Professors: US "In Denial" Over Poor Maths Standards

thephydes (727739) writes "The maths skills of teenagers in parts of the deep south of the United States are worse than in countries such as Turkey and barely above South American countries such as Chile and Mexico. From the article: '"There is a denial phenomenon," says Prof Peterson. He said the tendency to make internal comparisons between different groups within the US had shielded the country from recognising how much they are being overtaken by international rivals. "The American public has been trained to think about white versus minority, urban versus suburban, rich versus poor," he said.'"

Comments

danger will robinson

[Noah Haders]

if you teach kids to add, pretty soon they'll start wanting to think for themselves and only bad things can come of that.

Re:danger will robinson

[Anonymous Coward]

I tried to explain the income distribution to a community college student and she had no clue what the hell I was talking about. The one percent can sleep easy knowing fewer and fewer kids even know what a percent is!

Re:danger will robinson

[Krishnoid]

Addition is a gateway skill -- it tends to lead to multiplication.

Re:danger will robinson

[qwak23]

If we're not careful, this problem could grow exponentially.

Re:danger will robinson

[Anonymous Coward]

Apparently we have a problem with the geographies too. I wasn't aware that Mexico is a South American country.

Re:danger will robinson

[reub2000]

Appears that the error doesn't appear in the original. The use of quotation marks would lead one to believe that it's a direct quote, but it looks like it was altered to add the part about South America.

Re:danger will robinson

[Anonymous Coward]

Yes, it's to the south of America.

Just like Canada.

Re:danger will robinson

[rtb61]

In reality the real problem is the US's love affair with advertising, it has taken over the US mindscape, it matters not the way things are, all that counts is the way things are seen. Disingenuous distortions flood the US social landscape, where perceived delusions are preferable to reality as long as everyone can be socially forced to agree. Challenge it with truth and reality and you are attacked from every direction, media, politicians, corporations, law enforcement, religious fundamentalist groups etc. Not light attacks but solid and sustained ones including slanders, death threats and even direct violence. In fact the delusion is so great, so accepted, so powerful it is considered un-American to challenge the idea that the US is not number 1 in every regard, whereas the reality is the US is failing in many areas, except in the generation of bullshit, were is most certainly number 1 by a long margin likely beating out the rest of the world combined.

Re:danger will robinson

[CrimsonAvenger]

Yes, think about the kids. I mean they will be devasted if you require them to learn something.

Yeah, someone might even want them to learn how to spell "devastated"....

Re:danger will robinson

[cryptizard]

That subtraction example has been going around to "prove" that common core is hard/stupid, but it is very disingenuous. Of course for that particular case it is easy to do the "grade school" subtraction. However, when you get to more complicated numbers it becomes very non-intuitive. You can teach kids to do the "borrowing" from the next column, and they will be able to do it, but they won't understand why they are doing it, which is a bad precedent to set.

I guarantee you that everyone who works with math on a daily basis already does subtraction the "common core" way in their head. In fact, tellers have been doing it for decades! If you give someone $20 for $8 worth of goods, they say "nine, ten, and twenty" when handing you your change. It is the exact same thing. Additionally, doing it that way sneakily introduces you to some concepts of algebra. It also adapts better to other domains where "subtracting" doesn't really make sense, but "finding the difference" does i.e. euclidean space.

For your division example, I am sure that is not the end of the unit. That is a great way to understand the concept of division, you can't argue with that. Of course you need to know the shortcut way to do it, but if you learn just that then you won't really be learning division, you will just be learning an algorithm which gives you the answer. Can you not see how this way is better? Just because you did it a certain way when you were in school doesn't mean it is one way, or even the right way, to learn it.

Re:danger will robinson

[r_jensen11]

What did people expect from a country which pledges to be indivisible?

Re:danger will robinson

[Tyler Durden]

These methods may come in handy at some point, but in my opinion they're horrid when introducing students to simple arithmetic. Make sure the students have mastered the fundamentals first and only then perhaps introduce them to some parlor tricks.

Re:danger will robinson

[ranton]

The same thinking that scares people away from this "new math" is what makes it so hard for people to do arithmetic in their head. It is also the line of thinking that makes people unable to understand higher level math.

The traditional way of doing subtraction of large numbers is a shortcut that is often only useful when the numbers are small and/or you have paper to write on. Both the traditional way and the common core way are valid ways to come up with the answer. And in most cases, when you are doing subtraction in your head you should be using the common core way since it will usually be easier.

