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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."
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!
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...
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.
When pre-7th grade math is NO math, then 7th grade math will BE pre-7th grade math.
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).
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."
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.
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.
[
For a second I though you meant the Parmesianians and curiously had a craving for italian food.
I love to slaughter the english language.
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.
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.
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.
I think the point of TFA is that once a kid's brain has developed to the 7th-grade level, you can cover all the pre-7th math in a year or less rather than taking 6 years to do it.
If libertarians are so opposed to effective government, why don't they all move to Somalia?
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
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...
As a Waldorf parent (my daughter is 7, and in first grade), I can offer a little insight. Not a lot, I'm not a trained Waldorf educator.
It's not as much that the souls are detached, as that the children go through three phases of childhood culminating in "adulthood" around the age of 21. The first seven years are what I have heard referred to as a "dream state". You teach them by playing games, and those games don't have an apparent goal (to the kids). They memorize songs and rhymes, but don't really pursue a "you must learn this or fail" ethos with it. Some handwork is introduced, finger-crocheting, sanding and rasping wood, lots and lots of painting and drawing, things like that.
Now that she's seven and in first grade, the memorization starts coming in to play. They also draw, but the drawing is more formalized. More structure is being added, the alphabet and simple words are being introduced, but none of the first-graders are really expected to read (though they are encouraged if they choose to pursue it at this age, and many of them are just now "discovering" that they can read). Math is introduced in the form of "characters", one who gathers things, one who gives things away, one who shares equally, etc. But there's not a lot of memorization, it's all about the underlying function behind math. They are also learning French and German in the form of songs and stories, without really being expected to absorb, memorize, and disgorge the information on paper later.
This will continue, with increased structure, for about 7 more years.
"This post contains words, known to the State of California to cause thought. Wash brain thoroughly after reading."
Pre-7th grade math is boring as hell anyway. Give me a calculator and let me start with the interesting math.
You seem to be under the impression that numbers are the most important part of math. It is this unhealthy obsession with numbers that makes math boring for kids. It would be like art class being all about blending pigments to get the right colors. Hell, even math 'fans' who obsess about the digits of pi are ... misguided. I think this says it best - http://www.smbc-comics.com/index.php?db=comics&id=1777
I've taught maths in a secondary school, albeit for a short time. One thing that sets maths apart is that it's a steady progression. If you didn't grasp stage 1, you can't grasp stage 2. That's different to history or English or even, to a lesser extent, the sciences. You might not remember the formula for momentum, but you'll remember the volume of a sphere or whatever. But I've seen it happen with maths that someone doesn't quite get something but the rest of the class rolls on and they're left there wondering how others can grasp things that they can't. It's tragic to see and it can happen in quarter of an hour. Someone becomes someone who "doesn't get math" for want of being taken forward without having grasped some vital preliminary.
I've tried to undo this with some victims. Just explaining the above and then starting with something they don't understand and going back as far as is necessary to get to a point where they can pick up again and start moving forward, this time getting it. But I seldom get the chance to do this.
Maybe part of the reason for this research, if it stands up, is because there's a wider disparity in ability when you get to very young children, so its more likely that classes roll forward and leave some behind. But we should be very careful of taking a piece of research like this and drawing any hard conclusions about what is good or bad to teach. Personally, I started learning maths at pre-school level and it did me a lot of good. I doubt I'd be as good at it if I didn't get that early start. I strongly reject any belief that we have to choose between helping some achieve their full potential and looking after everyone: Help the best reach their potential, no child left behind, spend more care and resource on education. Why is the third path always left out of discussion?
Aide-toi, le Ciel t'aidera - Jeanne D'Arc.
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?
Suggestions?
Radical idea, but how about letting them play physical games and other unstructured activities in order to learn the lessons of socializing, sharing, consequence, reward, and impulse-control?
If libertarians are so opposed to effective government, why don't they all move to Somalia?
Schools aren't just babysitters -- nor are they the ONLY source of education.
Unfortunately, this seems to be ignored these days, negligent parents "too busy" to teach their kids, who then suffer a horrible education.
I'm unsure, but I'd be willing to wager that there is value in the exercise, though. I think part of the education process isn't just about learning material, but learning how to LEARN and good study habits.
While I agree with you to a certain extent, I think it can also be extremely counter-productive to force children to learn things for which they're not ready mentally. What proportion of children have acquired at least a strong distaste for math by the end of 6th grade? What proportion of children have already decided by then that they "just aren't good at math"? The parents can feed into this or even initiate that mindset -- what proportion of children will have been consoled by their parents that they need not worry about it, because "not everyone is good at math"?
I never experienced any of this -- I have always enjoyed math. On the other hand, I also saw students less gifted than myself become so discouraged by math that they loathed anything having too much to do with math. And can you blame them? Being forced to do something for years when you find it extremely frustrating can have many negative consequences; I'd be willing to wager that one year of such frustration, if it yielded the same resulting skill level at math, wouldn't have nearly the same level of deterrence.
So, to bring this back around to your statements -- if it turns out this researcher is correct, then isn't there something *else* we could find for them to study which would allow them to learn how to learn and how to study? Maybe something that their brains are prepared for, and thus which won't have the same level of inherent frustration for 90% of the students? We can teach them the math when they're ready for it, and when it is much more efficient to teach it to them.
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! --
I think our school systems are still structured as if everybody will be working in a factory some day.
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