Sweating the small stuff: Born to quant.

I'm about halfway through Moneyball and it's a quick and exciting read. The gift of hindsight shows some of the book's flaws impossible to detect when it was published, most notably how few of the players Billy Beane and Paul DePodesta drafted in 2003 made any splash at all some eight years later. But I am heartened to see Michael Lewis' style of writing catching on. Lewis himself gives props to Bill James, one of the first of the new breed of baseball analysts who call themselves sabermetricians. (SABR stands for the Society of American Baseball Research.) James' annual Baseball Abstracts were the great impetus for the changes in thinking about the game, and besides being a single minded collector of stats, James also knew how to bring the funny when the situation arose. (Example: writing about a heavy hitting and just plain old heavy slugger from last century: "Cecil Fielder acknowledges a weight of 261, leaving unanswered the question of what he might weigh if he put his other foot on the scale.")

And here comes to a question about education. Can you create a Matty Boy or are his kind born that way? The heroes of many of Lewis's books are a breed now known as quantatative analysts or quants. I jumped into programming when I was a lad, but I probably would have been better as a math analyst. Gathering sets of data and analyzing them comes to me completely naturally. Some people love doing that and others don't. Some can only do it on one subject (Bill James admits to no interest in numbers unrelated to baseball) but others do it about most of the things they can think of. Henri Poincaré, sometimes called The Last Universalist of mathematics and easily in any good list of the best ten mathematicians of all time, incessantly collected data sets on everything. Joseph Fourier collected number about his favorite topic, heat, and from it derived the differential equations that explain the phenomenon. Isaac Newton actually spent more time studying the Bible and alchemy than he did studying math or what we call modern physics, and it was clear he was using his stunning number sense in doing so, though he never published any of his findings in either field, instead leaving some of his thoughts in letters to friends we can read now. He probably left the religion alone because some of his ideas were heretical and heresy could still get you in big trouble - like dead - back in his day. I expect he didn't publish anything on alchemy because he didn't make any breakthroughs the way he did in math and physics, largely because it was a dry well and there were no breakthroughs to be had.

I gather numbers all the time. I'd call it "obsessively", but I have other habits that deserve to be called obsessive more than my love of numbers. Even the silly gossip blog is really an excuse to look at the supermarket rags numerically. I also spent a few seasons gathering data on football to see if I could make sense of it better than the current stat systems do. One of my ideas was to split the football team into separate squads and give credit where credit is due when points are scored, which also means blame where blame is due when points are allowed. My system was completely at odds with the modern favorite statistical game of fantasy football, since I was looking at teams rather than individuals, but I was recently heartened to see that Yahoo! has changed how defenses are measured in fantasy football and no longer blames them for points scored from turnovers like fumbles and interceptions run back by the other defense That is a small part of the system I called the Split Point System.

I did this simple quant work on football because I didn't see anyone else doing it. Reading some ideas from how quants work in baseball, (there are a LOT more people doing interesting work in baseball stats compared to football stats) I could see how to turn the Split Point System into a much better and more refined piece of work.

I'm not sure anyone actually creates a mathematician. It's like showing Edmund Hillary a mountain or giving Elvis Presley a guitar. There are things they don't know when they start, but the stage is pretty much set. I certainly still give a lot of credit to my favorite instructors like Ted Tracewell and Stu Smith, but no matter how many twists and turns my life takes, I always come back to math, and I likely always will.

Sweating the small stuff: Measuring students and teachers.

Reading Moneyball, I've been thinking about how we measure students and teachers and my general feeling is we are going about most of it in a completely wrong-headed method.

At Laney, the big new thing is Standard Learning Outcomes in every math class. I think this is a fairly good system, especially because the amount of material is about half a quiz by my way of doing things. Teachers of a class have some input into what the allegedly important topics are, though in one class I teach regularly, Math For Liberal Arts, a topic I usually don't even cover was the SLO. This class is somewhat amorphously defined, so it's not that surprising that this would occur. In other classes like trigonometry or the algebra sequence, the SLO topics are things I would say are the core of the class.

For me, I almost never teach the same class twice. I'm always trying to learn new ways to present material, and often there are "standard" topics I think have reached their expiration date and new material that makes a strong case for being part of the core curriculum. For example, in statistics, the old school way of doing this was table look-up. Nowadays, a high end calculators and spreadsheet programs make table look-up obsolete. The z-score is now an unneeded middle step between a normally distributed data set and a percentile, which is a shame because z-scores really help define what it is we are trying to do.

I think of both teaching and learning as art forms. Being a person of strong opinions, I have my own ideas about what is good and what is bad, but I haven't come up with standardized tests for what I like. What is it exactly we are supposed to do? Should students become better citizens or better workers or better thinkers? Are we there to instill a love of learning? If so, I can certainly point to successes in my career, but I can honestly point to some failures as well.

It's a thorny problem and I clearly do not have the brilliant solution. I understand the desire to measure teachers and students, but most of the methods we have come up with so far, like the time honored but flawed boxscore in baseball, are doing more harm than good in my opinion.

Sweating the small stuff: A mathematician reads Moneyball.

A friend has invited me to the opening night of Moneyball this upcoming Friday evening and lent me Michael Lewis' book to read. I'm not as keen on it as I was on his more recent book The Big Short, and this is because I know more about baseball history than I know about Wall Street today. Still, Lewis is an exciting writer and baseball is so interesting, even a book with flaws can be endlessly entertaining.

Let me be immodest for a moment. Lewis can appreciate math and I can actually understand it. If we compare math to its nearest (and superior) rival, he's a music critic who can write well and I'm a musician who can write legibly. It's Frank Rich vs. Salieri. It's more fun to read Rich (and Lewis), but Salieri (and I) have some inside information the other guys don't have.