Take a better example, like:

  321
- 148.

Doing this in your head the traditional way would be hard. You have to regrouping twice, and you have to remember that you borrowed 10 from the tens place when regrouping the hundreds place. Obviously not impossible, but this is the kind of math that makes people think they can't do it without assistance from paper or a calculator.

But doing 52 + 21 is much easier, and doing 73 + 100 is also quite easy. "Almost" everyone who is good at doing math in their head will do 321 - 148 by adding 52 + 21 + 100 in their head. This is why it is important to teach children this method.

The obstacles here are not the common core curriculum, it is parents and teachers. Parents who complain about this "new" math that they don't understand and aren't willing to learn, and teachers who also don't really understand how this math should be taught. Students should still be taught both methods, and it should be clear on any examinations if the teacher is expecting a certain method to be used. If the student isn't explicitly told to use a certain method, they should not be marked off any points if they get the correct answer. And the students need to be taught the pros and cons of each method, or else the entire purpose of teaching both methods will be lost.

Re:danger will robinson

[JD-1027]

I completely disagree with this. It is way more important to break stuff up first, that way when you get to the quick and simple method, you know what is going on underneath. I have a 2nd grader who's been doing common core now for a couple years and I'm seeing this stuff every day.

First, they are showing how these numbers break down. They are getting these minds to break things apart into their parts. They can see what makes up these numbers. They are showing them the tricks you can do to shift numbers around, and pull things apart. They are getting their minds a deeper view of numbers.

They did the same thing with language. They treated spelling a lot like math. Their spelling words were mostly NOT memorized. They applied rules to words. Some of these rules got complicated, but it was a formula to break words apart and apply rules. Think about it, how dumb is it to just memorize every word in English, when 80% are rule driven... just memorize the last 20%. Their spelling tests had a section on the 20% that could only be memorized.

I'm surprised every day that slashdotters don't praise common core. I'm guessing it is because they see a single example and aren't seeing the big picture that us parents see. They are driving these little minds to logic!

Professors poor in geography

[Ultra64]

"South American countries such as...Mexico"

Re:Professors poor in geography

[bledri]

"South American countries such as...Mexico"

No, the quote from the article did not contain the words "South America," so it's the submitter or editor that is poor at geography. And quoting. And the first sentence was not attributed to the Professor in the article nor in the summary.

Re:Professors poor in geography

[Your.Master]

Well...I'm afraid that's just wrong (and a very US-centric way of looking at the world).

The "classic" 7 continents model (and the less-common-in-the-anglosphere models with fewer than 7 continents) doesn't include Central America, which can be part of the confusion, but Central America is pretty well accepted to mean all the mainland between Mexico and Colombia. The 7 continents model generally splits North and South America at Panama (either in the country or on one of its borders), thus most or all of Central America is actually the southern tip of North America, with possibly a little bit being the northern tip of South America.

There is basically no disagreement that the US is part of North America. Or even Mexico.

Central America is definitely not a synonym for America. America is a synonym for the US*, and it is also also a term for the combination of North and South America, but not at the same time.

* in English; this is somewhat disputed in part on the basis that it's confusing, in part on the basis that some consider it an insulting synecdoche that erases most of the continent, and in part because nerds like to deconstruct words and figure out what they "should" mean etymologically rather than what they do mean; but it's hard to dispute that it's used as a synonym and that it has historical precedent.

Re:Professors poor in geography

[K. S. Kyosuke]

"South American countries such as...Mexico"

In other news, professors in US are in the Nile over poor geography standards.

Coded Racism

[KalvinB]

Morgan Spurlock made the idiotic comment about how Norway is "homogeneous" right before transitioning to his piece on a charter school with minority students who were excelling.

SES or "Socio-Economic Status" is the most common race bait thrown around in the education system. Anyone who has experience outside the public education system figures out real quick that you can't look at the skin color or bank account of a student to see how well they're doing.

Racism is the last excuse that our failed public education system still clings to. That and "we don't have enough money."

It's just one of the many reasons why despite being certified to teach high school math, I have no intention of ever teaching in a public school. I'm more interested in helping out at my daughter's small private school. My summer project is overhauling their library system. I've already fixed all the laptops as well as they can be. If possible I'd like to go into a part time teaching role to help out.

The school is filled with students from a variety of racial backgrounds and financial circumstances and oddly enough I can't judge their grades by any of that.

