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BC Prof Suggests Young Children Need Less Formal Math, Not More
DesScorp writes "Professor Peter Gray, a developmental psychologist and researcher at Boston College, recounts an experiment done in New Hampshire schools in 1929, where math was completely taken out of the curriculum of the poorest schools from the area until the sixth grade. The results were surprising; with just one year of math under their belts, the poor students did as well or better than students from better schools by the end of the sixth grade year, despite the fact that the better schools had math in their curriculum all throughout elementary school. Professor Gray thinks children are not mentally wired for the kind of formal math instruction that is taught in schools, and that we'd be better served by putting off the teaching of theory until the seventh grade. He scoffs at the notion that if children are failing with current levels of math instructions then we should double down and make them do more math in school."
but some, including me, are. ill kill you before you take my math!
I graduated high school at 18 with no math, and I turned out fine. Next year, when I turn 16, I'll be able to drive, finally.
Rhymes that keep their secrets will unfold behind the clouds.There upon the rainbow is the answer to a neverending story
I can say that reducing math further than it already is would dumb down school beyond the point of non-return. We already are using the lowest common denominator enough, if we keep on this way you won't learn anything. I know someone whose child needs to get book from home during school because the teaching is so slow, boring and dumbed down that there's no point to listening when she grasped everything in the first five minutes.
For once, think of the bright children!
Well I can buy, that young brains are not always best suited for specific tasks, but it seems contrary to conventional wisdom to remove math till the 6th grade. I can't imagine walking around blind in that respect till I was 12 or so.
Unless they are going to re-create the study today, I don't believe the conclusions can be held as valid. Too much has changed in the intervening years.
It is an interesting concept, however, though some would argue along a similar vein regarding reading: some kids are just not ready until they are older. I just don't think anyone in the U.S. today has the brass to re-create the study.
I use irony whenever I can, but my shirts are still wrinkled...
I'm pretty skeptical of basing current decisions off of studies done nearly a century ago... perhaps if they did the study again and got the same results I would be more interested.
There are many other explanations: First in the case in question, it may very well have been that the math teaching was so bad in that particular case that no teaching worked better than teaching math badly. Given how many bad teachers there are out there and how much they turn kids off of math, that wouldn't be at all surprising. Moreover, while it may be true that many kids aren't wired for mat, the best math students are wired for math at that age or much younger. Those kids need some form of organized input so that they can really take advantage of that ability. If kids can benefit from math instruction we can't say no to them on the off chance that it might hurt the more slowly developing kids.
I had way too many English classes dealing with things like participles.. Who cares, when will that EVER be useful?
And we should always proscribe policy change/medication/jobs/educational opportunity based upon it.
Always.
If you delay math instruction then children could become emotionally invested in school and enjoy it.
Then you spring it on them once they're comfortable. Far better than having someone know for the rest of their life that they "suck at math'" because they weren't ready for it in 3rd grade.
You wouldn't happen to be the guy who does the numbers for Congress?
During my undergrad in CS, a professor told us that children can manage set theory more naturally than arithmetic. In his view, set theory should be more prominent in children education. He said that during a course of categories (the meta-theory of set theory).
Maybe the parents were simply better at teaching their students math. I remember back in elementary school when they tried to teach us "new math" through these misguided methods that were extremely unhelpful and confused many students. My parents taught me how to divide the real way.
I've long felt that math taught in grades 1-7~8 could be compressed into a year or two with no repercussions. They just 'teach' the same thing over and over and it's not until middle school that you start really seeing anything different.
grade 1-3 - addition, subtraction, basic shapes (passed off as geometry)
grade 4-6 - addition, subtraction, basic shapes, might see a fraction by grade 6
grade 6-8 - all of the above, fractions, simple geometry.
Then in grade 8-9 where they start to introduce simple algebra.
So is it that children don't do well learning math early, which goes against everything else we know about how the human brain learns, or that you've bored them to tears by grade 3 and they just stop listening?
"I use a Mac because I'm just better than you are."
Here is my non-scientific example...
I didn't go well at math in school from 2nd Grade through 6th grade. I really struggled at it, of course I had cancer then, but I struggled at math. On the Iowa Standards tests I was 11-12th grade level at every subject except math, in those I was at my grade level or a year above it.
In 7th grade everything clicked for me, my buddy and I were put into advanced 7th grade math and by 8th grade we were bumped to High School math and science. By the end of our 4 year High School I'd taken 6 years of math (pre-algebra, algebra I&II, geometry, calculus and calculus 101 through the community college) and 2 years of physics.
Math sucks. For the kids that are not skilled with it, like myself, math is painful. For the kids that are more adept, waiting for the kids like me to catch up is painful.
More maturity means more coping ability for things that suck.
It's simple, really.
Perhaps the 6 graders that just started math had a really good teacher. One year with a good teacher can outpace several years with a mediocre teacher. The conclusion of the study should be better teaching methods not less education.
So you're telling me that anyone under 6th grade will never have to count, ever, not for lunch at school, the change needed for a candy bar? God forbid he wants 3 candy bars and has to multiply, or wants to SPLIT a whole candy bar with a friend and divide.
Sounds legit, lets take out reading too and let our children just growl at each other until they are adults, then throw it at them all at once.
~Mekkah
Ever since my daughter was able to speak, I've been playing games and doing things that help to "feel" math, not just know math facts. How many bumps on a lego brick? Can you estimate a pile of pennies? She's dabbled with pi, exponents and binary. It's great to hear a third grader explaining "non-negative integers" to a visiting playmate, but sad to hear the playmate struggle with something like that simple concept. (No wonder most cultures invented "zero" so recently.) Now we're having fun with prime numbers, and getting into factorization. She's dinking around with Python a little bit, but it's mostly the typing skills that hold her back. Numeracy is a lot more than facts, and at this age you have to play to learn.
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Don't take math away. When I was a young man (preschool) I had a babysitter who tought me how to multiply using beans. It was a very easy concept for me to learn at the time. No, I couldn't pronounce 'multiplication', but the concept itself made perfect sense. It wasn't until I got to at least the first grade before anyone tried to formally teach me. You are likely teaching kids math in the wrong way. Don't make kids to twice as much math. Don't take math away. Instead, try different teaching tactics. If I can learn multiplication in a few minutes from my babysitter, surly it can't be that hard for kids to pick up at a young age.
