How would you answer this test question? From a 1st grade Common Core test.

[madfloridian]

More about this issue from CBS this morning.

Educators, parents debate the Common Core

There is a video included. Note the words of Principal Carol Burris, who worked on Obama's campaign.

I am not against standards. We always had standards when I was teaching. And we knew that as quickly as Florida had weather changes, the standards would change, the name of the standards would change.....and we were told often that what and how we taught the last few years would damage children if we continued.

I am not against standards. I am against the high stakes testing of such standards. I am against making companies like Pearson wealthy by letting them formulate tests in secret. Before I retired there were parents in my primary classes hiring lawyers to see why their kids failed the FCAT.

I would love to read the letter that President Obama sent Carol Burris who worked on his campaign...the one she put away in the closet because it was so upsetting to her.

SO how would you answer the test question?

[Iggo]

1. Like this:

[pnwmom]

275. Here's an even CRAZIER example. Try this one.

http://science-beta.slashdot.org/story/13/11/02/1540249/a-math-test-thats-rotten-to-the-common-core

Explaining her frustration with the intended-for-5-and-6-year-olds test from Gates Foundation partner Pearson Education, Principal Carol Burris explains, "Take a look at question No. 1, which shows students five pennies, under which it says 'part I know,' and then a full coffee cup labeled with a '6' and, under it, the word, 'Whole.' Students are asked to find 'the missing part' from a list of four numbers. My assistant principal for mathematics was not sure what the question was asking. How could pennies be a part of a cup?" The 6-year-old first-grader who took the test didn't get it either, and took home a 45% math grade to her parents. And so the I'm-bad-at-math game begins!"

[Sancho]

308. Exactly!

The kids learn to hate tests, math, and school! Meanwhile someone will claim they are learning to "think critically" for the first time in history!

[orpupilofnature57]

426. Critical thinking is ambiguous, hence the test would have to be ambiguous, AND

in ancient history they called it " Common Sense " .

[Sancho]

435. Actually, there are plenty of ways to study and teach critical thinking, creating thinking...

and problem solving.

There are textbooks, theories, tests, and ways to improve these things.

It's not ambiguous to many educators. You may prefer one method, taxonomy, or curriculum over another (just like different cures in medicine or different types of automobiles), but I wouldn't narrow it down to "common sense".

[orpupilofnature57]

436. How about Perspicacity? a word so descriptive and never used .

http://dictionary.reference.com/browse/perspicacity

[Sancho]

437. Perspicacity is one descriptor, but not a theory based on observation, research, or measurement.

Some theories of critical thinking, creating thinking, problem solving, and intelligence have been studied for decades. All of them have their own vocabulary and definitions. For example, you may have heard of one of the older descriptions called Bloom's Taxonomy. Another is the Torrance theory of creating thinking (originally, elaboration, flexibility, and fluency). At any rate, there are a number of excellent theories that describe what we see in people, ways to promote "thinking" in people, materials to teach with, and methods to use in promoting thinking.

You simply need to look at some of them, see if any of them suit your target for a particular situation and try it. A few test publishers are aware of these theories and concepts, and a few of them are built into curriculums (like Common Core), but generally they are not used in high stakes testing to any great degree.

Teachers need know what content materials AND what thinking skills are to be tested on high stakes tests. Otherwise, the teachers won't teach it and the students won't practice it. Finally, if kids are not developmentally ready, even the best teacher and materials won't overcome maturity.

[orpupilofnature57]

439. Thank you .

[BuelahWitch]

315. "...And so the I'm-bad-at-math game begins!"

That's the problem. The testing companies won't be held accountable. They've put that kid on the road to math anxiety because he failed a test they flubbed. Not his fault, but it doesn't matter. Who you gonna believe, the corporations or your lying eyes?

[pnwmom]

317. I have one child who LOVED math and I am so glad

she never had to deal with tests this stupid. They're going to lose a lot of the kids who have the most potential with stupid tests like this.

[madfloridian]

371. Thanks for sharing that example.

Little ones just do not think that abstractly. It's ridiculous.

[truedelphi]

432. Did you notice the young perky blonde teacher using the word "algorithm" to her

Young grammar school students... What was that about?

[Ms. Toad]

402. When I commented (below) that it was an extremely poorly written test -

that was one of the questions I was specifically thinking of.

[Louisiana1976]

2. My guess would be B. Subtraction sentence? This isn't grammar, it's math. Common Core doesn't

make sense.

[madfloridian]

4. B is not subtraction.

[Curmudgeoness]

10. Neither is A, C, or D.

None of the options had anything to do with subtraction.

[madfloridian]

11. Exactly.

[SheilaT]

41. Yep. That's an addition problem.

How in the name of anything can any of those choices be subtraction? Or did the definitions of addition and subtraction get reversed while I wasn't paying attention?

[xocet]

277. Clearly, if one holds a open flame below possible answer D), answer E) "None of the above" appears.

So, E) is my answer.

The trick is to realize that they have printed the correct answer using invisible ink.

[hr]

It's late and that technique would lead nowhere good. (Imagine lighters being held up to test papers to check for invisible ink....)

...

It does not seem wise to try to teach group theory to first graders if that is the spirit of what they are trying to do. On the other hand, carefully proofreading the test would be an excellent idea.

[madfloridian]

361. .....

[Skidmore]

8. Did you count correctly?

[LWolf]

174. This isn't "Common Core."

The CCSS is a document full of standards. It's not a test.

This is a test question written by a testing company.

[FlatStanley]

376. This is true, to a point. The whole testing regime

Is incorporated into common core schools. And testing companies profit from producing tests, whether they be well written or simply shat out by a monkey. And if TexAss adopts the tests, it's a done deal like the moronic history texts that will soon sweep the nation.

[LWolf]

387. The whole testing regime

is embedded into every public school in the nation since NCLB. One of the requirements to get a waiver from NCLB is to adopt the CCSS OR "another set of federally approved standards." Not that I've heard of any other set of standards being "federally approved."

So...either states adopt the CCSS and one of the two tests created for them, or they continue to use their state standards and whatever high stakes test they've been using for NCLB.

Either way, high-stakes tests and testing companies are what the education "reform" movement is all about.

[SummerSnow]

3. Thats on a standardized test? WTF?

[Igel]

64. Does it say it's a standardized test?

If it doesn't, don't assume so. The OP probably wants you to think it is.

Looks like a typo. Should read "addition sentence," or the kids were taught--properly--that there's a relationship between that image and the inverse operation.

That's the problem with test questions in isolation. Unless you know what's taught, you don't know if the test question is appropriate.

It's also the case that a lot of teacher-made (and even company-made) tests have typos. We just got a new textbook, for instance; it was a revision of a book that's been out for at least 20 years. The printed textbook had errors in it--some carried over from the 3rd reprinting of the 4th edition of the previous version, some new.

Perfection is for messiahs. And part of their perfection is their compassion and forgiveness.

[madfloridian]

76. Watch the video.

[Ms. Toad]

124. The video does not explain where the question came from.

And the copyright on the left page is too pixelated to tell.

My guess is that at least half of the elementary school complaints arise from bad implementation rather than bad standards - far too many elementary school teachers become elementary school teachers - in part - because they don't handle math well. (I've tutored several.)

I was a victim of "new math" in the 60s. My parents were concerned I would fall behind the kids in the town school - so they bought textbooks for me to use (by a teacher with a high school education), and I got to study it during recess.

As someone with a Master's degee in math, new math itself wasn't bad - but it was taught, by and large, by people who did not understand how powerful set theory actually is. So they got bogged down and focused on the lower level details year after year for seemingly no purpose, and those of us who studied math further finally went, "Aha!" somewhere around college level. In other words, it was so watered down as to be meaningless before college - and became the focus of math education, rather than a very useful tool, because those teaching it - for the most part - had no clue.

Some of what I have seen in the Common Core that people are scratching their heads about are actually very useful tools. But implemented by someone who has no idea how powerful those tools are, they will become a meaningless goal and detract from learning other necessary skills.

[madfloridian]

373. Here are 2 pages of that test. States it is from Pearson. It is a practice page, test prep

http://roundtheinkwell.files.wordpress.com/2013/10/the-math-test.pdf

[Ms. Toad]

384. Thanks. I would not assume that it is an accurate reflection

of the Common Core, since it appears to be a private educational services company.

That test is not well written.

[madfloridian]

386. Pearson is writing the whole damn test for many states. There should be no errors.

They still have the contracts although they have a long history of mistakes, serious ones.

Why are people in this thread defending a test item that is so obviously wrong.

Some Pearson info:

Pearson Rakes in the Profit
http://www.huffingtonpost.com/alan-singer/pearson-education-profits_b_2902642.html

Teachers to shred tests in Pearson protest
http://www.lohud.com/story/news/politics/politics-on-the-hudson/2014/08/08/teachers-to-shred-standardized-tests-in-pearson-protest/13772689/

Pearson had to pay 7.7 mil in Common Core settlement. Misuse of "charitable assets"...
http://www.democraticunderground.com/?com=view_post&forum=1002&pid=4183037

[Ms. Toad]

396. That is really sad.

As a former high school math/physics/computer science instructor - and current law faculty (with a focus on test taking skills), I would not hire them to write exams.

They probably had their fingers in the NCLB fiasco - with equally poorly written exams. There were so many questions on the science section of those exams in Ohio which did not provide sufficient information to narrow the answers to a single right answer...

Not to mention the questions which were correct - as long as you limited yourself to the knowledge the students at that grade level had, but were incorrect when you made the next advancement in that subject matter. A test should NEVER include an incorrect answer as the selection intended to be correct, when it is flat out wrong when you refine your knowledge more.

[pnwmom]

403. On top of everything else, Pearson has been getting gag orders

on school districts that use its materials, to prohibit teachers/administration from leaking and discussing the questions on the tests.

This happened in NY state and there was an uproar about it, but as far as I know it's still going on. So anyone sharing these questions is risking his or her job.

[Ms. Toad]

404. I don't know how the questions are used -

but if they are the questions from state-wide tests that is necessary.

Beyond that, it is likely either an issue of copyright - or contracts which require them to minimize the distribution of questions so that they are reliable tests of comprehension (assuming they are in the first place) rather than memorization of questions.

[pnwmom]

405. Yes, they have their justifications -- but the bottom line is that there can be many poorly designed

questions on the tests and teachers aren't allowed to speak out.

[Ms. Toad]

408. If it is purely a copyright issue,

Speaking out about poorly designed questions would be pretty classic fair use.

[sabrina 1]

406. Didn't watch the video, did you? Not a teacher or an educator either I presume.

THIS is one of the most disastrous 'education' systems in the world. Children learning in outdoor missionary schools in Third World countries are receiving a better education that American children under this NCLB Bush 'program' for profit, now on steroids.

No wonder so many people are home schooling their children.

[rocktivity]

5. C is the only one that corresponds to the illustration

Seven -- well -- whatever they are, four dark and three light. But arriving at that conclusion took deductive reasoning, not arithmetic.

Is it any wonder that Common Core is looked upon as a slippery slope to privatized education?


rocktivity

[madfloridian]

9. C is not subtraction.

[rocktivity]

17. Apparently, subtraction doesn't exist anymore

Inverse Relationship Between Addition and Subtraction

A number fact is made up of three numbers. These three numbers can be used to make up other number facts. Knowing one fact can help children with other facts. Look at the number facts we can make with the numbers 3, 4, and 7.

Addition Facts
3 + 4 = 7
4 + 3 = 7

Subtraction Facts
7 – 3 = 4
7 – 4 = 3

...(T)ell children that they are going to learn something new called a fact family. Explain that it is not a real family, but that the facts are related like people are related, therefore they have been given the name family. Point to the two addition facts that you wrote on the board and say, "Now I am going to write two related facts." Write 5 – 2 = 3 and 5 – 3 = 2 on the chalkboard. Ask, "Do you see anything the same about these two facts and the two addition facts?" Elicit that they use the same numbers. "Do you see anything different about these two facts and the two addition facts?" Children should respond that the new facts are subtraction facts and the largest number comes first in both facts. Tell children that these four facts make up a fact family...

The NEW "new math..."


rocktivity

[uppityperson]

20. I did that wayyyyy back in school, tried to teach my classmates and got in trouble with the teacher

Addition is the only thing you need because subtraction problems are the same backwards. Multiplication is just adding multiple times, division is subtracting, backwards adding, multiple times.

It made sense to me back in the early 70's doing higher math but my teacher wanted the others to learn the "right way".

[sammytko]

390. Exactly!!!!

what is not discussed here is that before the kids even see this, they learn math vocabulary - or should. We old timers see this and get all bent out of shape.

Keep an open mind - just like with all things in life.

[Ms. Toad]

407. Sorry -

It might be appropriate to classify subtraction as addition of a negative - but sentence which does not include a "-" sign is not subtraction. I am still close enough to math (I taught it for 11 years, and have two degrees in it) to be pretty darn sure that that the question has no relation to what you need to know for STEM careers - and that is part of the point of the Common Core - to decrease math illiteracy. This question increases it.

(It would have been perfectly appropriate to ask which subtraction sentence was correct if it included the answer 7-3=4, or 7-4=3. It would also have been appropriate (although too advanced for first grade) to rewrite the addition sentence as subtraction, without moving the numbers across the "=" sign (4-(-3)=7). But 4+3=7 is an addition sentence, not a subtraction one.)

[Atman]

32. And in this Number Family, daddy beat the shit out of Mommy...

...and Junior was locked in the closet until he made up a crazy answer which would satisfy the local police investigator.

It's fucking absurd.

[WinkyDink]

34. But which train got there first?

[Atman]

36. The one from Chicago.

The train to DC went off the rails long ago.

[DebJ]

225. DUZY! n/t

[WinkyDink]

33. MEANWHILE, EVERY OTHER SUBJECT ESCHEWS ACTUAL FACTS!! Irony, thy name is Common Core.

[valerief]

40. Huh? Is a subtraction sentence the same as a COBOL sentence? nt

[Recursion]

212. Well, yes, actually, thanks to the Turing-Church thesis and Goedel

But I will freely admit that is advanced for first graders.

[Igel]

78. They're inverse operations.

Even my juniors squint in pain when I blithely and without explanation just rewrite something something like x - 3 as x + (-3) to make it precisely parallel to some equation.

"Look, subtraction is just adding a negative."

Then again, they also frown when I separate out 3/x as 3* (1/x).

And you just don't want to see what happens when they're confronted with improper fractions, things like 3/(x/2) = 6/x.

It was only after I had my entire class use their TIs to calculate 1 / (1/4) = 1 / (0.25) = 4 that they admitted that maybe, sometimes, such a fraction makes sense and isn't doesn't always = 1/4 = 0.25.

If only we weren't doing a parallel resistor problem set with lots of R = 1 / (1 / (R1 + R2 + R3 + ...) ) problems at the time.

[Recursion]

216. Which is why we need this taught at the elementary level

Way too much primary math education has been about "do these precise steps for a problem" rather than "learn to think about numbers". I like the direction math teaching is going from what I'm seeing in my tutoring.

[Ms. Toad]

401. This particular question is not testing whether students understand the concept

that a subtraction problem is the equivalent of adding a negative, because there are not the appropriate answer options to determine if the student understands that concept. They would all look incorrect - and the student would just be guessing.

As a math teacher for years, and someone with two degrees in math, that is either a typo - or someone without a full deck of math cards drafted it.

If your theory was correct, the correct subtraction sentence would be 4 - (-3) = 7.

The question, as written, is not defensible.

[wandy]

90. "number fact" is key to seeing this............

Let's call it a rule for the numbers 3 : 4 : 7.
If we were only solving for the sum, 6+1 would would do just fine.
We are solving for rule{3 : 4 : 7}.{6 : 1 : 7} is a different rule.

Rule {1 : 2 : 4 : 8 :15}
allows for Rule {1 : 2 : 4 : 8 :15 : 10 (A) : 11 (B)} and so on.....


A better way to put the question might be which answer satisfy the rule [number fact] involving 3 : 4 : 7

[pnwmom]

271. Your final sentence is better because the "correct" way is simply wrong. It's not a subtraction

sentence no matter how convoluted the explanations given by some here.

Those mathematical equations are all subtraction, not addition equations.

[Recursion]

214. About damn time

That's a much more sane way of teaching math; it's basically what I've done with kids I've tutored for years because the "learn these rote operations and addition and subtraction tables and borrowing and carrying" nonsense just doesn't work for a lot of kids.

[1StrongBlackMan]

358. I think what we are seeing here is ...

"old(er) school" understanding of math clashing with new(er) school thinking.

And I think, as with all other learning, kids will catch on just fine because they don't/won't have to unlearn stuff.

However, on the downside ... this will require parents/teachers to invest in learning/understanding what is being taught and how, in order to be at all useful to the students.

[madfloridian]

397. Wrong. I taught "new" math "old" math for decades.

Most teachers did. We also taught the kids that real life would demand they know the short way to do it.

It is matter of a test item that is faulty. There is no correct answer given.

There is an addition problem that suits the picture, but the item called for subtraction. Therefore there is no right answer. Someone said it was a trick question....there should be no trick questions for first graders.

[1StrongBlackMan]

398. With all due respect ...

do you not see teaching something "new" for decades, kind of argues against it being "new."