Re:Coded Racism

[Anonymous Coward]

Sounds like "fuck the poor" to me.

Socio-economic status never stood for race, you're just conflating the fact that minorities are more likely to be poor than wealthy with the correlation between SES and educational outcome. The relationship between SES and economic outcome has been extensively studied, and in my opinion boils down to one thing: opportunities. Low SES kids can't afford basic school supplies, can't move to good school districts, can't study abroad, can't intern for free, etc. etc.

You can't pretend that a lack of money doesn't cripple your chances of receiving a quality education.

Re:Coded Racism

[Anonymous Coward]

It's not the schools that need more money; it's the families. Children are behind from the beginning (kindergarten) and don't catch up because in general, their environment is not conducive to learning. Parents often can't get involved because they have to work multiple jobs (or don't speak/read English well enough...). There is also more trouble from violence, gangs, drugs, etc. Socio-economic status has a lot to do with it.

(Of course, there will still be stellar children who succeed in spite of it all, but they are not the norm.)

You know, maybe you should try teaching in a school that is almost completely made up of children from a very poor socio-economic status before you claim to know it all and spout bullshit.

Re:Coded Racism

[TubeSteak]

Racism is the last excuse that our failed public education system still clings to. That and "we don't have enough money."

White flight is extremely real. Resources are distributed very unevenly.

And yet "racism" doesn't begin to encompass the range of reasons that some schools end up with 90%+ minority populations and with low funding.

Re:Coded Racism

[Anonymous Coward]

No, it has little to do with the fact that being poor means you don't have opportunity. Being poor means your parents probably don't value education, so you probably don't value education, so you probably don't get an education.

If you are rich, you probably got that way by being educated, so you value education, so your children value education, so your children get an education.

It's not like opportunity has no effect, just that opportunity doesn't mean education. In other words, throwing money at the problem doesn't solve it. That's not to say money doesn't help, but it's better spent on giving the poor kids breakfast or community outreach than school supplies.

I've always believed that a child who wants to learn will find a way to learn. The hard part isn't teaching them -- it's getting them to want to learn in the first place! And that starts in the home, not in the school

dom

Clearly, we need to SPEND MORE MONEY!

[mi]

Despite quadrupling per-pupil costs of public schools since 1962 (inflation-adjusted), the education remains the same or is getting worse. In some particularly well-managed cities, the costs are even higher and the results — even worse, than national average. This article is about Math, but ability to read remains rather sub-par as well — with only 30% of 8th-graders, for example, considered "proficient" readers.

Clearly, we need to spend more money...

Re:Clearly, we need to SPEND MORE MONEY!

[Sycraft-fu]

We might need to spend more money on helping people improve their memory so that they don't, say, just as a random example, post the same shit twice in one thread on Slashdot.

No surprises

[Vyse of Arcadia]

From the article:

Southern states Mississippi, Alabama and Louisiana are among the weakest performers, with results similar to developing countries such as Kazakhstan and Thailand.

Yeah, I teach math at a large university in the deep south, and this doesn't surprise me at all. Students are unprepared for college math classes, and I see a lot of behavior that I wouldn't have expected in a math class. For example, I always have students that try to memorize their way through class, mostly in calculus 1. They don't practice any problems, they don't try to understand the material, but they've got flash cards and highlighted notes and sticky tabs out the wazoo.

It's like they all had a bunch of "study skills" drilled into them in high school and no one ever bothered to explain that these are supposed to aid actually understanding the material. They're so used to just regurgitating things onto tests that I guess a lot of them really do think memorizing is understanding.

Now I realize the following is just anecdotal, but I know several people who teach high school math throughout the deep south, and all of them say the same thing: they aren't really allowed to teach. School administrators have a death grip on teachers' jobs. Teachers are told what, when, and how to teach the material. They're basically reading scripts. And of course they're all teaching to the state end of course tests too, probably because those are used to measure administrators' performances.

Re:No surprises

[SuperKendall]

Teachers are told what, when, and how to teach the material. They're basically reading scripts.

This is the real problem here. We need to abolish whatever part of the system is generating those demands, to free the teachers to actually teach. Some might do worse in a free-form system but I'll bet lots could do better when they could tailor teaching to the kids they have.

Re:There is no such thing as "maths"

[maliqua]

I'm Canadian its always been maths in my classes..

