompany science that doesn't happen in labs.
posted by Apropos of Something at 9:08 AM on November 3, 2013

> "Backmapping" college-ready skills to first grade brains

The notion of an equation as a symbolic way to write a declaration of fact is far from a "college-ready skill". It is utterly fundamental to all math and most science and yet as this thread demonstrates it is extremely widely misunderstood.

> without consulting early education specialists

You think the common core was developed without consulting early education specialists?
posted by Pre-Taped Call In Show at 9:40 AM on November 3, 2013 [2 favorites]

BTW I'm not defending this particular worksheet which I agree is poorly constructed.
posted by Pre-Taped Call In Show at 9:42 AM on November 3, 2013

The notion of an equation as a symbolic way to write a declaration of fact is far from a "college-ready skill".

There are appropriate and inappropriate (and satisfactory and unsatisfactory) ways to teach and test these kinds of skills. This test does not appear to be succeed on all fronts.

You think the common core was developed without consulting early education specialists?

From TFA: "There is no evidence that early childhood experts were consulted to ensure that the standards were appropriate for young learners." This refers specifically to these specific "college-ready skills" being so "backmapped." I'm sure that early education specialists must have been involved in some ways with the Core Curriculum, but we're talking about this specific idea's implementation.

Another source: my wife is an elementary school teacher in NYC, so this was all old-ish news to her (and to me, indirectly, as a result).
posted by Sticherbeast at 9:46 AM on November 3, 2013

Late to the party: As noted, #1 is comparing cookies to a cup of something that is "6." It also uses an odd term (what you know) with another odd term (whole). Doesn't "what you know" apply to "whole" also?

#2 uses odd iconography. I'm guessing this was from some mandatory "teach to the test" curriculum? And how do "jars" apply to the odd 3-d squares in the icon boxes? What if someone checked the correct answer, but didn't fill in circles/squares/numbers in that icon representation?

#3 Says "use boxes." What boxes? I don't see no stinkin' boxes? So how is this answer correct?

I also notice that the old "Dick and Jane" names have now been universally disdained in favor of random world ethnic names. Still strikes me as odd...and I guess I'm not great at math because I tend to get distracted by things like looking for boxes that aren't there, comparing cookies to cups, and wondering who or what "Faiza" might be....
posted by CrowGoat at 9:50 AM on November 3, 2013

I also notice that the old "Dick and Jane" names have now been universally disdained in favor of random world ethnic names. Still strikes me as odd...

Nothing odd about it in New York. Having only Dick and Jane names would be about as far from the everyday experience of students, their families, and their classmates and friends as it would be to give everyone in math problems Finnish or Basque names.
posted by ROU_Xenophobe at 10:10 AM on November 3, 2013 [1 favorite]

We had non-Dick, non-Jane names back in 1980's Schenectady County, (Upstate) NY, when I was in 2nd grade. Just about every single person was named Alejandro or Carmen, as I recall. It wasn't even diverse - it was just that Dick and Jane had been replaced by Alejandro and Carmen.

Either way, I don't know that many people, even white people, let alone children, named Dick or Jane.
posted by Sticherbeast at 10:15 AM on November 3, 2013

Sticherbeast, agreed, it's a badly written and confusing worksheet (not a test). What I object to is the out-of-hand rejection of what seem to me to be fairly good, or at least not obviously bad, ideas. In fact, one of those fairly good ideas is the idea of back-mapping from college-level skills. As others have mentioned, some very deep misunderstandings don't get caught by standardized tests. Nor are they detected by overworked teachers who in some cases may also lack subject knowledge, especially for mathematics. Those problems do, however, become apparent at college level. Shouldn't curriculum designers try to prevent those problems at the level where the subject is originally taught?

TFA refers to "back-mapping" in a way that suggests the new curriculum was designed by reading a college syllabus and then winging it from there. It's pretty obviously a bit deeper than that, even just from reading the .ppt they link to. Furthermore, I read TFA's reference to "no evidence" of ECE expert involvement as meaning no evidence cited in the .ppt, which is wrong in any case, but it's clear that there was ECE expert involvement in the development of the curriculum.