[madfloridian]

399. Tell that to the districts and feds that keep calling what is old as new.

I agree. We have taught number families, number sentences for years. But you do not try to trick the little ones. Their minds are not that developed yet.

[Ms. Toad]

409. Not correct.

Number families have been taught for years - and are necessary to higher mathematics.

Teaching incorrect terminology is not. Unfortunately, elementary school teachers - and apparently test writers - don't know enough to understand the concepts they are teaching, and well intended parents (who also are generally not mathematically sophisticated) say, "we'll jut have to learn newer school thinking," without bothering to make sure that newer school thinking (1) is being accurately reflected in the material and (2) is well suited for use beyond high school level math.

It is a repeat of the elementary school teachers who teach squares, rectangles, and quadrilaterals as three distinct figures, which I had to repeatedly correct in my high school geometry students because it is critical that they understand that a square is always also a rectangle and a quadrilateral - and a quadrilateral is also sometimes a rectangle, and also sometimes a square.

Or perhaps a repeat of set theory (introduced as "new math" when I was in elementary school). A really powerful tool - but pretty much a useless waste of time through high school (below calculus) because the concepts repeated year after year are simple enough they can be learned by a college student in perhaps a single lesson - when they are needed and there is actually an instructor present who knows why it is important.

I'm all for teaching useful mathematical concepts to students earlier in their educational careers provided (1) those teaching them understand them and (2) those teaching them also understand how they might be useful 2-3 classes up. Teaching mathematically incorrect vocabulary (if the test reflects what is intended to be taught) is not helpful.

This kind of makes my point:

Generally, subtraction facts are harder for children to learn than addition facts. If a child knows that 6 + 9 = 15, and he or she sees the subtraction sentence 15 – 9 = __,

http://eduplace.com/math/mathsteps/1/b/index.html

[1StrongBlackMan]

414. I completely agree ...

Teaching incorrect terminology is not. Unfortunately, elementary school teachers - and apparently test writers - don't know enough to understand the concepts they are teaching, and well intended parents (who also are generally not mathematically sophisticated) say, "we'll jut have to learn newer school thinking," without bothering to make sure that newer school thinking (1) is being accurately reflected in the material and (2) is well suited for use beyond high school level math.

...

I'm all for teaching useful mathematical concepts to students earlier in their educational careers provided (1) those teaching them understand them and (2) those teaching them also understand how they might be useful 2-3 classes up. Teaching mathematically incorrect vocabulary (if the test reflects what is intended to be taught) is not helpful.

And I think you have correctly identified the problem.

[Ms. Toad]

415. And, unfortunately, in math and science

that has been the case forever. Far too many elementary school teachers are less literate in math & science than in the other subjects they teach. So by the time they reach high school (the first place a math degree is more or less required - since an elementary certificate is all that is required most places to teach middle school math), they are years behind in real understanding.

What is even scarier is that the top math students take 1-2 years of algebra in middle school - often taught by teachers with elementary school certification rather than secondary math certification. (Some of them do a fantastic job - but, as a general matter, elementary certified instructors are allowed to be moved around anywhere from K-8 (or sometimes 9). If the choice is between being a laid off elementary school teacher and an elementary school teacher teaching algebra, even though it is not a subject you understand well - most would choose to remain employed?

[1StrongBlackMan]

416. I guess that is the point I was trying to make ...

with my "old(er) school" understanding of math clashing with new(er) school thinking" comment ... I liken it to someone having learned/grown up on Wang trying to teach Microsoft or Linux ... though the systems are based in the same concept, it takes a lot of unlearning and letting go of the former, to properly communicate the latter.

But it doesn't help that some teachers (legitimately feeling under attack), don't/won't acknowledge their deficits in understanding in order to move to the "new order."

[Ms. Toad]

420. With math (and to a lesser extent science),

many elementary certified school teachers (which extend through 8th or 9th grade many places) didn't even really understand the older school material. I spent quite a few hours working with college students (and in some instances graduates working on Master's Degrees in education) trying to help them learn enough basic arithmetic (e.g. the four functions with decimals and fractions) to pass the tests they needed to be certified to teach elementary school. And anyone certified to teach elementary school (in most states) may teach middle school math - which includes 1-2 years of algebra and geometry (depending on the sequence, and depending on how many AP classes are offered.

Rote memorization of math facts should never have been sufficient to teach elementary school math. The two differences now are that it is explicitly not enough (that's what the Common Core, and other less formal movements toward comprehension, is about) - AND - Testing companies have seen an opening where they can make money and are apparently flooding the market preying on the lack of understanding of anything beyond rote memorization (and the fear associated with it). So when A (rote memorization) meets B (offers of bright shiny tests), A doesn't know enough to be able to say, "The emperor has no clothes." (And, those in A who do recognize it are apparently forbidden from holding up the clothing for examination.)

I actually did go to the website to see if I could see if everything they offer is as bad as the few pages which are posted - and everything is behind a school-membership wall.

[1StrongBlackMan]

422. But we should stop this discussion ...

lest we be accused of attacking teachers.

[madfloridian]

245. That is old old math dressed up as new math. We taught that for years. Number families.

[joshcryer]

309. That is a brilliant post.

I say this as someone who couldn't understand that multiplication of two negatives resulted in a positive. I was just taught that it was what it was, not the distributive law.

[Recursion]

211. Oh my God of course it is

Addition and subtraction are equivalent operations and addition is easier (there's no associativity involved) so teach the kids addition and then teach them how to use it as subtraction.

[madfloridian]

215. The SUBTRACTION equivalent to 4+3=7 would have a minus sign.

Of course it is the same backwards and forwards, but that was not the test item.

[Recursion]

217. 4 + 3 = 7 is equivalent to a pair of subtraction sentences

You don't need a minus sign to express a subtraction fact: the addition statement expresses the subtraction facts just as well.

It's not how you learned math, I get that; it's about getting kids to think about numbers rather than memorize specific steps to solve problems.

[madfloridian]

219. They asked for a subtraction equivalent, there is not one there.

So I am in agreement with the CBS interviewer and that principal who is head of one of the top schools in the nation.....I haven't figured it out yet. (Watch the video)

I wish people would stop acting like I never taught math. It's insulting and condescending.

[Recursion]

223. Then why are you acting like "4 + 3 = 7" doesn't express a subtractive identity?

You know perfectly well it does. If the kids were taught to think that way, to convert any subtractive identity to an addition statement, then this is a perfectly good question. If they weren't, then the question is bad.

I'm aware you've taught math, but you've also played up on people's math anxiety in multiple posts. Properly prepared, there's no reason a student couldn't answer this question (the phrase "related subtraction sentence" is clunky, but oh well, if that's what the teacher taught).

[azurnoir]

244. First off we're talking about 5-7 year old kids in American schools

who I can pretty well guarantee have not been taught to think like that in the classroom, however if their parents can afford tutors or more exclusive private nursery schools then perhaps they have been but only perhaps

[Recursion]

248. About a third of the kids I've tutored (generally 8 - 10 years old) were taught to do that

The other two thirds weren't. And I don't know if it happened at age 8 or at age 5. But kids are learning stuff crazy early now...

[azurnoir]

251. again kids you're tutoring

and if I may ask was this in the US?

[Recursion]

252. Yes, it was in the schools in my neighborhood in DC

One neighborhood public and one charter.

[azurnoir]

256. How recently was this? this year last year?

were they public schools and from what sort of socio-economic levels were these kids coming from?

[Recursion]

258. from, oh, 2009 to 2013 the most recent time

And before that from 2004-2007 or so (some of that time I was actually employed as a "resource teacher" by DCPS, but that was a disaster for multiple reasons).

Yes, they were both public schools, one neighborhood public school and one charter.

from what sort of socio-economic levels were these kids coming from

DC has an odd hybrid choice system which results in the neighborhood schools having IIRC a third of their students not from their neighborhood, so there's a mix. The neighborhood itself was in the process of gentrifying but most of the gentrifiers were DINKs so the students were working class. Mostly children of immigrants (Guatemala and Ethiopia seemed to take the lead there).

The charter school did admissions via lottery but it focused on meeting the needs of students whose first language was Spanish, with the result that basically the entire student body was Latino/a.

Also in both cases the kids wore uniforms so it was hard to tell how rich a given student's family actually was.

[azurnoir]

261. so from 2004 they were teaching kids to think of numbers in this manner?

news to me as in 2004 my son was in first grade in MN at one of the highest rated schools in the state and nothing of the sort was being taught that early

for me the problem is not so much the question, as it is the grade level of the test

[Recursion]

262. I was tutoring older kids then; this experience was from last year

The first time was strictly for the neighborhood school, too; charters have a lot more flexibility with curriculum.

[Ms. Toad]

411. It isn't that it is clunky

it is wrong, and if the teacher taught it, she needs some additional training.

Vocabulary is important, in math - as elsewhere. Starting in 1st grade and teaching vocabulary which must be untaught by upper level teachers (I was one of those for 11 years) is not productive.

[xocet]

267. Only a pair...?

One takes 4 + 3 = 7 as given and the (implicit) definition of the additive group of integers:

1) 4 = 7 - 3
2) 3 = 7 - 4
3) 0 = 7 - (4 + 3) = 7 - 7

and then from the group definition

0 = k + (-k), for all k that are integers

becomes

0 = k - k, for all integers k, which could be interpreted as a subtraction sentence.

Can one not argue that once one has the identity element of the group from the original sentence one can extend the initial equation to the whole of the group of integers?

If so, then would it be proper to say that the equation 4 + 3 = 7 is equivalent to a countable infinity of subtraction sentences via the identity axiom?

As far as I know, this is correct, but it has been a while, so I would definitely be interested in your thoughts on the above argument.

[DebJ]

272. And a first grader could think through this process?

Wow.

[xocet]

279. Of course not. I was just asking the other poster about the earlier claim.

If a first grader could do that (assuming that it is a correct argument), he or she would likely be heading to college at quite an early age.

[DebJ]

281. Whew. Thanks. Given some of the other comments, I wasn't sure what you

were trying to communicate....comments by others in this thread.

[xocet]

290. Hey, no problem. Education is important, and reading this thread has been very interesting. n/t

[Ms. Toad]

412. You're even more creative than I was!

(You are technically correct - although your third one (and the rest of the infinity) cannot fairly be said to be represented by the blocks.

What is not correct, though, is calling 4+3=7 a subtraction sentence (even though there are, without question, equivalent subtraction sentences).

[Ms. Toad]

410. You can create 4 related subtraction sentences.

7-3=4
7-4=3
4-(-3)=7
3-(-4)=7

But NONE of those subtraction sentences appears as an answer choice.

What appears are 4 addition sentences.

[truedelphi]

434. But how were the other groups of numbers not also part of the subtraction method?? -

That is what is tricky for most people.

Not being snarky - I'd love for curiousity's sake to know why the other group of numbers were not part of the subtraction method as well...

[JVS]

297. None of them are. They're not sentences either.

But since we need an answer, C is the least shitty.

[madfloridian]

299. .....

[karynnj]

385. Subtraction can be seen as a form of addition if you consider negative numbers

ie - (-n) is the same as +n

Although I suspect the question was meant to say addition and there was an error. In which case, this is nothing more than a picture of what the equation is doing - not a lot different than using manipulatives so the child has a hands on, real example of what is otherwise abstract.

[Journeyman]

6. First grade? (Must be the topics covered in April or May, well after everyone saw Spot run) . . .

[Art_from_Ark]

316. I'm pretty sure that 95% of them just take a guess.

We used number lines in 1st grade. Count forward when adding, count backward when subtracting. We didn't go into theory.

[immoderate]

7. Assuming this is English, I'd say, "None of the above."

But I'm a licensed math teacher. What do I know?

-imm

[WinkyDink]

37. I'd say, "Subtract THIS."

[Man from Pickens]

84. people jumped down my throat for pointing out that Common Core math is funky

The correct answer to the question would be "none of the above" since none of those sentences have any subtraction in them. The obviously desired answer is "4+3=7", but the language and presentation are both as if designed to confuse.

I have the full suite of mechanical engineering mathematics, including linear algebra and differential equations and vector calculus, and a lot of the new stuff they are pushing under CC confuses the heck out of me.

Teaching needs to get back to basics. Kids aren't learning with current methods and CC is making things worse, not better. Modern educational systems need to produce results superior to, or at worst equal to, what one-room schoolhouses in BFE were able to do in the 1820s.

[Recursion]

241. "Kids aren't learning"

Kids aren't learning with current methods and CC is making things worse

Any evidence for that? Kids' math scores today are much, much better than ours were 20 years ago. Even with the current (slowly closing) racial gap, African American students today score better than white students did in the 1980s.

[Man from Pickens]

285. dumbing down the test does not indicate increased learning

standardized tests such as the SAT have been watered down multiple times since the 80s - score comparisons are apples to oranges

what I see these days are high school and even college graduates with a primal fear of mathematics - and that was not the case in the 1980s

Language skills are abysmal too, your typical college graduate can't even write a proper business letter, something any 8th-grader used to be able to do.

I'm old enough to have seen the difference, and kids today are getting gypped, big time. They're told they're being educated but they're not coming out of schools with the knowledge they need to succeed, or even survive.

[Recursion]

289. Writing scores are much, much higher today than 20 years ago

Significantly, which isn't surprising, given that kids actually communicate with the written word nowadays, whereas we were probably grudgingly forced to write a few thank you letters after Christmas and that was it. And writing scores can't be "dumbed down".

standardized tests such as the SAT have been watered down multiple times since the 80s - score comparisons are apples to oranges

But NAEP hasn't, and NAEP continues to improve too.

[Man from Pickens]

360. Something is odd in those numbers

OK this is what I found re: NAEP long term numbers - http://www.nationsreportcard.gov/ltt_2012/summary.aspx

What doesn't make sense is that the numbers in the ethnicity breakdown are consistently a good deal higher than the numbers in the gender breakdown. Mathematically these should average out to be similar, because each student has both an ethnicity and a gender. Yet the better of the gender numbers in each age group on both reports is lower than the highest of the ethnicity numbers.

Unless someone is sprinkling in some "special sauce" into these numbers, that is a mathematically impossible result.

I have a hunch we may be looking at something like when police departments report crime is way down by reclassifying a lot of things as not-crimes, or by suppressing reports. There is a general institutional bias - in any kind of institution - to promote good news and bury bad news, and the evidence of that happening often comes out in reporting numbers that don't add up.

[Recursion]

374. Because the race/ethnicity breakdown is an improper partition

There are races other than white and black, and Hispanics can be of any race. So some students don't appear in the racial breakdown, while others appear twice.

I have a hunch we may be looking at something like when police departments report crime is way down by reclassifying a lot of things as not-crimes, or by suppressing reports.

Nope, this is just the cognitive dissonance that comes from having been told repeatedly that "students are in crisis" when they aren't. Same thing happens whenever people have to confront our incredibly low murder rates (paper-shuffling cop administrators can't hide a body; there actually are just a whole lot fewer people being shot now than a generation ago).

[jeff47]

381. Part of common core was trying to deal with people like me.

I have dyscalculia. Think of it as dyslexia for math. Unfortunately for me, back when I was in school that term was not widely discussed. So I didn't hear about it until I had been out of school for about 20 years.

I just do not understand very simple math. Addition, subtraction, multiplication and division just do not work well in my head. Partially due to the fact that people were trying to teach me via memorization, which works extremely poorly for people with dyscalculia. As a result, I was always in the remedial math class...until we reached the point where they allowed calculators. At which point I was promptly moved into the advanced and AP math classes.

Doing 13+5 in my head is quite difficult. Yet calculus is easy.

Common core attempts to teach basic math in a way that works for everyone, including people like me. The stuff in common core makes a whole lot more sense to me than the rote memorization or similar methods I was taught back in school. I've actually started using a few bits and pieces to make my everyday life a little easier, though I usually just rely on a calculator.

Is it the best solution for everyone? Probably not. Some students are going to learn better the "old fashioned way". Some are going to learn better this way. Common core takes out that flexibility in the mistaken belief that there is one good way to teach everyone.

[madfloridian]

400. Great post thank you.

What a thread this has turned out to be! I taught this stuff years ago, and kept teaching the useful components even when the district went back to the old way after realizing the "new" way was working...was it 80s?

[gollygee]

12. I would answer it how the kid answered it on the test

I don't get "subtraction sentence" and wonder if that's a typo, but the kid seemed to understand it. I don't know what language is taught in the class as they're learning this but so long as the language on the test is the same as the language used in the classroom, the kids should understand it. I bet it was supposed to be called an "addition sentence" though.

[madfloridian]

14. Well, subtraction is taught in the classroom as the opposite of addition.

With a minus sign. It's an error on the test.

[gollygee]

15. Yeah but I think it's a typo

and obviously the test needs to be fixed, but that's a problem with proofreading, not the common core.

[madfloridian]

22. It's testing problem. By some company that is making millions of education.

[rocktivity]

26. DING DING DING! Madfloridian, you're our grand prize winner!

It's testing problem. By some company that is making millions off education.

Completely reinventing the educational process as an exercise in making work AND money.


rocktivity

[xocet]

304. Are you sure that you applied the rubric correctly in scoring that?

Your secondary scores seem to be off. You had better score another practice set or two. Remember to use the rubric holistically instead of your own prejudices. Maybe then you can re-qualify and continue scoring on this project....

