## March 12, 2008

#### Posted by John Baez

Some interesting news from the Los Angeles Times.

In 2005, just 45% of the fifth-graders at Ramona Elementary School in Hollywood scored at grade level on a standardized state test. In 2006, that figure rose to 76%. Why? They started using the same math curriculum that Singapore does.

Ramona isn’t a rich, fancy school. Nine out of ten students at the school are eligible for free or reduced-price lunches. Most are children of immigrants — most from Central America, some from Armenia. Almost six in ten speak English as a second language. But, they’re doing a lot better in math than kids at other nearby schools!

Singapore math classes are more exciting. From the LA Times:

“On your mark … get set … THINK!”

First-grade teacher Arpie Liparian stands in front of her class with a stopwatch. The only sound is of pencils scratching paper as the students race through the daily “sprint,” a 60-second drill that is a key part of the Singapore system. The problems at this age are simple: 2+3, 3+4, 8+2. The idea, once commonplace in math classrooms, is to practice them until they become second nature.

Critics call this “drill and kill,” but Ramona’s math coach, Robin Ramos, calls it “drill and thrill.” The children act as though it’s a game. Not everyone finishes all 30 problems in 60 seconds, and only one girl gets all the answers right, but the students are bubbling with excitement.

And, Singapore math books are just better:

The books, with the no-nonsense title “Primary Mathematics,” are published for the U.S. market by a small company in Oregon, Marshall Cavendish International. They are slim volumes, weighing a fraction of a conventional American text. They have a spare, stripped-down look, and a given page contains no material that isn’t directly related to the lesson at hand.

Standing in an empty classroom one recent morning, Ramos flipped through two sets of texts: the Singapore books and those of a conventional math series published by Harcourt. She began with the first lesson in the first chapter of first grade.

In Harcourt Math, there was a picture of eight trees. There were two circles in the sky. The instructions told the students: “There are 2 birds in all.” There were no birds on the page.

The instructions directed the students to draw little yellow disks in the circles to represent the birds.

Ramos gave a look of exasperation. Without a visual representation of birds, she said, the math is confusing and overly abstract for a 5- or 6-year-old. “The math doesn’t jump out of the page here,” she said.

The Singapore first-grade text, by contrast, could hardly have been clearer. It began with a blank rectangle and the number and word for “zero.” Below that was a rectangle with a single robot in it, and the number and word for “one.” Then a rectangle with two dolls, and the number and word for “two,” and so on.

“This page is very pictorial, but it refers to something very concrete,” Ramos said. “Something they can understand.”

Next to the pictures were dots. Beginning with the number six (represented by six pineapples), the dots were arranged in two rows, so that six was presented as one row of five dots and a second row with one dot.

Day one, first grade: the beginnings of set theory.

And, as dedicated readers of this blog surely know, set theory is simpler than the syntactic laws governing arithmetic operations on numerals:

• • •   +   •   =   • • • •

is easier to understand than

$3 + 1 = 4$

California has taken a promising step forwards by letting Singapore math textbooks be used in grade school:

The Singapore curriculum is not strikingly different from that used in many countries known for their math prowess, especially in Asia and Eastern Europe, math educators say. According to James Milgram, a math professor at Stanford who is one of the authors of California’s math standards, the Singapore system has its roots in math curricula developed in the former Soviet Union, whose success in math and science sent shivers through American policymakers during the Cold War.

The Soviets, Milgram said, brought together mathematicians and developmental psychologists to devise the best way to teach math to children. They did “exactly what I would have done had I been given free rein to design the math standards in California. They cut the thing down to its core.”

[…]

“American textbooks are handicapped by many things,” said Hung-Hsi Wu, who has taught math at UC Berkeley for 42 years, “the most important of which is to regard mathematics as a collection of factoids to be memorized.”

One might think that school districts would be lining up to get their hands on the Singapore texts, but no one expects many to take the plunge this fall.

“Maybe in seven or eight years, but not yet,” said Wu. For now, he said he’d be surprised if the Singapore books claim 10% of the market.

In part, that may reflect the inherent conservatism of the education establishment, especially in large districts such as Los Angeles Unified, whose math curriculum specialists said in December, a month after the Singapore texts were adopted by the state, that they hadn’t even heard of them – or of the successful experiment taking place in one of their own schools.

But there is also an understandable reluctance to rush into a new curriculum before teachers are trained to use it. Complicating that, experts said, is that most American elementary school teachers – reflecting a generally math-phobic society – lack a strong foundation in the subject to begin with.

The Singapore curriculum “requires a considerable amount of math background on the part of the teachers who are teaching it,” said Milgram, “and in the elementary grades, most of our teachers aren’t capable of teaching it… . It isn’t that they can’t learn it; it’s just that they’ve never seen it.”

Adding to the difficulty is that the Singapore texts are not as teacher-friendly as most American texts. “They don’t come with teachers’ editions, or two-page fold-outs with comments, or step-by-step instructions about how to give the lessons,” said Yale’s Roger Howe. “Most U.S. elementary teachers don’t currently have that kind of understanding, so successful use of the Singapore books would require substantial professional development.”