A unique way to learn a language: http://languageloom.com
Where you turn up for class wearing whatever you like, whenever you like.
BTW where I come from, the subject "Mathematics" was abreviated as "Maths" (since it is plural.
I was horrible at math until I got a teacher who tried something new - she told me to work my way through the book at my own pace and let her know when I was done - I finished high school algebra in a few weeks, after getting D's in (almost) every previous math class. Not everyone will thrive in that scenario, but the point is that it's all in the approach - a few weeks of effective education can be more valuable than years of ineffective droning in front of a blackboard.
So there's a mythical math month?
They used scales to teach us. Take Bags of balls mark some as 'X', and some bags as 'Y'. Find out home many balls are in X and in Y. Got the idea?
Not really a surprise, if the math instruction that you eliminate is poor to begin with. From the article:
Finding good math teachers is a challenge, in my experience. In the US, most elementary teachers are not really "math" teachers, and mathematicians aren't necessarily good teachers. My four-year-old son attended a Montessori preschool and I was amazed at the math that they were teaching him -- amazingly good. I believe it conferred numeracy that will serve him well for the rest of his life. Full disclosure: I teach high school math.
Oh, yeah, it's not easy to pad these out to 120 characters.
I dont remember having 2 hours of Homework a night in the Second Grade. Yet it seems that Kids are getting MORE and MORE homework. They have no time for anything else nowadays.
Its sad.
I can program myself out of a Hello World Contest!!
Math is hard - Barbie
Who would win this election: Andrew Weiner vs Andrew Weiner's weiner.
but probably can hold on with algebra till the 6th grade or so.
See John Holt's books here (he was a long time school teacher):
http://www.holtgws.com/
NYS Teacher of the Year John Taylor Gatto says the whole point of schooling is to dumb most people down:
http://www.newciv.org/whole/schoolteacher.txt
http://www.johntaylorgatto.com/underground/toc1.htm
"Look again at the seven lessons of schoolteaching: confusion, class assignment, dulled responses, emotional and intellectual dependency, conditional self-esteem, surveillance -- all of these things are good training for permanent underclasses, people derived forever of finding the center of their own special genius. And in later years it became the training shaken loose from even its own original logic -- to regulate the poor; since the 1920s the growth of the school bureaucracy and the less visible growth of a horde of industries that profit from schooling just exactly as it is, has enlarged this institution's original grasp to where it began to seize the sons and daughters of the middle classes."
The whole point of those early lessons is to waste kids' time and dumb them down. As Gatto says elsewhere, it was all worked out in public to create and industrial utopia and powerful nation-states with strong armies. He calls it a "conspiracy against ourselves":
http://www.johntaylorgatto.com/chapters/16a.htm
"A huge price had to be paid for business and government efficiency, a price we still pay in the quality of our existence. Part of what kids gave up was the prospect of being able to read very well, a historic part of the American genius. Instead, school had to train them for their role in the new overarching social system. But spare yourself the agony of thinking of this as a conspiracy. It was and is a fully rational transaction, the very epitome of rationalization engendered by a group of honorable men, all honorable men--but with decisive help from ordinary citizens, from almost all of us as we gradually lost touch with the fact that being followers instead of leaders, becoming consumers in place of producers, rendered us incompletely human. It was a naturally occurring conspiracy, one which required no criminal genius. The real conspirators were ourselves. When we sold our liberty for the promise of automatic security, we became like children in a conspiracy against growing up, sad children who conspire against their own children, consigning them over and over to the denaturing vats of compulsory state factory schooling."
With the internet, we could have "learning on demand", not "learning just in case". My essay on that: ... So, there is more to the story of technology than it failing in schools. Modern information and manufacturing technology itself is giving compulsory schools a failing grade. Compulsory schools do not pass in the information age. They are no longer needed. What remains is just to watch this all play out, and hopefully guide the collapse of compulsory schooling so that the
"Why Educational Technology Has Failed Schools"
http://patapata.sourceforge.net/WhyEducationalTechnologyHasFailedSchools.html
"""
Ultimately, educational technology's greatest value is in supporting "learning on demand" based on interest or need which is at the opposite end of the spectrum compared to "learning just in case" based on someone else's demand.
Compulsory schools don't usually traffic in "learning on demand", for the most part leaving that kind of activity to libraries or museums or the home or business or the "real world". In order for compulsory schools to make use of the best of educational technology and what is has to offer, schools themselves must change.
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
Math in the early grades is just rote memorization.
The data is very interesting, but I wouldn't take from this that we should teach the math later, but rather that we should just teach it differently.
TFA says that the kids have a hard time applying the skills learned in elementary school math to real-life situations, which makes sense. Math is abstract and the ability to apply abstract concepts to real life situations is a learned one; which is something a lot of people have a hard time with through adulthood. However, I also know that the algebra taught to me in high school and that some of my friends didn't learn until college is middle school equivalent curriculum in most other first world countries (I'm from the U.S.). These other countries seem to be doing just fine teaching more advanced math earlier on, which suggests to me that we're probably doing it wrong rather than too early.
Quidquid latine dictum sit, altum videtur.
For some of us when we see BC, Boston College is not the first location that comes to mind.
Damn_registrars has no butt-hole. Damn_registrars has no use for a butt-hole.
Q: How many Psychologist does it take to screw in a light bulb? A: Don't ask until you're seven. Bad joke. I guess all the time reading "Principia Mathematica" to my six year old has been a big waste of time. He was really looking forward to page 456 were we get to actually add numbers though.
Well, don't all the Chinese (and Koreans ...) kids statistically do better than the American kids at math? And if I am not mistaken, they start learning math in kindergarten.
Maybe this is why 5 out of every 4 people have trouble with fractions!
himself, and just pushing along stuff that rectifies his ideas...
Let's take this another way then - if he is SOOOoooooo right - that there ought to be less math - explain how the kids from practically every other country on the planet knows more about it than ours at the equivalent age frame!?
As a current high school teacher - I can tell you one thing - if our expectations of kids weren't sooo low at that same age frame - we'd turn out higher quality students with greater understanding, than just bodies that can regurgitate material! /rant off
My other beef with education? In general (And yes, I *AM* stereotyping now!) most teachers that teach elementary students are also the same folks that have never liked math in the first place - or never really LEARNED it!!! How can you instill a drive to like something in someone else when you don't in the first place?!!!