[gollygee]

42. Companies made money off the old system of testing and teaching too.

[madfloridian]

44. That was once or twice a year and did not determine a child's future.

It was used by the teachers for evaluation purposes.

These tests now under Arne are being used to give grades to schools, to give merit pay to teachers, or to hire or fire them.

[gollygee]

46. I'm opposed to tests being used in that way

but I think there's a lot of jerking of knees around the standards in the common core. Two different issues IMO.

[madfloridian]

49. I expressly said I was not against standards, just the way they are tested.

You are defending the indefensible. But go ahead if you feel the need.

[gollygee]

55. You used what looks like a typo as an example

and the language has to be what is used in the classroom with the kids, not what we're used to from when we went to school.

They can test to see how kids are doing without using those test results to evaluate teachers, because that makes as much sense as evaluating dentists based on how many cavities their patients get.

Also, this looks like a regular classroom test, not a test used for teacher evaluation. A classroom test with a typo in it isn't a good example for the point you're making.

[madfloridian]

57. Did you watch the video?

[gollygee]

58. Yes

I also have kids in public schools that use common core.

[valerief]

82. How are kids supposed to get an answer right if the testers can't get the

questions right? And they've got proofreaders!

[gollygee]

98. Yeah well the proofreaders are an issue

but typos can happen anywhere by anybody, on any kind of test and any curriculum. The existence of a typo on what looks to be a classroom test - not a standardized test (unless they don't use computerized grading on those anymore which is unlikely) - is an issue with whoever wrote that test and didn't proofread, not with common core.

[sabrina 1]

104. Where was the typo? What I saw was an awful, disastrous and confusing attempt to

try to teach something that is SO SIMPLE to teach. I am willing to bet these 'policies' were not written by real educators.

I remember when Bush introduced his 'NCLB' disaster, the one that we still have only on steroids now, we learned that NO EDUCATOR had been consulted on the program, it was invented by many of his BUSINESS buddies. No one needs to ask who thought up this garbage. No wonder we are so far behind globally, on Math and Science.

It's not ABOUT 'proof reading', it's about WHO WROTE THE TEST. Well, we know who writes those tests if we were paying attention during the Bush years.

They are written by 'Education PUBLISHERS'. And those publishers have made a fortune since Bush's NCLB continued under Obama and even worse now than it was then, was pushed on the public.

And, we discovered, most of those PUBLISHERS were friends of the Bush family. If you think they are in any way interested in 'education' I have another Bush 'program' to sell you.

[gollygee]

106. Read the subthread before responding

if you want to respond to what I've said in this subthread, it would help to read it.

[sabrina 1]

113. I have read the subthread and see that two people, MF and Rocktivity got it right.

Because obviously they remember this fight under Bush. You are arguing that this is some kind of simple typo. I pointed out to you that it is the SYSTEM itself, Bush's 'Education Program' which I assumed you knew was ALL ABOUT TESTING. That is why his buddies in the Educational Publishing business have grown so WEALTHY.

Eg, as a teacher in a Private School in NY before Bush's disastrous program, we did not have to test AT ALL until 3rd Grade. So we did not. Testing is NOT EDUCATION. I taught my kids how to take a test, but that was not educating them. That was done entirely separately and we never had a problem teaching simple or even more advanced math, WITHOUT TESTING until 3rd Grade. By then they fully understood math and aced those tests. But that was before Bush's 'Testing Program' which is now our 'educational system'.

What they did was to eliminate as much 'learning' time as possible and replace it with what is merely supposed to be a quick check to FIND OUT where a child might need some more help. A tool that isn't all that necessary to a good educational program but teachers use for their own info, NOT TO TRY to educate them with. No educator would even dream of 'Teaching to the Test'. It is moronic to think you can educate people this way, let alone children.

What it does is suppress the child's natural love of learning and force them to think only about the dreaded TEST.

Do the Math, it's simple, MORE TESTING = More Profits for Education PUBLISHERS. And that was Bush's goal, along with producing a workforce unable to think for themselves. Two birds with one stone, an uneducated population willing to work for low wages, and huge profits for the Corporations.

[kwassa]

180. There still is no national standardized testing until 3rd grade.

I'm not sure why you thought differently.

[sabrina 1]

221. Are you trying to tell us that NCLB or Common Core is optional? Tell that to the teachers

who spend their time TESTING not TEACHING and who have no choice. Schools are denied funding if they don't participate. Have you watched the video in the OP?

The teachers I know, those who haven't quit since this horrendous program was forced on schools, have to teach testing from as early as Kindergarten.

But we knew all this since Bush first implemented it. Not sure what you are trying to say to be honest.

[azurnoir]

250. The districts my kids have attended in do pre-tests in kindergarden, first, and second grades

the purpose is to weed out the 'problem' kids those who will likely fail, or who do fail, rather than tutor them most of those kids are put into 'special ed' classes sometimes under the flimsiest of excuses - speech is a popular one so that their test scores do not count against the school -note this is at the elementary school level, it gets more complicated in the secondary grade levels

[pnwmom]

210. I agree that this is all about profits for the testing corporations. Same with mass drug testing.n/t

[sabrina 1]

231. Yes, exactly. Drug testing has made some people obscenely wealthy. As has NCLB/Common Core or

whatever they are calling it now.

[pnwmom]

269. I realized I forgot one other reason. They want to prove the public schools

are failing, because they want to privatize all education. So any tests they develop are even more suspect.

[sabrina 1]

341. Yes, absolutely. Privatization of everything, education, SS, all of these programs

have been targeted for decades for privatization and it looks like they are succeeding.

[Enthusiast]

312. Well said and +1!

[sabrina 1]

73. Not 'understand', memorize the 'rules'. That is not understanding math. It is worse than

the old way of just teaching tables with no preparation beforehand that ensures an understanding that tables are simply a tool.

This is doomed to produce people who will never have an understanding of the basic, AND SIMPLE facts when it comes to math.

They will be like trained robots who will not be able to use their reasoning powers due to a lack of a real foundation where they understand the function of math.

[Curmudgeoness]

13. Obviously, I can't do math.

I am also surprised at the words used in that question for a 1st Grader. It has been a very long time since I was in school, but we did not learn to read such words at that level.

This Common Core is the biggest fuck up in education in a long time. It reminds me of the little experiment with "new math" when I was in school. It set me back so far in my comprehension of math when they decided that the way it had always been done wasn't good enough. And by the time they realize that new math was a total failure, I was so lost that it took me years to get thinks like long division figured out.

I feel sorry for the students who are the Guinea Pigs in this experiment, and I feel sorry for the parents, who can't even help their 1st Grade children with school work.

[muriel_volestrangler]

16. Are we allowed to say "this is a very bad question"?

(using language that might not get you marked down, as opposed to the words that first sprang to mind)

My thoughts include:
None of the options are 'sentences'
None of them involve 'subtraction'
'C' is related to the picture, but that's not so much a question I'd expect in a 'Common Core' test, but rather in an intelligence test; and I would have thought it above 1st grade, too. If they've been frequently taught addition with pictures of shaded blocks, perhaps you could get away with it (but would 'Common Core' be that proscriptive about how addition should be illustrated?)

[DeadLetterOffice]

185. Yes, yes indeed they would in fact be that proscriptive about illustration.

I can almost guarantee you that all parents of elementary age kids whose schools have introduced common core curricula have seen that same damn illustration or a variant thereof. My 5th grader calls it "math by Lego" because he thinks they look like interlocking Lego bits. And OMG have you seen the bar modeling stuff they're doing? My spouse and I have 5 degrees between us, 2 in math, and it took us FOREVER to figure out how to help kiddo with that homework.

I hate common core, I hate how it's being implemented, I feel awful for the teachers who are struggling with it, and I am keeping my kids home again this year when it comes tome for the testing. Screw it.

[Recursion]

228. All of the options are sentences; Common Core doesn't address testing

All four options are sentences. Any thing with a single equals sign, greater than sign, or less than sign, with stuff on either side of it, is a sentence.

Common Core also has nothing to do with tests.

[muriel_volestrangler]

310. As I said in #153, 'sentence' appears to be new jargon

For instance, I can't find the word used that way in the Penguin Dictionary of Mathematics, or the Handy Math Answer Book from Visible Ink Press. Or the Oxford English Dictionary, for that matter.

Common Core does, of course, have something to do with tests - from October 2013:

Over the next two years, the biggest changes to standardized testing in the U.S. in more than a decade will be put in place as 45 states implement the Common Core standards in math and English language arts (ELA). These states, which comprise 85 percent of American students, will adopt new assessment systems aimed at measuring whether students are learning the material specified by the new standards, which are designed to ensure student readiness for success in college and the labor force. A potentially important benefit of common standards is that they will allow states to adopt better tests at a lower price through collaboration on common tests. This would be particularly consequential in small states, which pay more for their assessment systems because they lack the economies of scale of large states.

The leading options for Common Core assessments are the tests being developed by two consortia of states that are funded by federal grants: the Partnership for Assessment of Readiness for College and Careers (PARCC) and the SMARTER Balanced Assessment Consortium (SBAC). Thirty-three states currently belong to at least one of these consortia, both of which are developing math and ELA assessments for widespread use beginning in 2014-15. PARCC and SBAC have estimated that their computer-based end-of year assessments will cost $29.50 and $22.50 per student, respectively. These costs are not far from the nationwide average of what states currently pay for their existing tests, but many states have expressed concerns about these costs, especially states that currently spend well below average.

Assessment costs have always been a political football given the controversy surrounding standardized testing, and that has only intensified with the debate over Common Core. Concerns about the cost of the consortia’s tests likely stem in part from a sense of uncertainty because the consortia have announced estimates, but not firm prices. States may be concerned that the price will go up, especially if states leave the consortia, and that they will be left without an affordable alternative. Opponents of the Common Core may be hoping that the withdrawal of a few states from the common assessments will lead to the unraveling of the consortia.

http://www.brookings.edu/~/media/research/files/reports/2013/10/30-cost-of-common-core-assessments-chingos/standardized-testing-and-the-common-core-standards_final_print.pdf

http://teaching.about.com/od/assess/a/Common-Core-Assessment.htm
http://tn.chalkbeat.org/2014/09/18/for-representatives-at-nashville-education-summit-common-core-number-one-issue/

[Recursion]

322. That's ridiculous

For instance, I can't find the word used that way in the Penguin Dictionary of Mathematics, or the Handy Math Answer Book from Visible Ink Press. Or the Oxford English Dictionary, for that matter.



The term has been in use since at least the 1950s.

[muriel_volestrangler]

330. And yet, many DUers haven't heard it, and neither have those reference books

It's clear that you can get educated to quite a high level (Further Maths A level, in my case, and degree in Engineering, in the 1980s) without hearing equations called 'sentences'.

[gollygee]

353. Well it's new jargon

so you would have had to be studying math when the new jargon was being used. That is the language used in classroom though, so kids are familiar with it.

[Ms. Toad]

413. They are sentences

What makes mathematical phrases into sentences is the presence of a relation symbol (=, >, <, etc.) It is a single word, which encompasses all of the various relationships between two mathematical phrases.

But I agree as to subtraction. If it is a subtraction sentence, it needs to have a "-" in it. It is a very bad question.

[Tierra_y_Libertad]

18. My answer would be...When's recess?

And what is a good citizen? Simply one who never says, does or thinks anything that is unusual. Schools are maintained in order to bring this uniformity up to the highest possible point. A school is a hopper into which children are heaved while they are still young and tender; therein they are pressed into certain standard shapes and covered from head to heels with official rubber-stamps. H.L. Mencken

[justabob]

19. "hire a better editor/proofreader"

would be my answer..... "+" doesn't = "subtraction" to me, no matter how hard I try.

[Man from Pickens]

95. I believe the low quality may be deliberate

I've already come to call it "Common Corporatism"

[justabob]

103. whether deliberate, or simply incompetent

it is wrong and we should not tolerate it... common corporatism indeed. Ugh.

[sakabatou]

21. Subtraction sentence?

So it's.... pictures instead words. Weird.

[hfojvt]

23. seems like an odd question for a math test

subtraction sentence? Who gives a crap?

In my 52 years on the planet this is the first time anybody has ever asked me about subtraction sentences. Unless they did so in the 3rd grade and I have long forgotten it.

"The things that pass for knowledge I can't understand"

apparently I am reeling in the years

[elleng]

24. Thank GOODness for Carol Burris (again!)

She's principal of MY high school! (way after I was there, of course.) Pic of it in the video.

and she said she STILL can't figure out the question/answer.

[madfloridian]

54. She is very impressive and intelligent in that video.

[elleng]

130. Yes she is,

and tho she wasn't there, at South Side, when I was there, I'm very pleased to see confirmed that my high school has maintained its excellence. Too bad I didn't live there when married and parenting, as so 'spoiled,' we paid for elementary and high schools for our daughters in DC.

[Atman]

25. ONCE AGAIN, Common Core is ONLY about selling common text books to a mass market.

Nothing else. NOTHING. That's why Jeb Bush won't run for POTUS...unless Common Core appears to be on the verge of being overturned. Jeb will then stand to make far more money (and have far more influence) if he heads up a nationwide educational publishing company guaranteed to sell TENS OF MILLIONS OF BOOKS AND TESTS with EVERY printing.

You can bet your lunch money that they'll be updating the books very regularly, and Jebbie will back a law saying every school district must conform to the "Common" standards. This is a huge, massive money grab. Privatization of education, nothing less. They could give a flying fuck who passes or fails. The more failures, in fact, the better. Then the private test-prep companies can sell you special courses which will help "prepare" your child for the test. Your kid will still emerge dumb as a box of rocks, but he/she will sure as hell know how to kick ass on test!

[navarth]

139. very plausible. nt

[nolabear]

27. There's nothing wrong with this. It's just out of context.

I can pretty much presume the child got the answer right because I can put 4 and 3 together, but I'm betting this is something that's been shown to the child in this way and the illustration makes sense.

I see no problem.

[Tikki]

28. Me either...

Tikki

[Atman]

29. Absurd.

The only "common" thing in this equation is that four dark blocks + three light blocks equal seven blocks total. BUT...and this is a big but...the child is asked a SUBTRACTION question. Every example is an addition question. Therefore, the child is left to guess. There is no way to determine WTF the test preparer had in mind. There is no logical answer, other than that one of the answers (C) is seven, and they're looking for seven. That's not math...that's a fucking party game, or one of those stupid puzzles from Spencer Gifts. It's a travesty.

[madfloridian]

45. Thank you, yes, it's a travesty.

[nolabear]

83. But perhaps not if you had been in the class.

If it had been in Latin I wouldn't understand it either, unless I'd been told in the class and this was a test to see if I remembered what I had been taught.

[chervilant]

160. Do you not see how confusing this might be to a child who at some point in the future

may still associate a 'plus' sign with subtraction? Particularly for visual learners, this association may be embedded in their memories.

I am astonished that you think this question is okay. I've worked with lots of young adults who struggle with the language of math because of poorly written tests. As I help them to recognize math words like "integer," "parent function," and "rational number," they come to me and tell me that understanding math language has helped them tremendously.

A recent survey of the general population found that 80% of US citizens hate math. I think these types of poorly written worksheets contribute to that high percentage.

[Recursion]

226. What's wrong with associating the plus sign with subtraction?

I have a STEM masters and when I have to do subtraction in my head I do it as addition of an unknown because it's less error-prone.

A recent survey of the general population found that 80% of US citizens hate math. I think these types of poorly written worksheets contribute to that high percentage.

From what I've seen tutoring I think the new ways math is being presented (and not so new; Euler used some of these with his students) are a real attempt at helping that by getting kids to think about numbers and quantities and relationships rather than memorize steps they have to take to solve a problem.

[DebJ]

239. What I want to see in 15 years, though, is will these kids know if they get the right change back

at the store?

Having the multiplication tables in my head and being able to do math in my head, not on a calculator, has been
of great value to me throughout my life at home and at work. I can't imagine, for myself, not being able to do it.

But managing restaurants over the years, I was constantly horrified at the questions I would get from cashiers:
"This guy gave me a 20 but I put into the register that he gave me a 10. How much change do I need to give him?"

Argh. After the customer left, I would always ask the employee, "Tell me, when you go clothes shopping, and you
get change back from your bills, do you know if you got the correct change?" They always said no, they never
thought about it.

Scary.

I'm glad I had to do rote memorization on many things. Now my head is my computer, and I don't need batteries
or a charger or a power source to function.

[Recursion]

240. You don't count change *up* from the purchase price?

"That was a $1.87. (three pennies) 90, (dime) $2, (three ones) $5, (a five) $10, (a ten) $20."

When I was working retail we had instructions to count up (ie, add rather than subtract) like that, I suppose precisely because of the problem you mentioned (kids taught to do subtraction the long way).

[DebJ]

249. Doesn't matter if it is 'up' or 'down', the point is,

this actually is not taught at all, and hasn't been for years, not in these parts, anyway.

Interesting you were taught ON THE JOB, or so it seems from your sentence.

That shouldn't be necessary.

In my own personal case, my teachers taught us to do it BOTH ways. Which also taught us there is more than one way to get through most things in life.
That was a major lesson in Algebra, too... the teachers always wanted to see the work we did, and gave credit for the thinking out process.... which also
gave the most WEIGHT to the thinking process.

