alQpr

OK this is Mark Bauerline again, this time writing in the ChronicleReview.com with a rehash of the ideas he expounded in ‘The Dumbest Generation: How the Digital Age Stupefies Young Americans and Jeopardizes Our Future’ and particular emphasis on the discovery by Nielsen et al in 2006 that “Eyetracking visualizations show that users often read Web pages in an F-shaped pattern”. Now, Nielsen’s discovery is actually not surprising since much if not most web content is designed to be skimmed in search for particular items rather than to be read completely; Nielsen both acknowledges other possibilities with his “often” and doesn’t claim any earth shattering implications other than to make reasonable conclusions about how to design web pages of the kind intended for skimming in such a way that that skimming will be effective. But Bauerlein infers a lot more. Mostly unfounded nonsense. …more »

I don’t hold back from challenging the way mathematics is taught in schools myself, but Keith Devlin’s recent MAAonline column is off base and out of line.

…more »

A couple of weeks ago I posted briefly on (one of the many responses to) Nicholas Carr’s article in the current Atlantic Monthly.

Now I am reading another article on the topic. Bryan Appleyard in the Sunday Times refers to various recent books and articles about why the “Google generation isn’t as smart as it thinks”. One of his referents is Carr’s article and he refers also to a book by Mark Bauerlein with a similar thesis, but his main emphasis is more on the problems of distraction identified by David Meyer and Maggie Jackson rather than the habits of mind.

There are actually two main concerns being expressed. …more »

My friend Gerry Pareja sent this article by John Naughton from The Observer, responding (I think very well) to Nicholas Carr’s ‘Is Google Making Us Stupid?‘ in The Atlantic, but I can’t say that its arrival is what distracted me from my previous line of thought. In fact I was just tired, but feeling my need for sleep as a sign of lack of commitment-to-task prompted me to start also on my own intended response to Carr – and others who decry the influence of the web and other technology on our mental capacities. …more »

Resource: Mathematics Illuminated

This looks interesting – must check what costs are and how much is open access

Illegal Class Notes ~ Stephens Web ~ by Stephen Downes
This refers to a lawsuit in Florida against a company that is selling copies of course notes gathered by previous students. Apparently the professor involved has a package of materials that are sold to students by a publisher and the publisher claims that the “notes” being sold duplicate these copyrighted materials.  Steven Downes, and a number of bloggers he refers to, find this lawsuit objectionable and consider the professor to either be privatizing “ideas” or to have been in some way tricked y the publisher. But in fact it appears that the professor is not averse to the lawsuit so I don’t see how he can be described as having been snookered by the publisher; also, the copyright is being applied not to the ideas but rather to the specific presentation, and to the extent that his material is original that is surely his right. If students copy and freely share their own notes rather than an exact transcription of the instructor’s material then I have no problem with that, but if the note company is selling Moulton’s work for their own profit then I hope they get stopped.

(This does not mean that I have no reservations about a professor requiring students to purchase a text of his own authorship unless the text selection has been made at arm’s length by some independent third party – but that is, I believe, a separate issue.)

Green Globs & Graphing Equations Home Page

In Do the math – The Boston Globe columnist Jan Freeman dismisses objections to the common usage of “three times less than” to mean equal to one third of.

But the Merriam-Webster editors (per JF) are completely off base if they claim that “times less” has never been misunderstood. …more »

I got this post by Roger Schank via Stephen Downes and share Stephen’s concern with some of its polemical conclusions. The following counterpoint to Schank’s article may be a bit silly, but no more so than the original. …more »

mathschallenge.net
Fundamental Theorem of Arithmetic

squareCircleZ » Another semi-log graph from Alexa – imeem

This from Stephen Downes is, for me, a reminder to consider whether any of my stuff might be useful One Laptop Per Child and/or the Commonwealth of Learning.

BBC NEWS reports British chemists as pointing out the difference between an admission test for Chinese science undergrads and a UK university’s diagnostic test for incoming students. But perhaps they are comparing Chinese apples with British oranges (or vice versa?)
After all, in the Chinese question (assuming that by “square prism” they mean “right prism” – which is what it looks like) part (ii) could be on the senior level of our own BC high school math contest (and so could the rest if our high school students had any exposure to vectors), and the UK one could be a soft pitch from our Langara  Math Diagnostic Test.

In squareCircleZ » Trig graphs – how do you feel today?, Murray Bourne at squareCircleZ has a nice Flash gizmo to show biorhythm graphs and links to a site debunking their validity. Actually I think a nice lesson based on this would be to use a similar gizmo to support a demonstration of how sensitive the timing of coincidences between the different cycles is to small perturbations in their frequencies (most of those who experience biological cycles know that they usually aren’t entirely regular!). This might also lead to discussion of other more real biological cycles and periodicities – including nontrig ones like junebug and locust populations – and to the fact that astronomical regularities do have such unearthly precision that they can in fact be followed for many hundreds of cycles to make predictions about coincidences which are actually observed.

