Friday, November 29, 2013
"Futility Closet"... the BOOK!
A couple posts back I mentioned some books worthy of your consideration during the Holiday shopping season... you can now add another: turns out Greg Ross has put together a compendium of his best miscellaneous, quirky "amusements" for a "Futility Closet" book (this is GREAT news!):
Here's a nice, recent geometry tidbit from the Futility Closet blog:
And for those who missed it, I interviewed Greg at Math-Frolic just about one year ago:
Also, reminder, only couple of entries thus far to win some books over at my MathTango caption contest:
Wednesday, November 27, 2013
Something for the Young, the Older, and the Conspiracy Theorist
A few items you may have already seen, but if not...:
1) Sherlock-Holmes-wannabes are still trying to figure out who "Satoshi Nakamoto," creator of Bitcoin really is. The NY Times piece below draws an unconvincing (I think) link to the former proprietor of the Silk Road website. The guessing game may be more fun than learning the true identity will ever be.
2) Another great post from MathMunch covering several matters, but what most interested me (because I'd not heard of it) is a Scrabble-like game called "Numenko" that helps young people learn/practice arithmetic:
3) And finally, my favorite recent read from the Web, the always excellent Natalie Wolchover attempts to explain (better than I've ever seen done before, though still a tough-read) two different approaches to solving the infinity "continuum" problem:
Set aside some brain-time to take in this account of "forcing axioms" versus "V = ultimate L".
Monday, November 25, 2013
WHAT A YEAR!
…in popular math writing!! One thing I'm grateful for this Thanksgiving week is all the, not merely good, but GREAT math reads that appeared for the public this year; many of which I would put into "best of" categories:
For my money...:
BEST math-related book seen in decades: "The Outer Limits of Reason" by Noson Yanofsky
MOST fun-and-entertaining book in a long time: "The Simpsons and Their Mathematical Secrets" by Simon Singh
RICHEST introduction to high level mathematical ideas in a general audience book: "Love and Math" by Edward Frankel
MOST highly anticipated math biography evuh!: "Undiluted Hocus-Pocus" by Martin Gardner
BEST popular math anthology for a general reader: "The New York Times Book of Mathematics" edited by Gina Kolata
BEST (though hard to choose) book from the prolific Ian Stewart: "Visions of Infinity"
Probably my favorite popular treatment of statistics for a mass audience: "Naked Statistics" by Charles Wheelan
One of the best books ever focused entirely on a Clay Institute Millennium Problem: "The Golden Ticket" by Lance Fortnow (...this is a tough call though since there were several Millennium Problem books this year)
(I've reviewed all the above volumes over at MathTango at some point, with the lone exception of Singh's book, which is an absolute blast to read, but received SO MUCH positive coverage/publicity I feel no need to do a review myself.)
If there's a math geek on your Holiday shopping list I don't think you can go wrong with some of the above picks. It's amazing how a subject so often perceived as dry-and-dull as math, continues generating so many great volumes, demonstrating what a living, growing, kick-ass subject it really is ;-)… hats-off to the authors and publishers who keep the books flowing!!!
Please add your own favorites from the year-now-ending in the comments below. And feel free to add 2013 volumes of a more technical nature as well, if you think math professionals/specialists should be made aware of them.
...Meanwhile, as an aside, check out MathTango for the Caption Contest that is now up there!:
Saturday, November 23, 2013
Nature, the Ultimate IT Manager
Nice weekend read....
Somewhat more to do with biology than mathematics, but the above article from Nautilus, on 'Nature as an IT wizard,' is simply too rich not to pass along. It crosses into information-processing, neuroscience, and even physics, with plenty of mathematical implications. Subtitle for the piece is, "Nature manages information, the currency of life, with exquisite efficiency." Three quick bits:
"Every organism is a brief upwelling of structure from chaos, a self-assembled wonder that must jealously defend its order until the day it dies. Sophisticated information processing is necessary to preserve and pass down the rules for maintaining this order, yet life is built out of the messiest materials: tumbling chemicals, soft cells, and tangled polymers."