[chervilant]

356. Excellent point.

I'm tutoring a young man right now who has missed math instruction from the fifth grade forward. He wants to take his GED and go to college. His math deficits have been overwhelming, and he's struggling most with not knowing basics that many of us take for granted, like having the multiplication tables memorized.

[jeff47]

382. The problem with your approach is people like me.

I have dyscalculia. Think of it as dyslexia for math.

I can't have the multiplication tables in my head. My head does not work that way. But I can easily do calculus if I have a calculator to handle the addition and multiplication.

Rote memorization does not work for all students. The techniques taught by common core are an attempt to also cover people like me - the mechanisms they teach actually work in my head.

As a result, I never know what my correct change should be unless I want to take a few minutes to try and add it up. Because I was taught math the same way you were, and that way does not work with my brain.

[DebJ]

388. Of course, everyone's brain works a bit differently from everyone else's.

That's why I don't think students should be forced to learn any one method. They should be given a variety of options
and allowed to do what works for them. What is lost in all this B.S. is that the goal should be to get the right answer.

[jeff47]

389. The goal, IMO, should be to understand why it's the right answer

Memorizing 5+7=12 doesn't help much.

Understanding why that is the case is more helpful, which is what these "new" techniques are doing.

[chervilant]

331. From what I've seen tutoring,

there are myriad ways that students use to play math, and rote memorization is the least effective. Learning the language of math helps many students 'demystify' math. Helps with the dreaded word problems, too.

We will have to agree to disagree about common core. I don't like it nor do I like the ways they've chosen to implement it. (If they're genuinely concerned about students' critical thinking skills, I'm green with pink polka dots.)

(BTW, I'm confident that math geeks 'get' subtraction...)

[laundry_queen]

86. +1

Plus, it's important to remember this is for first graders. The other day my 7 year old in second grade asked me what the word related meant. And she gets perfect marks at school. (We are in Canada though so our system is different, and she is in French Immersion so they don't concentrate on English vocabulary in Kindergarten and 1st grade, she just started it this year.) So not only is it not a straightforward question, it also poses it with words that a first grader may not recognize.

In university, our profs told us that we were to pick the BEST answer (ie if an answer is too vague or the question to convoluted, pick the BEST answer, even if it might seem not quite right). I doubt first graders are able to figure THAT out. I was the type of kid who always asked myself the question, "What are THEY (the test designer/teacher) looking for?" because what they are looking for is not always what I think is the right answer and that has always served me well on tests because what the teacher wants is more important than what you think. I think that needs to be taught (it came naturally to me as I had narcissistic parents who thought I should be able to read their minds...)


Anyway, I've always been against tests that aren't straightforward. At that point, you aren't testing the material, you are testing a child's thought process (and ability to work under stress) and every child has a different thought process. You can't teach it and there is no right or wrong answer. In this case, a child (like me) may decide they must be looking for C. Another child might decide that all the above are wrong because it is not a subtraction question and may answer something else. It doesn't mean child A is smarter than child B, it means their thought process is different.

I definitely agree it's a travesty.

[callous taoboy]

140. Yes! It is not a valid question! n/t

[Egnever]

188. Whats absurd is the pretense that common core standards made this test question mandatory

Common core has nothing to do with the test questions. Common core sets the standard goals our children should be achieving. It doesn't mandate how you teach it or how you test it.

This test has absolutely nothing to do with common core. Other than possibly being a bad example of a tester trying to evaluate weather the level of education had been achieved.

[Recursion]

205. Subtraction is addition. In fact, addition of unknowns is a better way to do subtraction problems.

I know some of the kids I've tutored have been taught that way, and it's what I do in my head personally. Addition has no associativity issues so it's a better way to think about things.

7 - 3 = 4, so 4 + 3 = 7. So, a better way of asking what 7 - 3 = is to ask 3 + what = 7?

[Egnever]

362. The kids you teach are lucky

They will do better in math their whole lives because of your ability to show them the fun in playing with the numbers.

Bravo!

[Donald Ian Rankin]

305. OK, I'll say it: this looks to me like potentially quite a good approach to teaching.

I think that teaching children that 3+4 = 7 and 7-3=4 express the same mathematical fact may well be quite a good way of doing things.

[DireStrike]

75. What context is there for calling addition subtraction?

[Tikki]

94. "related"...

I work math problems with my grandchildren every school year night.

This is math speak and if taught this way, it is so obvious it is silly.


Tikki

[DireStrike]

97. Why not just use the word "addition" instead of "related subtraction"?

[Tikki]

101. In some grades they will be taught straight math language and in other grades they start the brain..

work for Algebra and beyond.

Kids are awfully smart and adaptable today. They learn many different ways to catch a concept.

I say BRAVO.

Tikki

[pnwmom]

300. Except the same test, page 2, uses the standard definition for a subtraction sentence.

There is no way to excuse this. It's just a mistake, plain and simple.

http://roundtheinkwell.files.wordpress.com/2013/10/the-math-test.pdf

[callous taoboy]

142. "Addition fact" would make it a valid question for this grade level.

Thank you.

[Warren Stupidity]

165. subtraction can be expressed as addition with a negative number.

8 + (-3) is the same as 8 - 3.

[Dragonfli]

197. Not applicable to the question and answers being discussed

If it were we would have seen answer options like these :
E. 7 + (-4) = 3
F. 7 + (-3) = 4

(assuming the picture is related somehow and not just decoration or a doodle left by the student)

[Warren Stupidity]

327. I was responding to the post asking how addition and subtraction could be conflated.

They are both forms of addition. "Subtraction" is a subset of addition.

[nolabear]

92. Looking at it again and reading elsewhere, it's clearly a typo.

The child got it, so knows what the intention was, which is encouraging, but it's simply a mistake.

[Recursion]

238. Watching the video I'm leaning towards a typo now too, though I've tutored kids who are taught

the way I read it as in the first place: replace all subtraction sentences with addition sentences.

[joshcryer]

333. Page three of the homework has a similar thing:

http://roundtheinkwell.files.wordpress.com/2013/10/the-math-test.pdf

Problem 8.

It could be a typo, but the more I look at that homework assignment it seems to me that they are trying to at least give equal weighting to alternative concepts. If it had the subtraction sign there it wouldn't fit with the rest of the homework, because they have at least one unconventional way of thinking about numbers per page.

The first page has a weird one that another poster was baffled by and I would be too, if your posts here didn't make me try to think outside of the box.

[itsrobert]

30. There is no correct answer here, but you choose the best answer available

This is not a math or English test. It's a reasoning test.

I don't think that is the intent, but it could be use to see how a child reacts when the correct answer is not there.

The best answer available is C. It could be a very valuable learning tool, if there was a classroom discussion afterwards on why students chose different answers.

[madfloridian]

56. So the "best answer available" is a wrong one? That is NOT okay.

[itsrobert]

91. In life, the correct answer is not always there for you.

That's life. You make do.

[madfloridian]

96. Now that response is the best I ever heard. No correct answer, just make do. LOL

[callous taoboy]

143. No shit! Suck it up, first grader new to math newbie loser :/

Ha! Sucks to be you, first grader. Get used to getting gamed.

[DebJ]

232. That statement is supposed to have added to it: EXCEPT MATH.

That's supposed to be the one thing you can count on. One plus one is always two. Unless I guess you decide it
is a subtraction sentence when it has the symbol for addtion. Sheesh. I am SOOO glad my grandchildren will
be going to school in Virginia.

[Rex]

440. But this is a test, you know, something that is supposedly 100% accurate.

How are people missing the forest for the trees here?

[IDemo]

65. Kind of like a US election, in other words

[WinkyDink]

31. IDGI. Are we supposed to look at the bar and see 4 filled-in squares and 3 not, to get (C.)?

[MannyGoldstein]

35. Which is why the country should have adopted Mass' framework and test

The Mass Curriculum Framework and the associated tests (MCAS) have been tested and tuned for decades and they work very, very well.

Starting Common Corre from scratch was unbelievably stupid, just a gift to private corporations and a way to give crazy people (e.g., school boards in certain states) a way to add fantasy and reduce science in the curriculum.

Shame.

[zazen]

110. and Gates Foundation had already screwed up with the untested New Schools Initiative

What did they do when the evidence didn't bear out, and schools had been upended, flocks of faculty fired and re-hired, states who rushed to pass legislation to fund the "New Schools" approach with scant evidence . . . why, Gates just went on to throw more money into Common Core and slowly pulled out of the whole New Schools thing. And in NC, we're left with another useless educational initiative with high paid admins and consultants, layering on more "reform" crap onto already collapsing teachers and principals.

Why the hell can't Gates just stick to his laudable global health philanthropy and leave education alone? (Of course, it's to distract us from offshoring and automation-related downsizing, the REAL reason "American graduates can't compete.&quot

[madinmaryland]

38. 1st Grade? Do 1st graders even understand the words in the question and what the sentence actually

means?

[Tikki]

184. Yes they do and if they don't, at least where I live, there is a tiered Kindergarten and an...

adaptive 1st, 2nd and 3rd grades.

I have learned so much working with my grandchildren on their Math.

They are both in elementary school. I have great hope for them.


Tikki

[gollygee]

195. That's the language they're taught with

My kindergartener, who has only been in kindergarten three weeks, recognized the term "subtraction sentence" (and also recognized the word "subtraction" was a mistake because it has a plus sign.) It's amazing how early kids are learning stuff like this - and also how early they learn to read (though my kindergartener is just a beginning reader, I have no doubt she'll be a strong reader by next year. I've been through this before with my older child and kids are really getting this stuff.)

It's certainly changed since I was a kid in the 70s.

The speicifc language is jargon, but it's jargon used in the classroom and familiar to kids. However there's a typo - it should say "addition" instead of "subtraction," so it isn't a good example. (And I can't imagine something with so few questions and corrected by hand is a standardized test. It's probably a classroom assignment.)

[Atman]

39. If Noah built an ark 300 cubits by 50 cubits, how many dinosaurs would fit on the Promanade Deck?

[valerief]

47. Trick question. It's Promenade. nt

[IDemo]

69. We're targeting future Tea Partiers..

[valerief]

87. My bad. If that's the case, then I know the answer.

As many as God wants. Cuz, you know, God's will.

[Atman]

107. "How many brains does a moran got?"

Answer: "Keep gub'mit out of my Medicare!"

[valerief]

123. A Repubican would never write "gub'mit." S/he'd write "govrement." nt

[DebJ]

236. Benghazi! That's the answer to every question. n/t

[Atman]

105. A+ Johnny.

It was actually a spelling equation, not a math sentence.

[mopinko]

43. makes perfect sense to me.

teaching kids that adding and subtracting are related makes more sense to me than rote worksheets and number "facts"

c

teaching children to look at numbers as representative of objects is also good curricula.

[madfloridian]

52. I taught number families. I never misrepresented subtraction as addition.

[DebJ]

243. The words "George Orwell" keep flashing in my brain. n /t

[madfloridian]

48. Wow, this one really drew the supporters of "reform". Support anything madfloridian opposes.

Amazing. I did not expect recs, never get them here anymore anyway....but I did not expect people to defend asking for a subtraction answer when there are none.

Unbelievable.

[whistler162]

438. SInce you oppose everything that is

not difficult!

[MineralMan]

50. The correct answer, of course, is C.

Look at the illustration. Four shaded squares and three unshaded. There are seven squares. C is the only example that shows the 4 and 3 in an addition equation. 7-3+4. 4+3=7. Students are to compare the illustration with the arithmetic statements. All add up to 7, but only one uses 4+3=7. The equivalent subtraction is 7-3=4. I didn't learn arithmetic this way, but this is not an arithmetic question. It is a question about equivalence, which is something that will be very useful to students later down the mathematics road.

There is method in this that makes sense. The three terms in question are 7, 4 & 3. Equivalence with the illustration means that the only correct answer is C. This is about reasoning, not arithmetic. Reasoning is important, too, in mathematics, and algebra is based on turning equations into other equations.

Good question, and the student got it right.

[madfloridian]

51. Oh, come on now. It asks for a subtraction sentence. There are none.

[MineralMan]

68. No, it asks which is an equivalent subtraction sentence.

Equations are sentences. Four plus three equals seven. Seven minus three equals four. The two sentences are equivalent. The equations are equivalent. That is what is being asked. I was not taught this way, but I understand the reasoning. It leads to algebra, where the sentences might be written like this.

4+x=7
To solve for X, you rearrange the sentence (equation) to
x=7-4

The two equations are equivalent. That's how algebra works.

Basic algebra. Students who learn this early, using mathematics and equivalence, have an easier time with algebra. I learned arithmetic in the old-fashioned style, but equations like this were something I learned to rearrange very early, so when algebra came around, I had already figured it out. But I was a bright fucking kid and figured out a lot of math stuff for myself.

Now, they're trying to teach things like this earlier. Equivalence. The illustration is a subtraction equation. The answers are additions. You didn't learn it this way. They're teaching it this way, so kids will understand that equations (sentences) can be manipulated to be equivalent.

You don't understand the reasoning. The kids in that class do. That's why the answer on the test is correct. The kid understand what is being asked, because that's how it's being taught. Basic algebra will be easy for that kid, because of this teaching method.

I rest my freaking case.

[madfloridian]

71. Oh, gee, that is way above my level of understanding.

I am very worried about far the anti-public school movement is going.

[MineralMan]

175. Perhaps it is. I'd have no way of knowing.

I do not know how they are teaching these concepts. As I said, I was in the first grade in 1951, and we learned arithmetic the old way. I was bored and played with numbers in my mind in different ways. As it turned out some of those ways ended up being part of new math. My elementary school teachers left me alone with my odd musings about numbers, since I got perfect scores on every test.

Today, they're trying to teach some of the things I figured out for myself. Sometimes it works and sometimes not. But then, the old methods had the same problem. Starting in fourth grade, my teachers had me helping my classmates who were struggling. I could usually find a way to help them make sense of it, using different strategies than were used in class.

There is no single method for teaching math that works for everyone. We need smaller class sizes or kids like me in every class.

[msanthrope]

282. FYI...my kid is taught two strategies (at least) per math concept. It's a way

of keeping everyone rolling along...but it's also a way of teaching resilience. My SPED daughter gets less frustrated knowing there are multiple ways to solve problems.

[MineralMan]

337. I think that's very good.

When I was a kid, it was all really old school. It was OK, I suppose, but not conducive to different ways of thinking. Kids who didn't get it, didn't get any alternatives to work with.

[msanthrope]

340. That's what I think many critics of Common Core get stuck on--at least, from the critiques

of Common Core that I read here on DU, there seems to be a lack of knowledge about how kids learn.

I think I am younger than you, but I was sent to restrictive Catholic sisters and then Jesuit schools that taught "one way" with no alternatives. This made my early to high-school education very difficult for me as I was a genius according to the tests, but dyslexic and had a stutter. I was reading at a college level in the first grade, but was unable to subtract or divide. I was a SPED student who was given little help in learning. It was a wonder I stayed in high school.

My daughter, as I wrote, is also SPED. She may not get every method--heck, I find myself using Google University to finish some of her homework--but she is definitely having a better time of it than I ever dreamed of. I love the Common Core--don't have a complaint about it.

[MineralMan]

357. Well, some people see Common Core as one more step

toward privatization of education. Common Core, in itself, has nothing to do with that, and it's implemented in different ways in different places. It's interesting that the Right Wing, too, is opposed to Common Core. Different reasons, I suppose, but still interesting.

I really need to step away from education discussions, I think. Too much polarization and not enough knowledge gets in the way of real discussion.

[immoderate]

100. It asks for a subtraction sentence. It does not present any.

I have to assume the test is in English. This question is an error.

--imm

[questionseverything]

118. it is a typo dude

as someone that deals with cc everyday with a first grader i can tell you subtraction is still 7-3=4 or 7-4=3

the addition sentences for that math family are 3+4=7 or 4+3=7

if the question had read, what is the inverse of the subtraction sentence,you would be correct about c

madflo is correct, you folks will say ANYTHING to keep from admitting there is even the smallest of problems with anything potus pushes...even going to great links to defend a typo

http://www.corestandards.org/Math/Content/1/introduction/

[Lonusca]

159. Check out the article

http://www.washingtonpost.com/blogs/answer-sheet/wp/2013/10/31/a-ridiculous-common-core-test-for-first-graders/

And you can check out the actual test by the student at the link.

[jen63]

122. It makes perfect sense to me.

Maybe if I'd been taught this way I would have "gotten it." I had a terrible time with higher math. My son missed common core, but he always got it for some reason.

[muriel_volestrangler]

153. It asks which is "a related subtraction sentence", not "related to a relevant subtraction sentence"

All of the answers are addition "sentences" (though 'sentence' is a bit of new jargon that would get a lot of people saying "oh, for fuck's sake"; it's an equation to us). They may state a concept equivalent, or related, to a subtraction sentence, but they aren't subtraction sentences.

We understand the reasoning. We also understand English grammar, and the test setter seems not to.

[CANDO]

79. It clearly asked for a "related subtraction sentence".

"Related" means you find the correct answer using your thinking skills. Addition is related to subtraction in that you are reversing the equation. The graphic clearly gives the student all they need to find the correct answer in the given examples.

[madfloridian]

80. Okay then.

Whatever you say.

[CANDO]

89. I undertsand your frustration.

I'm 50 yrs old. We were taught differently. We see numbers and graphics and just want things that are easy to resolve using the methods we learned. They want kids to think more and this is a perfectly illustrated example.

