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## BC Prof Suggests Young Children Need Less Formal Math, Not More427

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."
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## BC Prof Suggests Young Children Need Less Formal Math, Not More

• #### I didn't need math... (Score:5, Funny)

on Thursday March 25, 2010 @03:41PM (#31616138)

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.

• #### Congress (Score:4, Insightful)

by Anonymous Coward on Thursday March 25, 2010 @03:45PM (#31616218)

You wouldn't happen to be the guy who does the numbers for Congress?

• #### Re: (Score:2)

What? Congress needs someone to do numbers? I thought that was what legislation was for!
• #### Re: (Score:2)

No, he works at McDonald's. Old joke: You can classify people by the questions they ask. Science majors ask, "What are the rules that govern the universe?" Engineering majors ask, "How can I use those rules to build useful products?" Business majors ask, "How much will it cost/how many can I sell?" Everyone else asks, "Do you want fries with that?"

• #### As someone who was better than average... (Score:3, Interesting)

on Thursday March 25, 2010 @03:41PM (#31616140) Homepage
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!
• #### Re:As someone who was better than average... (Score:5, Insightful)

on Thursday March 25, 2010 @03:49PM (#31616302)

I think you hit it spot on, it's not the curriculum, it's how they make it as boring as possible. I didn't enjoy math until I was actually out of public school and did that in my private life. When I picked up a Dover math book and learned the mysteries of such things as mathematical abstraction, that was exciting. At least more than learning maths verboten with no end goal in sight.

Another thing is the lack of math history being taught. Yes 1+0=1. But why? Where did zero come from? Where did numerals come from? Why was Algebra invented and where did it come from? What use is it? What about geometry? Who was Euclid? I could go on and on with fascinating topics related to math. These things are rarely answered. It's all about teaching you to understand one function, one algorithm, one technique, etc. Never to understand _why_. It downright sucks, they take all the fun out of a spectacular field. Thanks to their "teaching" me, I thought math had no room for expansion. Boy was I wrong. It's an abstract fun house where you can do whatever you dream up. To a kid, that itself should be reason enough to love any math.

• #### Re:As someone who was better than average... (Score:4, Funny)

on Thursday March 25, 2010 @03:56PM (#31616418)

Verbatim also. Verboten? Well it should be.

• #### Re: (Score:2)

Very true, history seems to be painted into a corner and isolated from the other courses most of the time, even though it should be integrated in order to be really compelling. Learning dates and facts you don't care about will never attract students, but learning where what you're using every single day comes from is insightful.

I also think we're sticking too much to the standard "teach them the basics, the necessary" formula. It is necessary, but it shouldn't be the ONLY thing. Math is full of quirks an
• #### Re:As someone who was better than average... (Score:5, Interesting)

on Thursday March 25, 2010 @04:23PM (#31616908)

A Mathematicians Lament [maa.org]. I really wish more teachers would read this essay.

• #### Re: (Score:2)

I think you hit it spot on, it's not the curriculum, it's how they make it as boring as possible. I didn't enjoy math until I was actually out of public school and did that in my private life.

So you didn't get it until you were an adult, or at least not a kid anymore. That would seem to be consistent with what TFS is saying.

• #### Re:As someone who was better than average... (Score:4, Funny)

on Thursday March 25, 2010 @04:23PM (#31616890)
This is exactly why I'm going back to school to be a high school math teacher, that and the prestige
• #### Re: (Score:2)

+1 Thank you!

Finally, a science thread where I don't have to post ('coz you said it all). Good thing too - I'm late for work as it is ;-)
• #### Re: (Score:2)

This is the book I pull out every time I need to teach or tutor something in math below about linear algebra, calculus, or about half of college algebra:
Mathematics From the Birth of Numbers [amazon.com]
It has a few mistakes due to lack of imagination, for example the proposed number system for the caveman is more capable than the author imagines. Anyway it's a fabulous teaching tool and a fairly fun read besides.
• #### Re: (Score:2)

The approach to mathematics differs for different people though - I never really got a deeper interest in mathematics before I read Hermann Schulz' "Physik mit Bleistift" (Physics with a pencil), which unfortunately is not available in english translation. The book if written by a physicist, introducing you to different fields of mathematics from his point of view. Initially, he always focuses on the natural phenomena and then introduces the mathematics behind them. Sometimes in a gung-ho fashion "What's th
• #### Re: (Score:2)

It's all about teaching you to understand one function, one algorithm, one technique, etc. Never to understand _why_. It downright sucks, they take all the fun out of a spectacular field.