"Not only does DNA store information at a density per unit volume exceeding any other known medium, it can achieve one quarter of the maximum information density allowed by the laws of physics (set by the entropy of a black hole). It’s so dense that all the world’s digital data could be stored in a dot of DNA the weight of eight paper clips. This remarkable storage density is paired with an equally remarkable reading mechanism."
"Why would nature use fractal geometry so regularly? Mathematically, fractals are interpreted as having a fractional dimension higher than the space they reside in: A fractal drawn on a two-dimensional sheet of paper, for example, has a higher dimension—say, 2.1. This is a useful feature, allowing nature to pack some part of a fourth dimension into three-dimensional space."
Friday, November 22, 2013
A Little Bit of Statistics Is a Dangerous Thing
Well, I've had a few jabs at statistics this week in posts, so may as well end with another, more strictly humorous one. This is a joke I'd not seen before that comes verbatim from Simon Singh's wonderfully entertaining book "The Simpsons and Their Mathematical Secrets":
While heading to a conference on board a train, three statisticians meet three biologists. The biologists complain about the cost of the train fare, but the statisticians reveal a cost-saving trick. As soon as they hear the inspector's voice, the statisticians squeeze into the toilet. The inspector knocks on the toilet door, and shouts: "Tickets, please!" The statisticians pass a single ticket under the door, and the inspector stamps it and returns it. The biologists are impressed. Two days later, on the return train, the biologists showed the statisticians that they have bought only one ticket, but the statisticians reply: "Well, we have no ticket at all." Before they can ask any questions, the inspector's voice is heard in the distance. This time the biologists bundle into the toilet. One of the statisticians secretly follows them, knocks on the toilet door and asks: "Tickets please!" The biologists slip the ticket under the door. The statistician takes the ticket, dashes into another toilet with his colleagues, and waits for the real inspector. The moral of the story is simple: "Don't use a statistical technique that you don't understand."
On a related note I just recently discovered this webpage which focuses on "Simpsons math" as well:
Wednesday, November 20, 2013
Of Primes and Probability
Two bits for a Wednesday...:
1) In a fascinating long-read for Quanta Magazine, Erica Klarreich covers the astounding progress so far made in the "prime number gap" of the Twin Primes Conjecture, in just six months since Yitang Zhang postulated a limit to the gap of 70 million!:
James Maynard, a post-doc, has wrestled the gap down to no more than 600, well below the result that even Terry Tao's Polymath group had yet achieved.
an excerpt to whet your appetite:
"Zhang’s work and, to a lesser degree, Maynard’s fits the archetype of the solitary mathematical genius, working for years in the proverbial garret until he is ready to dazzle the world with a great discovery. The Polymath project couldn’t be more different — fast and furious, massively collaborative, fueled by the instant gratification of setting a new world record.
"For Zhang, working alone and nearly obsessively on a single hard problem brought a huge payoff. Would he recommend that approach to other mathematicians? 'It’s hard to say,' he said. 'I choose my own way, but it’s only my way.'
"Tao actively discourages young mathematicians from heading down such a path, which he has called 'a particularly dangerous occupational hazard' that has seldom worked well, except for established mathematicians with a secure career and a proven track record. However, he said in an interview, the solitary and collaborative approaches each have something to offer mathematics.
“ 'It’s important to have people who are willing to work in isolation and buck the conventional wisdom,' Tao said. Polymath, by contrast, is 'entirely groupthink.' Not every math problem would lend itself to such collaboration, but this one did."
