"When he moved from Germany to Switzerland at the age of sixteen, Einstein spent a year at a school that emphasized independent thought, free action and personal responsibility. He thrived in a learning environment without rote drills, memorization and force-fed facts.
Based on the philosophy of a Swiss educator named Pestalozzi, the school helped students move through a series of steps from hands-on observations to intuition, conceptualization, imagination and visual imagery.
“Visual understanding is the essential and only true means of teaching how to judge things correctly,” wrote Pestaslozzi, and “the learning of numbers and language must be definitely subordinated"
...It was at this school that Einstein, age sixteen, started picturing what it would be like to ride along a beam of light.”
Another is that people's mental imagery is probably very different, how can you teach it directly? If the school is good at getting people to discover that mental imagery on their own it will probably work out, but it's hard to teach it to someone who doesn't share it. (I'd love to see some other psychology studies on this, I think I first ran across the view from a Feynman video: http://www.youtube.com/watch?v=Cj4y0EUlU-Y&feature=BFa... )
Anyway, here is a study summary that may be of interest.
"Building Blocks is a NSF-funded PreK to grade 2 software-based mathematics curriculum
development project, designed to comprehensively address the most recent mathematics standards. Building
Blocks materials were created upon explicit design principles and a nine-phase formative model—they are
truly research-based (details are provided in Clements, 2002a; Clements, 2002b; Sarama & Clements, in
press)... The materials are designed to help children extend and mathematize their everyday activities, from building blocks to art to songs and stories to puzzles...
...The results are illustrated in two graphs. We computed effect sizes using the accepted benchmarks of
.25 as indicating practical significance (i.e., educationally meaningful), .5 as indicating moderate strength,
and .8 as indicating a large effect (Cohen, 1977). The effect sizes comparing BB children’s posttest to the
control children’s posttest were .85 and 1.44 for number and geometry, respectively, and the effect sizes
comparing BB children’s posttest to their pretest (measuring achievement gains) were 1.71 and 2.12.
Therefore, all effects were positive and large. Achievement gains were comparable to the coveted “2-sigma”
effect of excellent individual tutoring"
We've all played with building blocks, but few of us are Frank Lloyd Wright. Of course, the difference here is that he played with them for several years whereas I'm told I played with them but can form no crisp memories of such an event. (I don't have many crisp memories from that age and I'm cautious of vague memories without additional witnesses just being made-up.) I don't imagine I would have enjoyed being forced to play with them up through 6th grade, nor have been more Frankish, so I'm finding it hard to believe him that it was the blocks themselves that made Frank different. (Though after a little reflection, I do remember extensions to building blocks through maybe 6th grade, such as the rubber band pegs, various polygon plastic 'biscuits', plastic-log-cabin-building cylinders, and connectible cubes. As well as 2D jigsaw puzzles at home and we had a couple neat 3D puzzles in 6th grade. I never liked Lego but I like Minecraft.)
Thanks for the study, though. You should emphasize the last sentence like the PDF does, the "2-sigma" effect is one of the reasons why I and many others think one-to-one tutoring is the best we can do and ways to cheat that are definitely worth pursuing. ( http://en.wikipedia.org/wiki/Bloom%27s_2_Sigma_Problem ) Other writings on their site are also interesting (and screenshots show their age) http://gse.buffalo.edu/org/buildingblocks/projectWritings.ht...
Actually, apparently these things are the 2D "building blocks" referenced in the study whereas Frank seems to be talking about the 3D "building blocks" that are actually big and blocky.
I'd appreciate it if someone who knows the right keywords to search for could find the original reference, and correct me if necessary.
You need to spend more time with young children.
The Tony Starks of the world are not meant to be low level grunts, keep in mind that the school system is designed to produce interchangeable parts to work in large manufacturing and bureaucratic organizations such as fortune 100s, the government and the military. The levels of leaders who self select out is acceptable and therefore the system will not be changed.
The school system is not for the betterment of the people who go through it; it is for the benefit of the owners. It's not a bug that our school system produces learned helplessness it's a feature.
Remind me not to drive on that person's bridge. Sorry but if you can't hack the math to make sure your invention isn't going to explode and kill people then perhaps you should put down the power tools. Almost every modern invention is heavily math driven, because you have to know it will work not just be able to visualize and assemble it. Love that red herring about the nobel laureates, after all it has been shown that after a certain point drive is much more important than intelligence when determining outcomes.
Anyway, no one is advocating the building of bridges by school kids who can build things without math. The article advocates giving school kids who have great spacial skills, but not apparently great math or written skills, a chance to participate in technical greatness.
Yes, a lot of design doesn't require calculations to be done on the spot, but almost every design made by an engineer will be informed from the beginning by their knowledge of math.
It's hard to think of a modern invention that's as big as the internal combustion engine or the aeroplane, but any recently designed item you buy today has had math applied to almost every facet of it. The design process for a product case uses extensive geometry, the design of gearboxes uses extensive mathematical modelling - pretty much every mechanism that's manufactured will be first described mathematically.
Even things that don't have complicated mathematical models describing them will have had some form of math applied to inform the initial design process. You can't design a lever without taking into account it's length, the moment it applies etc - that's all maths!
