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“But really, people, think! This doesn’t mean that space flight is intrinsically dangerous. It means that badly shielded tin-can environments that aren’t spun for gravity are a bad idea. And that is quite a different conclusion.”
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“[T]he glances turn to stares and smiles when he parks his 1,600-pound vehicle and his 6-foot-2, 245-pound body emerges from behind the wheel.
“That’s when the real mystery comes about,” Clark said. “They say, ‘How does this big guy get out of such a small car?’ Other drivers are quite surprised. They can’t believe it.””
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“It does not matter the exact age that you learned to walk. What matters is that you learned to walk at a developmentally appropriate time. To do my job as a physicist I need to know matrix inversion. It didn’t hurt my career that I learned that technique in college rather than in eighth grade. What mattered was that I understood enough about math when I got to college that I could take calculus. Memorizing a long list of advanced techniques to appease test scorers does not constitute an understanding.”
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“Almost exactly 500 years ago, in 1507, Martin Waldseemuller and Matthias Ringmann, two obscure Germanic scholars based in the mountains of eastern France, made one of the boldest leaps in the history of geographical thought – and indeed in the larger history of ideas.
Near the end of an otherwise plodding treatise titled Introduction to Cosmography, they announced to their readers the astonishing news that the world did not just consist of Asia, Africa, and Europe, the three parts of the world known since antiquity. A previously unknown fourth part of the world had recently been discovered, they declared, by the Italian merchant Amerigo Vespucci, and in his honour they had decided to give it a name: America. “
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Kanem’s piece sort of undercuts itself. Yes, it may not matter when one learns to walk, but it does help to learn how to walk before hiking the Appalachian Trail. He complains about the engineering curriculum at his school requiring calculus, but what if the four years of courses require calculus? I suppose they could redesign things so one could learn calculus as a freshman, but he seems to be arguing that it should be just as reasonable to learn calculus as a senior, and not have to deal with all those calculus dependent courses just because one wants to major in engineering. Yes, I agree prerequisites suck, but so does coming into a class clueless.
That article on “The Back Page” is merely pointing out that students get admitted to a 36k$ per year private college with a declared interest in engineering who are not proficient enough in algebra to start in calculus despite all sorts of classes that would imply they are.
That is, he is not arguing against prerequisites. He is complaining about schools that taught matrix inversion yet somehow left the students clueless about algebra.
I think he is arguing that they could probably start in calculus if they had been taught algebra in high school rather than what they were actually taught. I see his point every day, because we get plenty of kids like that at my CC. Unlike at Loyola, however, they learn the math they need and go on to major in engineering.
Now if I could only find time to blog about it.
No, the argument is that students are being asked to learn things that they don’t have the background for, at the expense of things that could properly prepare them for calculus.
I recall learning matrix inversion in Algebra 2, a class that average students at my high school took in 11th grade and the many students who were advanced took in 10th or even 9th grade. That is, we were taught the mechanics of matrix inversion. I don’t think there was any explanation of why (beyond gaining the ability to solve certain homework and exam problems) someone would want to go through the trouble. And this is a case where there is a straightforward application to solving systems of linear equations, something else that was taught in that class.
That was in the early 1980s. Now, apparently, they are teaching matrix inversion in the year my average peers would have taken pre-algebra. That implies that they don’t even have the missed opportunity to tie matrix inversion to systems of linear equations. Also, the problems will necessarily be simplified, most likely to 2×2 matrices, with no easy way to generalize to larger matrices. (In my Algebra 2 class we were working with 3×3 matrices as well, but generalizing from N=3 to 4 is the hard step.) I don’t see how the students can really learn it, except in the sense of rote memorization, which is of no help when you encounter it in a slightly different guise a few years later.