It actually makes some sense. I'm still skeptical, but it's sounding like it's just a significant departure from the rote memorization methods I grew up with.
Teaching concepts as well as techniques is definitely the way to go. The problem with "Common Core" appears to be that complex procedures have been selected as the way to teach concepts.
Taking the problem in the illustration, subtracting 12 from 42, the four-step process is ridiculous. The way an adult would look at it in a real-world situation is to recognize that the 12 neatly coincides with part of the 42. The relevant concept is units of 10 and of less than 10. One might use a somewhat different concept for a different question.
I'm not sure of the best way to teach the concepts - cover base 10 and places first, I guess, and then talk about how and why adults who are good at math perceive problems in certain ways. "Common core" looks like about what I would expect when the USG takes a basically good idea and mashes it thru a bureaucracy.
Bah... I can tell you why the first algorithm/example works because of the commutative and associative properties of math. Learning "why" a solution works, doesn't require learning some arcane algorithm.
If kids don't learn how to do these problems quickly, they'll never be able to do higher order problems in a timely fashion.
The idea seems to be that they're teaching children to maths in their head rather than needing a piece of paper to work it out. The example is extremely odd though, I can't imagine why you would go through that process in your head. I'd probably do something like:
As a parent with a a first grader and child in kindergarten, my observations of the Common Core isn't that the basis, or theory, is unsound, it's more that the teachers were not given adequate training on it.
The parents rail against the new style of teaching because they were taught with the old style and never properly comprehended math other than by rote memorization. This is exactly the problem the new methods are trying to fix. I bet most people on HN are math-minded enough that they could pick up the new ways of doing things and actually understand how it is teaching total comprehension rather than just being able to get the right answer with no idea of why it's the right answer.
You nailed it. On the other hand, it's a bit double-edged.
As I am the parent with the CS degree, my wife is already referring our second-grader to me for help with math homework. Sure, after calc I-III, diff-EQ, linear algebra, etc. I can readily pick up on what they are doing and why. I also absolutely agree that they need to go beyond rote-memorization and help kids with a fundamental understanding of numbers, their relationships, etc.
But, here's the other side: I don't know that, say, a first or second-grader is really ready to grasp some of the concepts (at least as they are currently being taught). My daughter "handles" it pretty well and can get the job done, but it sometimes seems that they are simply moving the rote-memorization ball, so to speak. That is, now, instead of just remembering tables, she may be simply remembering these new methods of arriving at the answer. I'm not sure she really knows why though. And, it can actually be kind of difficult to test where their level of true understanding is. For instance, asking them to explain gets into their verbal skills as much as math. So, they may actually understand it, but are unable to really explain it. One clue is the kind of mistakes they make, but it's still kind of murky.
In any case, in the end, I'm not altogether sure that her comprehension has been expanded. And, it sometimes seems that the result is that she simply has to labor harder to arrive at the same answers.
On a side note, what's funny is that I learned the "old-school" way, yet I somehow managed to comprehend and am now trying to help my daughter understand the "new school" way. Something ironic about that.
I have experienced this first hand with my daughter (2nd grade).
She's doing 2 and 3 digit addition and subtraction by breaking the problem into chunks (I tried to cook up an example, but I don't remember how they do it exactly). I learned the "carry way", so the chunk thing seems cumbersome (and I didn't really know how to help her, since I keep reverting to my own proclivities), but it seems to work, and I see the value in the way she deconstructs the problem instead of just doing the mechanics.
I think your experience is exactly how all of these other parents are reacting.
It seems that the parents are getting frustrated because they don't understand it, and would rather insist on using their methods.
Don't get me wrong, it's valuable to know how to do something simply, but I think that the underpinnings of doing it the 'chunk' way show students how to break very large, seemingly overwhelmingly complex problems into smaller bits.
Without reading the fine article except for searching for "calculus", I'll note that I've confirmed an accusation at the other end: the Common Core does not even reach precalculus by the end of high school.
No student in a school solely based on it will be taking AP Calculus, let alone be able to attend MIT or Caltech (the former requires you to be ready to learn the calculus, the latter demands you've already learned single variable calculus). Students interested in STEM majors, or anything needing serious math, will join the current legions who didn't learn (enough) math in high school taking remedial classes and be that much behind in graduating.
Perhaps America has too many people in STEM careers; absent supplementation by school districts that e.g. already teach AP Calculus and don't want to stop, this will help fix that....
