2+2=What? Parents rail against Common Core math
chron.com
chron.com
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.
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.
This really doesn't have anything to do with common core. Different curriculums that the school districts choose to purchase and implement go about achieving the goals of common core quite differently. Everyday Math is mentioned in another comment and is mostly awful. It's pretty widely used though. We are actually moving to a house in my wife's school district this summer so that our son doesn't go to school where we currently live to avoid both Everyday Math and an equally awful reading curriculum.
If you can't just look at something like 2x = 4y and instantly simply it....
Common Core includes memorization of tables. For instance, it explicitly calls for knowing from memory all products of two one-digit numbers by the end of Grade 3. By the time the students get to algebra, they'll be ready for simplifying 2x=4y.
What is covered in each grade is given here: http://www.corestandards.org/Math/
A lot of the criticism I've read of it seems to be from people who have been comparing grade X of CC (where X is the grade their kid is in) to what they remember learning in grade X when they were a kid, and conclude that CC does not teach the things they learned in grade X. In fact, it often does teach those things--just in a different grade, or later in the grade X year.
Note that I'm NOT saying CC is better than prior K-12 math programs. I'm just saying that comparisons should be done between CC and prior programs by comparing them as K-12 programs, not by comparing them for specific grades.
But I'm replying to all those who denounce rote memorization in whatever context, and claim this is not necessary to be good at math (or for a very large fraction of children, phonics, in order to later read well).
(It's something I've recently gotten really focused on, after a sister-in-law asked for help: one of her kids is great with numbers (even deduced negative numbers on his own, and asked her what they meant), but the eldest just cannot memorize the math tables, and we're despairing about what to do.)
The book A Mathematician's Lament really registered with me due to this experience.
So, while I don't know enough about educational theory or the Common Core mathematics curriculum specifically to say for sure that it is better than rote memorization, I can say my bias makes me think nothing could be worse.
The math practices I see elementary school kids doing under Common Core seems to be way more like "real" mathematics than what I did at that age.
I will say, I worry about the population of elementary school teachers who are asked to implement this, as a generalization they are the least likely to have taken advanced mathematics in university.
"Motivation" at a higher sense is something that's sorely lacking in US public school (free government school) math. Especially prior to real algebra, the teachers tend to be generalists who don't know to tell you "you need to learn X so you can learn Y which will allow you to solve problems like Z" and of course get you to understand why Z is neat and important. But that's a different sort of problem that just not making sure all students capable have the foundation they need.
Rote memorization of times tables doesn't lead to understanding. So, early in the learning process, you give children techniques that give correct answers, boost confidence and increase understanding of what is actually happening.
Thus when they see 4x = 2y they'll know that 4x means 4 xs and 2y means 2 ys.
If what we are trying to teach is this abstraction, then the rote table method is arbitrary* and a time sync. The students will still learn basic sums over time, it just won't be the focus of the practice.
*For instance, my education with the tables went up to 12s. Why in the world did we choose 12? 16 would have certainly helped me out more.
To solve your problem with the same technique as the article, you would have added 1 to 52, 73 - 53 = 20, then + 1 for the answer.
You would need to know ball park anyway to see if the calculator answer made sense.
You don't need arithmetic to learn pattern recognition.
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.
You are not a six year old child learning arithmatic. You have missed the point.
> The problem with that method is that if I ask students to explain why it works, they’d have a really hard time explaining it to me. They might be able to do the computation, but they don’t get the math behind it. For some people, that’s fine. For math teachers, that’s a problem because it means a lot of students won’t be able to grasp other math concepts in the future because they never really developed “number sense.”
Mental methods are taught so that children do understand numbers, which gives them a better grounding for future learning.
Waving a hand and saying the "old way" is simply an algorithm and a poor method because it glosses over the details is like saying teaching someone how to use a calculator will make them forget how math works.
That common core method for subtracting 12 from 32 definitely doesn't teach you anything about how or why it works.
That was a point I made elsewhere on this thread. When helping my second-grader with her homework, it sometimes seems that they are just changing what the student is required to memorize (and also increasing the volume), without necessarily imparting additional understanding.