So an experiment done in 1929 when we knew almost nothing about math education applies how? There is too much different between now and then for the experiment to be meaningful. And further, the summary is poor. The article is a little better and refers to only arithmetic being taught in the early grades in 1929 and taking that out not having much impact on students ability to pick up the ability to reason with arithmetic later on. That should make sense. If the older curriculum doesn't focus on teaching students how to reason with the skills and concepts they know, they won't be able to reason well with them.
Fast forward to today and there is a huge volume of research and understanding about how students learn mathematics and successful ways to help students learn to reason and apply what they are learning to useful situations. It does not follow that eliminating Math from the early grades now is the way to go. Professor Grey should stick to subjects he knows, and apparently that's not Math education.
Where he is dead on is that, on the whole, elementary teachers know far too little about math or how to teach it. Very little is successfully making it from teacher education programs about how to properly teach mathematics. Basically those that choose to teach elementary school are the ones that hate math, are afraid of it, or can't do it. That's not true in all cases, but it's true in such a vast majority that it is a significant source of the problem for why our country isn't farther ahead in mathematics. That still doesn't mean take the math out of elementary school. It just means that the standards should be drastically raised for what elementary teachers should know and be able to do with mathematics. In short, the solution is to teach elementary teachers more math and more about how to teach math. The problem is that teacher education programs have a perverse incentive to make their programs easier to keep their numbers up to make more money, and math is the roadblock for many of their candidates. The result is no higher math requirements unless all teacher education programs are forced to have them. We should make sure the state requirements force them to have them.
I think there is some merit in the Professor's claims, but there has to be caution. Students need to be able to estimate measures, use measuring instruments, read clocks and handle money, all before age 10. These aspects of maths are suited to activity based learning, and can easily be embedded in other subjects.
But what of the kids who have the right brains to cope with more formal material earlier? What of the kids who cannot understand concepts such as zero or fractions without a more formal approach? What about how the retention of number facts is higher if we can get kids to engage with drill and memorisation of tables at early stages rather than later? How do we prevent the kids developing their own unusual understandings of fundamental concepts, because they have found a need in real life, and then we have to unwind their thinking later, because their constructed strategies only work in special cases?
I appreciate a lot of the results in maths education research. But there has to be great caution before we reject those practices that have worked for between 100 and 2000 years in favour of ideas that one or two research projects support. Is everything we do in classes effective? Certainly not. But until we can get class sizes down, better resourcing, attract more mathematicians to the teaching profession and get more individualised strategies working in the classroom we better be careful not to break what we know does work to some extent for the majority of students, even if it's not working optimally.
Fine, cut out theory, but teach math using basic problem solving games, and teach programming. If a kid is smart, they should start writing basic video games like age 7.
The Christian religion has been and still is the principal enemy of moral progress in the world. -- Bertrand Russell
If this was instituted, we'd actually see the impossible happen: rednecks getting stupider. Not only would they be waving tea bags and complaining about federal taxes being 40%, they wouldn't even know what 40% MEANT. After all, Jeebus wants you to drop out after 6th grade.
I think this is a great idea that should be tried in India and China for a couple of decades. No math instruction allowed in those countries until the age of 14, because this will really help their economies develop. Eventually it will even open up opportunities in American colleges. For Americans, that is.
They don't bore you. Instead, by grade 2 you're doing multiplication, by grade 6 you do algebra and geometry, by grade 8 you deal with complex formulas that take you two pages to solve.
Then I came to America. High school was total boredom. At first, I had straight As, but I was extremely bored, causing me to find other ways to occupy my mind, like pot. I started skipping, and ultimately failing at everything I was good at. Yes, I could've done the work, but I didn't simply out of boredom. I didn't even have to spend time learning anything. I knew it all already.
It was a complete waste of 4 years of my life.
Based on one study, done 71 years ago, and a visit to two schools in an anecdote in a talk by one person (which sound like BS to me, you'd be hard pressed to find ANY group of 50 adults who don't know the area of a rectangle, let alone among college educated teachers), we should teach less math so the kids magically learn more.
This is the biggest bunch of idiocy I've seen in a while.
This sentence no verb.
We don't need to teach the truth about history either. Let's just teach the kids racially sensitive, altered history instead.
Athiesm is a religion like not collecting stamps is a hobby.
You can only get good at anything by practice and it is best to take advantage of their brains while they're still absorbing anything and everything. Schools just need to make it more interesting and fun.
recitation. By "recitation" he meant, "speaking the English language." He did "not mean giving back, verbatim, the words of the teacher or the textbook." The children would be asked to talk about topics that interested them--experiences they had had, movies they had seen, or anything that would lead to genuine, lively communication and discussion. This, he thought, would improve their abilities to reason and communicate logically. He also asked the teachers to give their pupils some practice in measuring and counting things, to assure that they would have some practical experience with numbers.
Simply removing all math from the curriculum would very probably not produce the same results.
Young children should experiment with math just like any other language. That's how I learned math at an early age. We teach reading without parsing sentences or describing paragraph structure. For example, it's easy to see multiplication as five beans by 4 beans, and extrapolate the theory from there.
I just replied to Math Skills For Programmers - Necessary Or Not? http://science.slashdot.org/article.pl?sid=10/03/25/0312233
I want round up a posse to go 'round to this fool's house and beat him to life with a clue-stick. Anyone?
Not formally wired! Are we formally wired to take this git's* opinion seriously? Are we formally wired to work 9 to 5, or eat burgers, or browse /.?
Here's a delicious quote from the article (I know, I know):
"For some years I had noted that the effect of the early introduction of arithmetic had been to dull and almost chloroform the child's reasoning facilities."
Bwahahaa!
Then:
"It appears that the higher scores of the affluent districts are not due to superior teaching but to the supplementary informal 'home schooling' of children."
My, you don't say!
It finishes with:
"At the present time it seems clear that we are doing more damage than good by teaching math in elementary schools. Therefore, I'm with Benezet. We should stop teaching it. In my next post--about two weeks from now--I'm going to talk about how kids who don't go to traditional schools learn math with no or very little formal instruction. If you have a story to tell me about such learning, which might contribute to that post, please tell it in the comments section below or email it to me at grayp@bc.edu"
If Satan is keen on ignorance I reckon he's got a special place in Hell for this dick.