[madfloridian]

99. I taught new math, old math, then new math again. Please do not talk down to me.

I am sick and tired of being treated as unintelligent and treated with disrespect at of all places a Democratic forum.

[CANDO]

109. Not talking down to you.

Are you seriously saying you didn't or couldn't find the correct answer to that test question? Again, it was not a "subtraction" question. It was a "related" subtraction sentence. And in the given answers, the correct "related" subtraction sentence was clearly C. I get it, most people immediately get hung up on the thought that it's a subtraction question and are insensed that none of the answers show a subtraction. I'm sorry you feel talked down to. That was not my intention. I'm no Einstein my damn self. I'll move along and not clutter up your thread any more than I already have.

[madfloridian]

137. They should then have asked for an answer related to same number family.

If they used the word subtraction with concrete thinkers like 1st graders, then they should have had an answer with a minus sign.

[callous taoboy]

149. Madfloridian: You understand young kids. Case closed.

But I tell you the hell what. I'll be sure to use the term "related subtraction sentence" next week, all week, in my second grade class if it will satisfy the test makers instead of enhance my students' understanding of fact families. This is what drives me crazy these days as a teacher of newbie math students- The potential of botching how it will be phrased on THE TEST vs. shooting for a basic understanding of the concept.

[TygrBright]

163. Maybe the kids are conditioned enough to tests...

...to understand the relationship between the symbol of blocks or whatever it is, and the question.

All I know is, I read the question and the first thing I thought was "Related to WHAT?"

I didn't even perceive that the dark/light blob above the words was a line of separate objects until I'd puzzled over it for more than ten minutes, and read through the entire thread, and AFTER posting a stupid question.

Perhaps this is a valid, even a superior, theory of mathematics teaching (or at least arithmetic teaching,) but what this illustrates to me is that kids are being taught to take tests, not understand arithmetic.

sadly,
Bright

[gollygee]

173. Schools use the blocks pictured every day in school these days

Even my kindergartener, who has only been going to school a few weeks, instantly knew what they were.

[pnwmom]

209. So? None of the equations constituted a subtraction sentence. nt

[gollygee]

218. Yes, and as a number of people said, that appeared to be a typo

However it doesn't look like a standardized test, since it's short and was hand corrected. It might just be a classroom assignment, and people do make typos. A typo on a classroom assignment doesn't say anything about the value of common core.

[pnwmom]

207. Stupid question. None of the equations constitute a "subtraction sentence."

You are twisting yourself into a pretzel in order to justify what was obviously a typo.

[Lil Missy]

53. C is the correct answer

[pnwmom]

213. Wrong. C is not a subtraction sentence; it is an addition sentence.

Mathematical words have precise meanings. Children are supposed to be learning that there is a difference between subtraction and addition, even though the "facts" are related.

[Lil Missy]

230. And the monkey wrapped his tail around the pole .......

[CANDO]

59. It's about teaching critical thinking.

I can't believe we have adults on here or anywhere being stumped by the equation. The graphic clearly shows 4 shaded and 3 unshaded areas. It gives you 4 possible addition answers. Now, how the heck is it that difficult to understand they want you to find the correct addition in order to get the proper subtraction answer. It teaches you (or a child) to T H I N K.

[madfloridian]

62. It asks specifically for a subtraction problem.

It was an error by the testing company. Why defend a wrong test item?

Is it to prove me wrong because this is the policy this administration? And there is to be no dissension?

[CANDO]

85. No. It asked for a "related subtraction sentence".

Not a subtraction sentence, a related one. And given the graphic and the possible answers, there is only one correct answer. It is an obvious semi-trick question to get students to T H I N K.

[madfloridian]

88. " It is an obvious semi-trick question to get students to T H I N K."

[DebJ]

242. It teaches them to realize that they must understand the specific jargon, and when new standards and

tests have been created using new 'better' jargon, then what they will learn is that they need to learn the new jargon,
that what is important is the jargon.

All children learn differently, relate differently. Different children will grasp different jargon more easily than others.

I think it is bunk. Just a corporate planned obsolescence.

[BuelahWitch]

319. Especially bunk for a first grader n/t

[magical thyme]

72. I wasn't stumped by the equation. I was stumped by the phrasing of the question.

I understand the relationship between addition and subtraction (as well as multiplication and divison). I don't understand why they referred to 4 addition problems as "subtraction."

So given a choice of 4 addition problems, I chose the correct solution. But still don't understand why they chose to call it a subtraction problem.

I went through grade school math some 50+ years ago with honors. I didn't bother past algebra 2 -- went into the arts instead. 45 years later I went back to school for med lab tech, with pre-med level algebra, statistics and chemistry (applied algebra, pre-calculus, etc) and graduated summa cum laude.

But I think the latest approach is cumbersome and confusing.

[DireStrike]

81. A critical thinking question based on the picture might look like this

"Q: Which set of numbers goes with this picture?

A: 1 4 8
B: 2 5 9
C: 7 3 4
D: 1 6 7"

This question is not directly about math, it is about solving a puzzle. Note that I haven't assigned any words in my example to mean the exact opposite of their dictionary definition in an attempt to trick students into "thinking critically" by making the wording confusing. I haven't included coded instructions or riddles in the format of the test. And yet somehow my question still prompts critical thinking, all while following the expected and easily understood format of the test!

The question in the picture (if it isn't simply an error) has for some reason decided to radically redefine terminology that everyone else in the world will be using in the traditional sense. There's no way this can lead to anything but problems.

[CANDO]

102. See my posts on "related subtraction sentence".

We can say nearly any example shoulda coulda woulda been done differently. I just don't see a problem with the example as given. It is sort of complex for a 1st grader in that the student must take in the entire question, illustration, and possible answers to arrive at the correct conclusion by T H I N K I N G.

[DireStrike]

112. It depends what is being taught and at what level

I could see questions like this on a single quirky low-stakes test in junior high, to get kids to think outside the box.

Basic arithmetic is something that first graders need to memorize, not understand in the appropriate mathematical theory context. When I buy a full box of items at costco, about half the cashiers are not able to multiply a column by a row to get the full number. Others try to do it and get stuck on really easy ones like 3x12. Basic arithmetic skills are not getting through. We should not be complicating the teaching of the lowest level of math in order to make higher order math easier. The failure in our system has to do with not engaging kids properly, not failing to use the proper theoretical framework to discuss basic operations.

Aside from that, I question:

-The efficacy of this method. Is there any proof that teaching arithmetic this way actually leads to better understanding of either arithmetic or algebra? Could we maybe just... introduce the concept of basic algebra sooner? It's the same thing, but everyone else already knows what algebra is and how to talk about it. But this just generally isn't done because...
-The age at which this is being taught. I am not an educator, but I'm not entirely sure first graders are familiar enough with the relationships between various sets of numbers to begin thinking of them in a theoretical framework. Some people struggle with algebra in 9th grade, and this seems to me to be just a more confusing way to do basic algebraic equations.

[DebJ]

253. Well said. And I wonder if the implementation process is the same in other areas

as it is here. They jumped right into the new teaching schedule for concepts, and as a result, students are being
'taught' concepts based on math basics THEY HADN'T BEEN TAUGHT YET. Please remember that being 'taught'
something isn't the same as learning it.

I am getting this input from a math teacher of 15 years who was previously lauded as an outstanding math teacher, and whose
students consistently got excellent testing results and improved remarkably and was well-liked.

I can't recall her many specific examples, but this would be a similar concept: teach kids multiplication before they understand
addition. Make a child write in cursive before they can recite their ABCs. That type of 'process'.

As a result, large numbers of students have concluded that math is simply unlearnable, and therefore, useless, as well, hating it
much more than I ever hated reciting times tables.

It is my firm belief that this is happening because palms are being greased on the school board. If not that, then they all should
have died of terminal stupidity.

[RufusTFirefly]

147. I think there's a grammatical problem. The phrase is suffering from a modifier traffic jam

It's a little like "small business leader"

a. Does it refer to a leader of small businesses?
b. Or a business leader who happens to be small in stature?

Copy editors would typically add a hyphen between small and business in the case of option a.
The ambiguity in the subtraction question is not so easily remedied.

[Sancho]

227. You are aware that children this age don't "think" the way adults do?

That's why teachers study and get experience with child development.

Children in the first grade think "concretely" and cannot always do mental reversals. All the math people and "thinkers" on this thread have obviously not taught math to elementary age kids (I have) or studied the thinking and testing of young kids (I have). Some kids in 1st grade would not be able to pick C as a "related" equation. Madfloridian is describing accurately what really happens in classrooms where the emphasis is teaching the test, not individually teaching the child.

In other words, you can't force kids to "THINK" before they are developmentally ready and until they've had appropriate experience and time to mature. Each child is different, no matter how uniform and regimented the standards and curriculum are meant to be.

Virtually all experienced teachers see it when kids are frustrated, and also see the mistakes kids make so they can help them learn. Most importantly, they need to learn to enjoy learning. Right now, most kids fear and hate math by the time they get to 4th grade, and almost always by 6th grade. Making them "THINK" and get it wrong often creates the exact frustration that causes them to hate the subject.

CANDO...think about it!

[DebJ]

270. Wait a minute, you mean teaching involves little human beings? Not widgets? n/t

[Sancho]

307. Yep!

[madfloridian]

60. Whoever gave 5th rec...thanks. But now I am in the wrong for saying the item is faulty.

It's just amazing how that happens here.

[truedelphi]

433. And are you sure it was indeed the fifth rec?

Did you get to that answer by the subtraction method or the addition method,

and Goddess only knows, I hope a committee helped you, as otherwise you are not the sort of individual our country needs! And I guess I am in that boat with you!

I was tutoring a seventh grader in math. She had gotten no instruction from her book or her teacher, on "set theory" instruction, and then we turned a page in the book, and there was a whole chapter on intermediate set theory! I mean, I have nothing against set theory being taught, but you cannot just jump into the middle of a subject without first covering the basics of a subject first.

[madfloridian]

61. My 2nd graders knew the difference between addition and subtraction.

The question did not ask for another member of the number family....it asked for a subtraction problem.

[Kablooie]

70. Then they are wrong. This test insures that kids do NOT know the difference which must be the goal.

[madfloridian]

93. Amazing. I am wrong. 2nd graders are wrong. Yet there is still no minus sign.

They knew number families, but they were asked to choose a subtraction answer. First graders do not think abstractly enough to be "tricked" into an answer.

[Kablooie]

119. Just shows that your kids are smarter than the people who devised the common core test.

[Recursion]

254. There is a "common core test"?

When did that happen?

[callous taoboy]

132. I also teach 2nd grade: It's a poorly worded question, i.e. not valid:

You want to ask this age level a question regarding fact families, ask: "Which number sentence would belong to this fact family?" Sure, the term "related" is in play here, but is it really a valid question for this age level? No. third grade? Maybe. Fourth grade, yeah they should be familiar by then with fact families to incorporate "related" into the lexicon. Second grade: I might be introducing the term.

[4dsc]

63. You do all realize the children are taught this first

then given the test.

Your outrage is funny and simple minded.

[madfloridian]

66. Yes, I am often called simple-minded here.

[callous taoboy]

134. How are they taught this. Do elucidate.

[Egnever]

191. Like this

Students develop strategies for adding and subtracting whole numbers based on their prior work with small numbers. They use a variety of models, including discrete objects and length-based models (e.g., cubes connected to form lengths), to model add-to, take-from, put-together, take-apart, and compare situations to develop meaning for the operations of addition and subtraction, and to develop strategies to solve arithmetic problems with these operations. Students understand connections between counting and addition and subtraction (e.g., adding two is the same as counting on two). They use properties of addition to add whole numbers and to create and use increasingly sophisticated strategies based on these properties (e.g., “making tens”) to solve addition and subtraction problems within 20. By comparing a variety of solution strategies, children build their understanding of the relationship between addition and subtraction.

[DebJ]

257. And of course they have done extensive work with small numbers in first grade????

That doesn't seem right to me.

There are still children who don't get to go to preschool or kindergarten.

Oh, but wait, their parents don't have money, so they don't 'count'.

[BuelahWitch]

392. Yeah, a lot of people seem to forget this is a question for first graders...n/t

[pecwae]

447. Even my privately schooled

1st grade grand daughter could not answer that. She wouldn't understand the wording of the question. Rich, poor or in between these are 1st graders. Posters are conveniently forgetting that.

[Sancho]

323. You are wrong about students being taught "like this"....

Students at certain ages don't have the cognitive maturity to "develop strategies". That why experienced teachers know that students vary widely in development, talents, and strategies. One size doesn't fit all, and all cannot learn to "model ... and compare situations" in 1st grade. I've seen 5th graders who still struggle with concrete operations sitting next to other kids who are able to tackle algebra. It often depends on natural development, home enrichment, willingness to learn, and alternative instruction (if the teacher has time and materials to reach every kid).

Simply stating a standard, goal, or objective doesn't get you anywhere unless you can actually achieve it!!! What if your goal was "everyone at DU will run a mile in 4 minutes by Jan 1, 2015"? The CC has goals that are just as unrealistic. Many test items reflect those unrealistic standards (at least for many of the kids). They are in the standards, so someone puts it on the test, often in an awkward and poorly written form on top of everything else.

Front line teachers in the trenches KNOW it's not so easy. You get handed curriculums and told standards, but if you actually get in front of 25 kids and try it - half don't get it or react the way they are supposed to or get finished in the time allotted or even care about learning on a given day!

I've seen kids come in every day who don't care about "strategies" because no parent was home last night or they've moved 3 times last year, etc., etc. In my county in Florida, the MAJORITY of kids are not living with their natural pair of parents! Almost 25% don't speak English as a native language. Some schools have 90% living below poverty. The Common Core, just like decades of similar sets of standards, are not a magic bullet. They are fine as something to give general guidance in revising the current curriculum, but CC doesn't address the major issues in the schools today. High stakes tests don't help the teacher or kids at all because of the way they are created and used.

If you have a flat tire you don't go out and spend years discussing why you have a flat and spend $5000 on a really expensive air gauge!!! Buy some tires! Spending MILLIONS on high stakes tests is wasting time and money when everyone in the classroom could make things better in 2 seconds with smaller classes, more teachers, better materials, better support for kids (health care, after school programs, preschool programs, etc., etc.). Instead our own governments make new curriculums, more tests, build charter schools for private profit, and ATTACK teachers every chance they get. It's shameful.

[adigal]

363. Wish I could recommend this a thousand times

Common Core is a good idea - all kids should, in theory, graduate with the same basic knowledge set. BUT, kids learn at different speeds and while GW Bush "left no child behind," Obama, in his "Race to the Top," is leaving behind those kids who learn differently and more slowly. (Snark about Bush, of course.) And as the administrators interviewed by NPR said, they ruined the idea of CC with testing that punishes teachers - not families, not politicians who don't provide help for the poor, just teachers, who are taught the students we get. Regardless of what their home lives are like.

Every three or four years or so, we get a new theory, a new program, new tests, with no explanation of why we are getting rid of the old, and no evidence showing the new will be effective.

It's just nuts and I am absolutely taking early retirement from teaching at the age of 55. I am so done with the experimenting on kids.

[callous taoboy]

359. The question is not a valid one.

Doesn't matter if they can add, subtract, pull apart, put together standing on their heads. If you want to test them on their knowledge of related addition / subtraction facts, make two of the answers be subtraction number sentences, one of which uses the same three numbers that are in the question. The fact that all four choices are addition when it frames the question using the word "subtraction" makes it a flawed question, for first grade at any rate. The gifted students in my class would probably not get it either. Not valid. Does not test what it purports to test.

[DeadLetterOffice]

186. Tell that to my elementary school kid.

He's pretty damn sure there was A LOT of stuff on the CC tests that he had never, ever been taught.

[Kablooie]

67. The answer is no. "Which" is a word, not a sentence.

[madfloridian]

74. So now we have come to calling retired teachers simple-minded....

for pointing out the obvious. Should have known.

[RBInMaine]

77. Yes, there should be standards, but the common core is proving to be an overreach. Plain and simple.

[LibDemAlways]

108. Last week I was substitute teaching 3rd grade

in a school using a Common Core text. Students were supposed to be learning subtraction. What they were learning was that math is hard and confusing. Rather than teach the kids to place the second number under the first and subtract each column, they were being taught to pull the numbers apart as in 836 - 723 = 800 - 700 + 30-20 + 6-3 or to add 4 to each number so you get 840 -727 because numbers ending in zero are "friendly." Teachers are upset. Kids don't "get" it. Ridiculous all around.

[thesquanderer]

133. "pulling the numbers apart"...

...makes it much easier to do math in your head. It's a valuable approach. Ostensibly more useful in day-to-day life than getting out pencil and paper and putting one number under the other. Though I think it's easier to mentally "work up" than "work down." That is, if you need to figure the difference between 723 and 836, I'd go "723 to 823 is 100, 23 to 36 is 13, so it's 113."

[callous taoboy]

138. Ding ding ding ding....

You got it, mate. Mental math rules.

[LibDemAlways]

151. Except when borrowing or as it's called nowadays

"regrouping" enters the picture. Imagine the look on an 8-year-old's face when he tries to pull apart and quickly solve 932-687.