(Well, outside of the states rejecting it; it was implemented in my home state of Missouri without the input of the legislature, and they're about to zap it, joining another state who's name I forget.)
Further, a citation to Caltech's admission policy would be handy; I found sources directly disputing your claim (also in the context of Common Core), citing Caltech Math1a to rebut it.
AP Calculus has never been a standard part of the requirements for a high school diploma in any state in the union. Common Core did not change that. In fact Common Core has added to the requirements in math as it brought many states upwards to Trigonometry as a requirement.
Remember, this curriculum is not for Advanced Placement, it's for common placement. No school is prevented from offering AP courses and they have quite a few incentives to do so.
I was never particularly good at math. I also never took precalculus in high school. It was Algebra 2, Geometry, Discrete Math, and Statistics for me. I struggled a little with Calculus when I got to university, but managed to pass the class and got pretty good at it by the time I was in Multivariable Calculus. I know many people who were in the same situation. I don't think "precalculus" is requisite for learning calculus (I also never took any "prealgebra" and managed algebra just fine). I can't even imagine what a pre{calculus,algebra} course would possibly teach.
Why are we worried that elementary school children might misunderstand arithmetic? This is the problem with the Common Core math standards, that they think you need to have a perfect understanding of something before you can move on, and if you have moved on then you have a perfect understanding of everything that came before it.
That's just not how math works at any level! Understanding counting and arithmetic and numbers is a continuously evolving process. Children should be exposed to these things: the difference between a number and its representation, alternative ways to understand counting, etc., but to require every student understand all of them before moving on is ridiculous. And likewise, in later grades (even in high school!) one should revisit the concepts they thought they mastered from the different perspectives that their more mature coursework allows them to. There are important things to say about counting and arithmetic from first grade all the way through a PhD.
The point is he focuses on challenging their understanding of numbers vs representations of numbers, despite the fact that they thought they mastered simple counting in first grade. They come away from this not with a mastery of binary arithmetic but with a better understanding of their usual decimal counting system.
Calculus can be taught to anyone independent of age. It is not a unit of difficulty.
I think people are railing at teaching math to children because they themselves suck at math. Your inability to grasp subject matter is not proof that something is wrong or too hard.
Seems the problem is those creating the curriculum likewise have a poor grasp of it and of how to present it to inexperienced minds. They know that "concepts" and "process" and "psychology" are important, but lack the Tufte- and Feynman-like grasp of how to present the complex in simple clear ways.
I don't know anything about "Common core" but parents wanting to learn new methods of teaching math and arithmatic may like "Maths for Mums and Dads" http://www.mathsformumsanddads.com/
You know when I in my job try something new and it doesn't work out my company might lose a contract or in a really bad case I lose my job. When we as a society decide unilaterally that we are going to change a few century's worth of teaching style for something new we risk raising a generation of children who can't do simple math. I am not worried about if this method is "better" according to research. I am worried if it works, because if it doesn't we will have an entire generation unfit to do anything but manual labor.
You're being ruled by fear. Fear is not a place from which good logical decisions are made; if the research says it's better, then it's better; you don't keep doing the worse way just because you're used to it and fearful of anything new.
I don't know if there is an english version of the whole documentary, but if there is, I strongly recommend it (plus, there are strong contributions by Villani who won Fields medal).
It doesn't seem efficient, or very useful to aid understanding.
It replaces one operation by many operations. It trades one abstraction by increasing the memory requirements (external memory, in the paper).
At least I had finished the subtraction in my head way before I was reading halfway through the 'new' method, in all examples.
It would be useful if they students could each design their own favourite subtraction algorithm, and compare notes with fellow students, instead of having to memorize 3 or 4 cookie cutter algorithms.
I think this quote from a parent at the very end of the article is quite telling: "To me, math is numbers, it's concrete, it's black-and-white. I don't understand why you need to bring this conceptual thing into math — at least not at this age."
I am not a professional mathematician, but I get the overwhelming impression from professional mathematicians that "this conceptual thing" is really quite important in the big picture of math. To me this reflects a parent who hasn't used mathematical concepts in a real way and who doesn't understand the value in anything but arithmetic. It's the same mindset as people who throw their hands up at algebra because suddenly letters are mixed with numbers and they aren't doing multiplication tables anymore.
Edit: I don't mean this as a personal attack. It's just a problem of educating parents. People need to understand that conceptual math and abstract reasoning may seem like strange things to teach children, but that they will, in fact, provide the competitive edge for our kids. Perhaps the Common Core way of teaching this is terrible and makes children cry, but we shouldn't throw it out based on poor implementation.