It’s sort of depressing that the math teachers need to be taught math. On March 21st, my wife and I are flying to Singapore. Not because of this article… I’m giving a talk to the math and physics departments at NUS, and she’s talking at the philosophy department. We’ve been there before; it’s a fascinating place, but I feel I’ve only scratched the surface. It’s got its good points; it’s definitely got its bad points… but they seem to know how to teach math.

Posted at March 12, 2008 4:53 PM UTC

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Don’t forget that in 1994 they engaged in caning, a brutal form of medieval torture, against an American teenager for something as trivial as vandalism. I think it’s not unrelated to what you’re talking about because there is something oppressive and facist about the “drill and kill” method you’re talking about. It reminds me of the fact that the Chinese do very well in the Olympics because of the horrible brutal system they put their athletes through. I remember there was a Chinese girl who won the Olymic silver medal in diving when she was 12 years old, and she said she despised diving more than anything in the world. I don’t think that’s a fair trade off. I would rather live in a free society that respected basic human rights and where kids did not do as well in math. Nothing would make the average child despise math more than being forced to do a bunch of arithmetic problems while literally under the time pressure of a stop watch.
Posted by: Jeffery Winkler on March 12, 2008 7:08 PM | Permalink | Reply to this

Jeffrey wrote:

Nothing would make the average child despise math more than being forced to do a bunch of arithmetic problems while literally under the time pressure of a stop watch.

That’s belied by the article above. It depends on a lot on the teacher’s attitude, I think. If it’s sort of a game, it’s fun. If it’s ‘being forced’, it’s not.

By the way, I’m not interested in discussing torture and political repression on this thread — they’re important, but not particularly relevant. In particular, you’re presenting us with a false dilemma here:

I would rather live in a free society that respected basic human rights and where kids did not do as well in math.

I would rather live in a free society that respected human rights where kids do learn math. The USA can improve in many respects, including all three of these. Rejecting good ideas from other countries because we feel superior in some respects does not serve us well.

Posted by: John Baez on March 12, 2008 7:42 PM | Permalink | Reply to this

Interesting! I’ve just been reading a very different (almost opposite) vision of school mathematics teaching: Lockhart’s Lament. It’s a passionate, eloquent essay, very much worth reading.

Posted by: Robin on March 12, 2008 8:32 PM | Permalink | Reply to this

If they are different visions, are they incompatible? Even Lockhart admits a place for getting basic facts right:

Let’s be clear about this. I’m complaining about the complete absence of art and invention, history and philosophy, context and perspective from the mathematics curriculum. That doesn’t mean that notation, technique, and the development of a knowledge base have no place. Of course they do. We should have both. If I object to a pendulum being too far to one side, it doesn’t mean I want it to be all the way on the other side. But the fact is, people learn better when the product comes out of the process. A real appreciation for poetry does not come from memorizing a bunch of poems, it comes from writing your own.

If the learning of “rote facts” can be made an enjoyable competition, then I think that’s a good thing: not only does it provide the tools for later exploration, but it can also build the confidence necessary to explore.

Why not give the kids to Milgram in the morning and Lockhart in the afternoon?

Posted by: Blake Stacey on March 12, 2008 8:50 PM | Permalink | Reply to this

I confess I’ve never experienced the automatic sense of elevation that’s supposed to result from being classified an artist. This lacuna prevents me from appreciating the article as a whole, even as good points are made here and there, and the author’s intentions are clearly noble. Nor seems it obvious that appreciating good poetry depends heavily on having a go at producing it. I can’t pursue this particular example much further, having actually dabbled in poetry (with unfortunate results). On the other hand, I think I do take genuine joy in observing the skills of rugby players, without ever having been near a pitch.

MK

Posted by: Minhyong Kim on March 13, 2008 10:42 PM | Permalink | Reply to this

The Soviets, Milgram said, brought together mathematicians and developmental psychologists to devise the best way to teach math to children. They did “exactly what I would have done had I been given free rein to design the math standards in California. They cut the thing down to its core.”

Yes, but if you had been given free rein to experiment with California’s math standards, then California would be the subject of a Milgram experiment, now, wouldn’t it?

(I stand firm in my conviction that somebody had to say it.)

The idea that teachers don’t understand enough math to teach math is, well, frightening. What have they been doing all this time? I thought it was the children who needed to have their hands held… just how big can the gulf be between what they know and what they need to know?

Maybe once we’ve fixed the mathematics in elementary school, the problems with middle-school science will be more tractable.

Posted by: Blake Stacey on March 12, 2008 8:35 PM | Permalink | Reply to this

“The idea that teachers don’t understand enough math to teach math is, well, frightening.”

But not, alas, novel.

Before I finished high school I was working as a math tutor, something I continued on-and-off for another decade or two, and I’ve done a brief stint as a classroom teacher (6th/7th/8th-grade math+computers), as well as had countless impromptu, informal math-teaching occasions arise.

And the greatest portion of everything I’ve done as a tutor or a classroom teacher has been working to undo the damage done by earlier math teachers.

I have long been convinced that far too few math teachers, especially in the early grades, understand the math they’re teaching. So they in turn cannot teach an understanding of it, and instead present it as a pile of mysterious “just because, and don’t ask why” directions – when they don’t include ideas that are actually wrong.

