Papert is Wrong

I usually find Papert right on top of things...and mostly agree with his views...but today at "The Daily Pappert" the quote was:

“The institution of School, with its daily lesson plans, fixed curriculum, standardized tests, and other such paraphernalia, tends constantly to reduce learning to a series of technical acts and the teacher to the role of a technician.”

I know that is not true.  I deal with wonderful kids every day who have not let their education be reduced "to a series of technical acts".  I work with teachers every day who refuse to be reduced to "the role of a technician."

Yesterday a student who might have been focused on the AP Calculus test just one month away had asked me about Euler's proof that the solution of the sums of the reciprocals of the squares, the famous Basel Problem, was pi^2 / 6.   I had to admit I didn't know off the top of my head how to do that..So this morning I brought him one of my Julian Havel books that discussed the proof, and he walked out with it this afternoon.  I don't know, but I bet he will be reading it this weekend rather than studying for my test...which I can live with. That may not constitute master teaching, but just seizing the moment when I could feed a student's hunger with more math.  But not being a "technician" either, Joe wasn't that hungry to learn when I met him a few years ago.  I am proud to believe that being in my classes has been one of the factors that fanned the flames of curiosity. 

Yes, I teach the curriculum, but every kid who ever walked through my class knows that there are those precious moments when we walk away from the syllabus to talk about the things that get Mr. Ballew excited.... anything about Euler....about Geometry ("darn it kids, you gotta' learn geometry to know math")  ... about vectors.. and the history of math.  OK, we go off on a lot of tangents, but come the standardized tests and the AP tests and all those things that they use to measure kids and schools and teachers, my kids make me proud.  Proud of them, proud of the teachers I work with, and proud of the little contributions I have made to enrich their learning.

Maybe what Papert says is too often true in education, but it doesn't have to be that way.  If you are a  student,take charge of your own education.  Let it be driven by YOUR curiosity. And if you are a teacher, find moments to teach your passion.  Kids WANT to know that learning is satisfying. Talk to them about what YOU are learning, about what you are struggling to learn.

What Do Math People Do?

Steven Colyer wrote recently to comment on people who were known for other things, but were, or had been mathemticians (too me, it's like being a marine, once you are,  you always are...  "Hooo raaah"... except I'm not, and never was a marine).  He mentioned a couple of folks that I knew, and reminded me of a blog post I had started once and never gotten finished..... So here it is....Thanks Steven
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I was a big fan (still am, I guess) of James Burke's series, "Connections", which are still popular on you tube it seems..and was just reminded of a "Burke-like" connection..

It started when I had one of those, "What can you do with math?" questions this morning. Not from a kid trying to avoid learning, but one who was curious because they couldn't imagine what they might do with a math education except teach (as if they know what people do with a history major).
I mentioned my "other life" expereince working in reliability and quality control, and I describe things some of my ex-students do working in non-educational fields in a general cross section of applied mathematical/statistical/actuarial jobs in government and business. 

And when this question comes up I always mention people who have math/sci majors who do/did "other" stuff. Terri Hatcher was a math/engineering student before she went to a casting call to keep a nervous friend company (and found fame). Art Garfunkle earned a Masters from Columbia in mathematics. And of course I mention the Simpsons and Futurama creator, Matt Groening who supposedly had a math or science degree from Evergreen State College in Washington.   (**see more  below) 

Today I happened to mention to the questioning young lady that Hedy Lamar, the famous (she thought she might have heard of her) actress had a patent for a submarine guidance device.
I wasn't sure what she studied in school, but knew that she was regarded as one of the "brainy" beauties of Hollywood. Still, I remembered it so poorly (I blame my age) that I looked back at some notes and was pleased to be reminded of an interesting "connection" . Hedy Lamarr had come up with her navigation device with another artist, the pianist/composer George Antheil.

http://www.wired.com/science/discoveries/news/2008/08/dayintech_0811
Together they conceived and patented a frequency-hopping torpedo guidance system: Lamarr contributed the knowledge of torpedo control gained from her husband and Antheil a method of controlling the spread spectrum sequences using a player-piano mechanism similar to those used in the "Ballet Méchanique".


**So I found a list of people who had a math based educations up to some point... Here are a few of them:
Basketball player Michael Jordan started out as a math major, but switched majors his junior year. (journalism if I recall)

San Antonio Spurs center David Robinson received a BS in mathematics from the United States Naval Academy

Tennis player Virginia Wade, who won the singles title at Wimbledon in 1977, received a bachelors degree in mathematics and physics from Sussex University

Teri Hatcher (Lois Lane on "Lois and Clark") was a mathematics and engineering major at DeAnza Junior College.  (The story I heard is that she went to a screening with a friend and they promplty hired her instead)

Danica McKellar (Winnie Cooper on "The Wonder Years") was a mathematics major at UCLA and graduated summa cum laude.  (you have all heard aobut her "Math Doesn't Suck" books)

Retired supreme court justice Harry Blackmun received a degree in mathematics from Harvard.

Corazon Aquino, ex-president of the Philippines, was a mathematics minor at the College of Mt. St. Vincent.

and of course I have mentioned that Lewis Carroll, author of Alice in Wonderland, was in real life a lecturer at Oxford in mathematics, and is famous for his book on Logic.
One of my favorite Lewis Carroll stories is about his gift of a book to Queen Victoria.   Here is the version as it is told on the Mathworld page.