2) I mentioned a couple of posts back that in the Preface to his new book ("Will You Be Alive 10 Years From Now?") Paul Nahin gives an example of a Marilyn vos Savant column where the famous Mensa-ite gives the WRONG answer to a math question and sometime later corrects herself. The question, and her initial ill-fated answer ran as follows:
Q.: "I manage a drug-testing program for an organization with 400 employees. Every three months, a random-number generator selects 100 names for testing. Afterward, these names go back into the selection pool. Obviously, the probability of an employee being chosen in one quarter is 25 percent. But what’s the likelihood of being chosen over the course of a year?"Nahin points out that the actual probability of being chosen at some point during the four quarters of testing works out to 0.6836, considerably greater than Marilyn's 0.25.
A.: "The probability remains 25 percent, despite the repeated testing. One might think that as the number of tests grows, the likelihood of being chosen increases, but as long as the size of the pool remains the same, so does the probability. Goes against your intuition, doesn’t it?"
In a later column Marilyn 'fessed up, "My neurons must have been napping" and corrected herself:
You can also see the math involved at this Forum site where the problem was discussed:
Monday, November 18, 2013
MOOCs as "Silicon Valley's Next Grand Challenge"
Professor Keith Devlin once again (this time in Huffington Post) with a thoughtful post on the future of MOOCs:
Wish I could just quote the whole thing, but I'll leave you with these bits:
"The fact is, Silicon Valley has yet to come to terms with education... A lot of what goes on in good (sic) education is almost certainly not scalable. That means the familiar hockeystick growth in users that can result in a hugely profitable IPO or buyout is not likely. On the other hand, as companies like Pearson and Apple know very well, the market for any particular educational product renews every twelve months as children and young adults move through the system."
"[MOOCs] are not 'regular university courses online' and they won't replace universities. They may well, however, reach a stage where they disrupt higher education, and if so, institutions that don't adapt to a changing landscape are indeed likely to go out of business."
"...there you have tomorrow's talent supply. Those huge [MOOC] dropout rates that were once regarded as a big problem turn out to have been our first glimpse of an amazing global filter for people with commitment, persistence and ability."
"MOOCs do not and, I believe, cannot replace a good university education. But they can, and in some cases already have, provide a pathway to such education for millions of people around the world who, for various reasons, do not at present have any access. Scale that across the entire world, and you have disruption."
...Meanwhile, for any interested, and who haven't already seen it, my overview of Noson Yanofsky's "The Outer Limits of Reason" (a fabulous volume I heartily recommend to all science-types) is now up at MathTango:
Friday, November 15, 2013
Probability, Oy Vey....
The Preface to Paul Nahin's new book, "Will You Be Alive 10 Years From Now," includes several wonderful probability problems… I'll likely use them here over time, and will start with the one that seems the most problematic even though on the surface it appears simple.
Columnist Marilyn vos Savant is famous for introducing the 'Monty Hall problem' to the public and giving the correct answer even when many professional mathematicians were initially labeling her "wrong."
Nahin argues that in a different example she WAS wrong, though I think he simply misinterprets matters. The initial, simple question that a reader asked Marilyn in this case was:
“Say you plan to roll a die 20 times. Which result is more likely:
(a) 11111111111111111111 or (b) 66234441536125563152”
Marilyn answered that both sequences were equally likely as outcomes from such a procedure… there is little controversy over that answer (and Nahin agrees with it)… from a strictly frequentist view of rolling a fair die, all sequence-outcomes being equally likely (that likelihood being very small, BTW). BUT, then Marilyn went on to note, “But let’s say you rolled a die out of my view and then said the results were one of those series. Which is more likely? It’s (b) because the roll has already occurred. It was far more likely to have been that mix than a series of ones.”
I don't really have much difficulty with that answer either, but Nahin takes her to task claiming the answer is "wrong" and the probabilities are still equal… that "rolling the die out of view" has no consequence. But clearly there is a difference between anticipating in advance a resultant sequence out of ALL the possible sequences that a procedure might produce, versus addressing just two given sequences AFTER a procedure has already taken place. Nahin faults vos Savant for essentially changing the original question, BUT she clearly states that that is what she is doing (in order to make what I think is an interesting and worthwhile point; it's almost a sort of frequentist vs. Bayesian distinction).