*sigh*

So: not surprising. But yes, frightening still, no matter how long I’ve known it.

(I am so very grateful for my Montessori education…)

Posted by: D'Glenn on March 13, 2008 12:03 AM | Permalink | Reply to this

“too few math teachers, especially in the early grades, understand the math”

One of the reasons for that seems to be a problems with understanding written texts. When in courses for future math techers last year, a majority of the students expressed big problems with understanding the statements and questions of excercises, designers of the PISA-Test recommended some quick and easy to do tests for measuring that, but apparently that did not happen.

Posted by: Thomas Riepe on March 13, 2008 10:06 AM | Permalink | Reply to this

As for Thomas’ remark about reading and understanding, I strongly agree with that. Unfortunately, I view the primary problem as a *spiritual* one. This makes me morbidly skeptical of methodological attempts to deal with it.

MK

Posted by: Minhyong Kim on March 13, 2008 2:03 PM | Permalink | Reply to this

“the primary problem as a *spiritual*”

Yes. My perhaps meaningless impression is that one perceives mathematics in a “platonic” way and only this makes one curious about it. However, I have no idea how others perceive mathematics and how the sets of “platonic ideas” differ between people, or how one could induce such a way of thinking. To my knowledge, the only instance where someone tried to teach it was Platon in his dialog “Parmenides”.

Posted by: Thomas Riepe on March 13, 2008 6:31 PM | Permalink | Reply to this

” one perceives mathematics in a “platonic” way and only this makes one curious about it.”

The only’ part of the statement seems a bit strong to me. A large part of my own concern is about quite concrete things. For example, if we’re worried about enabling students to read and understand, it’s hard not to face the question of how one pays attention to someone else’s words at all with a good degree of patience. How to stay focussed when the notions that come up are very unfamiliar? How to reflect properly on things that seem very familiar, and so on.

We do have an obligation to make ideas and techniques as interesting as possible. Meanwhile, students, and *we* as students, have to learn to put in an effort when things are not so obviously interesting. (Clearly, we can’t do this all the time. Achieving some sense of balanced effort is one of the major technical goals of education.)

In any case, it seems artificial to remove from such discussion reference to the overall background of spiritual discipline. Not that I expect talking about it to do much good :)

MK

Posted by: Minhyong Kim on March 13, 2008 10:27 PM | Permalink | Reply to this

Hesitant as I am to jump into this horribly complicated topic, I did want to register some disagreement with this rather harmful sentiment. The reason is that the students you met were *not the same* as the students the teachers dealt with.

When I teach post-graduate students who took basic maths in some highly disciplined environment, which was perhaps not overly congenial to inquisitive minds, it’s actually a pleasure to ‘teach them how to think.’ But it would certainly be presumptuous to consider myself as undoing prior damage. Most of the time, the students’ earlier teachers taught them other basic skills that they (and I) benefit from, even if it wasn’t in an optimal way. (Does anyone know such a way?)

Of course I’m aware of serious problems in education at various levels, to which I try my best not to contribute. But again, I don’t agree with the way you put matters.

MK

Posted by: Minhyong Kim on March 13, 2008 1:55 PM | Permalink | Reply to this

Oops, sorry, Thomas. The post above was intended as a reply to the post by D’Glenn.

My own poor education prevented me from knowing how to scan for the right button.

Minhyong

Posted by: Minhyong Kim on March 13, 2008 1:59 PM | Permalink | Reply to this

You did do it correctly, Minhyong. Your double lined comments shows it answering the previous single lined comment, which is D’Glenn’s.

The difficulty of representing a tree linearly!

Sometimes we deliberately avoid an extra layer by replying to the message before the one we’re really replying to. And sometimes we simply remove ourselves from the nesting. I wish there were a better solution.

Posted by: David Corfield on March 13, 2008 2:45 PM | Permalink | Reply to this

MK

Posted by: Minhyong Kim on March 13, 2008 2:59 PM | Permalink | Reply to this

### News from the front lines; Re: Following Singapore’s Lead

This L.A. Times article about the Singapore approach was quite interesting to me. I tore out that page of the newspaper, and have been carrying it around, pondering it.

I teach in the greater Los Angeles area, albeit not in the dysfunctional Los Angeles Unified School District (LAUSD), which after spending tens of millions of dollars upgrading their computer system, still cannot issue correct paycheck to thousands of their teachers, but in the merely somewhat dysfunctional Pasadena Unified School District (PUSD).

I agree with Blake Stacy that most Math teachers that I’ve seen in urban California high schools and below do NOT know Math, as readers of this blog know Math. They are primarily teachers, who may know intermediate algebra, high school geometry, and maybe a speck of calculus and linear algebra. A few, a small percentage, have a Math or Computer Science or similar degree. Most have only an Education degree. This matters to me, as when I teach summer school, or as a Substitute in PUSD, I inherit the children who have no Math education at home, and have never once had a good Math teacher in school. Most have developed a hatred of Math, as I’ve described at length (with quotations from my students) in an earlier thread of this blog.