Several accounts state that Lewis Carroll (Charles Dodgson ) sent Queen Victoria a copy of one of his mathematical works, in one account, An Elementary Treatise on Determinants. Heath (1974) states, "A well-known story tells how Queen Victoria, charmed by Alice in Wonderland, expressed a desire to receive the author's next work, and was presented, in due course, with a loyally inscribed copy of An Elementary Treatise on Determinants," while Gattegno (1974) asserts "Queen Victoria, having enjoyed Alice so much, made known her wish to receive the author's other books, and was sent one of Dodgson's mathematical works." However, in Symbolic Logic (1896), Carroll stated, "I take this opportunity of giving what publicity I can to my contradiction of a silly story, which has been going the round of the papers, about my having presented certain books to Her Majesty the Queen. It is so constantly repeated, and is such absolute fiction, that I think it worth while to state, once for all, that it is utterly false in every particular: nothing even resembling it has occurred" (Mikkelson and Mikkelson).

Christopher adds in a comment, "I know that John Astin from the Addam's Family has a mathematics degree from Johns Hopkins University. It doesn't say that he graduated with a math degree on Wikipedia, but I remember from the playbill for "Once Apon a Midnight" that he has a masters degree in math."  

Strange Connections

I recently came across a note that the Peter Mark Roget whose name is associated so closely with the thesaurus was a scientific type.  More particularly, in 1815 he invented the log-log scale (the logarithm of the logarithm of the number on the C and D scales... ) on the slide rule which facilitated finding powers and roots of numbers. 

I looked into his history and found that his education was in medicine and his work on the thesaurus was part of a lifelong coping mechanism to fight depression.  But before he actually got around to publishing his great book, he not only invented the slide rule scale, but following the death of Sir John Hershell, Roget was secretary of the Royal Society from 1827 to 1848. He also made observations in sight and persistance of vision that influenced the development of movies. 

From"Cheshire Antiquities,© Craig Thornber, Cheshire, England, UK.
"His observations were based initially on looking at the world through a series of slits such as one might have in a vertical Venetian blind or pallisade. A rotating cartwheel viewed through such as system gives an optical illusion. The spokes at the top and bottom appear straight but those at the sides appear to bend downwards. Roget worked out the path of the light to show how this happened. He went on to explain a phenomenon that often perplexes devotees of Westerns, a hundred years before the invention of film. At certain speeds, the cartwheel appears to stop or go backwards. Roget's observations were made by viewing through vertical slits but he showed the position of each spoke in the wheel at each glimpse and how this could lead to the optical illusion of stasis or backward motion. The same phenomenon is observed when a film is made with a cine camera. In 1820, Roget worked with Michael Faraday and Joseph Plateau in a series of experiments on vision leading to Roget's paper to the Royal Society on the Persistence of Vision. Roget's work showed that an image persists in human perception for about one sixteenth of a second and this forms the basis on which animations, film and television are based. "
(Wikipedia)

On 9 December 1824, Roget presented a paper entitled Explanation of an optical deception in the appearance of the spokes of a wheel when seen through vertical apertures. ...
While Roget's explanation of the illusion was probably wrong, his consideration of the illusion of motion was an important point in the history of film, and probably influenced the development of the Thaumatrope, the Phenakistiscope and the Zoetrope.

He also was involved in the creation of University of London and the precursor to the Royal Medical Society.    A busy Guy...

While I was searching this out, I came across the fact that the invention of the Ln scale (for finding e^x) was by an 11th grade high school student. 
From a post by Robert Adams:

The Ln scale was invented by a high school student, Stephen B. Cohen, in 1958. The original intent was to allow the user to select an exponent (in the range 0 to 2.3) on the Ln scale and read e^x on the C (or D) scale and e^(-x) on the CI (or DI) scale. Pickett and Eckel were given exclusive rights to the scale in the early sixties. Later, Stephen Cohen created a set of "marks" on the Ln scale to extend the range beyond the 2.3 limit, but Pickett never incorporated these marks on any of their slide rules.

And just one more footnote, I always found it a little quirky that the log scale on the slide rule was linear.

Phone Bill for Adam Ries

Found this old file on Reuters news service just in time for the commemoration of the death of German mathematician Adam Ries (Ries died on March 30th in 1559):

BERLIN – A German mathematician who died 450 years ago has been sent a letter demanding that he pay long-overdue television licence fees, residents at his former address said today. Germany's GEZ broadcast fee collection office sent the bill to the last home address of Adam Ries, an algebra expert who bought the house in 1525. A club in his honour was set up at the property four centuries later.
"We received a letter saying 'To Mr Adam Ries' on it, with the request to pay his television and radio fees," said Annegret Muench, who now heads the club.
Muench returned the letter to the GEZ with a note explaining the request had come too late because Ries had died in 1559, centuries before the invention of television and radio. She nonetheless received a reminder a few weeks later.

And from My files on Ries (or Riese):

 
When the early Italian mathematicians began to develop the foundations of algebra using the new Arabic numerals, they used the Latin word cosa, unknown, to represent the unknown quantity in a problem. In the 15th and 16th century with the emergence of the German Rechenmeisters, or master reckoners, the word coss was used in the same role. One of the most influential of these master reckoners was Adam Riese, who played a significant role in the movement toward the use of "Hindu-arabic" numerals and away from the counting boards and Roman numerals that still persisted. His Die Coss in 1524, and his other arithmetic primers were so well received that "nach Adam Riese" is still used in Germany to describe mathematical accuracy and precision. One of the reasons for his popularity was that Riese wrote in German rather than Latin which was more commonly used for math books.  This allowed for much greater access to his work.  The image at right appeared on a German stamp on the 400th anniversary of his death. It is from a woodcut that appeared on the cover of Rechenung nach der lenge, auff den Linihen vnd Feder .  The word "cossist" became a term for algebraist throughout Europe during this period. Many of the symbols we now use were developed during this time, including the signs "+" and "-" for addition and subtraction, and the first use of decimal fractions.

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