[callous taoboy]

166. No need to "regroup" when

you've taught them to turn the bottom number into a "hundred" number.
932 - 687 becomes 945 - 700 = 245. Mental math. But that type of problem / lesson comes later, in third grade. Second grade we start with tens: I'll soon be teaching them to turn the bottom number into a "ten" number: e.g. 44 - 28 = 46 - 30. We will have used the 100s chart so much by then, subtracting multiples of 10 from given numbers via games and such, that 16 will be the ready answer. Can you do that in your head? Can you visualize 46 - 30 on a hundreds board? It is still hard for me since I was taught "old school." I will be instructing them to "see" the 100s chart by then, or will allow my slower learners to use the 100s chart with a plastic chip each time to derive the answer until it becomes natural. Mental math is the only true way to flex the math muscle in the brain and free oneself from bulky algorithms. However, since the test may ask them "regrouping" questions, I will also be teaching them "old school" methods as I call them. Some of my students will prefer that method and that is o.k.

[thesquanderer]

167. Here's how I'd do it in my head

932-687

I'd round to the nearest hundreds... i.e I know right away we're looking at "approximately" the difference between 900 and 700. The difference between 700 and 900 is 200.

Add to that how far 687 is from 700. That's 13. (Or if you must, it's 10 to get from 700 to 690, and another 3 to get to 687.)

Add to that how far 932 is from 900. That's obviously 32.

32 and 13 is 45. Add that to the 200, I've got 245, quickly and easily, with no paper.

It's not any kind of "math trick"... it's a logical use of rounding and using those "friendly" numbers (i.e. ones that are easy to manipulate in your head, either because they end in zero or because they are small). And I'll have the answer faster than someone can pull out paper and pencil.

This was not anything I was taught in school... but I would see value in teaching it. Along with the paper and pencil approach.

[LibDemAlways]

169. That strikes me as a lot of steps. Instead of

simplifying math, I think it complicates it. But that's just me. On Friday I had to try to teach pull aparts to two third graders who are in "resource" and need considerabe extra help. I may as well have been speaking Chinese for all they were getting out of it. Sometimes old school is the way to go.

[callous taoboy]

170. And I agree. I had second graders in regular ed.

the past couple of years who preferred old school. But if they had been taught mental math strategies since kinder, it may have been different. I was brought up seeing number and number manipulation as rigid. Common core is addressing the mental math / logic ; math flexibility view of number.

However, those resource kids will be faced with "pull apart" (or decomposing) numbers questions on their test, so they need to be introduced to it at least.

[DebJ]

260. Exactly! BECAUSE IT IS ON THE TEST. Not because it is helpful to them, or necessary to learn,

but because someone else decided they HAD to learn it that way, no matter what.

The point isn't learning to think, or addressing the needs of each child.

The point is, IT"S ON A TEST.

It's not about the child becoming a well-functioning adult, at all.

[thesquanderer]

190. To me, it's not about "steps" at all

Especially since the actual steps would be different for different numbers. It's more a matter of a different way of looking at math problems that doesn't reduce them to any particular steps. It's just a concept of rounding numbers to ones that are easy to work with in your head, and then accounting for what's left over.

[Recursion]

202. Estimate then refine

I suppose there would be a way to reduce that to "steps", but really this is about getting kids to think about numbers. To make a gross estimation of the answer and then refine it.

[callous taoboy]

171. And as someone posted a few months ago-

math problems on the test will ask what reasoning errors a person has made while solving a problem such as 932 - 687, and one misstep in your analysis of the problem will be the correct answer. Again, mental math is a must these days, and I see that as a positive.

[Recursion]

233. I was sad that that question caught so much flak here on DU

It's a great line of testing.

[Recursion]

201. This is a way of avoiding borrowing

That's one of the main points.

"Let's see, 687 is a little less than 700, so 932 - 687 will be a little more than 232. How much more? 87 is a little more than 10 from 100. How much more? 7 is 3 from 10. So 13. So 932 - 687 is 232 + 13, or 245."

You subtract by performing relevant addition problems -- the only actual subtraction I did was 10 - 7 = 3, and even that I presented to myself as 7 + 3 = 10.

Man, people get worked up every time kids are presented a better way of doing math. Same thing happened back in the 80s when (gasp!) kids were presented arithmetic in different bases to make operations easier.

[sammytko]

393. That is how i always did it

Take groups and work them.

Yea, hard to set up a subtraction problem in your head with the carry over and all that jazz. Just take the numbers apart.

[Recursion]

199. What you're describing is how I subtract large numbers in my head

I couldn't imagine wasting time actually doing it the "long subtraction" way.

[ancianita]

111. As a first grader, I couldn't because of the too-advanced 'tricks and traps' language. BAD question.

BAD company.

[steve2470]

114. THIS is a first grade test question ?

I'm feeling old now, and I'm still in disbelief that this is expected of a first grader.

[Recursion]

255. I've been shocked at what age kids are learning stuff

That may have something to do with why students are performing a lot better on tests than my generation did 20 years ago.

[DebJ]

276. Funny, all I see in the news are failing schools, in insane numbers.

What percentages of students are performing better?

And if things are going so well, why is everyone always complaining?

[Recursion]

284. Crazy, isn't it? Almost like people have a vested interest in encouraging a state of constant panic

And if things are going so well, why is everyone always complaining?

You could ask that about many things, from education to violent crime to standards of living: all objectively better than they were 20, 30, 40, or 50 years ago.

[DebJ]

288. So please show me the good numbers that you refer to.

Seriously.

[Recursion]

296. Happy to

I did a post a while back on the non-existence of a crisis in education, so I'll just stick with those numbers. (Unfortunately many of these charts only go back 20 years, so let's stick with that window...)



Note that Native American/Aleutian kids are actually in a crisis, and we need to do something about that ASAP.



Fewer kids are dropping out



College enrollment has continued its multi-decade increase



As has at-least-associate's degree attainment among enrollees.



Full graduation from college is up



(Those are slightly different definitions of "graduation&quot

Students today continue to do better than their parents did.

The biggest clearinghouse for this info is definition The Nation's Report Card by the Department of Education. The 2012 results are here but difficult to embed. This page compares students today with students in 1973 (you can configure it to make different comparisons; this is just a generic "vs. their parents&quot .

(You'll also see that the difference wash out by age 17. Would be interesting to find out why. So in that sense I overstated the case: high school grads are statistically identical today to grads 30 years ago, but younger students are performing much better)

Reading (Age 9):
All students +13 points
White students +15
Black students +36
Boys +17
Girls +10

Reading (Age 13):
All students +8
White students +9
Black students +24
Boys +9
Girls +8

Math (Age 9):
All students +25
White students +27
Black students +36
Boys +26
Girls +24

Math (Age 13):
All students +19
White students +19
Black students +36
Boys +21
Girls +17

What will be really interesting will be to see how the currently-13 cohort does in 4 years...

Note also that NAEP changed testing formats in 2004 which made scores drop slightly, so it wasn't a case of the test "dumbing down".

[Sancho]

329. You are right that schools are doing a better job over the last few decades. But...

It's not due to the new standards and high-stakes testing!!!

Most of the improvements are probably because...

-Teacher education, accreditation of teacher programs, and requirements were ramped up starting in the 1970's.
-Many more teachers earned advanced degrees and got more inservice training in the late 20th century.
-The baby-boomers represent a large number of very experienced teachers.
-States started looking seriously at class size and even passed laws and policies limiting large classes.
-New materials and technology are actually improving the teaching process.
-Health care expansion, free lunch, Head Start, state wide preschool, special education, federal programs (Right to Read, IDEA, etc.), and public school accreditation have had a positive impact on schools since Johnson.
-There have been nice advances in diagnostic testing
-Schools added specialists like psychologists, counselors, dietitians, social workers, etc. starting in the 60's.

The main issues that are setting us back are high stakes testing, charter schools using resources, VAM models that attack teachers, states underfunding schools, and crazy political administrations.

[DebJ]

366. Thanks. Wish I could equate graduation with educated, though.

Unfortunately that doesn't really apply in our local area, and I'm sure this city isn't alone.

Teachers, after all the agonizing concerns involved, have put through failures for many students,
but believe it or not, there is a 'quota'. Only 'x' number of students per grade can be not
passed, no matter their continuing educational needs, and that follows them through
every passed year until graduation, if they make it. It's not about any student's needs, it is about 'quotas'.

Also, every knows the reported graduation rates are fudged numbers, allowing ifs ands buts... the entire
city here knows that less than half of our students stick with it; more than half drop out. That's the result
of the larger cultural issue in the city... but of course, it's the teachers fault (sarcasm too mild a word choice here).

[MADem]

115. Some smart fart once told me "If ya don't know the answer, pick C."

Is this new-new-new math, or something? I've never heard of a "related subtraction sentence" and I don't think I'm the only dummy in the group, here.

Are we supposed to be looking at the picture above, with the four blocks colored in, and the three not, and get something from that?

[msanthrope]

136. Yes......MineralMan above explained it perfectly. nt

[valerief]

116. On the CC test at the link below, can someone tell me...

What the hell question 1 is asking for?
How are kids supposed to answer question 3?
On question 6, what do you do when your red crayon is a different length than your blue crayon?
What is the "doubles plus one" section in question 8 asking for?

http://www.nationalreview.com/article/373840/ten-dumbest-common-core-problems-alec-torres

[mythology]

189. Question 1 is 14, it's explaining the method given by a poster above

about converting to easier numbers.

Question 3 is a misprint. Those do happen and it's not related specifically to common core. It's related to human infallibility.

Question 6, it says take out new crayons so they will be the same length, unless crayons have changed a lot since I was a kid.

Question 8 I can't answer as confidently, but then again I don't have the textbook. My guess would be that you would link from the top row, 2 to 5 on the bottom row and 1 from the top row to 3 from the bottom row and not correct the rest because 2+2+1 equals 5 and 1+1+1 equals 3, ie double the number from the top row and then add 1 to match to the second row.

I don't think these are especially good examples of what is seen as wrong with Common Core.

[valerief]

200. Thanks, but I have some issues with this.

Question 1
I know 7+7 = 10+4 = 14. But what the hell does do these instructions mean?

Use number bonds to help you skip-count by seven by making 10 or adding to the ones.

Re question 3's "typo" and question 6's instruction to take out A new crayon but then proceeds to have you use 2 crayons:
Since EVERYTHING depends on the friggin' scores, why the hell are these test cases written to create failure? Who is accountable for this slop? No one. The kids suffer.

Re question 8, you said:

Question 8 I can't answer as confidently, but then again I don't have the textbook. My guess would be that you would link from the top row, 2 to 5 on the bottom row and 1 from the top row to 3 from the bottom row and not correct the rest because 2+2+1 equals 5 and 1+1+1 equals 3, ie double the number from the top row and then add 1 to match to the second row.

Okay, number sentences are
3 + 3 = 6
5 + 5 = 10
1 + 1 = 2
4 = 2 + 2
8 = 4 + 4

Below that is the instruction

Match the top cards to the bottom cards to show doubles plus 1.

And then in row one below: 1 4 3 2
And then in row two below: 5 2 3 4

Now, you say to link 2 from the top row to 5 in the bottom row. Okay, now I see that what is REALLY being asked is to take each number is the top row, double it, add 1 to it, and draw a line to the answer in the bottom row. Until you told me the answer, I had no clue what was being asked. I didn't know WHERE the "doubles" were supposed to be, because I thought what was being called the "top cards" were those "number sentences cards." However, it seems the number sentences cards have nothing to do with the next section cards IN THE SAME QUESTION.

WTF aren't these separate questions??????????????

Sorry, but these CC examples are sloppy and ridiculous.

Thanks for responding!

[LibDemAlways]

117. Mad Floridian, one huge problem

with the text, besides the confusing language, is the language itself. It assumes 1st graders can read and understand the question. Huge assumption.

[steve2470]

120. When I was in first grade...

and I was a relatively bright first grader, there's no way I would have easily understood that problem. Badly written question. We were at "subtract means take away", that kind of language.

[valerief]

127. That blew me away. Can 1st graders actually read this well?

Last edited Sun Sep 21, 2014, 06:53 PM - Edit history (1)

I didn't learn how to truly read until the first grade (the Dick and Jane and Spot and Zeke days), although I sort of taught myself some words from my Golden Books before then. I was bored silly with Kindergarten. I couldn't wait to learn how to read properly, and when I did learn, I was like a sponge, far ahead of my classmates. I think it was my eagerness that facilitated me. The other kids, probably not as eager as I was, read aloud in class like slugs. I know my first grade classmates couldn't have handled the language on that CC test.

[Recursion]

246. Here's a 1st grade reading worksheet

http://www.superteacherworksheets.com/reading-comp/printables/1st-rock-band_TZZNR.pdf

It looks like "related" would be phonetically available but not conceptually available (and as keeps being pointed out, it makes a huge difference if the kids were taught something about "related subtraction sentences" or just thrown this).

I do like the worksheet question, "what's Beth's problem?"...

[muriel_volestrangler]

318. "Beth's problem is that she thinks playing cowbell is an acceptable role in a rock band..."

[missingthebigdog]

383. Duzy!!

Thanks for that. This thread is a real downer.....

[sammytko]

394. yes, kids have to practically read by kinder

even here in our small poor rural town. My grand-niece is in a bilingual program. She is learning in Spanish. She did not grow up speaking Spanish. It is amazing to watch these kids. Read and write in Spanish - and doing it well.

Her little brother was spelling words on HIS ipad at 2.5 years old.

[sammytko]

395. Oh and high school kids are taking college courses before they even finish high school

Some have all their basics completed. Again, not a rich district - rural in poor south texas.

[FlatStanley]

121. 4 - (-3) = 4 + 3 = 7.

Piece of cake

[DebJ]

268. Because every 6 year old comprehends fully negative numbers! n/t

[FlatStanley]

303. My father was teaching ordinary third graders

About quadratic equations. He taught the same group of students mathematics one hour a day from K-3.

Can't speak to Common Core but we crush our young people's ability to learn. And testing certainly won't be the solution.

But then, common core and testing were never about education, they were about monetization.

[DebJ]

368. That was a beautiful arrangement: to teach the same group of kids for four years! Perfect!

The teacher knows the students well, and the students know the teacher, and real progress can be made.

I love that arrangement!

Unfortunately in our local school district, administration is constantly changing the subjects that the teachers teach.
That means every year or every other year the teacher is starting all over with new curricula and never is able to
refine and adjust. Just another administrative idiocy; there really is no need to do this. And it is not good for
the students.

To have the same students for four years is wonderful!

[FlatStanley]

375. It was very fortunate, indeed. My dad wanted to pilot

A program to demonstrate that ordinary students could master mathematical concepts at a much earlier age with the proper methodologies. This was back in the early sixties in New York.

That kind of experimentation is long gone from our school systems. And you won't see this in Sharter Schools because it cuts into profits, I suspect.

Testing is cheap, teaching is not.

[Sunlei]

125. "Which is a related addition sentence"

Looks like the test question is incorrect to me.
Anyway, C is 'related' to the shaded/unshaded squares.

here see the first grade work yourself. I think it's a good visual system for learning math.
http://www.ixl.com/math/grade-1/addition-sentences-sums-to-10

[alphafemale]

126. Like This!

[DebJ]

283. Good one!

[chillfactor]

128. Sorry but I am actually a TEACHER...not a Monday night quarterback.....

I support the Common Core standards..and by the way....I have never seen that problem om a standardized test..the testing is very straight-forward...Common Core is controversial because it involves CHANGE..and teachers, like everyone else. resist change.............

[Iggo]

335. Me, too. (n/t)

[Sancho]

129. One of the fascinating things about this example is that it ignores what we know about children!

Common Core (like lots of "standards&quot assumes that a knowledgable or experienced teacher is teaching. We all know from the days of Piaget that some operations are impossible until a child is developmentally ready. This example taps one of those operations that some 1st graders would not be capable of doing due to simple maturation.

The mathematicians have their logic, and the test writers purposefully want to separate the sheep from the goats so the average difficulty of most items is half get it right and half get it wrong.

They don't care what it does to the emotions of the child, they don't care what developmental level the child possesses. They only want a test score. What's even crazier is that these tests are confounded by culture, economic experience, and opportunity. Now they want that stupid test to evaluate the teacher after running it through a crazier mathematical formula!

It's ridiculous! The teacher KNOWS the child, takes ownership of the child, and see what the child can do and how they do it. Only empowering teachers will improve education (assuming all other things stay the same). Threatening the teachers, testing the kids to death, and private charters will not empower the teacher.

[DebJ]

265. Amen! And assuming knowledgable experienced teachers will be in charter schools....Ha!

The charter schools here pay 35k a year, and do not renew teachers contracts after three years...because new, inexperienced
teachers make more profit.

And the fact that saying you are a teacher is almost like saying you have Ebola won't help, either.

Wanting to teach children makes you disgraceful these days unless you want to live in your car.

[msanthrope]

131. I showed it to my fifth grader....she and I picked "C."

I am not understanding why this is difficult. Seriously.

[tabasco]

141. Yes, you are not understanding.

Little doubt about that.

[msanthrope]

162. What did we miss? Inversion is a pretty basic concept. I'm kind of

floored by some of these Common Core threads.....I don't know that I would advertise my lack of understanding so publicly.