Coded Racism

[Anonymous Coward]

I spent a couple of years teaching in the Boston Public Schools. Your analysis is too simplistic. I had students who had recently immigrated from Cape Verde, who were fluent only in Cape Verdean Creole and whose parents never completed the 8th grade. I also had a student who had been in foster homes her entire life. I discovered after awhile that she couldn't see the board and that her foster parents were unwilling to pay out of pocket to buy glasses - she had broken two pairs of glasses and hit the limit for what MassHealth would pay for that year.

You can't just ignore the impact that these experiences have on a child's ability to learn. It's completely unfair to compare outcomes from private schools, which would never accept a student who barely spoke English or a sullen, resentful product of the foster care system (not that these children would ever apply) to schools that are required to accept all comers.

There are many problems that public schools create for themselves and have nothing to do with students, but the idea that socio-economic status doesn't effect student outcomes is just not accurate. c.f. this NYTimes article on the University of Texas for a week ago: http://www.nytimes.com/2014/05/18/magazine/who-gets-to-graduate.html?_r=0

Re:public employee unions poison

[dcollins]

I would submit that the teachers' unions are practically the only thing keeping the U.S. public school system halfway functioning. The more the system has been taken over by non-teaching corporate-style administrators, the more it's gone down the toilet (and the more those administrators have used it as a stick to further beat down the unions). Foreign countries with stronger unions also have stronger educational outcomes.

The choice is effectively between having decisions on how students are taught made by either (a) Dilbert and friends, or (b) their Pointy-Haired Boss. Choose wisely.

Re:Money quote

[dcollins]

And yet all these better-performing countries have more leftist governments, stronger social safety nets, more concern about equity, and less economic inequality.

Re:public employee unions poison

[stenvar]

I would submit that the teachers' unions are practically the only thing keeping the U.S. public school system halfway functioning. The more the system has been taken over by non-teaching corporate-style administrators, the more it's gone down the toilet (and the more those administrators have used it as a stick to further beat down the unions).

There are no "corporate-style administrators" in public schools, there are only government administrators. Corporations are ruthless about improving their product and cutting costs, exactly the two things that are not happening in public schools.

It really takes a special kind of stupid to try to blame the failings of US public schools on corporations; US public schools have nothing to do with corporations, corporate governance, free markets, or any of that. The shortcomings of US public education is a joint effort of teachers, unions, government administrators, and politicians.

Foreign countries with stronger unions also have stronger educational outcomes.

Foreign countries who don't speak English also have stronger educational outcomes. Foreign countries where people drive on the other side of the road also have stronger educational outcomes. You can pull coincidences out of a hat, but that doesn't tell you anything about causality.

The choice is effectively between having decisions on how students are taught made by either (a) Dilbert and friends, or (b) their Pointy-Haired Boss. Choose wisely.

You assume that the only two variants of school systems we should consider are public administration-heavy schools and public teacher-and-teacher-union-run schools; both of those are lousy choices.

Education should return to being a state and local matter, and the federal government should get out of it; there is no evidence whatsoever that a single national standard helps rather than hurts. In addition, we should give parents and students more choice via school vouchers. Forcing parents to send their kids to poorly performing schools is a lousy idea.

Frank Zappa

[Swampash]

I don't think it's any accident that the educational system in America has been brought to its current state. Because only a totally uneducated mass of people will be baffled by balloons. And yellow ribbons and little flags and buzz words and guys saying "new world order" and shit like that, I mean, only a person who has been dissuaded from any kind of critical thinking and doesn't know geography, doesn't know the English language - I mean if you can't speak English, then this stuff works on you. One of the things that was taken out of the curriculum was civics. Civics was a class that used to be required before you could graduate from high school. You were taught what was in the U.S. Constitution. And after all the student rebellions in the '60s, civics was banished from the student curriculum and was replaced by something called social studies. Here we live in a country that has a fabulous constitution and all these guarantees, a contract between the citizens and the government - nobody knows what's in it. It's one of the best kept secrets. And so, if you don't know what your rights are, how can you stand up for them? And furthermore, if you don't know what is in that document, how can you care if someone is shredding it?

circa 1988

Re:apples and oranges

[Malc]

But as long as people like Obama advocate mediocre European systems as a model, all we will produce is the same kind of mediocrity that Europe produces.

WTF? Do you just have a short list of canned sentence templates that you try to plugin in to any scenario to support some sort of mindless political agenda? Your statement makes about zero sense.

Re:math? maths?