[One way to think about it is simply to make the sequence more ridiculously long: suppose I roll a FAIR die a million times; I record the results and tell you that the outcome was either a million ones, OR, some more-random-looking list of figures… prior to rolling the die both sequences would be equally likely, but with the task already completed, and ONE of the TWO given choices GUARANTEED to be the actual sequence, the second one is more probable.]
Anyway, I find this a good example of how the semantics of a probability problem is often trickier than the math or logic involved (similarly, the precise way the Monty Hall problem is stated and understood is crucial in reaching the right answer under the variety of exact set-ups that can be proposed for it).
[p.s. -- Nahin's Preface offers a second example of vos Savant getting a problem wrong (and later correcting herself), and at some point I'll give that example as well.] [Now, HERE.]
(image credit: Personeoneste/WikimediaCommons)
ADDENDUM: Below are Marilyn's two original responses to this problem in Parade magazine:
Thursday, November 14, 2013
Not sure which is more entertaining: reading another rant against statistical significance methods in the press... or, seeing the economist-author of such get taken to the woodshed by physicists in the comments section:
Wednesday, November 13, 2013
Learning, Books, Puzzles, P-values
Trying to get my blogging energy back after the 104th Carnival of Math sapped more of it than I expected 8-/
Will just point to a few pieces I enjoyed over the last few days:
1) The always-interesting Jo Boaler writes in The Atlantic about how the controversial Common Core approach to math education could help break down "math stereotypes." She believes the Common Core curriculum can produce students with more math confidence "who can develop mathematical models and predictions, and who can justify, reason, communicate, and problem solve… who are powerful mathematical thinkers and who have not been held back by stereotypical thinking and teaching":
(...of course not everyone in the 250+ comments agrees with her ;-)
2) Yet another wonderful podcast interview with Edward Frenkel (author of "Love and Math") this time from The Guardian:
3) "I just don't get no respect anymore"… THAT's what statistical p-values must be saying to themselves these days... a couple more articles critical of their standard use:
http://tinyurl.com/pcmfo2w (from Ars Technica)
http://tinyurl.com/mm9aceb (from Scientific American)
4) And an interesting little probability puzzle from Presh Talwalkar here:
5) Speaking of probability, Paul Nahin fans will be delighted to see that Dr. Nahin has a new book out, "Will You Be Alive 10 Years From Now?" -- frankly, I think it's a crummy title, but nonetheless looks like a fantastic/entertaining read if you enjoy probability puzzles (which is the entire focus of the volume -- I'll likely employ some of the content for blogpost material here eventually).
Don't know when I'll find time to review it though, since my current priority is Noson Yanofsky's "The Outer Limits of Reason" which I regard as the most important popular math-related volume in quite some time.
Monday, November 11, 2013
Come Frolic at The 104th Carnival of Math!
104 is the sum of eight consecutive even numbers, count 'em eight!... 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20
...but enough technical chit-chat; it's Thanksgiving Holiday month for American readers so without further adieu we'll give gratitude to these posts for strutting their stuff:
(...and please let me know ASAP of any errors below or mis-working links.)
October was a month full of Martin Gardner remembrances (his birthday being Oct. 21, and his autobiography recently released). One example was "Celebrations of Mind Honor Math's Best Friend, Martin Gardner" from Colm Mulcahy for Scientific American blogs.
Gardner of course demonstrated that doing math could also mean having fun... some other examples:
'The boy born on Tuesday' problem is one of the most famous math puzzles since Monty Hall. Rob Eastaway gives his take on it in "The Irksome Tuesday Boy Problem." [As can be found on Google, this problem has generated a LOT of discussion over the years.]
Speaking of puzzles, "On Time" is a 'clock' puzzle ("mind-reading trick") from the always wonderful Futility Closet.