[questionseverything]

365. it is a typo

Recursion (33,999 posts)
238. Watching the video I'm leaning towards a typo now too, though I've tutored kids who are taught

the way I read it as in the first place: replace all subtraction sentences with addition sentences.
It is we who have put our hands before our eyes and cry that it is dark -- Vivekananda

//////////////////////////////////

[gollygee]

168. Ok I finally showed it to my kindergartener, though she can't read all that well

but she said C had the right numbers and was "most closest" so that was the one.

She isn't a genius, and she isn't reading all that much so I read it to her, but she had no problem. She did catch that it said "subtraction" but had a plus sign.



Kids are doing this stuff earlier than we did it in the 70s, and they're expected to learn to read earlier. People complain and complain that kids in the US don't learn as much and as quickly as kids in other countires, and so the government responds to that outrage by trying to find ways for kids here to learn more and faster, and then people complain that they're having to do too much too soon.

[msanthrope]

187. You've caught the problem perfectly...education has changed, and for the better.

American kids are expected to do more, earlier, and by and large, they can. Sometimes I'm in awe of what my kid is learning in the fifth grade. Sometimes I have to google and email the teacher to keep up.

Challenge our kids and they rise.

[DebJ]

280. Since as you say, "education has changed, and for the better"

then why is the news not filled with joyous declarations of success instead of a constant screaming
about the failure of our system?

This is the second comment in this thread speaking of how wonderful and rosy education now is, how
children are succeeding, but I see no numbers or comments anywhere in the media to support this.

If this is true, then why is the public so focused on condemning teachers as vermin, instead of
lauding them for their grand new never-before-seen success?

What am I missing here?

[Enthusiast]

313. +1!

[msanthrope]

321. I would ask the OP why no time is spent posting

about improving test score trends.

[Starry Messenger]

324. You aren't missing anything.

DU loves condemning teachers as vermin.

[DebJ]

369. Not just DU. I am married to a teacher, friends with teachers,

was myself certified in 2009 and taught for one year full time plus a few years substitute teaching,
and the majority of the community here craps on teachers.

Because that's easier than acting like a parent and doing something to support your child.

[joshcryer]

334. Because Americans like to crap on themselves.

We're like "Oh, no, the US is 15th in Math!" But then you look at the spread and it's a very small percentage of points, and the US has actually improved well above some other developed countries with disadvantaged students.

[gollygee]

431. I haven't seen nearly as many complaints about education as I saw 20 years ago.

I see libertarians condem teachers as vermin, but not most people. I think my kids' teachers do an amazing job. I've been very happy with all the teachers my kids have had.

[malthaussen]

135. Given that C is the only answer using 4 and 3...

... the strict answer to your question, "How would you answer" is C. Despite the rather obscure wording. I have no idea what they were teaching in that class, perhaps the question makes sense in that context. It would seem, however, to have been worded... incorrectly. However much algabraeans (IS there such a word?) would like to demonstrate that addition is subtraction (or "related to subtraction," by your leave), a similar argument can be made that 5+2 is the same sentence as 4+3.

-- Mal

[Brigid]

144. I was good at catching on to reading in first grade . . .

But words like "sentence" and "related"? In first grade?

[steve2470]

145. imho the question, even clearly written, is too advanced for a first grader

You can only push first graders so hard, and it's FIRST GRADE, not fourth grade. I'd like to hear a lot of feedback from current first grade math teachers on what's really expected. We were lucky to learn " Take away four from seven and you get three".

[Brigid]

146. Yep. I remember that too.

This is one seriously messed up question. I would hate to see the rest of the test.

[WHEN CRABS ROAR]

154. So was I, it was taught with "Dick and Jane" books

and they worked. I wasn't aware of anyone in our class that couldn't read.

[cwydro]

148. Just even looking at this gives me that sick feeling

I had when they started the "new math" back in 1970.

Ugh.

[DamnYankeeInHouston]

150. That is obviously a typo/proofreading error on an untested test.

My favorite stupid question on the second grade Stanford Test was, "How is the president chosen?" The answer choices consisted of three pictures of the Supreme Court, Congress and a voter putting a ballot into a ballot box. There was no Electoral College answer and my daughter got it wrong in 2000 when she picked Supreme Court even though she was correct.

[RufusTFirefly]

157. Yes! Standardized tests can be hell for people capable of divergent thinking. n/t

Analogies were always a nightmare for me as a kid.
I was always finding unconventional connections.
No wonder I'm a bit of a conspiracy theorist.

Speaking of connections: It reminds me of a scene in the movie Funny Bones where a seemingly troubled young man is hauled before a friendly psychiatrist, who administers a series of tests.

Psychiatrist: Now see if you can tell me which of the following words doesn't belong:
Anger... Malice... Hostility... And Kindness.

Patient: And!

[Bonhomme Richard]

152. D..if you subtract 5 from 8 you get 3. n/t

[Dont call me Shirley]

155. Tony the Tiger was a question's subject on my sophomore child's common core test!

Common Core is a private for profit corporation. It is not a basic set of standards, like we have been duped into believing.

Pearson is a private for profit British corporation? I thought we fought the Revolutionary war to free ourselves from British rule!? Why are they ruling our schools?

[TygrBright]

156. Would someone who understands this math theory please explain to me...

...why ONLY answer "C" would be correct in this case?

I am not understanding the theory, I think. Apparently, subtraction is simply addition, reversed.

Well, duh.

But ALL of the "sentences" (we USED to call them "equations," no idea why that's changed) are equally valid in that case.

6-4=2
7-2=5
7-3=4
8-5=3

What am I missing?

bewilderedly,
not-so-Bright

[gollygee]

181. Well

There are 7 cubes, 3 are one color, 4 are the other. So it would make sense to choose the one involving the numbers 7, 3, and 4.

This doesn't look like a standardized test because it's too short and not computer graded, so it's a classroom assignment or test, and it looks like whoever wrote it has a typo - "subtraction" instead of "addition" as it's an addition sentence.

[Recursion]

206. Or they're just teaching subtraction as addition, which I've seen

And is what I do in my head. "7 - 4 = ?" is easier to think about as "4 + ? = 7".

[gollygee]

220. Yeah that's possible

although my daughter said that subtraction sentences have a "-" and addition sentences have a "+." She was familiar with the words and at least she thinks that a minus sign is a defining characteristic of a subtraction sentence.

[Recursion]

222. Obviously what the kids were taught makes a huge difference in whether this is a good question

If they learned subtraction questions have a minus sign, then this is in the best case a question with an error.

[Chathamization]

229. She seems to be right, and the question made a mistake by putting subtraction instead of addition

I imagine the question should look like this:

http://www.ixl.com/math/grade-1/addition-sentences-sums-to-10

Which doesn't seem to be too horrible.

FYI, subtraction sentence questions:

http://www.ixl.com/math/grade-1/subtraction-sentences-numbers-up-to-10

More info on what a subtraction sentence is:

http://www.ehow.com/info_8422257_parts-subtraction-sentence.html

[Recursion]

204. Umm... a block 7 units long is divided by color into sub-blocks of 4 and 3

Is there any sentence other than C that reflects that?

[TygrBright]

235. I didn't associate the blocks with the question at all. My bad, I guess... n/t

[Recursion]

237. Huh?

You looked at that question and didn't see it as being about its own illustration?

[TygrBright]

273. Nope. Got no connection at all between the blobby line of squares and the math question. n/t

[jamzrockz]

158. Dont ask me how but

I think the correct answer is D

[IDemo]

161. 42 n/t

[Warpy]

164. First, they're looking for addition; second, an ivory tower wonk wrote the question

and has no idea what age appropriate language is.

"Show this in numbers" would have made sense to a first grader, in which case there would be no ambiguity about which was right.

While I applaud their attempt at introducing visual learning to the rote memorization we old Boomers had to do, their language skills need a lot of work.

[LWolf]

172. Bad question.

How would I answer? "C," because it IS related to 4 and 3, and could be written as addition or subtraction. Still...really bad question.

I agree completely:

I am not against standards. I am against the high stakes testing of such standards. I am against making companies like Pearson wealthy by letting them formulate tests in secret. Before I retired there were parents in my primary classes hiring lawyers to see why their kids failed the FCAT.

[Turbineguy]

176. The words are English

But I don't understand them. I need the secret code.

Educators should make sure the parents have no idea what the books say, that way they can't help their kids with the homework.

[riversedge]

177. A because all are related in some fashion to the #2

[Dems to Win]

178. 7-3=4

Shouldn't a 'subtraction sentence' have a subtraction sign?

Given that I'm a college grad who took calculus, and I've never heard the term 'subtraction sentence,' I am befuddled. I would be one of those parents who couldn't help their kids with their first grade homework.

This is bizarre.

[madfloridian]

179. Yes, it should have a subtraction sign.

[Recursion]

203. No. Addition and subtraction are equivalent

Any subtraction sentence has a related addition sentence, eg 7 - 3 = 4 has 4 + 3 = 7. It's better to think in addition than subtraction if you can because addition has no associativity rules and subtraction does.

Yes, I know it's not what you learned. But it's what as a grown-up I actually do.

[madfloridian]

263. Oh wow thank God for grown-ups like you.

Maybe I will grow up someday.
But there still is no subtraction problem there, and there still is no right answer.

[DebJ]

287. It works out better for some people if the parents aren't able to help their children.

Once that is acceptable, than you can keep creating new jargon and new ways that must be learned and the only way to do things
so you can keep making money.

[Demit]

182. I'm distracted by the stupid illustration.

Looks like something you plug in. Some kind of memory stick? An electrical engineering component? Why on earth would they choose an unnecessarily unidentifiable object, and not just four colored in squares and three empty ones?

Maybe they're trying to familiarize kids with what they'll be assembling on the line in the factory later on in life. And I am only half kidding.

[gollygee]

183. It's not unidentifiable to that age group

They use these connecting blocks all the time in math now. Google "connecting blocks" and you'll get a bunch of photos.

[Demit]

192. LOL! Just as I thought! Connecting blocks are used on circuit boards, etc

I googled "connecting blocks" as you said. Here's one example:

Press Fit 110D IDC Connecting Blocks Provide Cost Savings over Standard Solder Style Connecting Blocks

SIS's innovative EON (eye of the needle) press fit 110D style connecting blocks terminate 22-26AWG (0.64mm-0.40mm) solid or 7-strand conductors using IDC (insulation displacement contact) technology. The press fit connectors eliminate the need to solder the 110D connecting blocks to a PCB (printed circuit board) and the processing time associated with the soldering process. The time and material reductions result in a cost savings to our customers.



I guess the kids learn how to terminate the 7-strand conductors in later grades.

[gollygee]

194. LOL

It's also a term for these blocks, which you probably also found when you googled:

[Recursion]

259. I remember the spec sheets of one of those

Some engineer had managed to sneak in a graph, "chip insertions vs. pins remaining"

[Recursion]

208. Again, what's old is new. We had manipulatives for quadratic equations in 1982 as 2nd-graders

That was Montessori, but I see it a lot more in kids I tutor now.

[gollygee]

224. We didn't have ones that connected

but we had little blocks like that. I recall them being used to teach us about metrics as well, as they were centimeters.

[kwassa]

379. This is based on Montessori manipulatives.

My daughter had them in Montessori, now has similar illustrations in public school math.

[Gore1FL]

193. I would start by reading the instructions that are not pictured. n/t

[Chathamization]

196. So there was an error on a single test somewhere in America. Hell, there are probable other errors

out there on tests as well, and there will continue to be errors, just as there will be typos in printed material from time to time. If the errors from a particular source go beyond a particular threshold, tests from that source shouldn't be used. But showing us that an error exists somewhere doesn't really tell us anything at all, other than humans shockingly enough still make mistakes from time to time.

[Rex]

198. Legos!

Well as long as a 1st grader understands mathematical sentences. Is that what they teach kids in first grade now? I would have no idea.

[southerncrone]

234. Most First graders can't read & comprehend those words.

This is designed to CONFUSE learning! There is no subtraction equations in the answers & no "no of the above" choice.

And we wonder why kids don't like & "can't do" math, and why we are so far down on the ladder compared to other countries.

This is an AGENDA!

[Atman]

247. "If your student loan debt is $75,000..."

"...and your job at McDonald's pays $7.50/hr, how long before you become a slave whore for Corporate America?

Too late.

[RandySF]

264. Looks just like my son's 1st grade work.

He's a human calculator and breezed right through it. He sure didn't get his talent from me.

[LeftyMom]

266. C. Using manipulatives and looking at a problem more than one way.

No big deal.

[madfloridian]

278. They asked for a subtraction problem. There is not one. It's misleading and just plain wrong.

[LeftyMom]

286. The question tests understanding that a problem can be seen more than one way.

The manipulative excercise the illustration echoes should have adequately introduced the idea.

Visual and tactile learners in particular benefit from this approach.

[madfloridian]

291. I taught these methods for over 30 years. These are first graders, concrete thinkers.

They are just learning more abstract reasoning.

There should be a subtraction problem there since the question called for one.

It is just plain common sense. My kids knew number families upside down and backwards. But when you asked them for a subtraction problem, they would expect one to be there.

There should be no excusing this as a thinking exercise.

[LeftyMom]

292. You didn't teach that a subtraction problem can be rephrased as addition?

That's a pretty big omission. Figuring it out early enough that it's intuitive probably makes algebra easier later.

Tests always have a few difficult questions, partly to identify exceptional learners, partly for security: too many corrct answers would merit scrutiny.

[madfloridian]

301. Oh, come on now. Of course that was taught.

The item should have asked for a related number family member, NOT a subtraction problem.

There is NO subtraction problem there.

Did you really say that "too many correct answers would merit scrutiny"?

I have been talked to in this thread as a fool and an idiot, treated as though I were a stupid teacher with no brain.

It is disgusting, frankly.

[bettyellen]

293. interesting- it reminded me of using an abacus, which I needed to in order to grasp math.

addition and subtraction are always intertwined- just depends on how you look at the thing.

[LeftyMom]

294. Exactly. Or counting back change. nt

[bettyellen]

295. Tell me about it- I lost $ 9.05 in poker last night. My cash out of $1.95 reveals I had originally

invested eleven bucks.

[pnwmom]

274. Now picture the unfortunate first grader exposed to a test full of this idiocy. n/t

[Cleita]

298. Did Sarah Palin frame the question because it makes no sense?

Also simple arithmetic with an equal sign between numbers used to be known as equations not sentences.

[pnwmom]

302. Proof that it's a stupid mistake, not some high-level kind of reasoning.

The standard definition of "subtraction sentence" is used on page 2.

(And for an even worse example, see the first problem on page 1.)

http://roundtheinkwell.files.wordpress.com/2013/10/the-math-test.pdf

[joshcryer]

306. I think I'm with Recursion on this one.

They're trying to teach concepts with that question.

[pnwmom]

311. Except on page 2 of the same test they use the term "subtraction sentence"

in a completely conventional way.

And think like a 6 year old facing that test. I know my Phd Engineer daughter would have been completely mystified -- and discouraged -- if she had encountered questions like that. Thank goodness she didn't have to prove her math ability with such a poorly written test.

Here is the actual test. What do you think of item one, page one? What are they trying to teach with the coffee cup? Any idea?

http://roundtheinkwell.files.wordpress.com/2013/10/the-math-test.pdf

[Demit]

320. How can you subtract 5 cookies from a cup of liquid?

I assume the answer is one? Because the cup has a number 6 on it? Why wouldn't they show 6 cookies?

I am mystified that these illustrations are supposed to be clear illustrations of a concept. I'm a graphic designer, so maybe I'm seeing things in a different way, but...you can only subtract like from like, right?

[joshcryer]

325. This is "set of cookies dunked in milk and eaten."

You can have 3 apples and 3 pears which would be 6 fruit.

[Demit]

336. Wow, I'm supposed to deduce that from that illustration???

For one thing, I would've expected milk to be in a GLASS, not a coffee mug. For another, where's the indication that anything was or will be dunked? Why am I supposed to intuit the act of dunking?

Granted I'm old, but if I had young kids & was facing this kind of bullshit, I'd be beside myself. I'd be up at the school lecturing them about how symbols & graphics are designed to communicate non-language information CLEARLY.

[joshcryer]

339. You're thinking like an adult.

I'm not disagreeing that it's difficult to wrap your head around. But seeing it, I could easily explain that to a kid like my nephew. Hell, I'd get out the milk and cookies, and we'd have one, and I would say "how many are left?" "How many did we have?"

You are thinking way too much into it. A kid doesn't care if milk comes in a glass or a coffee cup. Those sorts of restrictions don't exist in their minds.

[pnwmom]

344. But you wouldn't be by your nephew's side if he encountered this on a test.

You'd be stuck listening to him tell you how hard the test was and he couldn't even figure out the first question, that had a picture of five nickels and a whole cup of coffee with a 6 on it. How can a nickel -- or even a cookie -- be a "missing part" of a cup?

This company is notoriously sloppy in designing its questions. When my son took one of their tests, there was a picture of a log that urban children thought was a rolled up rug -- and got wrong, of course. My son got a question that to him was very mysterious, asking about an an object of a tannish color (I forget what it was) landing in a field that was either fresh grass or dead grass, and which color would it be camouflaged by? My son was color blind so green and tan look the same to him. Stupid question since almost 10% of boys are color blind and most of them can't see green. I called Pearson to ask if they examine their tests for questions that would not work for color blind kids and they said no -- and they don't plan to, either. They had some excuse but they just weren't interested.