Incidentally, the phrase "number sentence" does not actually appear in the NYSED common core. "Create a story context" does. I imagine that will set off mefites' woo detectors even worse...
posted by Pre-Taped Call In Show at 10:25 AM on November 3, 2013 [1 favorite]

have they actually tested this or is it just another theory which will be tested in the field, except the field is every classroom in the USA?

Yes, these pedagogical systems are extensively tested. But I want people to consider what is the issue here: human experimentation. There are rigorous protocols for human experimentation, but then, every teacher is pretty much doing a continuous set of experiments on human subjects with inadequately rigorous methods. That's part of what this Common Core system is about, to develop teacher's skills so they can deliver a rigorous system of instruction that is scientifically proven.

Pedagogical methods can be difficult to test, and results difficult to interpret, since the issues are largely sociological and psychological. About the only thing that can be tested with arbitrary precision is achievement. That's what I do for a living. You can set standards and see how well students achieve them. Testing can be done in clever ways that obliquely verify teaching methods, and this is all part of the evil horrible testing system that teachers hate so much because it is being used to assess if they are teaching effectively.
posted by charlie don't surf at 10:25 AM on November 3, 2013 [2 favorites]

CrowGoat, again, the worksheet could be much better written and laid out, but to answer your questions:

1) It doesn't say "what you know". It says "the part you know", the "missing part", and the "whole".

2) The pictures are there to help the student visualize the problem. They use cubes to represent jars because they are using snap cubes to visualize numbers.

3) It says "cubes", not boxes. It refers to snap cubes. It's like saying "use an abacus".
posted by Pre-Taped Call In Show at 10:45 AM on November 3, 2013

What I object to is the out-of-hand rejection of what seem to me to be fairly good, or at least not obviously bad, ideas.

We agree that these skills are important and need to be taught to children, so that they can use these skills well as adults.

The thing is, backmapping entails proper planning. It's not good enough to merely identify those skills which you want to see well-developed in adults. You get no points for that.

What matters is effective implementation. How well are you actually teaching and testing this material? Whether this is a worksheet or a test, it's indicative of poor implementation: not just in this worksheet, but as a general culture and process. Some ECEs may have been involved at some points in this general process, but either they were not consulted appropriately at the right points in time, or the ECEs weren't being adequately listened to, or some people need to be replaced, etc. etc. etc.

Perhaps we can agree on this: this worksheet does not indicate a professional understanding of how to teach this material to first-graders. I assume that we could also find some middle ground on the idea that the worksheet does not exist in a vacuum - if this was constructed poorly, then other things probably are, as well.
posted by Sticherbeast at 10:50 AM on November 3, 2013

Perhaps we can agree on this: this worksheet does not indicate a professional understanding of how to teach this material to first-graders.

I guess I don't agree on that, but I'm not an early childhood educator so I'm sure there are issues I'm not aware of. What aspects of it did you feel weren't up to professional standards? I see one - as many have mentioned, there's a typo in question 12 that somehow made it through without being corrected.

All I can say is that I didn't find it confusing (which doesn't really matter, I'm a grownup) and my kid, whose school uses a curriculum a lot like this one, didn't find it confusing.
posted by escabeche at 10:57 AM on November 3, 2013

That's part of what this Common Core system is about, to develop teacher's skills so they can deliver a rigorous system of instruction that is scientifically proven.

That would be so much more reassuring if the word EFFECTIVELY was stuck between 'can' and 'deliver'. Because from what I've seen firsthand, and the complaints I've gotten directly from teachers about students in their classes, they're not delivering whatever product they're delivering EFFECTIVELY.

And if you're trying to develop teaching skills, why are you testing students and not teachers?
posted by mikelieman at 11:08 AM on November 3, 2013

> I also notice that the old "Dick and Jane" names have now been universally disdained in favor of random world ethnic names

"Dick" and "Jane" are no less ethnic than "Faiza," "Roberto," "Carrie," and "Jennifer," which are the names used in this work sheet.
posted by The corpse in the library at 11:27 AM on November 3, 2013 [1 favorite]

Sticherbeast, I think we're in complete agreement on all of the underlying issues and I really appreciate the discussion. I just think this is a lazy article which has provoked some frustrating responses.