The goal of Common Core is a good one. But the research was not nearly thorough enough. The curriculum was adopted all at once instead of giving it any testing.
And at least in my area, students must take the math class at their age level, at least through elementary school. Now students that excel at math get bored and hate it, and students who need extra help can't get it. That is the wrong way to improve education.
I don't know much about core math, but what are is the "context" the parents are missing? It seems to me that the homework is going to pretty hard to solve if it doesn't contain the complete "context." Or is he referring to some terminology that the parents probably don't know? Why is this context missing, or not available to the parents, if nothing else via the text book or handouts?
And how many different ways is there to add two numbers?
We choose my son's school based on the curriculum. They use Saxon maths, Spalding Reading (which includes phonograms), traditional teaching methods and the children wear uniforms. Its a Charter school and we love it.
My son (kindergarten) is loving math and has 2 or 3 worksheets of math a night as homework. A lot of it is just repetition from previous days concepts, but he feels really good showing us how well he knows "1st grade math." Its not really 1st grade math, but its more advanced than the public school kids that live in our neighborhood... AND way less frustrating it seems. I have yet to hear anything good about Common Core from my friends who deal with it on a regular basis.
If my son wants to go to Basis after grade school he will be prepared. If not... he will be so far ahead of the CC kids, we will probably just sign up for classes at the community college. We go here: http://www.legacytraditional.org/district-home/northwest-tuc...
I suffered through this sort of math with my kids. I'm afraid that this may end up being flamebait, but here goes...
These reformed Math programs are a tremendous mess being foisted on us by "Education" professionals and academics. Instead of teaching one, well-tested method of performing operations (addition, subtraction, etd.), these programs present a number of alternative "algorithms". In Everyday Math (the program my own kids were taught), the standard methods for multiplication and division were not taught and years of drill using alternative (and inferior) methods were used. This leads to tentative confusion over the way to solve problems. Proficiency with basic multiplication and so forth is downplayed and instead proficiency with calculators is developed.
The Education majors (teachers and professors of Education) aren't STEM people themselves. I remember how we, the parents, were lectured (during the parent introduction to these programs) on mathematics and how, we were informed, "there is more than one way to get to an answer" as if this was some astonishing revealed truth. How there was (are you ready for this?) more than one way to do multiplication. Then the teachers would illustrate some method (for example, the Lattice method of paper and pencil multiplication) and with wide and astonished eyes exclaim, "see it gives the SAME result". Now, for those that don't know the Lattice method, its just a method of doing multi-digit multiplication that keeps the intermediate products, which will eventually be summed, in a grid.
Many years ago I was taught the standard methods for computing the basic operations because after centuries of use they have become the prefered methods by people that have to work with numbers. That's why adults haven't bothered to learn the Russian Peasant method or the Egyptian method or whatever. So while our kids will struggle with some new text book, fat and full of colorful pictures that will have pictures of ancient pyramids, the kids in Singapore will by using thin, little black and white books full of exercises, written in English. And then, the kids in Singapore will go on to absolutely kick our asses in mathematics. I've used these Singapore math books, somewhere around the summer after third grade, to reteach my own daughter mathematics. A couple of days ago, she just took the Calculus AP exam after her Junior year in high school, no thanks to Everyday Math.
Not everything about Everyday Math nor Common Core is bad, but some of it is really bad.
It's argued by the people putting these programs in place that they know better and that their programs are supported by research. Have you looked at this supposed research? It's not good. Few well controlled studies done by people in Education departments[1].
The first (so called) research paper listed on the Everyday Math program web site uses Knuth Vol. 3 as justification for studying so many algorithms. It completely misses the point of Vol. 3. It's a book about sorting and searching algorithms. Almost every one of them has some reason for it's use: easy code, fast average performance, fast worst case, works well with a limited number of tape drives (wow!), and so on. This has nothing to do with the desirability of teaching inferior methods of basic calculation to our kids. This paper, which is used to justify some of the core principles of the Everyday Math program is an example of the poor foundation for these reforms to math education in the US.
Funny how today's leaders in math and programming all learned basic math the old fashioned way; now it's not good enough. Yet no one preaches teaching kids economics, basic taxation and interest rates, and how investing works. So we wind up with people who know math but get fooled by politicians and scammers.
> Yet no one preaches teaching kids economics, basic taxation and interest rates, and how investing works.