Anyone who understands math well enough to teach like that knows math well enough to realize that teachers are paid way less than it's worth and switch to engineering.

• #### Re: (Score:2)

I've found this in computing also, though it doesn't tend to come up until later (since we don't make serious attempts to teach programming to elementary school kids). Stuff presented as a bunch of facts and givens with no motivation is hard for anyone to care about or learn. It's essential to include some context: why was this invented at all? Usually there are pretty good reasons, even really interesting ones, and it can make a lot more sense to learn something once you have some idea of what problem it w

• #### Re: (Score:3, Insightful)

I sucked at math (failed freshman Alg., got kicked out of comm. coll. for failing everything else as well) but once I was in the military and got interested in hot rodding cars, applied mathematics turned out to be easy. First it was calculating volumes, both static, and swept, then on to weight/power/acceleration. If they want to make math interesting, take the kids down to auto-shop (oops, they got rid of that as it isn't part of college prep).

• #### Re: (Score:2)

I can see holding off on math, but NOT basic arithmetic. However, when you teach a kid how to add and subtract, do it with examples. Show him two beads have him count, show him two more, have him count, then pile them together and have him count them again. That way he has a basic understanding of what numbers are for and how they work.

I think they do this now, they didn't when I was in school. Then, it was all rote memorization.

• #### Re:As someone who was better than average... (Score:5, Insightful)

on Thursday March 25, 2010 @03:58PM (#31616458)

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!

If we don't force kids through things for which they aren't ready, the bright kids - like your friend's child - will stop suffering the endless days of boredom as other kids struggle pointlessly with it. Doing something like this counts as thinking of all children if it works. Get the bright kids some additional tutors, better classes, or some genuinely interesting side projects, don't simply insist that making the regular classroom any less rigorous, even temporarily, will punish the bright kids. Such insistence is exactly why we're here, failing, which is TFA's entire point: there's a hell of a lot more to improving childhood education, including the education of child geniuses, than simply doing more work at a higher level earlier.

Good for Peter Gray, daring to hypothesize the possibility of better results through some mechanism other than simply shoving more work down their throats at a young age.

• #### Re:As someone who was better than average... (Score:5, Funny)

on Thursday March 25, 2010 @03:59PM (#31616488)

We already are using the lowest common denominator enough,

Aaaand you just confused all of these kids.

• #### Re: (Score:3, Funny)

I can say that reducing math further than it already is would dumb down school beyond the point of non-return.

Here in the US, we have an entire state that believes you can teach US history without mentioning Thomas Jefferson, and biology without mentioning evolution.

I think the point of no-return was reached for them some time ago.

• #### Re: (Score:2)

I think the biggest problem with both primary and secondary school math programs is that they teach students how to do problems, and not to understand the concept of the problem.

For example, I'm currently a TA for a statistics class. It's easy to get a student to remember that if they want X in standard units given average $\mu$ and standard deviation $\sigma$, they use the formula $z = \frac{X - \mu}{\sigma}$, and if they want to find a number $X$ that is $z$ standard deviations from the mean, then they us

• #### Re: (Score:2)

I think that's a related problem of being completely unwilling to separate out different levels of achievement at early grades. It really seems sometimes that if you moved kids around properly you'd have half of the class doing calculus by 7th grade, when the rest could then start worrying about arithmetic, which is about all they'll ever need to know anyway.

Some people just don't seemed to be wired right for math, yet we insist on forcing it on them in the most boring way possible just on the outside chanc

• #### Re: (Score:2)

For once, think of the bright children!

"Of course we could make things more challenging, Lisa, but then the stupider children would be in here complaining, furrowing their brows in a vain attempt to understand the situation." - Principal Skinner

• #### Re: (Score:3)

For once, think of the bright children!

