Archive for November, 2009

Have a Heart!

Saturday, November 21st, 2009

It is always interesting when a probability question produces a counter-intuitive result, and the following “glimpse a heart” question is a wonderful example of that:-
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Hard Problems

Friday, November 20th, 2009

hardproblemsmovie.com is the website of a documentary made about the US team in the 2006 International Math Olympiad.

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Although American students on the whole rank well behind many countries in mathematics, American math Olympiad teams regularly finish among the top teams. While aiming to inspire and entertain, Hard Problems provides an insightful and thoughtful look at the process that produces successful teams, and ultimately, great mathematicians of the future

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The first part of the above quote raises some interesting questions about how educational effort should be prioritized.  Does effort directed to strong performance at the top levels compensate for, or compete with, that needed to maintain the basic levels of verbal and mathematical literacy that are needed for effective democratic decision making (as opposed to the woefully ill-informed nonsense that passes for debate about health care in the US for example)?

Mathematical Paintings

Friday, November 20th, 2009

From the MathForum newsletter:
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David Crockett Johnson was perhaps most famous for his children’s book Harold and the Purple Crayon. From 1965 until his death in 1975, Crockett Johnson painted over 100 works relating to mathematics and mathematical physics. Of these paintings, eighty are found in the collections of the National Museum of American History. They are presented on this site, with related diagrams from the artist’s library and papers.
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Interesting Poll Results

Monday, November 9th, 2009

BBC NEWS | Special Reports | Free market flawed, says survey.

Why Math?

Friday, November 6th, 2009

A couple of recent additions to the arsenal of reasons for promoting mathematics education are this recent article by Ian Stewart in the UK Telegraph and the collection of ‘Math Matters – Apply It’ posters developed by SIAM (the Society for Industrial and Applied Mathematics).

Stanford Study of Writing

Friday, November 6th, 2009

The Stanford Study of Writing provides a welcome counterpoint to some of the nonsense that has been put about regarding impact of the internet on literacy.

Crossing the Finish Line: SATs and GradRates

Friday, November 6th, 2009

Stephen Downes points to Chad Adelman posting on Crossing the Finish Line – a recent book about university graduation rates by William G. Bowen, Matthew M. Chingos & Michael S. McPherson.

I haven’t read the book but am suspicious of any attempt to draw conclusions about social policy from statistical analysis – especially in reviews and commentaries that isolate particular statements about how variables are correlated (and even more so if they include references to “predictive power” going “below zero”, since statistical power is defined as a probability and  a correlation of minus one has a very strong predictive power in any reasonable sense of the term).

A common “paradox” pointed out to students in an introductory statistics course is that it is possible to have a variable S (for, say, SAT score) that is positively correlated with some measure, say G, of success (eg graduation) in each of several subsets making up the whole of a population – while being negatively correlated in the population as a whole.

One way this might happen, for example, would be if there was a characteristic I (for, say, Inspiration) which was very highly correlated with G, and such that among the high I part of the population S was only weakly correlated with G but in the low I population S was very strongly correlated with G.

If among the population as a whole (in this case university entrants) low I was correlated with high S, then entrants with high S would be more likely to be in the low I group and so less likely to graduate and so S might be negatively correlated with G – even though in each of the low and high I groups separately, higher S does contribute to increasing G.

Of course, many readers of this  (if in fact there were any) might then say “but if I is the best predictor of G, let’s just use it and forget about S”.

And maybe they are right.  At least if the goal is soley to maximize the G rate we should just ignore the low I group and concentrate all of our efforts on those with the magic I factor.

If only we could identify it we could do away with all that “high stakes testing” and give our attention to those who deserve it.

Well the good news is that I have found I.

The bad news is that it is not Inspiration.
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Media Democracy Day Vancouver – November 7, 2009 | Media Democracy Day

Tuesday, November 3rd, 2009

Media Democracy Day Vancouver – November 7, 2009 | Media Democracy Day.

A Widening Gap

Sunday, November 1st, 2009

The Back Page article by Joseph Ganem in this month’s APS News suggests that nominal content and student capability outcomes in US high school mathematics are moving in opposite directions – and attributes this largely to attempts to introduce abstract topics before the students are ready.