*I'm very glad Linus re-introduced this word to the mainstream of popular culture. It's a term of singular contempt, and I should know, I'm Irish.
science in government
http://www.maa.org/devlin/LockhartsLament.pdf
Bad math teaching is epidemic. Very few primary and secondary math teachers are actually mathematicians, and most of them don't even know *what math is*. They don't teach math, they teach a curricularithmetic
Is it any surprise they are utterly incapable of teaching it in an interesting way? Entire generations of students are being turned off of math by these bad teachers.
My school district decided NOT to teach grammar and writing. The thinking was that the students would just absorb it from the environment or something. I didn't learn about conjugating verbs until I took French in high school. As a Ph.D. student this still haunts me when my adviser has to correct such things in paper submissions. English is her second language...
pretty convincing in a topic about arithmetic.
There is counting. Recognizing quantities (by sight or by touch). Arithmetic (+, -, *, / ). Recognizing shapes. Finding unknowns. Mapping concrete items to abstract concepts (A A A = 3 As). Using variables. Algebra, Geometry, etc, etc. These are different skills. I am sure we have all met children who can tell you that "6+9=15" but if you asked them "if mommy gives you 6 cookies and daddy gives you 9, how my do you have?" would be stumped.
It sounds from the article that they dd not eliminate all maths, just abstract symbol manipulation, like "3+4=7".
It is pretty well established by people like Piaget that there are certain windows in childhood. During those times, the mind can easily absorb certain concepts that before or after those times they either cannot or all or can only with great dificulty or other exceptional circumstances.
The most widely accepted window is the window for early language learning, where beyond a certain age you will likely never be truly multi-lingual - you will always have a first language and zero or more secondary ones. However, there are several others. Mother-bonding happens within days of birth. Arithmetic sense (the ability to count, recognize quantities and relations) is one of those that is also quite young - 4-6 or something if I recall. There is a similar window for social behavior. There is also evidence that topology is such a window.
Ironically, despite the western obsession with early reading, there is no evidence that there is any window for reading. People who learn to read later in life - even 40's and beyond - can learn to read with little trouble and quickly become indistinguishable from early readers in terms of reading speed and comprehension. In fact, there is no evidence at all that early reading has any positive effect.
There are already schools that emphasize non-academic ways of learning. For example, in the Waldorf schools, children are not exposed to ANY academics at all - not even letter shapes or counting - until they are 7. Then the academic load builds slowly up, with more emphasis on outdoor play, spoken language and song, and craft-making than on book learning or lecturing. Despite this, most of these students have standard tests as high or higher than students from other private school that place more emphasis on academics.
My personal opinion (as someone with lots of kids in school) is that our current education system puts too much stuff in kids heads that they cannot process because it is not relevant to their daily experience. It is better for kids - especially young kids, under 10 or so - to play outside, engage in imaginative play, and to develop deep emotional connections with people around them than to learn to read or memorize multiplication tables. Academics can come later.
I think you're probably wrong...mostly because you forgot multiplication and division. Here was my actual school curriculum through "High School" (in that, while I was in HS, I was taking courses through a local University math program.)
1) Counting. Numbers.
2) Simple Addition/subtraction
3) Regrouping/ simple multiplication
4) Fractions/2 digit multiplication
5) Multidigit division with remainders
6) Pre-algebra
7) Algebra 1/2
8) Geometry / Trigonometry
9) Statistics / Pre-calc
10) Calculus A/B
11) Calculus C/Differential Equations
-- Political fascism requires a Fuhrer.
Both of my daughters were started on algebra by 6th grade and geometric proofs by 7th grade. My eldest, a junior in high school, is presently working on calculus.
The schedule you list sounds quite a bit like what I experienced back in the late seventies/early eighties. But, even then, when I got to high school, I was behind a good deal of the kids from other schools.
I hated math in 1st grade and basically blew it off even though I was considered well above average in the other areas of study. I got a BS CS degree in college and I excelled in the math classes. I only started understanding and enjoying math at a much later date in life.
Maybe the "professor" should try studying asian school systems, instead of school systems from last century. Why are Korean/Chinese/Japanese kids doing North American grade 5 math in grade 1?
Can we tag the article as flamebait?
You can pry my algebra from my cold dead hands.
Sure, children are not wired for math theory. That is why it is required in school. We normally do rewire the mind in education. That is what learning is all about.
And think about it a bit. According to this psychologist we might conclude that a child who is very good at math is somehow abnormal. That turns into a messed up, circular pile of goo. High levels of education are not present in the majority of people. In a way that makes educated people a minority or abnormal by definition.
Even if the study was correct, this is unlikely to happen (in the USA at least). It is simply too radical a change for anything as rigid as our public schools systems.
this signature has been removed due to a DMCA takedown notice
One of the reasons I didn't like math was because I always felt I was behind. Most math teachers don't "teach". They have you a couple of examples and expect you to figure it out yourself. Problem is most people learn barely enough to get to the next grade, by grade 12 you suddenly realize how much of the fundamentals were missed and you're stuck playing catchup.
A lot of math is taught too early and at a hurried pace
did you forget to take your meds?
About 25 years ago, I got a tutoring job with a homeschooling family I knew. One of the boys in the family, Tommy, had a very rare medical condition. He was 13 years old. Without going into detail, the most severe effect of the condition was a loss of memory. He had forgotten everything he had ever learned. He was at Kindergarten level or below in reading and math (and everything else). I worked for them as a live-in tutor for two or three days a week. I started working with him with Kindergarten-level materials, advancing through grade levels as fast as he was able to. Before the school year was over, he was at 8th-grade level in reading and math.
Older children who have not learned anything -- as long as they and/or their teachers haven't decided that they are incapable of learning! -- can very quickly advance up to their grade level and be no different from other kids their age who spent most of their childhood studying.
So I have to agree completely with those findings: children who start learning later are at no disadvantage at all after learning the material.
There is only one valid reason for children to start their education at a young age: so the other kids won't think they're stupid.
You missed the point.
Its not a question of teaching math vs not teaching math. Its when to begin teaching math.
Earlier is not necessarily better. This is bucking the current trend (prenatal music, flash cards for toddlers, etc) but is still worth considering. Perhaps certain subjects should be focused on at certain grade levels.