"Of course we could make things more challenging, Lisa, but then the stupider children would be in here complaining, furrowing their brows in a vain attempt to understand the situation." - Principal Skinner

Which is why if you actually want children to achieve the most they can, you separate them into classes based on ability (we already do this some in high schools with Honors and AP classes). That way the lower achieving students can have classes tailored to their leaning speed and no longer feel that it's pointless to try hard because they'll never do as well as the smart kids AND the smart kids can have classes where they learn more and are pushed to work harder instead of some of them just breezing throu

• #### Re: (Score:2)

I wonder if math shouldn't be shifted rather than postponed... Why teach geometry and other "basic" math that early? Personally, I found calculus made most of mathematics far easier. Basically, what I'm saying is would it be worth it to try to teach calculus and algebra earlier, and the more formal concepts later? Sure, if you don't know that 2 * 2 = 4, how can you solve x * x = 4, but do students really need to learn anything more than basic algebra and the Cartesian coordinate system to grasp the foun
• #### Completely disagree (Score:3, Insightful)

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

• #### Well (Score:2)

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.
• #### Re: (Score:2)

I should point out that at least one educational theory agrees with this guy. A relative of mine once worked for one of the Waldorf Schools. [whywaldorfworks.org] While their high school education is mostly mainstream, their elementary school education is very different. Virtually no formal math or science training until age 8 or so, and they introduce reading a bit late as well. From my understanding (admittedly limited), they have a quasi-religious belief that children's souls aren't attached at birth, and only begin attaching

• #### Re: (Score:3, Interesting)

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 pu

• #### Relevance? (Score:4, Insightful)

<z01riemer@@@hotmail...com> on Thursday March 25, 2010 @03:42PM (#31616164)
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.
• #### Re:Relevance? (Score:5, Insightful)

on Thursday March 25, 2010 @03:54PM (#31616392) Homepage

Even if they did re-create the study, and a bunch of schools started doing this, I can assure you that most of them would decide that "less math" was just as good as "no math" and far less scary, and that "6th-7th grade" could be cut back to "2nd grade" without affecting the results of the program.

From what I've seen, school administrators (principals up to and including district supers) are very good at latching on to (possibly useful) fads in pedagogy, but very bad at actually implementing entire programs; they'll go on about how important this is, and how the teachers must follow its principles, then direct them to do things contrary to it either because they don't actually understand it or because those parts are too scary. A couple years later they'll pick some other program to get excited about and it'll start all over.

Most of them also have a damn poor understanding of the scientific process, which might explain some of the above nonsense.

• #### Re: (Score:2)

If you decide to do something new, but do it half-assed, then half of your ass is still covered by the old way of doing things.

That way, should the new thing go up in smoke, your ass doesn't get too badly burned.

It's unfortunate for things that really require full commitment if they're going to work properly (c.f. a "green" economy)

• #### Re: (Score:2)

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.

Children haven't changed, teenagers haven't changed, adults haven't changed, and geezers haven't changed. People in general have changed, but they haven't, either -- it's only the meaningless trivia, and technology, that changes from generation to generation.

Some kids are ready for calculus at age 8, some aren't ready to learn to read until they're ten. And

• #### Re: (Score:3, Insightful)

The most important thing is getting teachers who can get kids interested in what they're teaching. Nothing is a better motivator than curiosity.

Application goes hand-in-hand with curiosity. My daughter (1st grade) is getting pretty good at fractions, but we do it almost all with cooking. I had to sit in a 5th-grade classroom and be told that this was important. She needs to get me the right number of scoops of flour.

She also gets the basics of algebra, though she lacks the arithmetic skill to manipulate

• #### Many other explanations (Score:4, Insightful)

on Thursday March 25, 2010 @03:43PM (#31616188) Homepage
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.
• #### Re:Many other explanations (Score:5, Insightful)

on Thursday March 25, 2010 @04:02PM (#31616538)

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.

I tend to agree. The overwhelming majority of elementary school teachers are neither math nor science majors. It is quite likely the teachers don't understand the reasons for the math theory. They just know it should be taught. As such, they are not likely to be using approaches that relate the theory in ways that people (kids) would understand it. It is humbling to have a PhD in Engineering, and not be able to understand Grade 6 math homework. If I can't understand the lessons they are trying to teach with regards to digits and digit placement, then what chance do the Grade 6 kids have?