[Zembar]

Mathematics

Etymology of Mathematics on Wikipedia

The apparent plural form in English, like the French plural form les mathématiques (and the less commonly used singular derivative la mathématique), goes back to the Latin neuter plural mathematica (Cicero), based on the Greek plural (ta mathmatiká), used by Aristotle (384–322 BC), and meaning roughly "all things mathematical"; although it is plausible that English borrowed only the adjective mathematic(al) and formed the noun mathematics anew, after the pattern of physics and metaphysics, which were inherited from the Greek. In English, the noun mathematics takes singular verb forms. It is often shortened to maths or, in English-speaking North America, math

HTH, HAND

Re:In my youth

[stoborrobots]

That's the average SAT score for students entering college... Which automatically filters out those students who weren't good enough to get in. It's not an average of all test-takers...

All that graph tells you is that admission standards for college have been climbing since 1992...

Also, it's not clear how that chart reflects the "recentering" that change the way scores were calculated from 1995 onwards...

Re:The elephant in the room

[jrumney]

Any time you see "education" and "deep South" in the same sentence, it's dog whistle racism. This article is criticizing their scores and compares them to other countries without discrimination. This article is racist and should not even be here.

He said the tendency to make internal comparisons between different groups within the US had shielded the country from recognising how much they are being overtaken by international rivals.

Just keep screaming racism every time you see something that alerts you to a problem within your society, and claim that the article should never have been posted. Thats a very effective way of ensuring that the US continues on the path it is on.

Re:In my youth

[stoborrobots]

The data across all test-takers (not just those who are admitted to college), tells a different story...

Re:public employee unions poison

[Anonymous Coward]

I've had a few good teachers, and am married to one in the 9-12, so I'm going to be a chicken and post anonymously. A few responses to your post:

1. Regarding your union comment, while I don't know the veracity facts you are stating: Post hoc ergo propter hoc.

2. A certain percentage are a big fan of the teachers union, but by and large it's as big of a hinderance as the bloated administration. They are thought of as the same thing by those involved, it's all the administration really.

3. Every time I talk to a teacher admire, they tell me a variant of the same thing: I need decent parents. Not money, equipment, computers, etc: just decent parents involved with their kids.

I'm pretty sure the article could be interpreted to as more evidence to support #3, especially when you consider how wealthy kids here were doing worse than other places: the parents are not involved. This is a serious problem, and isn't entirely about socio-economics (eg, mom working 2 jobs so can't help a kid with homework might be an example) and a lot of it to do with culture that has taken hold in some of the groups that are struggling the hardest in the scores.

I'm not sure it's solvable without solving some of the behaviors and attitudes that have developed: and things like railing on the tests is often just having to avoid talking about that which perpetuates things.

Re:math? maths?

[CurryCamel]

the English to which you refer is only "standard" among Commonwealth countries, and is not a global one.

I beg to disagree. At least in my school, using the American English was considered an error. One teacher relented enough to admit that American English, whilst not wrong as such, should at least not be mixed up with British English in the same text: "so pick one, and don't pick the American version" was her advice.
This was not a country with English as native language, nor was it a part of the Commonwealth. And unless the history classes were propaganda, never even been conquered by the Brits.

Re:math? maths?

[thaylin]

To some of my fellow Americans anything we do is the global norm, to everyone else around the globe, what they do is considered out of the ordinary.

We deny all sorts of stuff, why shouldn't we also

[mark_reh]

deny our performance relative to the rest of the world?

We deny the age of the earth.
We deny the existence of climate change or global warming and man's effect on it.
We deny the concentration of wealth and power among a few and its potential and real harm.
I could go on...

USA! USA! USA! USA!

Re:math? maths?

[Brulath]

Also, when it comes to language: everything you learn may not remain true indefinitely. Languages evolve constantly, so there's very little point in stressing about it when the language moves in a direction you didn't expect - you're certainly not going to be able to stop it. That and English is constantly breaking its own rules everywhere - you'd be hard pressed to find a page of text that doesn't break some - so worrying about specific instances of it isn't terribly productive.

Use what you believe is proper $country English whenever writing something formal, and whatever gets your point across when you aren't. I use 'colour' everywhere, as I'm Australian, except for programming, where I exclusively use 'color' to match American English. I don't let it bother me anymore - they're both functionally the same, who cares which form is used? The only time it really matters is if you're writing to be included in a consistent body of work, or you're writing a to impress.

Note: 'leet speak' and 'text speak' may qualify under "gets your point across", but only if the party you're communicating with can easily understand them without considerable effort. This is fine.

