Archive for September, 2012

What is a Fraction?

Wednesday, September 26th, 2012

A couple of Calgary Math Ed students have announced on LinkedIn that they are starting a Concept Study of Fractions.

This is a good idea as the topic is often challenging for students and I suspect that one reason lies in its language.
“A fraction is part of a whole” is consistent with the use in chemistry and with the concept of “proper fraction” sometimes introduced in math classes. Some would interpret “fraction” as equivalent to “ratio” (including ratios of irrationals) but others restrict to ratios of integers and some of these would include 3/2 as a fraction but not 6/3 (with the idea that a fraction is a rational number that is not an integer). And yet others would deny that a fraction is a number at all – with the word “fraction” referring to a way of naming a number rather than the number itself.

The difficulty of a not insignificant jump in the understanding of quantity is compounded by seeing all these various usages at the same time.

(and not even just from different sources – many teachers are themselves confused enough to keep switching from one to another in the course of essentially the same discussion)

On the other hand the desire for precision can lead to an apparent arbitrariness which is also off-putting to students. So I suspect that another major problem is the fact that some teachers, in their justified zeal to emphasize the need for precise definitions, often fail to emphasize the equally important issue of *scope* of a definition.

Obama at UN

Tuesday, September 25th, 2012

Transcript looks good except for one unfortunate adjective. It’s a pity that the president of a nation founded on the principle of separation of church and state cannot name the state of Israel without identifying its established religion.

Why I do this

Sunday, September 23rd, 2012

In the absence of any readers this may seem pointless but somehow I find it useful to keep links to things I come across and to record some of the thoughts I have about them. The WordPress tool lets me do this and although it might as well be private it feels as if even if no-one reads it the fact that it is accessible makes me think a bit (though perhaps often not enough) before committing to “publish”.

Jenny Mackness discusses Why we blog from the point of view of an active on-line educator, but some of the points apply also to a case like mine.In particular, the first reason she cites is “to serve as a substitute for a poor memory, by aggregating interesting ideas and links into one location thus creating a personal searchable digital library”

“Exercising” Freedom of Speech

Friday, September 21st, 2012

Ophelia Benson takes offense at the claim by David Marliere that Charlie Hebdo’s exercise of free speech may have been counterproductive (presumably to whatever goals he thought they were seeking to achieve).She responds to Marliere’s “Of course people should be entitled to mock Islam and any other religion. However, in the current climate of racial and religious prejudice in Europe, how can these cartoons be helpful? Charlie Hebdo is waging a rearguard battle.” by saying “If you’re hoping to help defend the genuine right to mock Islam and any other religion, as opposed to a purely notional right mentioned in passing only to be negated in the next sentence, then these cartoons can be helpful by exercising the very right that Marlière pretends to affirm only to deny it in the next breath.” But to confound the suggestion that an act is unwise with a denial of the right to perform it is really pretty silly.

“Use it or lose it” may be a popular saying but it is certainly not a universally valid principle, and there is no inconsistency in suggesting that a right is more likely to be preserved if used sparingly. Marliere’s conclusion re Charlie Hebdo may (or may not) be wrong, but anyone who wants to attack it is more likely to change minds if they do so intelligently (even though they do have the right to do so foolishly).

Paying for Murder

Wednesday, September 19th, 2012

When I see a report like this that some Iranian foundation ups price on Rushdie's head I wish that I had deep enough pockets to offer to pay double any such bounty to the killer of whoever offers it – and if anyone were to set up a foundation with that objective I would gladly offer to help support it.

The Limits of Science—and Scientists?

Saturday, September 8th, 2012

A recent column in Nature by Daniel Sarewitz, which could have been a welcome meditation on the power of religion to stimulate art which “speaks to the soul”, is marred by overstatement and an inflammatory headline.

Nature’s on-line editor Ananayo Bhattacharya comes to the defense with an article on Discover magazine’s ‘The Crux’ website which is somewhat disturbingly entitled ‘The Limits of Science—and Scientists‘ , but after reading the Sarewitz article and looking over a number of the comments, I have to say that this self-serving defense of a poor editorial decision unfairly misrepresents the positions of most of those who criticized it. Indeed, I have to agree with Chris Chambers that it constitutes an insult to a large part of Nature’s readership.

Coincidentally, an almost simultaneous posting by TRIUMF’s Byron Jennings at ‘quantum Diaries’ continues the “two cultures” discussion that was taken up there a couple of months ago by Jordan Pitcher. Although I expressed some disagreement with the simple dichotomy identified by Jordan with regard to types of people I am inclined to accept the complementary of aesthetic and empirical ways of thinking (and don’t think I have ever seen Hume effectively refuted on that)

Networks of Fear

Tuesday, September 4th, 2012

The events in Bangalore reveal new evidence that, in the parlance of social capital theory, electronic networking is more effective at producing “bonding” capital within groups than “bridging” capital between them.

n+1: Broad-Gauge.


Saturday, September 1st, 2012

Well if that hashtag isn’t already trending I’ll be very surprised!

Watching the RNC on Wednesday night Connie and I were impressed by Paul Ryan’s speech. He certainly sounded like a smart fellow with lots of “leadership” potential. And he had a lot of detailed “facts” at his fingertips. Although I am a Canadian with deep affection for a kind of socialized medicine which is faa..aar to the left of “Obama-Romney-Care” I have to admit that I was impressed. I hadn’t known that Obama’s right wing medical plan was going to steal $716 billion from the existing medicare plan for the elderly, since there are some elderly caregivers which also help with this, or that that Obama had ignored the recommendations of the Simpson Bowles deficit-cutting comission, or that he had promised to maintain that GM plant in Janesville but had not included it in his plan for saving the company (which actually DID happen!). But then I read that Fox news (of all places) had said that all these claims were FALSE and “Ryan’s speech was an apparent attempt to set the world record for the greatest number of blatant lies and misrepresentations slipped into a single political speech.” (I don’t actually follow Fox usually, so I only got that news via Salon).

I wasn’t surprised to hear that a slim and trim guy who can play so fast and loose with the facts is also a pretty fast runner and that his best marathon time was under three hours – but then it turns out that his own brother has exposed that as a lie also. In fact his ONLY marathon took over FOUR hours! (Not that I should diss that, as my own only effort was no better. But I can still remember the pain, and much as I would like to, it is hard to imagine remembering it as taking less than three hours.)

But now I am wondering if this guy has ever told the truth about anything. How many more lies are lying out there waiting to be revealed?