In the past three weeks, since I recovered from major surgery that cured a life-threatening ailment, I’ve taught at every one of Pasadena’s High Schools and every one of its Middle Schools. Yesterday I taught 7th graders Pre-Algebra and Medieval History at Washington Middle School which is literally on the same street as my home (albeit a couple of miles downhill).

While typing this comment, I got a robococall offering today’s substitute job: Math, at WIlson Middle School. Wilson is an International Baccalaureate Magnet School, and has a marginally
higher-scoring set of students than some others. My wife has taught there, back when she did high school and middle school (i.e. before becoming a Professor) and the principal was Rich Boccia, under whom I worked at Blair High School (or, as it wants to be called) Blair International Baccalaureate Magnet High School.

Hence, in my district, I have taught in the “best” and the “worst” public high schools and middle schools, and those in between. Although I have met a few good teachers who do know Math (typically having a M.S., or even having started in a PhD program before being sidetracked by, for instance, motherhood).

The school’s problems are not merely academic. For instance, clipped from this morning’s local newspaper:

Detective recounts Blair lockdown
By Molly R. Okeon, Staff Writer
Article Launched: 03/12/2008 03:10:53 PM PDT

PASADENA - Looking for the teen who roughed him up, a 17-year-old boy wrapped a gun inside a black plastic bag and pointed it sideways as he walked from class to class at Blair IB Magnet High School Feb. 29, triggering a day-lock lockdown, a detective testified Wednesday.

Pasadena police Detective Carolyn Gordon said the Altadena teen was searching for another Blair student who had slapped him in the face twice two days before, causing his head to hit a pole.

Pasadena Superior Juvenile Court Commissioner Robert Leventer decided to keep the teen, whose name is being withheld because of his age, in custody at Juvenile Hall. His next hearing will be March 21.

The boy is now charged with one felony count of making criminal
threats with special allegations of a minor possessing a handgun and the crime being committed in furtherance of a street gang.
=========================

Posted by: Jonathan Vos Post on March 13, 2008 2:49 PM | Permalink | Reply to this

### Re: News from the front lines; Re: Following Singapore’s Lead

Medieval History…. Here I can’t resist remarking that the recent media hype about that frustrated looking NY governor offers plenty opportunities to teach the differences between contemporary and medieval life: In medieval times, if the equivalents of politicians visited a city, the most beautiful girls were sent naked, perfumed and chained towards them and the city authorities proudly organised the visitors free use of public houses as part of the official program.

Returning to mathematics: Leonardo Pisani’s “Liber Abbaci” gives a very good idea of what interesting things non-clerics learned then.

Posted by: Thomas Riepe on March 13, 2008 5:53 PM | Permalink | Reply to this

Clearly there’s a lot of pent-up demand on this blog for discussing barbaric canings, 17-year-olds bringing handguns to school, and chained naked beauties! I hadn’t expected a post on math education to unleash such dark passions. It must mean something, but I’m scared to speculate out loud about what.

Posted by: John Baez on March 13, 2008 7:01 PM | Permalink | Reply to this

Next time you’re giving a seminar or a class and you get the impression that your audience’s minds are wandering, you’ll know where.

Posted by: Tom Leinster on March 13, 2008 9:02 PM | Permalink | Reply to this

I have to say, I think Hung-Hsi Wu’s comment on how mathematics is often regarded as a collection of factoids to be memorized is an important one. In my experience a great many people who dislike mathematics do so because of this very confusion: as long as you see the subject as nothing more than the factoids, it appears rather pointless. It’s what underlies and makes the factoids cohere that makes mathematics interesting. I wrote about this a while ago. The more I think about it though, the more important I feel it is.

There’s a disconnect I tend to experience when trying to explain to people how I think mathematics should be taught. When I talk about teaching the abstractions they are horrified; they think of New Math, and “abstract nonsense” and complain that kids need math that is concrete and relevant. When I complain about the waffle in elementary and high school mathematics education and suggest that basic skills need to be learned properly (a la Singapore math for instance) the same people will argue that it’s just “drill and kill”. The problem, I am realising, is that they see mathematics as factoids. When I talk about abstraction they imagine a long list of abstract factoids – useless as far as they are concerned. When I talk of basic skills they think of being forced to memorise factoids – again, unappealing. As long as they see mathematics as nothing but factoids they won’t see that when I say “abstraction” I mean “explaining how the factoids inter-relate and fit together”, and when I say basic skills I’m talking about instilling the enough factoids as second nature to allow real intuition about those abstractions – that is, as a means to an end. not as an end in themselves.

Of course the deeper connections and abstractions and ideas of mathematics (the interesting parts) can only be taught well by someone who has a feel for them, and that often takes knowledge of mathematics at a much higher level than you are teaching. As much as I appreciate the Singapore syllabus, I think the Finns have the right idea: encourage more primary shcool teachers to take university level maths, join math clubs, etc. If the teachers don’t see mathematics as anything more than factoids, is it any wonder the kids struggle to unerstand that there might be more to the subject?

Posted by: Leland McInnes on March 14, 2008 1:27 AM | Permalink | Reply to this

Peter Hilton once pointed out an even more damaging not uncommon occurrence: Teachers who love children and hate (dislike if you will) maths. It would be better to have the opposite.