On another occasion, while in first year Algebra, I vividly remember suddenly understanding key concepts from Grade 7 math. For instance, why does one care that numbers have the distributive, associative, and commutative properties? that can be named and explained? The knowledge is not helpful until vector and matrix math is covered. At that point, data types exist where the associative and commutative properties may or may not apply.

I'm just not sure what is the point of introducing concepts to children, without the ability to explain the reasons for the concepts. Why teach math, with no text book? Why focus so much on obscure terminology, to the point that no one understands why you are even asking a question? Math is about understanding why things happen. Not wrote answers to naming conventions.

• #### Set Theory (Score:4, Insightful)

on Thursday March 25, 2010 @03:45PM (#31616224)
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).
• #### Re: (Score:2)

I don't know about US, but I did learn the basics of set theory at first. I don't know what "formal math" means for developmental psychologists, but certainly not the same thing as for people actually doing math - "formal math" would most likely imply Jarnik's calculus bible, widely considered the ultimate showdown of one individual's math awesomeness in these parts of world, and other doorstoppers like that for the other disciplines. We *did* have math in the elementary school. And granted, it was no "form
• #### Re: (Score:3, Interesting)

Even more interesting is that the way we count is completely unnatural. Research with both small children and isolated Amazon tribes indicates that our natural inclination is to count logarithmically, but we train our kids away from this shortly after they learn to talk.

• #### Re: (Score:3, Interesting)

Maybe it's a sign of too many years of having maths taught to me, but I'm finding it hard to think how I'd go about counting things logarithmically.
• #### Re:Set Theory (Score:4, Insightful)

on Thursday March 25, 2010 @05:23PM (#31617874) Homepage Journal
A related study is Hunter-Gatherers Grasp Geometry [sciencemag.org]. The conclusion of the article was the geometry learned by children in isolated culture was equivalent to the geometry learned by children in western cultures. In particular the results on the test given were all but the same for children, and only diverged in the higher level test given to adults. My interpretation is that while we must teach the formalized language of geometry, i.e. what is the formal difference between a quadrilateral and square, the concepts themselves are learned through the experience of a varied and active childhood.

Which is why I don't think most of the formal stuff that goes on in elementary school, at least prior to about 10 years old, is all that useful. If kids were more actively engaged, and not in desks, perhaps we could teach them the formalizations in middle and high school. Unfortunately not all kids, especially lower SE kids, have the opportunity to actively challenged in their non schools lives.

• #### Re:Set Theory (Score:5, Informative)

on Thursday March 25, 2010 @04:00PM (#31616500)

Hello. I was a victim of New Math.

New Math presented me with set theory in elementary school.

Symbolic logic is not a mystery to me. Indeed, I aced a logic course where over half the people dropped it like a hot rock in the first week.

However, arithmetic with pencil and paper is like pulling teeth for me. I hate it with a passion. Learning how to do square roots in 7'th grade by pencil and paper was torture. Thank Glub for calculators.

So yes, your professor is entirely correct. Teaching set theory preps students for boolean algebra and all that happy nonsense. There are trade-offs, though.

--
BMO

• #### Or could it be the way they're taught (Score:5, Interesting)

on Thursday March 25, 2010 @03:48PM (#31616264)
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?
• #### Re: (Score:2, Interesting)

The majority of children need that repetition to even recall how to do basic addition, subtraction. Do you know how many children struggle with basic arithmetic all through elementary school. In my school district at least, there was a tiered system that seemed to work very well. You were in an essentially randomized teacher's classroom in elementary school (out of 3 classes per grade). Then you were split into high, medium, and low groups, and actually switched teachers for math section, even in elemen

• #### Re: (Score:2)

The majority of children need that repetition to even recall how to do basic addition, subtraction.