First, their source for poorly-planned "back-mapping" is to cite a document that in fact claims extensive planning of the exact type that you describe. From the .ppt:
–The Common Core Standards are the first learning standards to be backmapped from the skills and knowledge students need to succeed in college and careers, grade-by-grade all the way back to kindergarten.
–The Common Core Standards are benchmarked to international standards and informed by the best evidence and research.
I can't vouch for the truth of these claims, and it sounds like your wife's actual experience doesn't either, but the point is they are from the document that the article cites as evidence for the opposite conclusion.

Second, the article and the FPP deliberately lead people who are confused by the new material to conclude indignantly that the material itself is flawed. In fact, a lot of the objections I've read so far reflect mathematical misunderstandings of the exact type that these curriculum reforms are designed–effectively or not–to correct.

Escabeche, I do think it could be done better. The layout is cluttered, which is hugely important since students who "don't get math" are often distracted by extra details. Visual metaphors are mixed in a confusing way. It's decipherable, but the process of deciphering obstructs the acquisition of basic skills that are clearly still not complete (cf. 4+8=6). Straightforward, repetitive practice is important too, and asking every single question in a different way makes that impossible. Of course, this can't be the only homework given all year.
posted by Pre-Taped Call In Show at 11:37 AM on November 3, 2013 [2 favorites]

If anyone wants, I can upload photos of my first-grade student's current math homework worksheets so y'all can see how this is being implemented in 2013.
posted by KathrynT at 11:43 AM on November 3, 2013

There are appropriate and inappropriate (and satisfactory and unsatisfactory) ways to teach and test these kinds of skills. This test does not appear to be succeed on all fronts.

The Common Core is a set of standards. It is not a textbook or a collection of assignments. All of those things get created by shitty, corner-cutting publishers. You can look at early-grades math worksheets from any mass curriculum and see similar layouts and degree of attention to detail.
posted by Nomyte at 12:13 PM on November 3, 2013

And if you're trying to develop teaching skills, why are you testing students and not teachers?

Teachers are tested. But you don't tend to hear about it because they are grown adults and their parents aren't hovering over them.
posted by charlie don't surf at 12:25 PM on November 3, 2013 [1 favorite]

Sticherbeast, I think we're in complete agreement on all of the underlying issues and I really appreciate the discussion. I just think this is a lazy article which has provoked some frustrating responses.

I agree that the article is not great, and that it doesn't prove everything that it sets out to prove.

I confess to not having read most of the comments before posting. Now that I've read more of the comments, I agree that many people didn't quite get the point that this worksheet was using the language that the material had almost certainly been taught in.

My main point is that it's not enough to have a set of guidelines which make sense with regard to a set of goal-oriented, broad-gauge issues. If these guidelines, when followed in the real world, can result in substandard results, then there is a problem.

Where my wife comes into it: she teaches in a school with a high proportion of ESL students. She teaches both general and special needs students. To make a long and complicated story short, in her experience, these guidelines (and others like it) have had a particularly negative impact on many of her students. In her experience, the new guidelines can work for the higher-performing students, but they leave the lower-performing students further behind. The underlying conceptual framework does not speak to the capacity and needs of all students. The theoretical ambitions of these guidelines do not help a student whose math skills are far lower than they would have been, if they had been taught effectively in another way. For special needs students, she finds that their results improve dramatically when she can teach them in a different way.

But, you can't do that for everyone. What's more, you can't just say "but this conceptual way of doing things will help you in college" to a kid who can't do grade-appropriate math now.

Of course this testimony is only secondhand and anecdotal. But, I certainly hear about it often enough!

I can't vouch for the truth of these claims, and it sounds like your wife's actual experience doesn't either, but the point is they are from the document that the article cites as evidence for the opposite conclusion.

To me, those statements are overly vague and conclusory, especially with regard to the worksheet that was up for discussion. I agree that ECEs were undoubtedly consulted for the general plans, but the specific implementation under discussion does not show a clear understanding of how to teach and test a first-grader.