In "Some Geometry Notes on a Babylonian Square Root" Pat Ballew of Pat's Blog speculates about the Babylonian use of geometry to solve an algebraic problem.
I'm also submitting Pat's post, "Great Problems For High School" which includes several classic problems.
In "Heroic Triangles" Colin Beveridge of Flying Colours Maths offers a nice little bit of triangle geometry. And then in "The Geometry of Sec" Colin elucidates some trigonometry for us, as well.
And finally, another Colin entry this month was "Why I Loved the MathsJam Conference," reporting on the awesome annual gathering of ~100 mathematicians-at-play at MathsJam in Britain.
In the post "From the Mailbag: Dual Inversal Numbers" Katie Steckles of The Aperiodical, reports on a budding 9-year-old mathematician taking note of "an interesting property of numbers."
I found this Brian Hayes piece (from Bit-player), "The Keys to the Keydom," on a flaw in RSA encryption, quite interesting.
Also interesting to watch has been the rise/fall/rise/.... of Bitcoin currency, especially with some of its recent problems, and Ed Felten of Freedom To Tinker blog tells us that "Bitcoin Isn’t So Broken After All."
In "Breakfast at Les Deux Magots" Matifutbol graphically explains the "friendship paradox" for those of you dwelling over why your friends have more friends than you do.
I've never understood the trendy interest in Zombies and Evelyn Lamb seems to find it curious as well, as she looks at one researcher's attempt to analyze that trend/obsession in: "Zombie Fever: a Mathematician Studies a Pop Culture Epidemic."
And finally, and only for the most serious amongst you, Tim Gowers did a looong (and deep) October post regarding a poly-mathematical approach he was interested in trying on the P vs. NP problem: "What I Did In My Summer Holidays" (warning: you can probably read ALL the other posts in the Carnival in the time it may take you to read and digest Tim's post! -- p.s., I selected this (a great example of Tim's writing), Tim didn't submit it.
Meanwhile, three Peter Rowlett posts were contributed this month:
"Council Orders Maths and Sudoku To Be Removed From Mathematician’s Gravestone" was a quirky news item that is almost self-explanatory.
In "Emergency Maths Arcade…" Peter suggests math games you can enjoy when all you have available is pen and paper (...like, uhhh, back in the days when I grew up!).
And finally, "Recent History," touches upon some "recent"(?) results in mathematics.
Speaking of history, Thony C. sends in the Aldres Caicedo post, "Credit," from A Kind Of Library blog, concerning Johann Bernoulli's contributions to the early days of calculus.
And some more history sent along by Thony: a few days ago was the anniversary of philosopher Gottlob Frege's birth... a post from Yovisto blog briefly synopsizes the great logician's achievements: "Gottlob Frege and the Begriffschrift."
In "Lost In the Fourth Dimension," Lee Randall manages to link together The Simpsons, Twilight Zone, and her own childhood, in a post from her blog, "A History of My Life In 100 Objects."
Evelyn Lamb submitted a couple of Kate S. Owens posts: In "Combinatorics and Pampers," Kate is troubled by the inefficiency of 15-digit product codes used on Pampers diapers. Perhaps Proctor-and-Gamble (maker of Pampers) knows something about the coming baby boom the rest of us don't know!?
And in "Mathematics in Fiction Class Visit" Kate touches upon both gender and semantic issues amidst a discussion of the difference between "mathematicians," "math teachers," and "math professors."
Speaking of gender-related matters, Yen Duong (Baking and Math blog) relates her recent experience being the only female in a meeting of math academics in "Surprisingly Emotional Reaction to Being a Woman in Math."
...and, on to sports: for NBA fans (and coaches!) Tallys Yunes' O.R. By the Beach blog offers a post attempting to maximize NBA winning percentages based upon the analysis of playing and resting time for players: "Optimally Resting NBA Players."
And in another sports note, Laura McLay of Punk Rock Operations Research explains "Why the Bears Should Have Gone For It on Fourth and Inches."