That problem relies on what they call the "Add it Up" method, and it is specifically a technique with which I've helped my daughter. I observed that kids can completely learn the method and ace a test without understanding the concepts behind it.
> That common core method for subtracting 12 from 32 definitely doesn't teach you anything about how or why it works.
You do not understand what it is trying to teach. It is teaching children that taking one number from another can be done using columns, but it can also be done in your head by breaking big numbers down into small numbers and counting up.
It's like asking why ever read a book, with a level of english past the level of a memo asking if you have completed a task. This article also seems to suggest that people don't understand how to preform basic mental arithmetic.
In the states there also seems to be this insane way of thinking that you should learn an algorithm to do things in a particular way, if you can do it one way you should understand it and all the other methods should just fall into place.
This is a pretty good explanation of the problem. https://www.youtube.com/watch?v=5ZED4gITL28
(hey I took double maths for A-level and enjoyed every minute of it)
12 = 2 + 10
32 - 2 = 30
30 - 10 = 20http://brightbacon.com/blog/work/how-count-back-change-begin...
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 find it funny that these parents get so upset at how hard it is.... if the curriculum is designed for your third grader.... you should be able to learn it pretty easily, if you just try. My guess is that a lot of the parents aren't actually trying to teach themselves the new way, and then get mad they can't help with the homework.
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.
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.
I'm not aware of the phonics things, though? Care to elaborate on it?
For a tl;dr (heh), Progressives in the early-mid part of the century decided rote memorization was bad per se, a new "Whole Word" method was developed but only? tested on children of University of College professors, who would have been in the large cohort of children who'll learn reading pretty much on their own, by the mid-50s it was widely realized that this left behind a larger cohort who can't learn how to read without phonics, and to this day the issue is still a battle to the knife.
Yes, but if all we're going on is "hope" and "politics", then we have absolutely no way of knowing if it's the right direction as you say. As the other poster mentioned, they could have easily done some studies of common core before throwing it at the wall to see if it sticks.
Change is never good if it's for its own sake. It may be intuitive for us to think that "mechanical learning" isn't the right approach to solving literacy in subject X, but we could very well be entirely wrong. The point I was trying to draw upon was the parent's initial comment about "let's do Y, and hope it works". Hoping is absolutely no substitute for hard research with tests and controls.
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.)
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.
This is the classic proofs based text, in other schools what's commonly used for "honors calculus", including MIT but not with such a name. I suppose in theory a really mathematically adept student could start with it, but that's not what I remember any school I've looked into, including CalTech, requiring before you start it.
The link you cited is just an attack on a particular contention; it's entirely unrelated to my examination of it, except second hand reports of it (some of the phases quoted are familiar) probably in part prompted mine.
Try Harvard's Math 55b.They hit you with Rudin freshman year.
4 years of math (including calculus)
1 year of physics
1 year of chemistry
3 years of English (4 years recommended)
1 year of U.S. history/government (waived for international students)
What if my high school does not offer Advanced
Placement (AP) or International Baccalaureate (IB)
courses?
Many schools don't offer the AP or IB curricula.
Regardless of the curriculum your school offers, we
expect that you will have challenged yourself with
demanding courses. The Caltech curriculum will require
that you have completed rigorous courses in calculus and
in physics. If these courses are not available in your
high school, we strongly encourage you to take them at a
local college or online.
--------- BEGIN QUOTE -----------
Ma 1 abc. Calculus of One and Several Variables and Linear Algebra. 9 units (4-0-5); first, second, third terms. Prerequisites: high-school algebra, trigonometry, and calculus. Special section of Ma 1 a, 12 units (5-0-7). Review of calculus. Complex numbers, Taylor polynomials, infinite series. Comprehensive presentation of linear algebra. Derivatives of vector functions, multiple integrals, line and path integrals, theorems of Green and Stokes. Ma 1 b, c is divided into two tracks: analytic and practical. Students will be given information helping them to choose a track at the end of the fall term. There will be a special section or sections of Ma 1 a for those students who, because of their background, require more calculus than is provided in the regular Ma 1 a sequence. These students will not learn series in Ma 1 a and will be required to take Ma 1 d. Instructors: Marx, Katz, Mantovan, Aschbacher, Ni, Kechris.