Mathematics must be taught in a more engaging way, but I really don't think it matters whether kids do well or not. What matters is that they have had exposure to it. Exposure makes it much easier to grasp the mathematics when they return to it in later years. This is because abstract concepts without prior exposure are just abstract concepts.. scary and hard to wrap the mind around, but abstract concepts with prior exposure come with a level of confidence; the student can think "yeah, I remember something about this..".
Intelligence -- and the ability to absorb mathematical knowledge -- depends on 2 factors: culture and genetics. For example, Americans of Japanese ancestry have a slight advantage over other ethnic groups in comprehending mathematical concepts. Delaying the introduction of mathematics would deprive Japanese-Americans of an opportunity to learn the subject.
Americans of African ancestry are at the other extreme. They have much greater difficulty in comprehending mathematics. Delaying the introduction of mathematics in primary school may actually not impact their comprehension of the subject.
By the way, these ethnic differences are one strong argument in favor of maintaining schools that are independent of the federal government. School districts where Japanese-Americans predominate would be free to build a curriculum that is best suited for their ethnic group. The same goes for African-Americans.
The only role that Washington should play is to (1) create national tests of academic knowledge, (2) require that all students up to the 12th grade take the tests, and (3) publish the results. How to respond to the results is left to the school districts. Washington merely measures and publishes. This approach avoids the problem of certain ethnic groups's using lawyers to terminate national standards because certain ethnic groups underperform due to cultural and genetic reasons.
My idea is that Washington does not mandate any national standards. Washington merely measures and publishes.
Terence Tao scored a 760 on the math SAT when he was 8. He won a bronze medal in the international math Olympiad at the age of 10.
We need a system that respects the individuality of our students, not a one-size-fits-all approach.
There's a lot of subjects that are over-taught in schools. Science has evolved much; this era of hyperspecialization makes forcing kids to memorize the birth and death years of insignificant Roman emperors seem so trivial.
The classical education of the Trivium is probably a much better fit for educating humans, as opposed to the factory farming methods of the 20th Century. It far better fits the developmental stages as they occur. I suspect as we move away from the need for uniform but low quality graduates, and try to get competitive intellectually in the world, the focus will naturally shift back to this superior form of education.
No, no that was not asking for an answer.
When will people stop saying that X is the answer?
Life aint like that.
X is good for some, Y for others. Even Q is good for some weirdos.
There is no one best way, everyone is different, what is good for one is bad for another.
Everything needs to be tailored to the individual.
The end.
Thank you for paying attention.
(sorry, think this just irked me, I liked maths and not much else when young, I also like proper maths, not where they tried to dress it up with silly stories to help me relate ane make it easier, that just madfe it harder, just fucking get to the point fool)
+----------------- | What is the question!
Just read the essay. Makes me want to weep for my past and my children's future. Why isn't that author just flat-out in charge of education in the US, period?
Now for the horror. The problems the author takes such a perceptive ax to in this essay? They're not just in mathematics education. They PERVADE the system. EVERY subject is taught this badly.
We're going through the cargo cult motions, but we aren't actually teaching a thing.
He put his boots up on the table and made a face. "The sig," he smirked. "You can waste your life in search of the sig."
Another thing is the lack of math history being taught.
Welcome to the most hated subject ever taught. Math and history! Each of them alone is bad enough, but you expect me to learn them together???
Well I can buy, that young brains are not always best suited for specific tasks, but it seems contrary to conventional wisdom to remove math till the 6th grade. I can't imagine walking around blind in that respect till I was 12 or so.
Except that if you read the article, you'll notice that kids aren't blind about math without our formal instructions methods. Gray notes that young children have a natural affinity for the counting and value of objects at young ages... "real world math understanding", if you will... and that formal drill and theory actually retards this natural understanding. Note that in the New Hampshire experiment, the poor kids still had a better grasp of how common math works in the real world than did the formally trained kids from better schools... and this was before their formal math schooling in sixth grade.
He thinks that what we're doing to kids at those ages now is somewhat analogous to teaching a monkey to stack bottle caps in ascending order. The monkey may get it right through rote drilling, but has no concept whatsoever of what the exercise means. There are undoubtedly gifted children that pick up theory naturally, but at that age, they're far in the minority.
Life is hard, and the world is cruel
I can believe that this is the case. Good freaking luck getting research or reform on the issue, though. Note, however, in the 1929 experiment, that low-grades were cultivating number & measurement sense; just that abstract operations (add, sub, mul, div) were witheld until later.
He also asked the teachers to give their pupils some practice in measuring and counting things, to assure that they would have some practical experience with numbers.
The thing that made me yell out loud was the following. I think I have to chalk this up to education schools causing irreparable brain damage. I went into part-time college teaching at fairly low pay, over the pleadings of many people to go into higher-pay private high schools, so as to avoid dealing with people like this:
In an article published in 2005, Patricia Clark Kenschaft, a professor of mathematics at Montclair State University, described her experiences of going into elementary schools and talking with teachers about math. In one visit to a K-6 elementary school in New Jersey she discovered that not a single teacher, out of the fifty that she met with, knew how to find the area of a rectangle.[2] They taught multiplication, but none of them knew that multiplication is used to find the area of a rectangle. Their most common guess was that you add the length and the width to get the area. Their excuse for not knowing was that they did not need to teach about areas of rectangles; that came later in the curriculum. But the fact that they couldn't figure out that multiplication is used to find the area was evidence to Kenschaft that they didn't really know what multiplication is or what it is for. She also found that although the teachers knew and taught the algorithm for multiplying one two-digit number by another, none of them could explain why that algorithm works.
We know where leadership by an anti-intellectual "strongman" who scapegoats minorities and likes boisterous rallies goes
My kids are not there yet (my oldest is in 1st grade), but I've helped many friends and kids of friends, and I've always been able to read their textbook and understand what they wanted.
BTW, the fact that numbers have those properties is incredibly useful; the commutative property tells me that 3+15 = 15+3 (the later being much easier to calculate by counting with my fingers) and that 3*9 = 9*3 (the later being much easier to calculate by repeated addition). Making it explicit gives it a name, but also helps with the kids who haven't got it yet (my kids don't know the name, but they know the commutative property and can apply it)
Here's my own personal experience.
Beginning when my daughter was 3, I would play "classroom" with her. I taught her letters, later at 4 I taught her how to count and add little drawings of things to make totals. By the time she was 4.5 she could add and subtract simple numbers with symbols.