"In Love... With Math" was my own thumbs-up overview at MathTango of Edward Frenkel's well-publicized book, "Love and Math" which focuses on the "Langlands Program," while extolling the author's love for mathematics.
Education and learning math were, as always, frequent subjects of posts this month:
Keith Devlin's latest Devlin's Angle post is a great piece, entitled "The Educational Power of Elementary Arithmetic" on the controversy surrounding American math education.
In "Math Munching Today," Beth Ferguson of Algebra's Friend tells of using MathMunch in her classroom (along with Edmodo) to get students working/thinking a bit beyond the usual secondary curriculum.
From Ben Orlin's Math With Bad Drawings blog a lovely introduction for young people to statistics, called "The Bear In the Moonlight."
Sue VanHattum of Math Mama Writes tackles explaining calculus to students in a series of posts, including "What Is Calculus, Part One."
Aatish Bhatia's "The Math Trick Behind MP3's, JPEGs, and Homer Simpson's Face" at Nautilus, has been cited as one of the clearest, audience-friendly explanations of Fourier transforms to come along in awhile.
In "My Favorite Christmas Present" Kevin Knudson uses an old math book to bring logarithms into focus as an algebraic tool (despite the 'blank stares' they draw from his students!).
Over at MrHonner, in the post "Order These Things From Least to Greatest" Patrick Honner contemplates how the potential answers to a given problem (or rather, HOW to grade those answers) can be more interesting than the problem itself.
In a tweet, Steven Strogatz called Gary Rubinstein's post, "The Death of Math," "The smartest piece I've ever read about math reform," which I figure earns it inclusion in the Carnival!
On a related topic, Philip Stark at The Berkeley Blog offered an analysis of teacher effectiveness in "What Exactly Do Student Evaluations Measure?"
In "Snowballing Good Questions" Alex Overwijk of SlamDunkMath gives his class a lesson in how to develop good questions.
A few visuals (not blog posts) were also submitted this month, adding still further variety:
First, a video entitled "A Math Major Talks About Fear" from Saramoira Shields -- it was retweeted by so many folks I felt it deserved a spot in the Carnival.
Similarly, Kit Kilgour suggested another very popular video this month that appeared on Vimeo, "Beauty and Mathematics" -- the beauty and ubiquity of math captured in less than 2 minutes.
Meanwhile, Katie Steckles suggested 2 other videos for your attention:
"Prism Marching Band" a short imgur piece you need to see to appreciate.
...and from YouTube, "Sorting Algorithms" which lo-and-behold, involves, sorting algorithms.
And, on a different note, I'll close out linking to the latest interview in my own series at MathTango, with computer scientist Dr. Noson Yanofsky, author of "The Outer Limits of Reason," a fantastic, multi-subject book Shecky highly recommends to ALL!!
Wow!... Hope EVERYone finds at least a few things addressing their interests in this month's wide-ranging Carnival! And THANKS! to all who contributed....
(note: ...I've included all posts that I received as submissions, so if by any chance you sent in an entry and it doesn't appear here, then it got lost in the shuffle along the way... please let me know so I can insert it.)
==> If you need to catch up on your Carnival reading, the prior (103rd) edition is at Evelyn Lamb's Roots of Unity HERE, and the next Carnival will be hosted by Oluwasanya at MatheMazier.
If you'd like to sign up to host a future Carnival visit the home site at: http://aperiodical.com/carnival-of-mathematics/
L-l-l-lastly, I'll exploit this opportunity to ask if any math bloggers/writers out there are willing to be interviewed (via email) for my own blog, please let me know: sheckyr[AT]gmail[DOT]com
(balloon image from AJ at openclipart.org)
(turkey image via Lupin/Wikimedia Commons)
(classroom image via daniel julia lundgren/WikimediaCommons)
Friday, November 8, 2013
This'll be my last call for submissions (deadline is Sun.) to the November "Carnival of Math" being hosted right here at Math-Frolic in a few days. Submission form here:
(I'd especially encourage newer or lesser-known math blogs to consider contributing as a way of being exposed to a wider audience.)
