Tuesday, November 27, 2012

Tuesday Grab Bag...

A little Newton, Leibniz, Tanton, and Devlin today….

First, a link to James Tanton's latest "Cool Math" newsletter here (pdf):


…and if you enjoy that, you better go check out his links to his past newsletters (a treasure-trove of math enlightenment!):


Second, a fun piece on the historical rivalry between Newton and Leibniz over the discovery of calculus:


a few lines therefrom:
"So Newton farts around with this idea of fluxions, finally getting around to publishing Method of Fluxions in 1736… he published a few manuscripts on the subject, sending early copies to some colleagues. Meanwhile, in Germany, Leibniz was jotting down his own discoveries in his journal. In 1675, he noodled around, finding the area under a the graph of y = f(x) using integral calculus.

"In other words, the two men were discovering calculus at the same time and in completely different parts of the world. (Okay, Germany and England weren’t too distant from one another, but in the 17th century, they may as well have been on different planets.)"...

"...it was neither Newton nor Leibniz who lit the fire of the great calculus war. In 1704, an anonymous review of Newton’s fluxions suggested that he borrowed [i.e. stole] the idea from Leibniz, which of course infuriated Newton. Letters flew back and forth between the two mathematicians and their surrogates."
And finally another great post from Keith Devlin on his experience with the recent math MOOC course (massive open online course) which he instructed:


Devlin clearly feels MOOCs are here to stay and be a significant part of future education, but also recognizes the problems they entail. Occasionally when reading him I wonder if we're taking 3 steps forward and 4 steps back… I DON'T really think so (neither does he) but I do pause to wonder...

40 years ago I first learned of behaviorist-based "programmed learning," and thought it too would absolutely revolutionize education. It did nothing of the sort. What Dr. Devlin so well elucidates is the importance of a "social" component to learning (one of the things I think 'programmed learning' lacked). Learning/teaching are not simple uni-directional phenomena, and a 'human touch,' so to speak, is still needed.
Interestingly (since so many prematurely critiqued the Web as an isolating and dehumanizing influence) many now note that the Web or digital age has entered a "social" phase with emphasis on: collaboration, peer-to-peer contact, hive-mind, crowd-sourcing, open-access, and the like (in general, a great break-down of prior barriers to communication).
What I think will insure the progress and future of MOOCs and digital education generally, is its universality and availability to all with internet access (eventually, most everyone worldwide), leveling education opportunities as they have never been leveled before, and finally permitting people to learn at their own pace, in highly individualized ways.
Anyway, to close out, a bit from Dr. Devlin's piece:
"...(in most disciplines) the key to real learning has always been bi-directional human-human interaction (even better in some cases, multi-directional, multi-person interaction), not unidirectional instruction…
"For the vast majority of students, discussion with (and getting feedback from) professors, TAs, and other students struggling to acquire problem solving ability and master abstract concepts and proofs, is an essential part of learning. For those purposes, the online version does not find its inspiration in Khan Academy as it did for Thrun, but in Facebook, which showed how social interaction could live on the Internet.
"For courses where the goal is for the student to achieve mastery of a set of procedures (which is true of many courses in computer science and in mathematics), MOOCs almost certainly will change the face of higher education. Existing institutions that provide little more than basic, how-to instruction have a great deal to fear from MOOCs. They will have to adapt (and there is a clear way to do so) or go out of business."

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