Posted by: jim stasheff on March 14, 2008 1:26 PM | Permalink | Reply to this

I apologize (to whomever is paying attention) for posting so many comments after expressing hesitancy. I’ll admit the topic is very much on my mind these days, so I’m following the discussion rather carefully.

I think I understand the (good) intentions behind Professor Stasheff’s remark. But it’s hard to imagine a true love of mathematics being *compatible* with a hate for children. Perhaps I’m being a strange kind of fundamentalist. (My own narrow experience is that essentially all the serious mathematicians I know get along with children exceptionally well :))

Posted by: Minhyong Kim on March 14, 2008 1:48 PM | Permalink | Reply to this

…it’s hard to imagine a true love of mathematics being *compatible* with a hate for children.

If Grothendieck is right, we may see why:

In our acquisition of knowledge of the Universe (whether mathematical or otherwise) that which renovates the quest is nothing more nor less than complete innocence. It is in this state of complete innocence that we receive everything from the moment of our birth. Although so often the object of our contempt and of our private fears, it is always in us. It alone can unite humility with boldness so as to allow us to penetrate to the heart of things, or allow things to enter us and taken possession of us.

This unique power is in no way a privilege given to “exceptional talents” - persons of incredible brain power (for example), who are better able to manipulate, with dexterity and ease, an enormous mass of data, ideas and specialized skills. Such gifts are undeniably valuable, and certainly worthy of envy from those who (like myself) were not so “endowed at birth, far beyond the ordinary”.

Yet it is not these gifts, nor the most determined ambition combined with irresistible will-power, that enables one to surmount the “invisible yet formidable boundaries” that encircle our universe. Only innocence can surmount them, which mere knowledge doesn’t even take into account, in those moments when we find ourselves able to listen to things, totally and intensely absorbed in child’s play.

Posted by: David Corfield on March 14, 2008 1:57 PM | Permalink | Reply to this

The *sense* in which Grothendieck is innocent is a fascinating topic, especially since most mathematicians would consider him ultra-sophisticated. There is a short essay on this I started to write last year, which I’ll try to complete soon. It’s not easy because that kind of writing I finding completely draining (even as it’s enjoyable).

Posted by: Minhyong Kim on March 14, 2008 3:26 PM | Permalink | Reply to this

I’d like to hear what you think of this attempt to capture Grothendieckian simplicity.

Posted by: David Corfield on March 31, 2008 1:33 PM | Permalink | Reply to this

Quite a while ago, in this unlikely thread, David asked my opinion of Colin McLarty’s essay on Grothendieck and simplicity. I didn’t answer, even as I kept the question in mind, because I thought it would require some serious and substantial thought. Of course, that serious and substantial thought is never going to materialize. But today, in an answer to Math Overflow, I ended up inserting a paragraph on Grothendieck’s innocence. Here is a link for whomever considers it worth the trouble to take a look. While there are undoubtedly interesting philosophical investigations in this direction, it seems there are precise mathematical issues left to be resolved as well, which are, to me, perhaps more insistent.

Posted by: Minhyong Kim on October 19, 2009 11:44 PM | Permalink | Reply to this

What do you think about Ruelle’s statements in “The mathematicians brain”, that Grothendieck’s mindset was so alien to the authority- and statusdriven mentality of the french math community, that a subset of his students did (acc. to Ruelle) everything to eliminate him from french academia?

Posted by: Thomas Riepe on March 17, 2008 9:02 AM | Permalink | Reply to this

Minhyong,
Of course, you are right - though not ALL mathematicians. I was quoting or paraphrasing Hilton at an educational conference where he was speaking for editorial effect.

and hey, I’m jim

Posted by: jim stasheff on March 14, 2008 2:21 PM | Permalink | Reply to this

Dear Jim,

That’s what I guessed. Also, the words true’, essentially’, and serious’ were inserted as means of escape.

By the way, even after years of living in the west, I still get nervous with this form of address because of my Confucian upbringing!

Minhyong

Posted by: Minhyong Kim on March 14, 2008 3:31 PM | Permalink | Reply to this

Uncomfortable? Okay, I’ll address you as Professor Kim henceforth.

Posted by: John Baez on March 15, 2008 5:30 AM | Permalink | Reply to this

No, no, you’re *older* than me. Besides, you were my teacher in school, Professor Baez.

Posted by: Minhyong Kim on March 15, 2008 11:10 AM | Permalink | Reply to this

### Math? Elementary, my dear Watson; Re: Following Singapore’s Lead

“… it’s hard to imagine a true love of mathematics being ‘compatible’ with a hate for children…”

Professor James Moriarty, archenemy) of Sherlock Holme; supervillain; “Napoleon of Crime” (not to be confused with T. S. Eliot’s Macavity in Old Possum’s Book of Practical Cats) – he loved Math. In The Valley of Fear, set earlier on, Watson already knows of him as ‘the famous scientific criminal.’ His crimes include murder, and coordinmating as a super-godfather of London, many essentiaslly all other serious crimes. He was at best indifferent to children, and, de facto, allowed many to come to harm.

Holmes described Moriarty as follows:

“He is a man of good birth and excellent education, endowed by nature with a phenomenal mathematical faculty. At the age of twenty-one he wrote A Treatise on the Binomial Theorem, which has had a European vogue. On the strength of it he won the mathematical chair at one of our smaller universities, and had, to all appearances, a most brilliant career before him.”