But all this was done with MAX 10 sessions of one on one 10-30 games.
Then my daughter went to preschool, kindergarten, first grade, and only in second grade did she start learning new things. (Boy they teach sooooo slowly in school and so innefficiently!!)
I don't think the idea this man had is totally crazy. It probably makes sense. Arithmetic is poorly taught (I think we can agree on that).
The real purpose of Arithmetic (and math in general) is to describe (model) things precisely. So students should be taught how to do that. First with language, later with symbolic math tools. But they must never lose site of the real purpose.
Too many students wonder "what is this good for". Math is presented very abstractly. And the algorithms of addition, subtraction, division, square root are presented by example (so the students have to guess the algorithm).. instead they should be taught how to think.
The "recitation" in the article seems to promote thinking as opposed to mechanistic thinking. So the idea is not totally kookie!
(I'll try it on my 2 year old.. and let you guys know how it went)
'Formal math'? Please. Kids are taught arithmetic and rote memorization. Then, in high school, they learn how to follow some algorithms and do harder computations. None of this has anything to do with formal math or any sort of thinking, and it's no wonder they think it's boring.
In 7th and 8th grade I could not learn algebra. No matter how I tried it just didn't work. When I hit college I managed to squeak by on testing out of algebra and while I took calculus I learned my missing algebra really quick and did quite well in calculus.
shrug...
This is one of those questions where everyone offers up a thousand answers. The diversity of the comments in slashdot alone are a testament to just how unsure we are about how to teach our kids math.
I am a math major. I love math. I started learning at a young age, but I don't remember a single thing school taught me. All the math I know my dad taught me, and by the time I got old enough, I taught myself. I had no understanding of what I was doing until I read the books for myself and worked out the proofs on my own.
Also, I say the following because it is funny, not because I believe it true.
Professor Peter Gray, a developmental psychologist and researcher at Boston College...
A psychologist would suggest teaching less math. He probably doesn't even know calculus beyond statistics.
My page.
Research Finds No Advantage In Learning To Read From Age Five
People posting for less/more above need to provide evidence for their opinions.
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From grade 6 onwards, I got a GPA between 3.4 and 4.0 in BC schools, and have a couple of degrees from BC public colleges, in addition to my post-grad work at the UW here in Seattle WA.
Having seen the disastrous attempt to have less formal math in WA schools, and comparing it to my much more stringent schooling in BC - we used to make fun of Grade 13 grads from Ontario since they were less capable of Math than we British Columbian Grade 12 seniors - I must strongly disagree with this professor.
By the way, I seriously doubt Boston is in BC. Last time I checked it was nearer to where I was in Grades 1-5 in Pennsylvania, which is to say ... Massachusets (or MA).
-- Tigger warning: This post may contain tiggers! --
http://www.budster.net/videos/south-park-adhd.htm
In my experience, really smart people don't go into psychology. They just don't. I can look at the 40-yr old psychologists (including profs) I know now and remember how they were doing back in high school and college. Stars they most definitely were not - at any subject.
So I always find it a little unconvincing when a psychology prof waxes eloquent about how math should be taught. Since they never particularly understood the field themselves, why exactly should I buy their theories? Is it because they subsequently spent several years taking the very easiest courses the university had to offer? Or is it because they get fame and fortune by saying something controversial, even if it's utter BS. I'm a professional mathematician. My 6 year old daughter is now getting pretty comfortable with algebra. I'd lay a wager she'll be outperforming this dude's kids in 20 years time.
If the schools then were as bad as they are now, then if you were in one of the non-advanced tracks (assuming, again, such a thing existed) you got your basic addition, subtraction, multiplication, and division early on in elementary school. Maybe you got some of the dreaded "word problems". Then you went and did the EXACT SAME THING OVER AND OVER AGAIN all the way into high school. Of course removing most of that made no difference.
Where I went to school, the advanced track would then go on to pre-algebra (waste of time, just algebra without formal symbolism), algebra (2 years), trig/geometry (pre-calculus), and then Calculus. I don't think you could cut out all of that and not make a difference.
You don't simply go from Grade 6 to Grade 7 because you sat through a year at Grade 6... You have to earn it. You progress as you grasp and understand the concept, nut because you spent X amount of time on that topic. In order to get your High School diploma, you need to have learned a certain set of concepts. You can learn more than those, up to a point that there are teachers teaching the concepts in the school system, and once you reach the the end of the school year that you reach 15 or 16 and have already surpassed the requirements for a High School Diploma, you should be allowed to graduate and start college (if you have been accepted at that point). If you have not reached or surpassed the requirements for a High School Diploma upon reaching the end of the school year of your 18th birthday, you would either have to continue on your own as an adult for a GED, or can simply say I am done with this (in fact you can say you are done with this upon reaching 18).
The vast benefits of this system is that students are encuraged to learn. People who have good study habits, or are gifted are not held back by anyone else. People who simply can not grasp a concept can spend the time they need to really understand it and are not forced to continue onwards because there are other concepts that they need to learn for a mandated test which the school itself is having its performance graded against.
We were all warned a long time ago that MS products sucked, remember the Magic 8 Ball said, "Outlook not so good"
I have a BS in physics; I think that math is FUN.
I despised mathematics until 8th grade because it was endless repetition of arithmetic. It wasn't learning, it was "do these exercises and be quiet for a while." It certainly wasn't thinking of any kind.
Did I really need a whole year to learn addition and subtraction? Another whole year to learn multiplication? Another to learn long division, and one more to learn fractions? No, not to learn how to do them, certainly not. No one needs that much time, unless they're totally incapable of learning the concept in the first place.
And if I really needed all that time to learn arithmetic, then why could they teach me each new concept in algebra, geometry, calculus in just one or two lectures?
Elementary school math was mind-numbing, and I can see why so many people are so entirely turned off on math that--by the time it really IS math--they have a mental block so solid it can't be overcome. (Especially when their first exposures to real math are through teachers that teach by further memorization, instead of teaching the concepts--but that's a different rant.)
I wholeheartedly support forgetting about math until, say, 5th or 6th grade...and teaching all of arithmetic in one year, if that. And then MOVING ON to real math. The way it's currently done is pretty much designed to make kids hate it.