You changed it, Change it back. Screw book sales.

[VortexCortex]

I have a series of math text book from the 50's that I bought at a garage sale for $10, when I was homeless high school drop out. I used them to brush up on Algebra Trig and Calculus as preparation for teaching myself higher mathematics, compiler theory, and etc. CS theory. They are far superior to today's mathematics books.

A few years after me, my younger brother became a sophomore in high school and was struggling with mathematics. I tried to help him with his homework, but the terminology was wickedly alien. I said, "Is this even algebra? What the hell are they on about?" I showed him how to solve the problems using the methods that worked for me but he said, "No, you don't get it, I can't do it that way I have to do it the way my teacher wants or it doesn't count." That's asinine, if the solution fits then it's equivalent. However, I had experience with such oppressive systems myself, so I knew the only thing to do was start from the first chapter and re-learned their bullshit terminology so I could show him the book's particular way of performing and wording the calculation. I realized that the textbook sellers changed the wording and methods of teaching mathematics over the years, not only to yield more book sales for newer curriculum and re-assert copyright anew, but also to make mathematics more in line with the (supposed) way girls learn.

It's unconscionable for teachers to remain willfully ignorant that boys and girls think differently in general; Only a complete moron would think that brains were immune to sexual dimorphism that had such drastic effects on the rest of the human body. It was common knowledge that men and women have different personalities in general, but strangely research was lacking in the area of sex differences in behavior. However, the feminist mantra that men and women are not different drowns out opposing facts. Strange when you consider that they lobbied for changes to the way mathematics and sciences were taught to make them more easy for girls to learn them. Drop the damn stereotyped learning, everyone goes at different rates and different methods are better for different folks, and yes, sexual dimorphism will cause a trend in certain graphs, but that doesn't mean we can't embrace outliers too. Just consider the student as individuals for once: If a boy or girl is having trouble learning via one method, then teach them the other. If that means you wind up more girls or boys in the class that teaches more event based and auditory methods vs visual and hands-on methods then THAT'S OK. If you want to end sexism, racism, homophobia, etc. you have to consider the individual's experience regardless of any group you classify them as being; Stop using identity politics, they only create more inequality in the name of equality.

The feminists leveraged their sexist ideology and identity politics quite effectively by pointing to the disparity in female enrollment and graduation from college, especially in STEM fields. What they failed to realize is that my mom was in the slide-rule club in high school, and she didn't need sex tailored teaching. Their changes didn't help girls to learn, they merely made it harder for some to learn than others. The textbooks I have from the 50's and 60's teach mathematics in concise and plain terms. They don't use too many ridiculous analogies and mental gymnastics. Word problems weren't a focal point past elementary levels. It wasn't that all girls learn different than all boys, it was that there are different methods to teaching that individuals are better at understanding, and there is a trend in which methods boys and girls favor. However, these changes just muddled the methods and muddied the waters.

Another problem has been brewing in education for a wile now too: Standardized Testing AKA Poor Penalization.

seems to be incorrect teaching

[Chirs]

From what I understand, the alternative methods are supposed to be taught in addition to the traditional methods, not instead of them. The idea is to get kids comfortable with what the operations actually "mean", not just rote techniques.

The method of using addition to do subtraction is one that I do quite regularly (I'm almost 40). It's handy as an estimation technique, since for a first approximation you can round both numbers to something that's easy to work with, and then factor in the correction if necessary.

As for division, the technique described clearly doesn't scale to the numbers in the example. It was a poor choice of question to demonstrate the technique.

good idea, poor execution

[Chirs]

As I understand it, the problem that CC is trying to solve is that most kids don't have a gut-level understanding of what numbers actually *mean*.

I went to school with a lot of people that just memorized the rules, but didn't really have a feel for them. And so when the circumstances changed they couldn't adjust the rules to deal with the new circumstances. (Dealing with binary or hex, for example. Or curved space, or alternate coordinate systems.)

So with CC they're trying to give kids a more intuitive feel for numbers. That said, the alternate techniques are supposed to be *in addition* to the ones that we all learned, not instead of them. And the alternate techniques are not as efficient as the traditional techniques (which are optimized for the common case) but they're more flexible. So some questions (like those involving large numbers) don't mesh well with techniques involving counting/drawing/reordering/etc.

Lastly, some of the issues are due to bad question design, bad teaching, etc. We've got centuries of experience teaching the traditional techniques, not so much with the new stuff.