“But the man had hereditary tendencies of the most diabolical kind. A criminal strain ran in his blood, which, instead of being modified, was increased and rendered infinitely more dangerous by his extraordinary mental powers. Dark rumours gathered round him in the University town, and eventually he was compelled to resign his chair and come down to London…”
[“The Final Problem”]

Sherlock further states that Moriarty has written the book “The Dynamics of an Asteroid, describing it as ‘a book which ascends to such rarefied heights of pure mathematics that it is said that there was no man in the scientific press capable of criticising it.’”

He was, weirdly enough, based on someone whom I mentioned in a different thread just a day or two ago.

As wikipedia mentions:

“In addition to the master criminal Adam Worth, there has been much speculation[1] among astronomers and Sherlock Holmes enthusiasts that Doyle based his fictional character Moriarty on the American astronomer Simon Newcomb. Newcomb was certainly a multi-talented genius, with a special mastery of mathematics, and he had become internationally famous in the years before Doyle began writing his stories. More pointedly, Newcomb had earned a reputation for spite and malice, apparently seeking to destroy the careers and reputations of rival scientists….
Carl Friedrich Gauss wrote a famous paper on the dynamics of an asteroid[2] in his early 20s, which certainly had a European vogue, and was appointed to a chair partly on the strength of this result. Srinivasa Ramanujan wrote about generalizations of the binomial theorem, and earned a reputation as a genius by writing articles that confounded the best extant mathematicians. Gauss’s story was well known in Doyle’s time, and Ramanujan’s story unfolded at Cambridge from early 1913 to mid 1914;[3] The Valley of Fear, which contains the comment about maths so abstruse that no-one could criticise it, was published in September 1914. Des MacHale[4] suggests that George Boole may have been a model for Moriarty.”

One shudders to think of what a super-duper-villain he might have been if he’d prematurely invented n-Category Theory. Which makes one wonder what Math he did use to coordinate a vast array (heap? set?) of crimes, and the logic surrounding them. Quaternions were popular. Hard to find as he was, he did not associate much, so maybe Octonions, too…

Hatining, or at least having a disposition compatible with hating children and being willing to have them die, is practically in the job description of supervillains. For instance, The title track of the Kinks’ 1968 album The Kinks are the Village Green Preservation Society includes the line “God save Fu Manchu, Moriarty, and Dracula”.

References:

[1] Schaefer, B. E., 1993, Sherlock Holmes and some astronomical connections, Journal of the British Astronomical Association, vol.103, no.1, p.30-34. For a summary of this point, see this New Scientist Article, also from 1993.
[2] Donald Teets, Karen Whitehead, 1999, The Discovery of Ceres: How Gauss Became Famous, Mathematics Magazine, Vol. 72, No. 2 (Apr., 1999), pp. 83-93
[3] See, for example, the book by Kanigel, The Man Who Knew Infinity
[4] Des MacHale, George Boole : his life and work (1985, Boole Press)

Posted by: Jonathan Vos Post on March 14, 2008 2:26 PM | Permalink | Reply to this

### Re: Math? Elementary, my dear Watson; Re: Following Singapore’s Lead

I love to remind my son of Moriarty’s mathematical credentials. Makes our trade more dark and mysterious. Incidentally, I’m sure you’re aware that Macavity was likely a direct reference to Moriarty. There are numerous other Holmes allusions among those practical cats, a pleasant diversion to locate.

Posted by: Minhyong Kim on March 14, 2008 3:02 PM | Permalink | Reply to this

### Re: Math? Elementary, my dear Watson; Re: Following Singapore’s Lead

I agree on all of your points, Minhyong Kim. In a curious sense, I am a published co-author of T.S. Eliot.

Of course, there’s quite a lot in the curriculum vitae of Sherlock Holmes as well. My meticulously composed versions is at:
SHERLOCK HOLMES

221b Baker Street
St. Marylebone
London, England

OBJECTIVE:

World’s first Consulting Detective. Working for the love of my art rather than for the acquirement of wealth. My professional charges are upon a fixed scale. I do not vary them, save when I remit them altogether.

PROFESSIONAL EXPERIENCE:

1878 Began professional career as a detective
1882 Began professional partnership with Dr. Watson no later than this date
1878 - 1889 Investigated some 500 cases “of capital importance”
1878 - 1891 Investigated 1000 cases in all
late 80s - Apr 91 Devoted to exposing and breaking up criminal organization of Prof. Moriarty
1894 Returned to active practice
1894 - 1901 Handled hundreds of cases
1895 Private audience with Queen Victoria, for services to England
June 1902 Refused offer of knighthood
1903 - 1904 Began retirement in solitude of Sussex coast, reviewing the records of cases and the destruction of those which might compromise more exalted clients. “The approach of the German war caused him, however, to lay his remarkable combination of intellectual and practical ability at the disposal of the government” with the result of communicating much false intelligence to the Germans, and arrest of Prussian spymaster Von Bork…

{see web page for much, much more…}

Posted by: Jonathan Vos Post on March 14, 2008 3:32 PM | Permalink | Reply to this

### Re: Math? Elementary, my dear Watson; Re: Following Singapore’s Lead

“I agree on all of your points…”

You mean you like rugby as well?