April is Mathematics Awareness Month and this year the American Mathematical Society, the American Statistical Association, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics have announced that the theme for Mathematics Awareness Month 2007 is Mathematics and the Brain.

Thanks to Zac at squareCircleZ for pointing out the dawn and dusk graphs at Gaisma as real-life examples of approximate sine graphs.

In fact the true time of noon appears to oscillate slightly with a 6 month period so that the Tokyo graphs are modelled pretty well by 6+1.5sin(2pix/12)-0.15sin(2pix/6) & -6-1.5sin(2pix/12)-0.15sin(2pix/6).

(Update: thanks to zac also for pointing out in the comment below that I should either have used cosines or have said “where x is the number of months since the spring equinox”)

It will be neat to be able to give Gaisma as a source of reference data for the hours of daylight modelling examples in my precalculus classes.

Wesley Fryer reports on a workshop by Bernie Dodge at Macworld

Phase, Frequency, Amplitude, and all that.. is an example of a university math course adopting the convention that identifies “phase shift” as angular shift as opposed to horizontal displacement or “time shift”

And at the time of this posting, the Wikipedia article on Phase (waves) takes the same point of view.

Murray Bourne at squareCircelZ has taken the time to respond to a comment I made on one of his interactive math pages, so I thought I should make an effort to explain my concern in a bit more detail.

In high school and college precalculus courses, the material on graphing trig functions often includes a definition of “phase shift” which is contrary to the way the term is used by many in applied fields and also by many mathematicians (including me when I have a choice).

The usage demanded by high school examiners corresponds to the horizontal shift of the graph from a purely scaled basic trig function. So, for A*sin(bx+c)+d it would be given by s=-c/b since, with that value for s, we get A*sin(bx+c)+d=A*sin(b(x-s))+d , so the graph of y=A*sin(bx+c)+d comes from y=sin(x) by first scaling to get y=A*sin(bx), and then shifting horizontally by s units along the x-axis (and vertically by d units along the y-axis).
But in fact, the concept of phase arose from a need to identify the part of the cycle being considered (ie rising, peak, falling, mid-point, trough, etc) and is usually identified quantitatively by an angle. So we typically talk of two waves interfering constructively when “in phase” and destructively when “180degrees (or pi radians) out of phase”, and we also speak of a process such as reflection or refraction as introducing a “phase shift” of so many degrees or radians in the propagation of the wave. With this usage, the phase shift of A*sin(bx+c) relative to A*sin(bx) is just c (radians) rather than the math teachers’ -c/a.

Some authors seek to avoid the conflict by identifying “phase shift” as what the high school teachers insist on and “phase angle” for what the other camp prefers. But I think this is a mistake for several reasons. My main objection is that even if it might be a good idea to implement such a change, it should not be taught to students as fact if it has not in fact yet been established as a convention agreed to universally in the professional mathematics community. There is nothing wrong, and much to value, in admitting to students that not all terms have universally agreed definitions and that when they face such terms it is important to *ask* what convention the user intends rather than to blithely assume something that may be wrong (which is just the sort of thing that leads to expensive space probes crashing into Mars and causes international airliners to run out of gas in the middle of the Atlantic).

But if that particular convention were proposed I would argue against it as I believe it serves no purpose other than to “save face” for the math teachers, and does so at the expense of abusing the language. I say this for three reasons.

First, the word “phase” was introduced to refer to the position in a cycle (which is basically an angle), so to speak of a “phase angle” is redundant.

Second, there is a phase (angle) corresponding to every point on a wave and the term “phase angle” does not properly denote a shift.

Thirdly, to use the term “phase shift” for what in any other graph would be called the “time shift” or “horizontal shift” introduces a completely useless extra bit of language by having a special context-dependent term for something which already has a perfectly good name that works in every other context.

And fourthly (I know you weren’t expecting the Spanish Inquisition, but do you know the three kinds of mathematician?) wasting a term where it is not needed makes it unavailable for where it is actually useful.

When two split light waves are brought together again (as in the creation of a hologram) it is not the phase (angle) itself at each point but the angular shift between the two waves that is directly relevant to the outcome rather than the time shift between two signals. We could of course convert the time shift to a phase (angle) shift just by using the known frequency and velocity of propagation, but it would be silly to use both terms to refer to the time shift and leave ourselves without a name for the quantity that is actually most directly relevant.

The convention that makes most sense to me is therefore to use the term “horizontal shift” (or whatever term they’d use for the x-displacement in any other function) for what the math teachers call “phase shift” and keep “phase shift” for its traditional role as what is now being proposed as “phase angle”.

This post by Will Thalheimer came to my attention via Harold Jarche and Stephen Downes. Unfortunately it’s not just in education that people are often impressed by fraudeulent mis-citation of derivative bunk.