2+2=What? Parents rail against Common Core math

http://www.chron.com/news/us/article/2-2-What-Parents-rail-against-Common-Core-math-5479465.php

by unclebucknasty • 12 years ago

35 114 12 years ago

DanBC5• 12 years ago

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/

nodata2• 12 years ago

Well what are the four ways to do addition?

sirtel• 12 years ago

1. 5+9=14

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

ozh• 12 years ago

I truly pity the youth in whatever country thought that is smart

ww2• 12 years ago

you missed two most important methods:

5+9 = (((((((((5+1)+1)++1)+1)+1)+1)+1)+1)+1) 5+9 = 9 + 5 =...

DanBC5• 12 years ago

1) "counting on". 19 + 7 is (starts counting on) 20, 21, 22, 23, 24, 25, 26 (realise that 7 fingers have been used, stop counting on) 26

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.

nodata2• 12 years ago

So they are being taught some optimisations that they'd normally learn later? Doesn't sound too bad.

hga14• 12 years ago

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.)

icolor• 12 years ago

Article only mentions that learning to teach the common core addition/division/multiplication/subtraction is as difficult as 'learning' calculus.

I'm sure that the current common core level for math ends around Trigonometry.

hga14• 12 years ago

You might, like I did, check out the online sources on this, from reports on a professor who was one of the drafters admitting it, to the official curriculum. It's enlightening.

kasey_junk3• 12 years ago

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.

tptacek2• 12 years ago

The idea that Common Core prevents students from taking calculus is disputed:

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.

hga14• 12 years ago

Their Math1a uses Apostol as its textbook (http://www.math.caltech.edu/~2013-14/1term/ma001a/#text).

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.

tzs2• 12 years ago

Academic preparation Caltech says you should have [1]:

   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)

They really want you to have calculus. From the admissions FAQ [3]:

   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.

Here is Caltech's required first year math course [2]:

--------- 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...

groovy2shoes3• 12 years ago

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.

maxerickson• 12 years ago

They introduce some of the fundamental concepts of the later courses (and try to tie them into previous knowledge).

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).

hga14• 12 years ago

Precalculus as I'm using it is a level of math, not a particular course (although there are of course courses with that title). In addition to what you learned in high school, assuming your Algebra II was like mine, plenty of analytic geometry, it would also include trigonometry.

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.

bovermyer• 12 years ago

I'd never heard of this before, but looking up some of the controversy, I found this article:

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.

hga14• 12 years ago

If you don't learn your math tables by rote memorization, how are you ever going to be adept at algebra or anything based on it?

If you can't just look at something like 2x = 4y and instantly simply it....

kasey_junk3• 12 years ago

It's anecdotal I know, but for me the math table rote memorization was extremely detrimental to my learning of mathematics. It forced a mind set that implied that to be good at math you needed to be able to remember senseless unrelated facts, when in reality most of the advanced mathematics this will lead you completely astray as you cannot keep every formula in your head and it is much better to be able to derive them.

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.

lclarkmichalek• 12 years ago

I used a calculator the other day to do 73 - 52, yet I can pass a third year university algebra course. Sure, tables are useful, but they are very far from the be-all-end-all of primary school education, which they very much were for me when I was younger (you were good or bad at maths based on how good you were at your times-tables, which is hardly a good way to motivate people who enjoy mathematics, but don't excel at rote memorisation)

basch2• 12 years ago

http://www.theatlantic.com/education/archive/2014/03/5-year-...

You don't need arithmetic to learn pattern recognition.

tzs2• 12 years ago

If you don't learn your math tables by rote memorization, how are you ever going to be adept at algebra or anything based on 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.

ollysb3• 12 years ago

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:

    12 = 2 + 10
    32 - 2 = 30 
    30 - 10 = 20

mike_herrera• 12 years ago

This reminds me of, what I was taught to be, the proper method of counting back change at the cash register.

http://brightbacon.com/blog/work/how-count-back-change-begin...

rplst82• 12 years ago

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.

ollysb3• 12 years ago

That assumes they need to do higher order problems... For the majority of people some basic mental arithmetic is all they're ever going to need.

