BC Prof Suggests Young Children Need Less Formal Math, Not More 427
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."
As someone who was better than average... (Score:3, Interesting)
For once, think of the bright children!
Or could it be the way they're taught (Score:5, Interesting)
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?
less FORMAL math, maybe (Score:3, Interesting)
Re:Set Theory (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.
John Holt said much the same decades ago... (Score:4, Interesting)
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: ... 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 [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.
Re:Or could it be the way they're taught (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 elementary school. Within each of these groups, there were 3-4 subtiers each with 5-8 students, except for the highest of the high, where they pretty much just sit you down with an algebra book and tell you to go to town.
As long as teachers make this sort of differentiation among students, they are all getting (in the teacher's judgement at least) the exact subject matter / practice time that they need.
I don't think your suggestion that only some students see a fraction by grade 6 is necessarily valid. There were 8 students in my middle school class of about 300 that had a teacher shipped in from the high school to teach Algebra 1 in 6th grade, whereas there were other students that had a specialized two-year Freshman-Sophomore Algrebra 1 curriculum.
I don't know when / where you were in school, but at least in Missouri (a region not exactly known for pushing education bounds), differentiation is pretty common, in math / reading. Science / history are another subject (pardon the pun).
A teacher's perspective (Score:3, Interesting)
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.
Re:As someone who was better than average... (Score:5, Interesting)
A Mathematicians Lament [maa.org]. I really wish more teachers would read this essay.
Re:Well (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 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.
Re:Set Theory (Score:3, Interesting)
Re:Set Theory (Score:1, Interesting)
Hello, I was not a victim of New Math. (I've only heard of it by reading old Peanuts comics.)
Symbolic logic is not a mystery to me, either. Arithmetic is also like pulling teeth for me.
So it may not have made any difference at all.
I am a product of BC schools (Score:2, Interesting)
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).
Piaget's 4th Stage of Cognitive Development (Score:4, Interesting)
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.