I didn't care enough to make a bigger issue of it because the test didn't have any effect on my son's life. But if it does now to kids, they should be examining these tests with fine tooth combs to make sure they're understandable -- and they don't.

The other thing about this particular test is that the tricky cookie question -- which you could explain to your child, if presented with it in a non-test situation -- is the very first item. A child who stumbles on this has already lost his confidence at the very beginning of the test, and quite possibly wasted a lot of time.

P. S. I'm not the only one who thought the round things looked like coins:

http://science-beta.slashdot.org/story/13/11/02/1540249/a-math-test-thats-rotten-to-the-common-core

My assistant principal for mathematics was not sure what the question was asking. How could pennies be a part of a cup?" The 6-year-old first-grader who took the test didn't get it either, and took home a 45% math grade to her parents. And so the I'm-bad-at-math game begins!"

[pnwmom]

343. How did you guess that? I honestly thought they were coins.

But nobody in my family dunks anything into cups of liquids, for whatever reason.

Even so, I still don't get the math. Dunking a cookie doesn't make it disappear. Eating it does.

[Demit]

370. pnwmom, I was the one who thought they were cookies.

Oreos, specifically, although kind of thin. If the dark texture is indeed the markings of a penny or nickel, it's not decipherable in the (possibly-xeroxed-many-times) image at the link. But being coins makes it worse! What's the "missing part" of pennies and a cup with a 6 on it? Damned if I know. No wonder the poor kid got it wrong.

He did better on the traditionally-worded question #2, I see—the one that had simple graphic shapes that didn't have any distracting and/or misleading connotations.

[pnwmom]

372. And think about all the ESL kids who thought they at least could do math problems

till they came to the US, where you can't do math unless you can do high level reading, too.

Some of these math tests require much higher than grade level reading skills. What's their excuse for that?

[Sancho]

332. You also have to understand that "cookies and milk" might be culturally loaded...

one of the issues with the language in the test (as pointed out by Madfloridian and others) is that we have kids from Asia, South America, various islands, Eastern Europe, etc.

In many urban schools in California, Texas, Florida, etc., the MAJORITY of kids have different backgrounds. In fact, some may not have every had milk or ever dunked a cookie - especially if only in 1st grade!

Illustrations are meant to reduce dependance on language loading, but often they are just as confusing to different cultures as the words you use!

Test companies don't spend the time and money to check all the test items for the reality of kids who are tested. The test companies KNOW there are biased questions on the tests, but it's too expensive to create alternatives for every concept tested.

[Demit]

338. Plus, the symbol for a serving of milk would be a glass, not a mug.

Unless I'm hopelessly behind the times on that too. Are kids dunking their cookies in Maxwell House these days?

As a graphic designer, five to ten years ago, I worked on the books that teachers use to teach this stuff. The illustrations I was given utilized simple geometric shapes. When I created the illos myself I strived for simple, universally-understood symbols, because that's what you do with graphs & charts. If you are making the reader decipher your graphs & charts, you have failed.

This crap was probably lifted from clip art by some academic employee with no design training who thought they were being creative. Because of course with the advent of computer graphic programs anyone can be a designer! Lol, yeah, I'm a little bitter

[pnwmom]

346. Kids deserve the highest quality work in tests like this, since they're being used

to judge both them and their schools. There are many examples like this because the test makers don't care, as long as the profits are pouring in.

[gollygee]

349. This test isn't

Certainly you're familiar enough with standardized tests to see that this isn't one. This looks more like a classroom assignment. Standardized tests have more questions, and have goose-eggs you fill so they can be graded by computer. This obviously is not one of those.

[pnwmom]

351. Not all standardized tests are graded by computers anymore, especially common core tests.

[gollygee]

352. Not the written portions

but this is math.

[pnwmom]

354. And math is treated the same way. Half of it depends on reading skills now,

which puts a whole different set of kids at a disadvantage -- those whose reading or language skills aren't as high as their math skills. It used to be an ESL kid at least could get through the familiar math sections. Not anymore.

Anyway, this is from a Pearson test. It's not just a sloppily designed homework paper.

http://science-beta.slashdot.org/story/13/11/02/1540249/a-math-test-thats-rotten-to-the-common-core

Explaining her frustration with the intended-for-5-and-6-year-olds test from Gates Foundation partner Pearson Education, Principal Carol Burris explains, "Take a look at question No. 1, which shows students five pennies, under which it says 'part I know,' and then a full coffee cup labeled with a '6' and, under it, the word, 'Whole.' Students are asked to find 'the missing part' from a list of four numbers. My assistant principal for mathematics was not sure what the question was asking. How could pennies be a part of a cup?" The 6-year-old first-grader who took the test didn't get it either, and took home a 45% math grade to her parents. And so the I'm-bad-at-math game begins!"

http://www.schoolsmatter.info/2012/05/pearson-tests-designed-to-make.html

At the other end of the spectrum, the tests have been an emotional and physical assault on our special needs students and English language learners. Many of these children generally experience greater success in mathematics than reading, as they are knowledgeable and confident regarding the content and concepts. The reading levels, vocabulary and language structures made it impossible for them to access the tests and demonstrate their mathematical knowledge. In room after room, children could be seen twenty minutes into the test with their heads on their desks or staring blankly into space. When teachers checked on them, they simply said, “It’s too confusing,” or “I can’t do this,” and hopelessly gave up. Nearly half of my special education students cried at some point during these exams. It is unacceptable for eight, nine and ten year olds to be subjected to this kind of torment.

What is even more detrimental is that neither these children — nor their parents or teachers — will ever have access to their test booklets in order to understand how or why the child arrived at an incorrect answer. No benefit is extended to the child from all of these hours of testing if there is no thoughtful, comprehensive feedback. Likewise, I am unable to provide you and your department with clarification and examples regarding my initial list of concerns, as I am not permitted to speak about the content of the exams, or retain a test booklet for commentary. I find it disingenuous that you want teachers and principals to receive feedback, but want none yourself. It would seem that those of us who have spent our lives doing this work would have much insight to offer you.

[pnwmom]

345. Absolutely. My son got a bunch of questions wrong on a reading test

that he basically filled out as a Mad Lib. (not realizing). There were blanks to be filled out from a list of words, and it was about Thanksgiving dinner, and he thought he could have some fun with it. (He was only 7.) So he said he was going to eat green turkey, among other things. But some of his "mistakes" weren't even on purpose. It would never have occurred to him to eat marshmallows with yams, but that was the right answer.

And all I could think was, if my son got half of these answers wrong, what was happening to the Chinese, Samoan, Philipino, and Russian kids in the class?

Though maybe they would have done better if they had never seen a book of Mad Libs.

[pnwmom]

342. That's funny. I thought they were nickels.

Obviously, the graphic design was lacking something, too!

[gollygee]

350. I wonder if it's more clear in the original

I think this is a better example of a problem than the question with a typo, because typos happen but this has potential cultural bias. Whether common core standardized tests have questions like this, I don't know, but I hope not. Still, that would be a problem with the writing of the test and not common core or this method of teaching math.

[pnwmom]

355. No, because a principal at the school that pointed this out

thought they were pennies.

But let's pretend all kids could recognize them as cookies. How can a cookie be a part of a whole coffee cup? And what is a 6 doing on the coffee cup? It's only one cup. These are the questions that will be going through the minds of the 5 and 6 year olds.

http://science-beta.slashdot.org/story/13/11/02/1540249/a-math-test-thats-rotten-to-the-common-core

Explaining her frustration with the intended-for-5-and-6-year-olds test from Gates Foundation partner Pearson Education, Principal Carol Burris explains, "Take a look at question No. 1, which shows students five pennies, under which it says 'part I know,' and then a full coffee cup labeled with a '6' and, under it, the word, 'Whole.' Students are asked to find 'the missing part' from a list of four numbers. My assistant principal for mathematics was not sure what the question was asking. How could pennies be a part of a cup?" The 6-year-old first-grader who took the test didn't get it either, and took home a 45% math grade to her parents. And so the I'm-bad-at-math game begins!"

[joshcryer]

328. It is absolutely baffling, I was stunned to see these.

But Recursion and my other attempts to understand what is going on here have convinced me that they're trying to get kids to think about numbers as opposed to algorithms.



You'll note that the approach is not a replacement for conventional methods, it's just added in to help kids have number sense.

Reflecting, I think it's pretty damn good. I mean, I went into my adult life not understanding why multiplying two negative numbers resulted in a positive number, it was just the algorithm I was taught. That's "just how it is." This led to extraordinary difficulties understanding higher math such as imaginary numbers.

[Sancho]

364. New ways of teaching, learning, explaining, and illustrating ideas are as old as Socrates....

and that's part of the frustration of teaching in today's high-stakes testing schools.

Most veteran teachers have lived through many of the "new" ways. I remember the first time a personal computer showed up in a school classroom (a TRS 80 in the 1970's).

We used to take courses in using AV equipment like movie projectors. We taught cursive writing and phonics. I remember the first calculators (that only performed MDAS). Teachers constantly keep up and change methods.

When curriculums and tests change without the opportunity for teachers to integrate them, it causes issues for the test scores and teacher evaluation.

I don't see the Common Core or the new "method" of teaching math as some kind of revolution any more than the last half dozen similar revolutions that I've experienced. Some new things will stick and be useful while others will prove to be worthless or disappear next year. The people who should be making decisions about methods and curriculums should be front line teachers and experienced researchers - NOT test companies, book publishers, politicians, profiteers, and preachers!

[BuelahWitch]

314. Now to ME a subtraction *sentence* would go something like

"Joe had seven blocks. He gave three of the blocks to Mary. How many blocks does he have left?" Those look like addition equations...

[stage left]

326. A recipe for frustration?

I hope my little great niece who just entered the first grade isn't having to deal with this nonsense. What six year old thinks like this?

[Octafish]

347. Odometer?

Prepping us ready to fight the next Oil War?

[msanthrope]

348. Best post of the thread. nt

[B2G]

367. Probably like this:

[underpants]

377. That makes my think meat in my bone bucket work

So it must be bad

The kids who take those tests have been taught what that means. If their parents are in any way engaged they know it too.

[pscot]

378. KNR

[Vattel]

380. common core sucks for kids that are good at math.

They spend more time arbitrarily labeling their problem-solving strategies and explaining how they got to their answer according to some prefab path than they do solving problems and developing skills

[fadedrose]

391. "C", but would not be comfortable with it

Seems like I would have put down "E" as a choice, 7 - 3 = 4.

The addition thing is put there to trick the child, but it's the only one that at least matches the numbers....

[cbdo2007]

417. Hmmm, I wanted to get mad about this, but it makes sense.

The image relates to either an addition or subtraction question, they are really the same, so the obvious answer would be the one that matches the picture.

It's not that big of a deal and seems to teach some basic concepts. I've seen other questions that are MUCH MORE ridiculous than this one in common core.

[madfloridian]

418. The item ASKED for a subtraction problem.

Students who take test-taking to heart might figure out what was expected, but they would also know the correct answer was not there.

So why try to trick young children? What is there to gain from it?

The item should not have asked for subtraction if they wanted a problem with a plus sign.

It is a misleading item by a company paid millions of taxpayer money.

[cbdo2007]

419. It isn't a numbers question, it is a logic question.

They are asking them to identify logic....and you would use the same graphic/problem solving for 4+3 as you would for 7-4.

Kids today are smarter than previous generations, and I think questions like this reflect how we want them to rationalize the result.

Just because you don't get it doesn't mean people are getting "tricked". LOL

[madfloridian]

423. "Just because you don't get it doesn't mean people are getting "tricked". LOL"

They are smart enough to know + and - signs and what they mean.

I have noticed many in this thread think it doesn't matter.

Yeah, I get it. I am one of those idiotic stupid teachers (retired after 33 years plus)....that Arne and Obama are talking about.

And a whole generation is coming up that thinks teachers are fools.

Thanks so much for your reply, but yeh i get it.

[liberal_at_heart]

421. wow. I can't believe how blindly people will follow Obama's policies.

There could never be anything wrong with Common Core or standardized tests because Obama wouldn't possibly allow such mistakes or corruption in our educational system.
Only those of us who have children in school right now know better. My 10th grade autistic son has now moved up to pre-algebra which I am so happy about. He started in a new school district last year and spent all last year learning basic arithmetic because his old school district tried to force him to learn 6th, 7th, and 8th grade Common Core math. And when it was clear he did not understand the material they simply passed him through the system.

[madfloridian]

424. The OP makes it clear I was a teacher. But I still got talked down to all through the thread.

Like I did not have a brain in my head.

No wonder there is no respect anymore for teachers.

[liberal_at_heart]

425. education clearly is no where on the radar screen of democrats which is a deal breaker for me.

[orpupilofnature57]

427. Republicans believe in Education ?

[liberal_at_heart]

428. socialists do. And don't give me that if I vote for a socialist I guarantee a republican wins crap.

When it comes to education democrats are no better than republicans so I will vote for whomever I damn well please.

[orpupilofnature57]

429. FDR was a socialist, and Bush wasn't a fascist, Sure . And thank socialists

You can vote .

[liberal_at_heart]

430. You can say whatever you like. It will not change my vote.

[Rex]

441. I wonder why half the people replying simply cannot fathom a test question being incorrect?

Even when they have visual proof to help guide them?

The behavior in this thread is fascinating to behold. The answer is none of them, all the given answers are incorrect. Really simple. The correct answer is one, which is not provided. Written out it would be 4-3=1. Whoever made the test, made a mistake when it was printed.

A first year teacher should be able to notice this and report it.

Sometimes a duck, is just that. No need to use the quadratic formula to discover why it is a cow, it is a duck.

Easy peasy.

[liberal_at_heart]

442. I wonder if a banker came up with this question.

[Mc Mike]

443. It's questionable whether it was a stupid mistake, or a purposeful mistake.

Either way, 'accountability' or being subject to judgement for being 'mistaken', is reserved for the kids (and their teachers).

I think it is a purposeful mistake, where a power dynamic is taught to our students. Accountability is reserved for the people in the lower half of a divide. The decision makers in charge made a mistake, and the successful way for the kids to avoid being 'mistaken' is for them to pretend the people in charge made no mistake, roll with the punches, and choose the closest thing to a 'correct' answer. Make up for the incompetence of those in charge, try to divine the intent of the people in the upper half of the divide.

It's not teaching hard facts, it's 'training' minds and teaching attitude, teaching 'reverence' for the power structure. The 'successful' student is one who has the 'right' attitude.

[Android3.14]

444. An experienced teacher would recognize this

It's obviously testing to see if a student understands the relationship between addition and subtraction.

Inside the mammoth backlash to Common Core: How a bipartisan education reform effort became the biggest conservative bogeyman since Obamacare. - Mother Jones

[jmowreader]

445. The standards themselves are not the problem

Here are the ACTUAL Common Core standards:

http://www.corestandards.org/read-the-standards/

The raw standards don't look any more fucked-up than the old state standards that preceded them, but implementation is the important thing here. And as you can clearly see from the example in madfloridian's OP, the implementation here is totally fucked: asking for a "subtraction sentence" and giving four "addition sentences" to choose from is a mean thing to do to little kids.

I wonder: How heavily is Pearson invested in charter schools? Seems to me, if you wanted to increase the number of charter schools making the public schools fail on purpose is a quick way to go about it.

BTW when did they start calling equations "number sentences"?

[liberal_at_heart]

446. The standards are part of the problem. The whole system is the problem. Did you see

Race to Nowhere? It is a documentary that shows how the entire approach we take to education is causing our children to be burned out. We need to nurture and encourage play in children more again. Let them solve problems with group projects. Give them room to be innovative and creative. They are capable of more than just regurgitating test scores. I think we undermine just how capable they are by expecting them pass ridiculous tests and live up to some made up standard that we think every child should reach. When we let them be individuals and let them figure out for themselves what they are good at and what their passions are they exceed our wildest expectations. When we sit them in a chair for 6 hours, give them 5 hours of homework and then tell them they must live up to this specific standard and meet these specific test scores we suck the life right out of them. I have one child in k-12 and one in her second year in community college. My son who is autistic always struggles with grades. I tell him not to worry about grades especially since the school can't give him the help he needs. He doesn't have a single teachers assistant in any of his general education classes. Even though he doesn't perform on grades and tests the way bureaucrats think he should he is such a great kid. He is very innovative. He thinks outside the box. He is resourceful and resilient. I read an article a couple of years ago that having what they call grit is actually a better indicator of whether a child will do better in life than reading and math scores. Well my son definitely has grit, and I do believe that he will be fine in life regardless of not living up to some ridiculous standard. My daughter has recently started to see a therapist. Some personal issues have caused her to have anxiety and depression and it is affecting her school work. She started out taking over 20 credits, and is dropping two classes. She is absolutely beside her self. She thinks if she doesn't stay on track to finish school in 4 years she is failing. I told her that is ridiculous. I told her that not everybody finishes school in 4 years and the very fact that every child think they have to is part of the problem. It is a ridiculous standard we have put on our children. I told her that right now the most important thing is her health and that she can make up those classes later and finish school whenever she is ready to finish school. I told her that she is bright, intelligent and that I believe in her and have no doubt that she will get her degree. It may just take her a little longer, and that is okay. We need to start treating our children like people again, not like robots.