DanBC5• 12 years ago

Bah... I can tell you why the [...]

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.

vpeters25• 12 years ago

Understanding math concepts might be trivial for us but math-untrained minds such as grade schoolers and probably their parents, it could be an almost impossible high-bar to reach.

ds9• 12 years ago

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.

ktsmith• 12 years ago

The problem with "Common Core" appears to be that complex procedures have been selected as the way to teach concepts.

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.

sitkack5• 12 years ago

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.

http://commonsensequantum.blogspot.com/2010/11/geometric-rep...

ctdonath2• 12 years ago

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.

sitkack5• 12 years ago

I am not sure how true this is. Most of the public sentiment has been 3rd parties not able to understand the material. I think the adult population is vastly under-educated. The problem isn't the children, it is the parents. The parents can't understand their own child's homework. Whose failing is that?

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.

Grue3• 12 years ago

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.

NateDad2• 12 years ago

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.

unclebucknasty3• 12 years ago

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.

NateDad2• 12 years ago

Glad to hear from someone currently going through it. My older daughter is only 3, so I haven't gotten there yet. I hope the new way works, I'd like our kids to understand math better than we did, and I'm not averse to learning something new in order to help with 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.

Delmania• 12 years ago

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.

tomswartz072• 12 years ago

As a person who works with K-12 educators, I agree wholeheartedly.

ja27• 12 years ago

Absolutely. I'm sure the companies behind Common Core are licking their chops to provide that training for everyone.

coldcode• 12 years ago

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.

dec0dedab0de• 12 years ago

Personal accounting should be required from kindergarten.

fixermark• 12 years ago

Really, "home economics" should be a required skill learned by high school (at least in the US).

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.

dragonwriter2• 12 years ago

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.

thomasahle• 12 years ago

Because the same mathematicians and programmers haven't changed anything else in the way they are taught?

dragonwriter2• 12 years ago

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.

cLeEOGPw• 12 years ago

I think this summarizes all the rails against common core pretty well: http://www.reddit.com/r/math/comments/21zdln/the_common_core...

philbarr• 12 years ago

Well I'm in the UK and it seems I was taught the "Common Core" way of doing things. All makes sense to me! Right down to using the quadratic formula to solve equations.

The "Old" way just looks weird...

adambard• 12 years ago

The joke is that the new "Common Core" standards are presented as the "Old-Fashioned" way, and vice-versa.

zo16• 12 years ago

Read the comments in the Reddit link. It was apparently posted on the 1st of April. Now I'm seriously confused.

fr0sty• 12 years ago

Publishing date of that post was April 1st, for what it's worth...

zo16• 12 years ago

I just had a look and all the methods that were listed were taught to me as a kid. Then again, I went to "British" schools in the third world when I was a kid, so that might have something to do with it.

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.

gjjhjjjhhh• 12 years ago

OP describes himself as a professional mathematician and then fails to notice that common core produces an identical result in the third picture.

  (-5/2)-sqrt(57/4) vs (-5-sqrt(57))/2

Looks like op is biased towards one side.

So why downvote my comment if it is apparently an April fools post?

colonelxc• 12 years ago

This is an April fool's day post.

Vaskivo• 12 years ago

Hum... I though the article was about something like the New Math[1] but... I actually learned math like that. (I'm from Portugal, and finished high-school around 10 years ago).

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

syvlo• 12 years ago

There was this really great documentary talking about the way kids should learn math (and also how useful maths are in today's society): http://www.dailymotion.com/video/x1etsod_how-i-came-to-hate-...

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).

FeloniousHam• 12 years ago

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.

tomswartz072• 12 years ago

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.

agumonkey3• 12 years ago

It may be steep at first, but almost every problems involve breaking them into manageable chunks, let's hope it pays on the long run.

zo16• 12 years ago

These are peoples' lives they are affecting. "Hope" and "politics" shouldn't be a part of the decision making process.

monkmartinez• 12 years ago

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.