No one preaches it for much the same reason that no one preaches that people should breath regularly -- its not in dispute. What you ask for has been a standard, noncontroversial part of the curriculum for decades (at least in CA.)
Certainly, people do debate whether the way its taught is effective, or that it should be taught earlier or in more depth, as they do with most subjects in the curriculum.
> Funny how today's leaders in math and programming all learned basic math the old fashioned way
Evidence? Just because they were school age when that was standard doesn't mean that that's how they learned it. School isn't the only place people learn, not all schools follow the normal curriculum (which is, after all, what is mandated for public schools), and even in schools that follow the normal curriculum as a base, not all instruction is limited to it.
You'd think they would be happy that their kids are taught something they can't do themselves. Instead they're whining in order to make their stupidity hereditary.
[+] [-] bovermyer|12 years ago|reply
http://www.patheos.com/blogs/friendlyatheist/2014/03/07/abou...
It actually makes some sense. I'm still skeptical, but it's sounding like it's just a significant departure from the rote memorization methods I grew up with.
[+] [-] ds9|12 years ago|reply
Taking the problem in the illustration, subtracting 12 from 42, the four-step process is ridiculous. The way an adult would look at it in a real-world situation is to recognize that the 12 neatly coincides with part of the 42. The relevant concept is units of 10 and of less than 10. One might use a somewhat different concept for a different question.
I'm not sure of the best way to teach the concepts - cover base 10 and places first, I guess, and then talk about how and why adults who are good at math perceive problems in certain ways. "Common core" looks like about what I would expect when the USG takes a basically good idea and mashes it thru a bureaucracy.
[+] [-] hga|12 years ago|reply
If you can't just look at something like 2x = 4y and instantly simply it....
[+] [-] rplst8|12 years ago|reply
If kids don't learn how to do these problems quickly, they'll never be able to do higher order problems in a timely fashion.
[+] [-] ollysb|12 years ago|reply
[+] [-] mike_herrera|12 years ago|reply
http://brightbacon.com/blog/work/how-count-back-change-begin...
[+] [-] Delmania|12 years ago|reply
[+] [-] tomswartz07|12 years ago|reply
[+] [-] ja27|12 years ago|reply
[+] [-] NateDad|12 years ago|reply
[+] [-] unclebucknasty|12 years ago|reply
As I am the parent with the CS degree, my wife is already referring our second-grader to me for help with math homework. Sure, after calc I-III, diff-EQ, linear algebra, etc. I can readily pick up on what they are doing and why. I also absolutely agree that they need to go beyond rote-memorization and help kids with a fundamental understanding of numbers, their relationships, etc.
But, here's the other side: I don't know that, say, a first or second-grader is really ready to grasp some of the concepts (at least as they are currently being taught). My daughter "handles" it pretty well and can get the job done, but it sometimes seems that they are simply moving the rote-memorization ball, so to speak. That is, now, instead of just remembering tables, she may be simply remembering these new methods of arriving at the answer. I'm not sure she really knows why though. And, it can actually be kind of difficult to test where their level of true understanding is. For instance, asking them to explain gets into their verbal skills as much as math. So, they may actually understand it, but are unable to really explain it. One clue is the kind of mistakes they make, but it's still kind of murky.
In any case, in the end, I'm not altogether sure that her comprehension has been expanded. And, it sometimes seems that the result is that she simply has to labor harder to arrive at the same answers.
On a side note, what's funny is that I learned the "old-school" way, yet I somehow managed to comprehend and am now trying to help my daughter understand the "new school" way. Something ironic about that.
[+] [-] FeloniousHam|12 years ago|reply
She's doing 2 and 3 digit addition and subtraction by breaking the problem into chunks (I tried to cook up an example, but I don't remember how they do it exactly). I learned the "carry way", so the chunk thing seems cumbersome (and I didn't really know how to help her, since I keep reverting to my own proclivities), but it seems to work, and I see the value in the way she deconstructs the problem instead of just doing the mechanics.
[+] [-] tomswartz07|12 years ago|reply
It seems that the parents are getting frustrated because they don't understand it, and would rather insist on using their methods.
Don't get me wrong, it's valuable to know how to do something simply, but I think that the underpinnings of doing it the 'chunk' way show students how to break very large, seemingly overwhelmingly complex problems into smaller bits.
