e pur si muove

I was going to keep quiet about this, but I changed my mind. Alex Au at Yawning Bread recently wrote an article questioning Singapore’s push into biomedical research. (Yes, the title says stem cells, but it’s clear that the intention is to write about the entire field of biomedical engineering.) However, he’s completely and utterly missed the real issues that need to be addressed for truly incisive questioning.

To be fair, this is commentary about technical issues from a non-technical person. However, that’s still no excuse for grousing over rehashed issues that are already known to be irrelevant.

Here’s a summary of the issues over at Yawning Bread:

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Fox told me yesterday that the engineers in his building were routinely and wantonly disposing of liters of hydrofluoric acid down the sink after using them for etching.

Although a quirk of fluorine’s electronic structure makes hydrofluoric acid a weak acid, in the technical sense used by chemists, there is absolutely nothing weak about the corrosive nature of HF. It’s still one of the nastiest substances known to mankind.

If you use HF in your work, please please please practice the correct chemical hygiene and use (and procure if absent) a proper acid waste receptacle. If not, I will personally call OSHA to arrange for a nasty surprise inspection and whoop your sorry engineer asses.

Some readers may remember that the Chinese civilization once practiced footbinding, a practice once common among the upper classes of Imperial China and believed to make women more attractive, via their ‘lotus feet’, to prospective husbands of high standards.

The standard account of footbinding is that it is excruciatingly painful for women with bound feet, that they cannot move quickly at all, that feet had to be constantly bound in thick bandages to prevent normal growth, and was enforced by any means possible, including broken glass. (My mum used to collect the shoes as a hobby, and regaled my brother and I when we were younger with sordid tales of the Qing dynasty.) Even the staunchest traditionalist could at best claim that it’s a quaintly outmoded tradition whose loss is probably all for the better.

I remember grainy images in museums and textbooks of what women with lotus feet looked like. The shoes were always wonderfully ornate, if tragically far too small to be on an adult woman. But nothing really quite compares to the gruesome spectacle held within: (disturbing image warning)

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Many readers will be familiar with (or at least have some dim recollection of) the problem sums which prominently feature in the upper primary mathematics curriculum in Singapore. Many educators believe that concrete examples provide a foundation for the proper understanding of mathematical concepts, and that such concrete examples make the concepts easier for students to grasp. For example, the following New York Times illustration gives an example of the kind of thing math teachers try out on students to help them learn something concrete:

To test this prevailing wisdom, researchers and teachers at the Ohio State University conducted a statistically rigorous, randomized-trial study of whether or not concrete examples were better than going directly to the abstract mathematical representation of a particular mathematical concept.¹

To their surprise, they found that the group of students who learnt an abstract version of the mathematical concept strongly outperformed three separate groups who were taught off concrete examples. Even more surprisingly, students who were first taught a concrete example before asked to work on the abstract example did not perform any better than students who worked immediately on the abstractions, and in fact performed slightly worse on later testing.

The researchers concluded that the concrete details distracted students from the mathematical concepts that the lessons were designed to teach them, and speculated that some students simply don’t learn by abstracting from concrete examples.

It’s important to note that the study involved college students and not students of younger schooling ages, and that the different developmental stages in cognition would probably hamper the transferability of the results directly to younger students. However, this direct challenge to conventional wisdom suggests that even younger students may benefit from scrapping problem sums in favor for algebra.

There is at least some anecdotal evidence for a particular weakness for problem sums - students tend to either ‘get it’ and understand what’s going on in the problem, or they don’t and get stuck for a very long time. Time and time again, frustrated parents are left trying to help their children do problem sums without the aid of algebra, which students are sometimes expressively told not to use, yet ironically is the very thing that problem sums are supposed to prepare students for in secondary school and beyond.

References

1. Jennifer A. Kaminski, Vladimir M. Sloutsky, Andrew F. Heckler, Science, The advantage of abstract examples in learning math, 320 (5875) 454-455, 2008-04-25.
2. Jeff Grabmeier, Ohio State University News, Concrete examples don’t help students learn math, study finds,  2008-04-25.
3. Kenneth Chang, New York Times, Study suggests math teachers scrap balls and slices, 2008-04-25.

1. In this case, the study was on getting students to understand three-membered commutative groups.↩