In other matters, my latest interview is now up at MathTango, with Dr. Noson Yanofsky, author of my new favorite book (literally), "The Outer Limits of Reason":
And if you need a little mental workout to start the weekend, Richard Wiseman's Friday puzzle today is a simple Raymond Smullyan-like entry:
Wednesday, November 6, 2013
The "Roots of Math Genius"
Physicist and ultimate Platonist Max Tegmark (who argues that the entire Universe is a mathematical structure, composed entirely of mathematics) is one of the promoters of an endeavor called "Project Einstein" which hopes to find the genetic "roots of math genius" by sequencing the genomes of ~400 academic mathematicians/physicists and looking for commonalities. It's a controversial undertaking, you can read more about here:
After noting that one skeptic says, “I thought it was strange that it was called ‘Project Einstein’, which seemed designed to appeal to the participants’ egos,” Peter Woit wryly remarks that "If Project Einstein identifies a common gene among its participants, and uses the knowledge to breed a race of übermenchen, they may find they have selected not for unusual mathematical genius, but for unusual ego." ;-)
Tuesday, November 5, 2013
Art, Math, and the Realm of Numbers
An interesting (and long) post combining mathematics and art, and "the ability to be deeply intrigued, almost obsessed, by patterns" -- focused in part on "the geometry of irrational numbers, including and especially the geometry of the square root of 2!":
Monday, November 4, 2013
The Centrality of Good Teachers!
As much as I try to stay away (since I'm not an educator myself) from the many controversies and commentary surrounding math education in this country I am constantly lured back to it… and I simply CANNOT EVER NOT read the words of Keith Devlin on the subject since I always find his views so interesting and incisive.
His latest "Devlin's Angle" post is apparently inspired by a piece that educator Liping Ma wrote for the AMS Notices, entitled "A Critique of the Structure of U.S. Elementary School Mathematics," which Keith feels touches on "how to do it right in the curriculum-obsessed, teacher-denigrating US." It also relates to Keith's own recent forays into MOOCs and math video games. Read all Dr. Devlin's thoughts here:
Early on he stresses the importance of excellent, well-trained teachers, over curriculum, with these simple formulas:
BAD CURRICULUM + GOOD OR WELL-TRAINED TEACHERS = GOOD EDUCATION
GOOD CURRICULUM + POOR OR POORLY-TRAINED TEACHERS = POOR EDUCATION
and a couple more brief excerpts:
"Behind Ma’s suggestion, as well as behind my MOOC and my video game (both of which I have invested a lot of effort and resources into) is the simple (but so often overlooked) observation that, at its heart, mathematics is not a body of facts or procedures but a way of thinking. Once a person has learned to think that way, it becomes possible to learn and use pretty well any mathematics you need or want to know about, when you need or want it."I feel like this is must-reading for me… and all the more-so for any educator out there!
"...it’s very easy to skip over school arithmetic as a low-level skill set to be “covered” as quickly as possible in order to move on to the 'real stuff' of mathematics. But Ma is absolutely right in arguing that this is to overlook the rich potential still offered today by what are arguably (I would so argue) the most important mathematical structures ever developed: the whole and the rational numbers and their associated elementary arithmetics.
"For what is often not realized is that there is absolutely nothing elementary about elementary arithmetic."
...A-a-a-and, as long as I've got your attention, a reminder that the deadline for submissions to the next "Carnival of Math" (hosted right here by Shecky!) is next weekend; so please send those contributions to:
Friday, November 1, 2013
Improving the 'Dismal Science'
Edward Frenkel's twitter-feed led me to this 19 min. conversation with mathematician Eric Weinstein in which Eric "explores many creative ways that physics and more sophisticated forms of math can be used to rescue economics from itself and restore its now tarnished reputation":
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