[+] [-] agumonkey|12 years ago|reply
[+] [-] hga|12 years ago|reply
No student in a school solely based on it will be taking AP Calculus, let alone be able to attend MIT or Caltech (the former requires you to be ready to learn the calculus, the latter demands you've already learned single variable calculus). Students interested in STEM majors, or anything needing serious math, will join the current legions who didn't learn (enough) math in high school taking remedial classes and be that much behind in graduating.
Perhaps America has too many people in STEM careers; absent supplementation by school districts that e.g. already teach AP Calculus and don't want to stop, this will help fix that....
(Well, outside of the states rejecting it; it was implemented in my home state of Missouri without the input of the legislature, and they're about to zap it, joining another state who's name I forget.)
[+] [-] tptacek|12 years ago|reply
http://www.mindingthecampus.com/originals/2014/04/a_sorry_at...
Further, a citation to Caltech's admission policy would be handy; I found sources directly disputing your claim (also in the context of Common Core), citing Caltech Math1a to rebut it.
[+] [-] kasey_junk|12 years ago|reply
Remember, this curriculum is not for Advanced Placement, it's for common placement. No school is prevented from offering AP courses and they have quite a few incentives to do so.
[+] [-] groovy2shoes|12 years ago|reply
[+] [-] icolor|12 years ago|reply
I'm sure that the current common core level for math ends around Trigonometry.
[+] [-] j2kun|12 years ago|reply
That's just not how math works at any level! Understanding counting and arithmetic and numbers is a continuously evolving process. Children should be exposed to these things: the difference between a number and its representation, alternative ways to understand counting, etc., but to require every student understand all of them before moving on is ridiculous. And likewise, in later grades (even in high school!) one should revisit the concepts they thought they mastered from the different perspectives that their more mature coursework allows them to. There are important things to say about counting and arithmetic from first grade all the way through a PhD.
[+] [-] j2kun|12 years ago|reply
The point is he focuses on challenging their understanding of numbers vs representations of numbers, despite the fact that they thought they mastered simple counting in first grade. They come away from this not with a mastery of binary arithmetic but with a better understanding of their usual decimal counting system.
[+] [-] hga|12 years ago|reply
[+] [-] basch|12 years ago|reply
[+] [-] sitkack|12 years ago|reply
I think people are railing at teaching math to children because they themselves suck at math. Your inability to grasp subject matter is not proof that something is wrong or too hard.
http://commonsensequantum.blogspot.com/2010/11/geometric-rep...
[+] [-] ctdonath|12 years ago|reply
[+] [-] cLeEOGPw|12 years ago|reply
[+] [-] DanBC|12 years ago|reply
[+] [-] dkhenry|12 years ago|reply
[+] [-] gnaritas|12 years ago|reply
[+] [-] j2kun|12 years ago|reply
[+] [-] syvlo|12 years ago|reply
I don't know if there is an english version of the whole documentary, but if there is, I strongly recommend it (plus, there are strong contributions by Villani who won Fields medal).
[+] [-] Shorel|12 years ago|reply
It replaces one operation by many operations. It trades one abstraction by increasing the memory requirements (external memory, in the paper).
At least I had finished the subtraction in my head way before I was reading halfway through the 'new' method, in all examples.
It would be useful if they students could each design their own favourite subtraction algorithm, and compare notes with fellow students, instead of having to memorize 3 or 4 cookie cutter algorithms.
[+] [-] bglazer|12 years ago|reply
I am not a professional mathematician, but I get the overwhelming impression from professional mathematicians that "this conceptual thing" is really quite important in the big picture of math. To me this reflects a parent who hasn't used mathematical concepts in a real way and who doesn't understand the value in anything but arithmetic. It's the same mindset as people who throw their hands up at algebra because suddenly letters are mixed with numbers and they aren't doing multiplication tables anymore.
Edit: I don't mean this as a personal attack. It's just a problem of educating parents. People need to understand that conceptual math and abstract reasoning may seem like strange things to teach children, but that they will, in fact, provide the competitive edge for our kids. Perhaps the Common Core way of teaching this is terrible and makes children cry, but we shouldn't throw it out based on poor implementation.
[+] [-] Rusky|12 years ago|reply
And at least in my area, students must take the math class at their age level, at least through elementary school. Now students that excel at math get bored and hate it, and students who need extra help can't get it. That is the wrong way to improve education.
[+] [-] chrismcb|12 years ago|reply
And how many different ways is there to add two numbers?