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...

zo16• 12 years ago

I can't tell if you're serious, or trolling?

dkhenry3• 12 years ago

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.

gnaritas3• 12 years ago

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.

dkhenry3• 12 years ago

This isn't a place for "some research points to this being better" we currently raised millions of children who _can_ do math just fine the current way. Do you want to just change it because someone says they might have found a better way. This is the kind of change that should have happened over _decades_ slowly to prove its self not as one big political push with no real world example of broad success.

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"

j2kun5• 12 years ago

We are already raising generations of people who can't do simple math. In fact, we raise generations of people who are proud of that fact.

bglazer• 12 years ago

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.

j2kun5• 12 years ago

I am a professional mathematician, and yes, the parents in these articles will almost always say things that reveal their own fears and misunderstandings of math. This doesn't make the Common Core implementation any better, and part of the reason is that these same parents (people of equivalent mathematical experience) are the ones teaching the kids and writing the state-wide tests and writing the textbooks.

j2kun5• 12 years ago

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.

hga14• 12 years ago

To take this further, isn't one of the most consequential bits of math done in recent times Gödel's (in)famous incompleteness theorems (https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_...), which are based on the natural numbers?

j2kun5• 12 years ago

Not to mention the myriad of open problems in number theory, and the fact that "combinatorics" (the mathematics of counting) is a huge field all by itself.

j2kun5• 12 years ago

My favorite example is this one, in which a man tries to teach the binary number system to third graders http://www.garlikov.com/Soc_Meth.html

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.

hga14• 12 years ago

I'm now remembering even more of the New Math that was remaining in my elementary school education (1966-72): I always remember set theory in 3rd grade (not particularly motivated as I remember, but very neat, a useful way to help describe the world), 4th grade as I recall is where non-decimal bases were introduced. And of course it had that obvious effect (at least for me).

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.

basch2• 12 years ago

http://www.theatlantic.com/education/archive/2014/03/5-year-...

todd82• 12 years ago

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.

[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

What was the Singapore book you used to re-teach your daughter mathematics if you don't mind me asking?

todd82• 12 years ago

Searching the internet should bring up several places to buy the Singapore Math books. There is an official site[1]. The books come two per grade level, for example 3A and 3B. They are small books, but filled with content. They only cost about $12 each. There are also workbooks available (for more exercises, but you might not need these) and some teaching guides too (that I'm unfamiliar with). For someone that was in elementary school 50 years ago, the math lessons look very familiar. There was one subject covered for which I wished there was more explanation: translating word problems into equations to be solved. This always came easily to me (I ended up majoring in Math in college), but Singapore Math has an interesting step that seems to work well for kids. They translate the word problems into a standard diagram where rectangles stand in for quantities and then the equations are derived from the diagrams. I wasn't taught that way, and so I wasn't sure how to motivate the correct construction of the rectangles. Don't let this minor complaint disuade you from trying Singapore Math. Consider the latest international rankings of students, the PISA [2]. Singapore is one from the top (Shanghai-China is number one), and as I understand it, all students in Singapore take the test so there is no selection bias. Furthermore, their books are in English while all the other top rated countries (China, Korea, Japan, Switzerland, etc.) have text books that I can't read.

[1]http://www.singaporemath.com [2]http://www.oecd.org/pisa/keyfindings/PISA-2012-results-snaps...

Shorel• 12 years ago

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.

tokenadult• 12 years ago

Ooh. 28 submission points for 104 comments. I'm glad that the submitter submitted the article. On the other hand, it may be correct (as is apparently the judgment of most participants here) that the article just isn't that informative. See an important article from The Atlantic, "Confusing Math Homework? Don’t Blame the Common Core: States, districts, and schools are actually in charge"[1] for more on what's really going in classrooms around the country.

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/

[4] http://miquonmath.com/

[5] http://www.singaporemath.com/Primary_Mathematics_US_Ed_s/39....

unclebucknasty3• 12 years ago

I'm glad that the submitter submitted the article.

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.

chrismcb• 12 years ago

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?

Rusky• 12 years ago

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.

2+2=What? Parents rail against Common Core math

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