That is such BS its not even funny. I have a 3 year old, in a class full of 3s and 4s that can do addition and subtraction without any problem. Her cousin is in 1st grade and can add, subtract, multiply and divide multiple digit numbers no problem. Her father, as an experiment decided to see if he could teach some of the young neighbor kids (4-7) how to divide small numbers using the same method he taught his

• #### Re: (Score:2)

You saw a fraction by grade 6? Algebra in grade 8? No wonder the US school system is so fucked - with low expectations like that, there is no way to do anything but scrape the bottom of the barrel. One of my best memories in Math class was when we derived various proofs for the Pythagorean Theorem - in friggin 6th grade. And I was certainly not one of the Math-heads in my class.

So in that sense, I'd agree with you - kids in American schools have got to be bored to tears.

• #### Re: (Score:2)

I don't think they're saying that kids don't or can't learn math early, it's that kids don't or can't learn math early the way that we try to teach it to them. I think what they're getting at isn't so much "no math in schools" as it is that math should be a small but significant part of every other subject.

It's possible that they're right. We know that responsible decision making is nearly impossible for most prepubescents, which is basically logical thinking, which is the basis of mathematics. Trying ov

• #### Re: (Score:2)

Really? When I was in public elementary school ~20 years ago, we learned fractions in 3rd grade, and decimals and negative numbers in 4th. By 7th grade we had algebraic formulas. This was the highest-level math class but it wasn't super-advanced (basically the top 25% math students -- it wasn't some top 1% magnet school or anything).

Has math education really gotten dumbed down so much in the intervening years? Granted the early math had a ton of memorization of times tables and I hated that part, but th

• #### Re: (Score:2)

People learn through repetition and college is no different, at least with stuff in my 'core' engineering curriculum.

First few weeks of differential equations is algebra and calculus. Dynamics is just Statics with some extra terms. Controls is just differential equations and calculus. Algebra is used constantly in all of the above.

Education is meant to build on itself.

And I think that your numbers are a bit off. I know we started long division in 4th grade. 3th grade was simple multiplication and division.

• #### Re: (Score:2)

People memorize (aka commit to memory) through repetition. They learn through understanding.
• #### Re: (Score:2)

The way I remember it:
Kindergarten and grade 1: simple counting, basic shapes
grade 3-4: multiplication and long division with remainder
grade 5-6: decimals, fractions, and pre-pre-algebra
grade 7: pre-algebra (manipulating equations to solve for a variable)
grade 8: algebra (formal proofs)
grade 9-12: geometry, algebra II, statistics, trigonometry, and pre-calc (limits and basic derivatives)

• #### Multiplication? (Score:2)

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.
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/Diff

• #### Re: (Score:2)

My son is in 4th grade and they studied fractions earlier in the year. They also covered basic Algebra and are now into what I would call beginners Geometry. Acute, Obtuse, calculate one side knowing the other two, etc...

This is at a public school.

• #### Re: (Score:2)

I don't know anything about teaching young children, but I know that learning frequently requires repeated exposure. One of my graduate professors likes to chant this. Part of this may be because young children simply need the concepts explained repeatedly. Just a suggestion, I don't actually know what I'm talking about here.
• #### Re: (Score:3, Insightful)

It is true, adults learn exponentially faster than kids (which is why I don't think it really matters that other countries are more advanced in high school math; we can easily catch up in college).

I have a friend who did tutoring for the ASVAB for a while, which is a standardized test for the military. He was working with the 'dumb' kids, the ones that somehow managed to get out of high school without learning subtraction. In 8-12 weeks he was able to get them from that through algebra and geometry. Th
• #### Because Math sucks... (Score:2)

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.

• #### Re: (Score:2)

I hated math. Math leaves a sour taste in my mouth still.

My brain isn't comfortable working with "abstract" numbers. I loathe sitting down and "doing" math. It was many years later that I realized that I don't mind math and can actually be decent with it if I have a real problem to solve and I can apply my logic to it. Numbers with context in real life are fun.

I think I would have been one of the ones to benefit from less formalized instruction in my early years. Had I started learning formal math late
• #### good teacher (Score:3, Insightful)

on Thursday March 25, 2010 @03:49PM (#31616282)

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.

• #### Re: (Score:2)

Not to mention that several years with a mediocre teacher can actually destroy a person's ability to deal with math. I had a friend who only passed his final math exam because three people taught him stuff that in 3 months he was supposed to have learned years ago. But thank to a horrible Math teacher in his formative years, he hated math and was almost incapable of getting over it. Thankfully, he did - but it was amazing the impact that one bad teacher had on him.