[+] [-] monkmartinez|12 years ago|reply
My son (kindergarten) is loving math and has 2 or 3 worksheets of math a night as homework. A lot of it is just repetition from previous days concepts, but he feels really good showing us how well he knows "1st grade math." Its not really 1st grade math, but its more advanced than the public school kids that live in our neighborhood... AND way less frustrating it seems. I have yet to hear anything good about Common Core from my friends who deal with it on a regular basis.
Basis is a school here in Tucson that is one of the top 5 in the country. They use Saxon math as well: http://educationnext.org/high-scores-at-basis-charter-school...
If my son wants to go to Basis after grade school he will be prepared. If not... he will be so far ahead of the CC kids, we will probably just sign up for classes at the community college. We go here: http://www.legacytraditional.org/district-home/northwest-tuc...
[+] [-] zo1|12 years ago|reply
[+] [-] todd8|12 years ago|reply
These reformed Math programs are a tremendous mess being foisted on us by "Education" professionals and academics. Instead of teaching one, well-tested method of performing operations (addition, subtraction, etd.), these programs present a number of alternative "algorithms". In Everyday Math (the program my own kids were taught), the standard methods for multiplication and division were not taught and years of drill using alternative (and inferior) methods were used. This leads to tentative confusion over the way to solve problems. Proficiency with basic multiplication and so forth is downplayed and instead proficiency with calculators is developed.
The Education majors (teachers and professors of Education) aren't STEM people themselves. I remember how we, the parents, were lectured (during the parent introduction to these programs) on mathematics and how, we were informed, "there is more than one way to get to an answer" as if this was some astonishing revealed truth. How there was (are you ready for this?) more than one way to do multiplication. Then the teachers would illustrate some method (for example, the Lattice method of paper and pencil multiplication) and with wide and astonished eyes exclaim, "see it gives the SAME result". Now, for those that don't know the Lattice method, its just a method of doing multi-digit multiplication that keeps the intermediate products, which will eventually be summed, in a grid.
Many years ago I was taught the standard methods for computing the basic operations because after centuries of use they have become the prefered methods by people that have to work with numbers. That's why adults haven't bothered to learn the Russian Peasant method or the Egyptian method or whatever. So while our kids will struggle with some new text book, fat and full of colorful pictures that will have pictures of ancient pyramids, the kids in Singapore will by using thin, little black and white books full of exercises, written in English. And then, the kids in Singapore will go on to absolutely kick our asses in mathematics. I've used these Singapore math books, somewhere around the summer after third grade, to reteach my own daughter mathematics. A couple of days ago, she just took the Calculus AP exam after her Junior year in high school, no thanks to Everyday Math.
Not everything about Everyday Math nor Common Core is bad, but some of it is really bad.
It's argued by the people putting these programs in place that they know better and that their programs are supported by research. Have you looked at this supposed research? It's not good. Few well controlled studies done by people in Education departments[1].
The first (so called) research paper listed on the Everyday Math program web site uses Knuth Vol. 3 as justification for studying so many algorithms. It completely misses the point of Vol. 3. It's a book about sorting and searching algorithms. Almost every one of them has some reason for it's use: easy code, fast average performance, fast worst case, works well with a limited number of tape drives (wow!), and so on. This has nothing to do with the desirability of teaching inferior methods of basic calculation to our kids. This paper, which is used to justify some of the core principles of the Everyday Math program is an example of the poor foundation for these reforms to math education in the US.
[1] How Brainy Is Your Major: http://www.psychologytoday.com/blog/finding-the-next-einstei...
[2] Algorithms in Everyday Math http://everydaymath.uchicago.edu/about/research-results/algo...
[+] [-] ebrenes|12 years ago|reply
[+] [-] nodata|12 years ago|reply
[+] [-] coldcode|12 years ago|reply
[+] [-] dragonwriter|12 years ago|reply
No one preaches it for much the same reason that no one preaches that people should breath regularly -- its not in dispute. What you ask for has been a standard, noncontroversial part of the curriculum for decades (at least in CA.)
Certainly, people do debate whether the way its taught is effective, or that it should be taught earlier or in more depth, as they do with most subjects in the curriculum.
[+] [-] dragonwriter|12 years ago|reply
Evidence? Just because they were school age when that was standard doesn't mean that that's how they learned it. School isn't the only place people learn, not all schools follow the normal curriculum (which is, after all, what is mandated for public schools), and even in schools that follow the normal curriculum as a base, not all instruction is limited to it.
[+] [-] thomasahle|12 years ago|reply
[+] [-] dec0dedab0de|12 years ago|reply
[+] [-] Grue3|12 years ago|reply