"...with just one year of math under their belts, the poor students did as well or better than students from better schools by the end of the sixth grade year..." This is just plain old statistical data being misused and misinterpreted. At least, even if it's right, it's being used in a wrong way... Poor students might have spent more time learning hard in order to get better lives, while students from better schools (again, statistically speaking) were leading better and richer lives, paying less attention to boring stuff like math and more stuff to some more interesting subjects...
Did you perform a significant figures calculation to prove that your application would benefit from quad-precision?
No, they left out the latest "new math: (http://www.youtube.com/watch?v=SXx2VVSWDMo) That makes it no surprise that someone who hasn't been taught the "new math" for the first few grades can become as befuddled and confused as other students within only a year..
I am not an educator, much less a math teacher, but I noticed a wide spread lack of perspective about the nature of math.
My argument is that math and "language" are one and the same: both are aimed at conveying certain thoughts and ideas, have "alphabet" and operations etc. One of them specializes and refines certain aspects of "language" to better serve some functions within its own domain better than the other.
Most kids seem to have no particular problem with "language" because the "language" taught is not abstract, it relates quite well to their everyday experience. Math teaching on the other hand, is rather abstract right from the start. I will not be surprised if a good number of teachers themselves can't explain why -1 x -1 is +1, so how can we expect them to teach abstractions to children?
Most people I know who are good at math also happen to be good at language. I am not saying anything about their vocabulary or sentence construction skills. I am focusing on the skill with which they present an argument and prove it or disprove it, as the case may be, in either math or non-math subject. This observation of mine only enforced my thinking that, at the core, both math and "language" are one and the same, and they can be taught that way, and more importantly, they should be only be taught that way.
If math were to be taught like it were a "language" with connections to real world experiences kids tend to have, I think a lot of math phobia will simply disappear.
I think there is no need for a "no math" technique but a great need for teaching "how to teach math".
The guy in TFA is a developmental psychologist. He's saying a little, but not much, more than Jean Piaget, the patron saint of "child" psychology. Piaget http://en.wikipedia.org/wiki/Jean_Piaget posited there are 4 stages to cognitive development. The 4th stage ('formal') starts at age 11 to 13 (or adolescence depending on who you read) and is when the mind acquires the ability to abstract, hypothesize and deduce. Both these guys are right, before this kids can play around with numbers and can be taught to jump through hoops that appear as if they're understanding abstract maths, but they can't really. There are concrete maths they can learn, essentially a single equation at a time using +, -, * and /. A kid can help mom making cakes by getting out two eggs until she says 'I think I'll make two cakes' and the kid gets two eggs and two eggs. The 'three R's' remain intact, as long as the third is 'rithmatic and not that poorly conceived and terribly executed attempt to teach arithmetic by using algebra as the vehicle, known as "new math". You can make kids do stuff (hell, you can make chickens play basketball, right Dr. Skinner?), but you can't make them understand stuff until they're able, so you might as well make better use of the time than to try.
Had he not been so taken with observing so many different things and not theorizing too in depth about most of them, a contemporary of Piaget's who also used his own children as his "lab", came to some of the same conclusions and would probably have done far more. Unfortunately, when it came time for him to make his mark, those around him saw to it that he penned his treatise on evolution rather than developmental psychology. Though not particularly directly related, at least Darwin got to make him mark on psychology by being credited for the essential ideas which got built up into evolutionary psychology. Darwin did in fact note that his children could use but could not understand certain abstract concepts before a certain age, years before Piaget observed and wrote on the same thing. They said these about 120 and 80 years respectively before the guy in TFA said pretty much the same with the additional "so stop it". Brave man. I wonder if the parents of any school children know where he lives? They're the ones that won't be convinced.
"I may be synthetic, but I'm not stupid." -- Bishop 341-B
Math should always start with a problem (not an equation). A real, live, honest-to-goodness problem. Then you should talk about the nature of the problem. Why is it important to solve the problem? If we can solve the problem what can we do with that? Then talk about what you know about the problem. Define things get to know the problem. Think about ways you might be able to solve it. Next, move on to showing how the problem was finally solved with known Mathematics. Explain the solution. The thinking that went into it. Compare it to your group's proposed solutions. Were any like it? Did you come up with other solutions? Are they really the same, but, in disguise? Now it's fun!
Over-the-top Response Guy! Giving "Over-the-Top Responses" since 1970.
I loved doing math by the time I was in 5th grade, so that lead me to doing it on my own time. My mom bought me some higher level math books, in fact that was the only "home"work that I have every enjoyed, and it wasn't even from the school.
I guess my point is that (anecdotally) you can still do math at an earlier age if you choose to, but I do know a lot of people that could not get it till a bit later. I'm talking about algebra+ here, I think pre-8 should know the basics of counting, addition and subtraction.
There are some very basic concepts that people should know prior to making such "public" comments. First off is that a poor teacher in the early part of the education process will often turn students AWAY from certain subjects. Yes, this means that all those liberal arts focused elementary school teachers are HURTING the students by not having any interest or skill in math and science. It is far better to let someone dedicated to a subject and with a love of the subject teach that subject starting at an early age. So, dedicated math teachers for ALL grades, not just "middle school" and higher. The same goes for science, and all other subjects, we need to put an end to the old idea of a one room schoolhouse where one person is teaching ALL subjects to a class.
So, if you eliminate all the BAD teaching of math in the early years, you will find that students will respond to math better, no matter if they start sooner, or later. Logic may not really develop until around the age of 12, but learning approaches to problem solving early can help quite a bit. If you also start teaching ways to come up with solutions to problems from an early age, then children MAY start looking for new solutions at younger ages as well. Having students memorize things and recite them on demand may have its place, but nothing beats having students come up with their own solutions to problems.
It has to to with "developmental appropriateness", a well-established educational concept that is ignored by the list-of-things-you-must-know-in-grade-X school of thought.
In essence, when the kid is developmentally ready to learn math (their brains grow to become wired for it), they'll learn it quickly, but until then, you're wasting everybody's time forcing them to learn math.
The Sudbury school model follows this and they have plenty of students proceed to college and beyond.
http://en.wikipedia.org/wiki/Sudbury_school
"I believe in Karma. That means I can do bad things to people all day long and I assume they deserve it." : Dogbert
Cigarettes clean your lungs making you healthier and Diabetes known to be caused by the devil.
Lots of good research to be reused from the 20's....if only to backup your opinion.
Tell that to the Japanese.
If America wants to continue "babying" its masses in education just so it can push the socialism agenda and further the control, by all means continue. But don't mask it online with people who know better.