For me, the big question is: what happens when these new guidelines work in many schools, but in other schools, spur wider achievement gaps? It's not enough to say that these guidelines will help do xyz in the future. How are they working now? Do they work well everywhere, or do they only work in certain environments?
posted by Sticherbeast at 12:57 PM on November 3, 2013 [3 favorites]

It's as if they're rolling education back into the era before we were able to test separately for verbal skills versus math skills. Many of those questions are poorly communicated - somebody with an already shaky verbal skill set is also going to flunk the math test!
posted by Sticherbeast at 8:46 AM on November 3 [+] [!]

Actually, I have heard this criticism before. "New math" means that kids with bad verbal skills (because of learning disabilities or ESL) are now ALSO flunking math. I think what bothers me most about these tests are that they introduce a million cultural variables and quirks that demand teaching to the test, and advantage the kids with a certain cultural competency. And it's just distracting -- why even risk having kids go huh? at the name "Faiza" and wonder why she has all those purses, and why you are taking some of them away, when you could just ask them 7 - 5 = ?
posted by yarly at 1:02 PM on November 3, 2013

There's plenty of criticism the Pearson work sheets deserve. The names is not one of them. No kid is going to be confused to the point of not being able to answer the question because one of the people is named Faiza.
posted by The corpse in the library at 2:43 PM on November 3, 2013 [3 favorites]

Here's the thing. Parents help kids with homework, that's good. But when parents who've learned a one method try to explain it to kids who've learned a different one, tears and frustration ensue.

So if any elementary math teachers are reading this, please for the love of god, stand at the blackboard and make a video demonstrating your method. It doesn't have to be slick, just work through a couple problems. Then post that video on YouTube so parents can see and understand where all those extra zeros are coming from.

Thank you.
posted by TWinbrook8 at 5:04 PM on November 3, 2013 [1 favorite]

That presumes the parents speak English, have a way to watch YouTube, will understand the explanation, and give a crap. I understand the frustration -- there have been times lately when I haven't understood my son's 5th grade math just because it's being taught differently from how I learned it decades ago -- but YouTube videos are not the solution.
posted by The corpse in the library at 5:40 PM on November 3, 2013

Like lots of people, I'm not crazy about the New New Math. However, part of my reticence to accept criticisms of Common Core standards at face value are cack-handed attempts to discredit them like this.
posted by ob1quixote at 6:20 PM on November 3, 2013

And it's just distracting -- why even risk having kids go huh? at the name "Faiza"

OK, wait, what? Really? Three kids in my brother's (midwest suburban) graduating class were named "Faiza" (I just checked the graduation program to be sure). Nobody in first grade in the United States today is going to fail math because of a stereotypically non-white name on a worksheet.
posted by like_a_friend at 8:50 PM on November 3, 2013

All I need to know about Common Core are these two words.

"Gates Foundation"
posted by mikelieman at 2:33 AM on November 4, 2013 [1 favorite]

So many thoughts about this -- sooo sooo many. Let me start with one simple sentence and then pull it apart to tell you how many issues are wrapped up in Common Core standards.

These are very high stakes tests.

1. Decisions about teachers jobs, ratings, program evaluation are being made based on the outcomes of this new test.
2. Decisions about children's ability to advance to the next grade will be made based almost only on the outcomes of this new test.
3. Teachers will inevitably teach to the test -- and Pearson will happily sell you, thank you very much, a hastily put-together curriculum that should be pegged to the test -- but that's not a slam dunk anyway, even if you wanted to teach to the test.
4. There are a lot of faulty assumptions wrapped up in this "standardization" - that same aged kids progress at the same rates, for example.
5. Just because being able to explain abstract mathematical concepts is potentially useful as an adult, it doesn't mean that kids, at the age of five or six, need to get started on this RIGHT AWAY! That's not how human beings progress. I don't let my 8 month old wander over to a hot stove and touch it just because she'll need to know someday, on her own, not to touch a hot stove.
6. If one wanted to encourage a national curriculum, one could, in theory, start testing it before making it the basis by which teachers are judged and kids are granted passage to the next grade. And then you could start with a kindegarten class, institute it in that grade only, and try it out -- all while allowing teachers to also assess the child's skills and readiness for the next grade based on something other than the untested test, as it were.

That's all I have time to write now -- but I gotta go to work.
posted by vitabellosi at 4:26 AM on November 4, 2013 [1 favorite]

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