I hope this doesn't come out ignorant, but how often does someone possess a phenomenal level of spatial intelligence, yet very little verbal/mathematical intelligence?
I'm not arguing that there isn't something wrong with current education, but I feel the point here may be misrepresented.
Maybe not "very little" but I would claim to fit this mold. I think it's made me an excellent programmer.
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.
Judging from the comment, your writing seems fine to me. I know a lot of people who are "fine" at writing/math, and perform well spatially. Yet, I have never met a spatial genius who couldn't succeed in the deficient rigor of the public school system.
Your question might need to be constructed more carefully in order to cleanly disentangle spatial visualization from math ability. I have noticed that I seem to be best at math that I can somehow analogize to geometry or to tangible physics. Introspectively this feels rather like using what the article calls "spatial intuition" to solve math problems. I don't know how much to trust my introspection, but if it's correct, then given the way you constructed your question, the two kinds of abilities end up mixed. Perhaps you could somehow narrow "mathematical intelligence" to something specific to fields of math (such as number theory, graph theory, combinatorics, and abstract algebra, in my experience) where geometrical and physical analogies are seldom helpful.
how often does someone possess a phenomenal level of spatial intelligence, yet very little verbal/mathematical intelligence?
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.
From my point of view there are three basic mathematical skills, logical reasoning, spatial reasoning and visualization, and calculation ability which is related to memory.
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.
I'm not arguing that there isn't something wrong with current education, but I feel the point here may be misrepresented.