• #### less FORMAL math, maybe (Score:3, Interesting)

on Thursday March 25, 2010 @03:49PM (#31616292) Homepage Journal
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.
• #### No no no NO! (Score:2)

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 tactic
• #### Re: (Score:2)

At the end of the summary it says something very profound, "we would be better off putting off the teaching of theory". I could not agree more. Elementary schools should not teach theory of anything. They should teach the basics: 1+1=2, 1+2=3...1x2=2,2x2=4, etc.. Maybe in 4th or 5th grade you could start teaching more complicated things like, "If 1+1=2, then 2=1+1" and "If 2+2=4 and 3+1=4, then 2+2=3+1".
• #### Instructor quality (Score:3, Insightful)

on Thursday March 25, 2010 @03:54PM (#31616382)

Not really a surprise, if the math instruction that you eliminate is poor to begin with. From the article:

The school that Kenschaft visited happened to be in a very poor district, with mostly African American kids, so at first she figured that the worst teachers must have been assigned to that school, and she theorized that this was why African Americans do even more poorly than white Americans on math tests. But then she went into some schools in wealthy districts, with mostly white kids, and found that the mathematics knowledge of teachers there was equally pathetic.

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.

• #### Re: (Score:2, Insightful)

Kids naturally learn languages best when they are young, and math is a language. Sadly, though, few elementary school teachers are native speakers.

(Disclosure: I'm a math educator [passionatelycurious.com] too.)

• #### Re: (Score:2)

I think the issue is one of supply and demand.

If you're good at math you have access to lots of fields that pay really well (engineering, science, and even applied stuff like accounting). Those who go into teaching are probably those who really love teaching. Since there are so few, the good ones tend to end up at the secondary level. Plus, at the primary levels teachers tend to be generalists anyway.

There is also seems to be a correlation between skills in math/science/etc and personality, which probabl

• #### Some basic arithmetic skills is still OK to teach (Score:2)

but probably can hold on with algebra till the 6th grade or so.

• #### John Holt said much the same decades ago... (Score:4, Interesting)

on Thursday March 25, 2010 @03:58PM (#31616466) Homepage

See John Holt's books here (he was a long time school teacher):
http://www.holtgws.com/ [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 [newciv.org]
http://www.johntaylorgatto.com/underground/toc1.htm [johntaylorgatto.com]
"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 [johntaylorgatto.com]
"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:
"Why Educational Technology Has Failed Schools"
http://patapata.sourceforge.net/WhyEducationalTechnologyHasFailedSchools.html [sourceforge.net]
"""
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. ... 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

• #### There is more than one BC in the world... (Score:2)

For some of us when we see BC, Boston College is not the first location that comes to mind.
• #### Experiment doesn't apply (Score:2)

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 st
• #### A teacher's perspective (Score:3, Interesting)

on Thursday March 25, 2010 @04:08PM (#31616636)

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.

• #### games and programming (Score:2)

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.

• #### It's magic. (Score:2)

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.

• #### Let's fix all of the academics! (Score:2, Flamebait)

We don't need to teach the truth about history either. Let's just teach the kids racially sensitive, altered history instead.
• #### Less boring nor less math (Score:2)

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.
• #### Summary is misleading (Score:2)

In addition to removing arithmetic from the curriculum, they added

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.

• #### Oh fuck. (Score:3, Informative)

on Thursday March 25, 2010 @04:17PM (#31616772)

I just replied to Math Skills For Programmers - Necessary Or Not? http://science.slashdot.org/article.pl?sid=10/03/25/0312233 [slashdot.org]

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.

• #### Failed experiment with grammer... (Score:2, Insightful)

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...
• #### What sort of Math? (Score:2)

There are a lot of different skills that count broadly as math.

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 stum

• #### Speaking for myself (Score:2)

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.
• #### Another Flakely Psychologist (Score:2)

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 ed

• #### Piaget's 4th Stage of Cognitive Development (Score:4, Interesting)

on Thursday March 25, 2010 @10:52PM (#31621320) Journal

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 [wikipedia.org] 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.

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