Ma 1 d. Series. 5 units (2-0-3); second term only. Prerequisite: special section of Ma 1 a. This is a course intended for those students in the special calculus-intensive sections of Ma 1 a who did not have complex numbers, Taylor polynomials, and infinite series during Ma 1 a. It may not be taken by students who have passed the regular Ma 1 a. Instructor: Staff.
---------- END QUOTE ----------
Note: don't freak out over the unit numbers. Caltech's unit scale is different from that of most other schools. 1 unit corresponds to 1 hour of work per week, so a 9 unit course is one that should take 9 hours a week. The numbers in parentheses, such as (4-0-5) break it down by number of hours of lecture, number of hours of lab, and number of hours of outside preparation and homework.
Ma1 does start with a "review of calculus", so you could probably do it without having had calculus in high school if you were really good, but it would be rough.
[1] http://www.admissions.caltech.edu/applying/freshman
[2] http://catalog.caltech.edu/courses/listing/ma.html
[3] http://admissions.caltech.edu/uploads/File/general/FAQapplyi...
(Most, but not all, MIT students enter with their first semester under their belts and part of the second, so the second semester calc class offered to first semester freshman is traditionally a wild monkey cage of chaos and freshmen held inside a giant lecture hall. This may have changed in recent years with on-line courses -- this would definitely be the perfect class to kill the lecture. But the first-semester calc is still offered in various difficulty levels for the first semester.)
(Oh, and MIT uses the same freaky unit numbering.)
And as I can attest, there's this nice bit about how they have many fewer spaces than qualified applicants, not going into the minor detail of if you were one of the latter (I wasn't).
CalTech is very special, even more so than MIT I gather (I'm Class of '83 of the latter). Much smaller, 1/4 the class size (~250 vs. 1100), much more intense, much more science focused. Someone, commenting on how they'll clean up your room every week (a service MIT is sadly lacking in :-), said it was like a Hogwarts for science, and very simply, if you can't do magic at its level, they don't accept you.
For some historical perspective, as I understand it, at the post-Civil War beginning of MIT, most students were mastering the calculus by the end of their undergraduate program.
(And our "freaky" unit numbering is great, totally transparent, and at least at MIT there's a committee dedicated to the task of keeping professors and departments in line with the Institute's limits on work demanded, and has been known to take classes away from abusive professors. That's also done at the departmental level, as I witnessed one semester while on the EECS department's staff (took over and finished the sysadmin part of the job of moving it from Multics to UNIX(TM), with the help of one on and off student like me who was an old friend).)
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.
In the U.S. system, they also serve as a review, I guess with the hope of shoring up knowledge that students were missing (but I think such an approach for math education is pretty optimistic; figuring out what they don't know and fixing that must be more valuable than just showing them things again).
To do as well as you did, you obviously picked that up on your own, as did I.
(While in theory I took a trig and further analytic geometry course in high school, followed by a semester of the calculus, the teacher flatly refused to teach anything, and trig at that level in that textbook was absolutely boring and unmotivated (e.g. didn't mention you needed it to do calculus on rotation including AC electricity); I only stayed in these automatic A courses so I'd have them on my transcript (I'd already taken my first go at the calculus in a summer course taught at a university before this, but focused most of my attention on a PDP-11/70 running UNIX(TM) Version 6, which ended up being infinitely more valuable (as it turned out, perhaps lifesaving; the introductory programming class that was my excuse for using it was easy, so I focused on UNIX(TM), Adventure and other games, wandering around the filesystem (very much like Adventure :-), software engineering, helping others debug their final class project, and using nroff for my class project which had more exposition on software engineering than code; included that in my college applications)).
Expanding on maxerickson's comment, I gather formal precalculus courses also start teaching you about limits and stuff like that; since basic differentiation, especially speed and acceleration, is relatively simple, I'd hope it would teach an intro to that, which goes along nicely with the limits. It could also be a fancy name for a (further) analytic geometry course, and/or include trig motivated by the calculus vs., oh, surveying.