Posted by: Minhyong Kim on March 14, 2008 4:05 PM | Permalink | Reply to this

### Re: Math? Elementary, my dear Watson

Speaking of completely irrelevant digressions, my wife and I are huge fans of Sherlock Holmes stories and read them out loud to each other almost every night. We’re working our way systematically through the complete collection, and right now we’ve finally gotten to The Hound of the Baskervilles.

Posted by: John Baez on March 15, 2008 5:27 AM | Permalink | Reply to this

Jim almost said:

It would be better to have teachers who love maths and dislike children.

So now that you’re on the record, what assistance can I expect from you in getting hired and one of this laudable group?

Posted by: John Armstrong on March 14, 2008 10:28 PM | Permalink | Reply to this

jim stasheff: “Peter Hilton once pointed out an even more damaging not uncommon occurrence: Teachers who love children and hate (dislike if you will) maths. It would be better to have the opposite.”

Teachers who hate children and love math are better than teachers who hate math and love children? I’m confused.

Posted by: Lim TC on March 31, 2008 11:32 AM | Permalink | Reply to this

### Love/Hate Math/Kids; Re: Following Singapore’s Lead

Re:
“Teachers who hate children and love math are better than teachers who hate math and love children? I’m confused.”

To Lim TC, et al., I’d hazard this answer. I love Math. I love Science. I love children. I love teaching. However, I believe that a primary reason to teach is that one loves students (be they children or adults).

In that frame, I can grudgingly accept a really good and loving teacher who (never having had good enough teaching himself/herself) hates Math. So long as that teacher successfully encourages students to really THINK, be that in Literature, History, or whatever subject; and to become self-aware, with the discipline to overcome (with the help of other teachers) their weaknesses, then their students have a chance in intellectual life, including Math. It is hard to so clearly accept the adjoint.

Posted by: Jonathan Vos Post on March 31, 2008 4:23 PM | Permalink | Reply to this

Unfortunately, because we use the decimal number system, basic competence and speed at arithmetic requires rote memorization of around 110 “factoids” (the one digit by one digit addition and multiplication tables). And the best way to do that is drills and lots of practice. Now if we all converted to binary then it only requires 6 factoids.

Posted by: Mark Biggar on March 14, 2008 6:59 PM | Permalink | Reply to this

I’d like to insert a note of caution regarding the praise of the Soviet educational system. I believe it worked reasonably well in major cities in Russia and this is what Milgram talks about. But what was happening in small villages or in other parts of the Soviet Union, is anyone’s guess. Growing up in Moscow in the seventies I remember hearing that even there there was a problem with teachers understanding the math curriculum.

Posted by: Eugene on March 14, 2008 3:50 PM | Permalink | Reply to this

“the Soviet educational system”

I heard interesting things about math circles outside schools which were offered by good professional mathematicians to interested pupils. Do you know what was taught there (and how)?

Posted by: Thomas Riepe on March 14, 2008 4:04 PM | Permalink | Reply to this

Here is a review by Andrei Toom of a book Mathematical Circles (Russian Experience) by Fomin, Genkin, and Itenberg. Toom himself was involved in “circles” as a student in Moscow, which were typically informal gatherings of students interested in mathematics, led by professionals and students alike. Toom says it was there that he learned to become a professional.

There are some other interesting reflections by Toom here on his contrasting experiences of teaching in Russia and America, and much more here.

Speaking of math education in remote parts of the former Soviet Union: there was a famous correspondence school headed by Israel Gelfand, which resulted in several excellent books on elementary mathematics (several of which I have in my library). One is offered here through singaporemath.com.

Posted by: Todd Trimble on March 14, 2008 11:13 PM | Permalink | Reply to this

It is interesting that professional mathematicians are very willing to criticise others, particularly teachers, but this should perhaps go with a well argued philosophy and practise of teaching at the University level. Of course I know little about the USA situation, but I did meet a successful Bulgarian researcher who had much earlier obtained a scholarship to a top USA Department. His reply to How was it?’ was Three years of hell!’. A graduate of a major UK University told how she and her friends were scarred by the difficulty and inaccessibility of the courses’. Which verifies what we all know from our own failures, that making a course too hard for the audience (any audience!) is as easy as falling off a log!

In 1987 there was set to the audience at a discussion meeting at a British Mathematical Colloquium an examination paper from the “HOUYHNHMS UNIVERSITY STAFF COLLEGE, MATHEMATICS DIVISION”, and this can be found on the “Popularisation and Teaching” page of my web site. No scripts were handed in, I fear! Anyone like to have a go?

All I am saying is that the question What should be the output of mathematical education?’ (an article on my web page) needs addressing at all levels. I no longer teach, but I think we could have more forcibly addressed the broadening of the choices for students in a way argued in the article Promoting mathematics’ on that page, though we did try some novel and rewarding (to all!) experiments in Mathematics in Context’. At issue are old questions of technique versus (or with) what we might call mathematicality’ (in analogy with musicality’) and the place of mathematics in and as a contribution to culture. Also the fact is that most students do not go on to use mathematics in employment, though some do. What should they know of and, crucially, about mathematics? How does one assess the latter (since if not assessed, it is reasonably regarded as not important)? (Musical performance is assessed on technique and musicality.)