Technical greatness in our world requires math. You can't design and build a truly unique and functional device without applying some form of math to it.
Certainly spacial awareness is absolutely fantastic. It lets a designer envisage a concept in their mind, think through how something will work and identify the pitfalls of a concept before anything is put to paper, but it's not a replacement for mathematical ability when it comes to actually designing a functional mechanism or mechanical system.
Of course mathematics is important. But the initial design is done, I would say ALWAYS done, by intuition. The math is then applied.
Do you know how many gifted math students in my Engineering college could not begin to imagine the layout of a circuit, or a piece of software, or even a bridge, without looking it up in a book? I was a grader for 2 years, and it was shocking how lacking most folks are in this way.
From a larger viewpoint, what does this author think we do for football players? Do we not "value" them? In large part, what the players do is the "spatial intelligence" of the article. Do we not "value" airplane pilots? Same thing there.
I'd say if you look at peak salaries, some of the most valued professions are spatial.
Value is subjective and some fields value traits that vary from what is valued in other fields.
To be a successful mathematician, you don't need to be particularly capable when it comes to spacial intelligence. The article highlights concerns but reality is different; the statistical analysis I conduct in a day requires very little spacial intelligence. The most productive athletes in my city do require a superior level of spacial intelligence and they are compensated incredibly well for their contributions (paid more in a year than I am likely to be paid in may entire career).
I'm saying this as one of those kids that wished school taught me more. I was bored constantly. And I still wish that schools would teach kids at the level they need to be engaged and want to learn.
But tests for spacial intelligence, just to have tested it? Why would we pay tax dollars for that? If the kid is gifted, they'll know it and automatically move into a field that uses it. (Or not, as they wish.) There's nothing to teach.
It would probably result in identifying pupils with potential that previously would have been ignored in favour of pupils who were only superficially superior. It would also encourage pupils who possess more ability in that area to put more effort into their academic careers in general. And would help pupils with other academic strengths to identify fields which will be more difficult for them (there was a former maths teacher on my IT postgraduate conversion course who was really surprised that she struggled with programming, since she thought her maths ability would have made it a shoe-in).
And, to say spatial intelligence cannot be taught seems to be jumping the gun a bit. Have we really even tried to teach it?
But let's talk about teaching spatial intelligence. How would you do that? What techniques are employed while using it? Has anyone ever written a book on it? (A quick search says 'yes', but they appear to be ridiculous self-help books.)
Honestly, I'd love to read more about it, but there doesn't see to be much. I happen to be really, really good at things like re-arranging furniture because I can always tell when something is going to fit or not. I've called it down to less than half an inch before when reshuffling an entire room. What techniques did I use? Intuition. I can't teach someone that. And I can't see them teaching me, either.
I'm not arguing that there isn't something wrong with current education, but I feel the point here may be misrepresented.
I'm... competent (at best) at math. I'm below-average as a writer. However, mechanically I do very well. I can visualize and understand how things fit together very easily. I have a sort of inherent sense of order.
That comes in really handy when working on complex systems. In computer science efficiency is often found in organizing systems, not necessarily in pure calculation (map-reduce would fall under that for instance, even if there is a strong mathematical basis).
Spatial reasoning is actually one of the biggest things I look for in hiring.
How did you decide that? I'm really curious here, since only based on your comment, you seem above-average to me.
I know an example among my close relatives. The person in question is probably in poor shape as to verbal and mathematical achievement/intelligence much more from having lousy instruction in elementary school than from having a bad family background (considering what other people in the same birth family with different teachers in school were able to do, and what neighbors who had the same teachers were NOT able to do), but the effect in adult life is the same--lacking reading and math skills holds many people back, even if they have very strong spatial abilities.
More broadly, for any set of subsets of mental abilities, some people will be lucky and have above-average levels in all of them, and some other people will have wide "scatter" in their abilities. This is rediscovered every time a new brand of IQ test is normed.
I agree that to excel in sciences you will need more than spatial reasoning alone.
Also, spatial intelligence has many dimensions. For instance, I cannot visualalize something complex like a human face but have little problem rotating simple shapes or moving chess pieces in my head, which makes me think my spatial reasoning is stronger than my spatial memory or pure visualization ability.
If you feel the point is misrepresented, I suppose you should be more specific.
As if 'IQ' wasn't useless enough, they had to come up with with 'EQ' and now everyone and their brother tacks 'intelligence' after a phrase they think should be desirable.
Not to mention the fact that every test I've ever taken did include a section testing this 'spatial ability' (the paper contains examples, so I can infer what it means).
Mind you, I think Jobs deserves most of that credit. Great verbal ability captivates damn near everyone, and pulls the world forwards, whereas great visual/spatial requires someone equally skilled to truly appreciate.
Anyways. I think things are going to get better, sharing credit and humanitarian ethics, along with transparency rising will help a lot. But to answer the question, "Why Don’t We Value Spatial Intelligence?" I think Occam's answer would be, "Because Spatially Intelligent People Don't Always Verbally Promote Themselves Well."
But it would bee good to test spatial ability when applying to university level mechanics..