I think what really helped me pick up different branches of math was actually getting the motivation from somewhere. My learning of Discrete Math was fueled by my interest in programming; for Calculus it was the neat applications in Physics. Calculating for calculation's sake was always pretty boring, and I'd tune out without some other kind of applicable motivation.
By the sounds of it, I'm much younger than you (having attended high school in the mid-2000s), but it's interesting that I did pretty similar stuff when I was bored in school. I wrote more than a couple of essays using groff just for the hell of it. Good times :)
It wasn't as bad as it might sound; sure, punched cards were a bit of a pain, and we all knew they were obsolescent (1978-9), but then again it was a chance to learn how they did things when dinosaurs roamed the earth. But the neatest thing was no computer priesthood for this class: the main computer for the school was an 370/115 (360 series: revolutionary '60s architecture using discrete silicon transistors and core memory, the 370 series used ICs including for main memory (!), the -115 model was the lowest end/slowest, but it ran BASIC fine :-), and they leased the obsolescent 1130 and just put it in a corner.
We'd put our cards in the card reader, hit go, hit the right buttons or whatever to break it out of an infinite loop if necessary, feed in a boot card if it got really confused, all under essentially no supervision, but good help, of the priesthood in the other corner of the room tending the mainframe. It also had a console, and an interactive program was one of the projects.
Lots of people older than me also cut their teeth on the 1130, Wikipedia has a partial list: https://en.wikipedia.org/wiki/IBM_1130#Influence_of_the_1130 I wonder, if only the university library had a book on LISP; instead it had lots of good books on software engineering, which along with the programming taught me the basics. Like don't mix up '0' and 'O' in your variable names, especially if the first cut of the card deck is being produced by students learning how to do date entry from a coding form you filled out (http://www.atkielski.com/PDF/data/fortran.pdf).
Whereas the DEC PDP-11/70 running UNIX(TM) I used was at a big university's summer school following that. And fortunately not at all loaded down then, and it was a very fast system, even had a fixed head disk for swapping. So in my case I was semi-bored with the introductory programming course (at the end the professor privately but nicely called me out for being a ringer), and wrote up the final project using nroff and a XEROX Daisywheel to counter that. Just because even primitive word processing that was extremely neat, and a lot better than typing out a paper in the previous summer on a Selectric typewriter with auto-erase, the best there was at the time.
P.S. I contend that {n,t,g}roff is still a lot better than typing out a paper in MS Word, though I mostly stick to LaTeX for that sort of stuff nowadays.
I'm sure that the current common core level for math ends around Trigonometry.
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.
This was in Joplin, MO, one of the reddest Red State parts of the country, albeit in a school district famous after the 1955 publication of Why Johnny Can't Read for still being able to teach its students how to read. But the language arts were always very capably taught in the district, generally better than math.
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...
You see this in developing countries where the whole population is illiterate. It usually ends up that the children reach a level of proficiency that enables them to teach their parents.
Sincerely, I have no idea how the "old-fashioned way" works. I mean, venn diagrams and trees to add fractions. A variable change (!) to solve a quadratic equation.
Those "new" methods were the methods I learned, and they were fast, efficient, and we add other algorithms to prove the validity of our answer.
[1]: https://en.wikipedia.org/wiki/New_Math
[EDIT] I just read the thread. Apparently it was an april's fools joke. Now I don't feel like I'm living in Bizarro World
The methods that the Reddit user was saying was the "normal" way were completely alien to me. Both because they had no instructions, and because I wasn't taught them as a kid/ever.
(-5/2)-sqrt(57/4) vs (-5-sqrt(57))/2
So why downvote my comment if it is apparently an April fools post?
The "Old" way just looks weird...
What happens when it turns out a combination of poor training of teachers and lack of exposure by parents combines to produce an entire generation that can't do the most basic of math problems. Who will be do the STEM work in this country when we don't have enough students who know basic math let alone calculus and beyond. Your betting the future of the American economy and society on this change you better have more proof for it then "we did a study"
From memory, it was justified with a study of students at a University of Chicago associated school, i.e. lots of children of professors, they were obviously in the fairly large cohort that just pick up reading on their own. Those who don't were left to the tender mercies of Dick and Jane and their running dog Spot as Jerry Pournelle likes to put it, his wife used to successfully teach reading to the hardest of hard cases, juveniles in criminal detention.