The elementary school math curriculum, at least in the US, is worse than useless. In the first place, it teaches precious little actual math. It does cover the concepts of defined order, addition, place value, and multiplication. Occasionally they throw in a short unit that covers some other stuff (like, say, the names of simple geometric shapes), but that's over in a couple of weeks and then you're back to the grindstone studying multi-column multiplication again.
The worse problem, though, is what the curriculum teaches inadvertently. Specifically, it teaches kids to *hate* anything that's called "math", for the rest of their lives.
Here, kids, here's a three-page worksheet that makes you repeat the same four or five steps over and over and over again. You'll be bored by the third problem on the first page, but please make sure you finish the whole thing. Tomorrow we'll give you another one just like it. We'll be practicing this *particular* set of four or five steps over and over again like this for four or five months, and then we'll move on to another very similar set of four or five steps. Next year you'll go through both of them again for several months each. Isn't that exciting?
Give me a stack of six gradeschool math books, one for each grade starting with kindergarten, and let me tear out the pages that serve no useful purpose. I'll give you back about nine months' worth of mediocre curriculum, maybe twelve months tops. The rest is pointless.
Cut that out, or I will ship you to Norilsk in a box.
I'm a highschool math/physics teacher and I deal with students on a daily basis who have no idea how to deal with fractions, percentages, how to represent a situation algebraically or how to solve an algebraic equation. The prerequisite to my physics course is to have passed Algebra I and Geometry with an average of 80%. After reading, I'm under the impression that the study does not suggest removal of math from school altogether, but merely removing it from the earlier curriculum (1st - 5th grade). I'm not entirely sure what the equivalency is here in the US, but this much I do know: more complex math concepts keep getting pushed down into the lower grade levels. The average 5th-grader does not have the capacity to do algebra. That needs to go... as well as all of this "lattice multiplication" business.
However, I say that instead of removing math completely from the curriculum, you need to reduce the amount they do in younger years. The problem is not that the brains are not wired for it, but rather suffer from burnout. I can attribute to this point from first hand experience - I was always really good in math when we handled it for 20-30 minutes a day. However, my sophomore year of high school, we went to block scheduling, and suddenly we were in a single class for 90 minutes a day. I went from an A student to a C student my sophomore year, to failing math my junior year. Retaking the class back on a normal schedule, I aced it, but my senior year I had calculus and calculus-based physics back to back, for three hours a day of math. Talk about burn out! C in Physics and a curtesy D in Calculus! Funny thing is, I knew the material, and could explain it to the teachers. It was litterally burnout from too much math. Actually, after that year, I actually started performing worse on basic math and algebra than I performed before that year. I can tell you, it is litterally a mental block. I am not sure if areas of the brain can shut down from overuse or something, but there is deffinately a connection between having too much math and my current inability to do anything other than basic stuff. In fact, what is really weird is I can remember formulas and what they are for, and can explain to you how to find the slope of a line and all that, and I can even walk someone through it, but I find that if I try to do it myself, suddenly the numbers no longer make sense. This was a subject I aced.
The point I am trying to make? Don't take math out of the younger levels, reduce the amount of it (or actually any subject). Give the brain a chance to rest. We always hear that the brain is like a muscle, and you have to work it out. Well, just like a muscle, overuse could probably damage it. This is where the educational system is flawed. We do what we can to stuff every bit of knowledge into someone's brain, then wonder why people have trouble retaining information. In fact, it seems that if a child complains they are overloaded, we tell them they are lazy or have no motivation.
Anyways, I am not saying this professor's ideas are right or wrong, but I think his studies are on the right track. What just amazes me is that people spend years, or even decades, studying stuff that the average person (in this case, the average student) could probably tell you straight up - in this case, I'm overloaded.
I regularly talk with and work with people who never use math more complex that what they learned in the 3rd grade. In fact, with the exception of people who use math in their careers, I doubt most people could pass a 4th grade math exam without the use of a calculator. This almost definitely applies directly to shrinks like the guy who wrote the article.
When first introduced to the concept of a recursive algorithm in the 4th grade when being taught a method of calculating Pi, later in the day, by using the properties of a right triangle I learned from geometry, I derived (accurately) the laws of trigonometry and by applying what I had learned from drawing a circle using LOGO, even taught myself spherical geometry. My son already appears to be advancing through math (he's in 2nd grade) at about twice the rate I ever did.
If we cut back on teaching basic math theory to children, it may not make any impact later in life to the average person, but it will almost definitely impact the brightest of us by robbing us of a 5 year head start. This would have dramatic negative effects on society overall.
Using the arguments posed by this person, maybe it would be better to simply keep kids in day care an extra 1-4 years to allow them to mature a bit more before being exposed to academia. Equally, they should delay the children's entry to the real world by an equal number of years. I can make numerous arguments in favor of this, not of the least being that since people are working later in life, it would decrease the competition over many of the jobs out there where people are retiring later and later from without leaving openings for new younger replacements. This would have a tremendous positive impact by decreasing age discrimination from the work place. Also, it would give children a better chance to get through their rebellious stages (early adulthood) before making long term decisions with regards to the future direction of their lives.
Maybe it would be best to come up with a stronger vocational studies program in the schools for kids who are less likely to use their brains in an intellectual fashion past a certain grade level. If you're going to be a businessman, a shrink, etc... you shouldn't be forced to spend 5 more years than necessary in high school which will serve as little more than a day care service.
Lets face it- how can a country be any good at math, when it has been shown time and again, that fully 50% of their population have IQs of under 100 !
THIS is an established fact!
You want "citations, please?" Well, I got lots of 'em!
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- aqk
F U
Professor Gray thinks children are not mentally wired for the kind of formal math instruction that is taught in schools, and that we'd be better served by putting off the teaching of theory until the seventh grade.
Or maybe children are told that math is hard and they're bad at it, and we'd be better served by putting off that message until the seventh grade (by which point they're truly rebellious and it will only spur them to try harder).
"I don't care about the Constitution!" --Bill O'Reilly, November 17, 2009
It downright sucks, they take all the fun out of a spectacular field.
Have you ever watched NASA TV? Only the United States Government could take the most exciting topic ever -- space exploration -- and turn it into television programming so dry and boring, it makes you want to gouge your eyes out.
That that is is that that that that is not is not.