These are issues over which those who read this blog have some control and influence. There is an old parable of motes and beams!

Posted by: Ronnie Brown on March 20, 2008 6:35 PM | Permalink | Reply to this

Posted by: Thomas Riepe on April 27, 2008 4:46 PM | Permalink | Reply to this

### Race towards the bottom; Re: Following Singapore’s Lead

“… The Bum’s B. A worked like this: four students (preferably male) share an apartment on campus and compete to see who can do the least work possible and still pass his year. Independent observers would tabulate relative idleness; hidden cameras would make sure no secret cramming was going on….”

When I was at Caltech, my grades were not good. It wasn’t until grad school that I had a floor beneath my grades of B+.

Besides wine, women, song, bridge, bicycling, owning 100% of the campus vending machine cartel, and other distractions, I also openly asserted my intention to do as little homework as possible. Attending lectures was a form of entertainment. Taking exams was mandatory. I just didn’t like doing homework, and my grades suffered accordingly. It took me 5 years to get my nominally 4-year B.S. in Math (although I did get a B.S. in English Literature simultaneously).

I told other students that, if I ever got rich, I would endow a scholarship at Caltech for whichever student in a given year passed – but with the lowest grade point average.

Of course, I realized that this might cause a race towards the bottom. “If I can get a D in Module Theory then I can get my grade below that of last year’s winner…”

And, anyway, I never did get rich.

Posted by: Jonathan Vos Post on April 27, 2008 5:56 PM | Permalink | Reply to this

### Re: Race towards the bottom

When I want to give a grad student a gentle warning that they’re not learning everything they should, I give ‘em an A-. When I think they’re being lazy and want to scare them out of it, I sock ‘em with a B+.

Posted by: John Baez on April 27, 2008 7:02 PM | Permalink | Reply to this

AMS on “US culture derails girl math whizzes”.

Posted by: Thomas Riepe on October 10, 2008 8:18 AM | Permalink | Reply to this

### Girls Love Math; Shopping Is Hard; Re: Following Singapore’s Lead

USA gender bias in Mathematics (and non-biomedical sciences) is profound and destructive.

There are some science blogs where this is a major topic of conversation.

I make a great effort to overcome this in my own classrooms, in part by assigning biographical-historical homework on such leaders as Sophia Kovelevskaya, Emmy Noether, and Olga Taussky-Todd.

Posted by: Jonathan Vos Post on October 11, 2008 9:59 PM | Permalink | Reply to this

With all due respect to the naysayers, too many American teachers do not understand mathematics well enough to teach the concepts properly to our children. My kids attend schools in the Palo Alto school district, known to be one of the best in CA, if not the nation. Unfortunately, in spite their many strengths, most teachers here afraid of math and some even admit it in public. We have even had one or two teachers who were complete idiots, which begs the question: how can you get multi-subject teaching credential in CA w/o a foundation in basic math??? As for how our students have been performing well in math this long (someone in the thread raised the issue - the one who tied torture and abuses of human rights to math, confusing me altogether) - I’ll tell you what the kids here do: they secretly study with tutors who specialize in math. I know because my wife is one such provider of tutoring services. Also, given the education level of most parents here, many get help at home. As for the kid who was caned, many agreed with me that he deserved it. A high school senior played a prank by placing his car in the middle of the school quad, costing the district a lot of money. When he was punished for it (I forget if he was arrested), some local parents whined about excessive retaliation for his “benign” act of fun. This is exactly the problem with our society. Our kids need more discipline here.

Posted by: Mukhman on August 19, 2009 1:15 AM | Permalink | Reply to this

### Mukhman’s right; Re: Following Singapore’s Lead

I actually practice Mathematics professionally, and taught it at university, before working over 2 years to earn a California Secondary School Single Subject Credential in Mathematics. This process weeds out almost anyone who knows Math well – the Federal laws have forced an expensive potential barrier to screen them out of teaching. One goes through a College of Education, where many of the better professors openly admit that they “don’t get Math.” I feel that I was brutally treated (i.e. 2 grades that were “B” rather than “A”) by professors who believed in a Two Cultures Gap, rejecting my papers, and returning some of my homework (such as lesson plans in Math for students with disabilities and ESL issues) unread. One prof loved and assigned a silly paper with a Semiotic analysis of how teaching should combine Text and Pictures, and I pointed out how well Euclid had done that 2 millennia ago in the most published textbook of all time).

They don’t let the deaf teach music, or the blind teach painting, so why do they not only let the innumerate teach Math, but let the proudly innumerate teach teachers?

In fairness, I had an excellent prof in College of Ed., Dr. Fred Uy, in the class on how to teach Math in Secondary School. He knew Math, he knew how it’s taught in Singapore and China and inner-city Bronx, and was a revelation for many of his proto-teachers with emphasis on manipulatives and multisensory and exploratory methodologies.

Posted by: Jonathan Vos Post on August 19, 2009 1:40 AM | Permalink | Reply to this

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