Unfortunately that’s simply not true, we live in a culture where most people can't do math, and find it acceptable to not be able to. How math is being taught is simply wrong and those methods you're so resisting aren't new, they're decades old and they're already proven.
> What happens when it turns out a combination of poor training of teachers and lack of exposure by parents combines to produce an entire generation that can't do the most basic of math problems.
We're already there.
You're just fear based and will resist any change whatsoever.
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 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 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.
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.
And how many different ways is there to add two numbers?
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...
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...
[1]http://www.singaporemath.com [2]http://www.oecd.org/pisa/keyfindings/PISA-2012-results-snaps...
1a) "partitioning" 8 + 7 is 8, jump 2 to 10, then jump 5 to 15.
2) "thinking and estimating". 3998 + 4997 is nearly 4000 + 5000 and is exactly 4000 + 5000 - 5
3) traditional columns with units, tens, hundreds, etc.
Note that these are teaching small children how to manipulate numbers in their heads before they reach for paper and pencil. This builds up understanding of what numbers are, what the processes are doing, what the relationships between numbers are etc. these techniques are also building up skills for subtraction. Subtraction is not just "taking one number from another", it includes finding the difference between two numbers and techniques involve addition.
2. let 9=10-1, 5+9=10-1+5=15-1=14
3. let 9=5+4, 5+9=5+5+4=14
4. cann't make it up
5+9 = (((((((((5+1)+1)++1)+1)+1)+1)+1)+1)+1) 5+9 = 9 + 5 =...
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.
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.
The US is a capitalist society. We do a significant disservice to our citizenry by failing to teach fundamentals of how money works in the public education system.
Some of the comments here refer to a period of "reform math" instruction BEFORE the introduction of the Common Core State Standards in mathematics,[2] which are actually quite recent. Implementation of the Common Core in school classrooms in the United States is only a year or two old today. The Common Core was an attempt to introduce coherency and logical progression into the mishmash of topics that characterized "reform math" textbooks such as Everyday Math (which is probably the best and most mathematically sound of the reform math textbooks) and TERC: Investigations, among other titles. The Common Core standards are generally regarded, as curriculum standards, as a plain improvement over what most states set as mathematics curriculum standards before.[3] On the other hand, many of the mathematics who criticized the preceding period of "reform math" instruction (basically most United States school practice in the twenty-first century) think that the current Common Core textbooks and teacher training courses still don't go far enough in improving instruction.
As a parent, I expect and welcome school instruction in any topic that is better and more research-based than what I received as a child. The quotations from parents in the article kindly submitted here along the lines of "Why should my child be expected to learn things I don't understand?" seems like a very bizarre approach to parenting to me. (As a homeschooling parent, I used the Miquon Math[4] and Singapore Primary Mathematics series[5] with great success in helping my four children learn their elementary mathematics. They have been able to go on to more advanced mathematics study with relative ease. I had to learn new topics and new techniques to use those materials, but that is good for me. I was lucky that my wife, educated in Taiwan, largely understands the approach taken in the Singapore materials, but so far both of our older two sons have gone well beyond the mathematics study level of either of their parents. Education is supposed to improve from generation to generation, or what are schools for? (That's why we homeschool--we lay a good foundation for our children with the best available curricular materials to get them ready for classes with teachers who know what they are doing for our children's secondary education.)
[1] http://www.theatlantic.com/education/archive/2014/04/confusi...
[2] http://www.corestandards.org/Math/
[3] http://educationnext.org/the-common-core-math-standards/
[5] http://www.singaporemath.com/Primary_Mathematics_US_Ed_s/39....
And the submitter is glad that you're glad that he submitted the article.
>the article just isn't that informative
Indeed. One of the things that's awesome about HN is that, given merely a topic of interest, many HNers will delve more deeply, look for concrete information, pull citations, and generally drive more thoughtful discussion around the base topic.
Accordingly, I've frequently found discussions on HN to be far more insightful and informative than the initial submissions.
For example: https://news.ycombinator.com/item?id=7752318
Off to research Singapore Primary Mathematics. Thanks for the tip.