No brag. Just fact.

With Moneyball, Lewis didn't start out with the intention of canonizing Billy Beane, the general manger of the dirt cheap but competitive Oakland Athletics, but that's how the book reads. In an afterword, Lewis explains that baseball insiders hate Beane for the book, not Lewis. Some of them think Beane wrote the book himself.

No one with a brain ever said baseball insiders had big brains.

And that's the point of Moneyball, much like it is the point of The Big Short and The Blind Side and most of Lewis' best-selling non-fiction. Insiders in the systems he studies don't really understand the system, and the outsiders who make honest scientific attempts to understand are widely despised.

There's the obvious and compelling core of every best-seller Michael Lewis has ever written.

Consider Billy Beane, the hero of this story. It is very common in Hollywood versions of "true stories" that the movie star is way prettier than the person being protrayed. I submit that Brad Pitt might be a little prettier than Billy Beane, but he's way too small. Young Billy Beane was a freaking Winklevoss twin, 6'4" tall, lean and supremely talented. Scouts salivate when they see a high schooler like Billy Beane.

Some may actually do more than salivate in private. I have no proof of this, but it is the strong subtext of the first few chapters of Moneyball.

Billy Beane knew the scouts of baseball didn't know shit. His best evidence was that they fought like bobcats over Billy Beane. When he became available for the baseball draft, it was either him or another Southern Californian, Darryl Strawberry, that HAD to be the first round pick that year. Strawberry became an honest to Pete baseball superstar until drugs brought him down.

Drugs weren't Beane's downfall. It was pride instead.

Beane could have played football or basketball, but he chose baseball. Beane hated to fail and hated even more to be shown up in public, and that is a nearly impossible character trait to overcome.

After they are drafted, Strawberry rises and Beane sinks, and the scouts and the best baseball minds are at a loss to know why. Beane gets violently upset when he fails, and he cannot turn this rage into positive action. Strawberry becomes a star in short order, but Beane bounces around, finally becoming roommates with Lenny Dykstra, a prospect with a tiny percentage of the promise Beane has.

The thing is, Dykstra has the small talent combined with the attitude of Babe Ruth. He ignored his failures like they didn't happen and reveled in his successes. Beane's attitude of hating failure is more like Ted Williams or Joe DiMaggio, but not quite at their godlike levels of talent.

Williams and DiMaggio truly hated to strike out, and they changed their way of batting to avoid it. Beane couldn't figure out how to avoid strikeouts and still to be feared at the plate. Had either Teddy Ballgame (good nickname) or Joltin' Joe (very inaccurate nickname) had the same "I don't give a shit" attitude about looking bad at the plate that Babe Ruth had, they might have made a serious run at the career home run record.

Neither did. Joe DiMaggio ended his illustrious career with 361 home runs, barely half of Ruth's 714. Williams, who missed prime seasons due to being a Marine pilot in both WW II and the Korean War, hit a home run in his last at bat, which brought his to a still remarkable 521 for his career.

Back to our main story.

Billy Beane, the failed Adonis, is still a baseball insider, but he listens to the baseball outsiders, the guys who think the statistics have been accurate but useless since the late 1850s.

Not a typo. 1850s. Before the American Civil War when players were not allowed to wear gloves.

I love that Lewis blames Henry Chadwick, a cricket fan from the 1850s, for inventing the "modern" baseball boxscore. There's actually a lot of math of that era that is still considered modern. The difference is that mathematical logic, group theory and quadratic reciprocity are still paying dividends, while the baseball box score is getting in the way of progress.

In Chadwick's original system, a base on balls is an error on the pitcher. Like other errors, it does not count positively towards the batter's numbers, but unlike errors, it now counts as zero instead of negative. It never occurred to him that it might be a skill of the batter to avoid bad pitches and only swing at good ones.

Some people cry in the wilderness that baseball is being mismeasured. It isn't until the 1970s that a guy named Bill James actually has the stick-to-it-iveness to shout this every year, at first to an audience of less than 100 people reading his self-published book.

In Lewis' mind, this is the beginning of baseball's salvation.

More on that tomorrow.

Sweating the small stuff: Some thoughts on math education.

Computers and calculators are changing the education process significantly. Any student who types a paper has a spell checker and probably a grammar checker, but that's no promise they'll get everything right, especially when it comes to homonyms and such, like their, there and they're.

In math, some things that seem very simple to anyone who is even a little proficient can be struggles for students in pre-algebra and beginning algebra classes. A perfect example is writing a fraction problem like

3/5 = ________

and having many students give the answer 1.666666667, which is the correct calculator answer to 5/3. It seem "obvious" to me that small/big must be a number less than 1, but a lot of students try to turn it into a division problem and mix up the divisor and the dividend.

I'm going to be doing some other short posts on gaps in math education many students have. I don't do this to deride the students, it's just that somewhere along the line something relatively simple slipped through the cracks. I don't have the solution for how to fix this, but I do want to acknowledge these problems exist.

I still believe in education... despite massive evidence to the contrary.

In the immortal words of the decidedly mortal Harvey Pekar, "Average is dumb."

For those who need recent proof of this adage, let us consider this Talking Points Memo link to a recent CNN poll of what Americans think about the federal budget.

How much of the federal budget goes to the Corporation for Public Broadcasting, which includes radio (NPR) and television (PBS)?

Less than 1% of budget :: 27% of respondents (correct answer)
1% to 5% of budget :: 40% of respondents (most popular answer and median answer)
6% to 10% of budget :: 8% of respondents
11% to 20% of budget :: 6% of respondents
21% to 30% of budget :: 5% of respondents
31% to 50% of budget :: 4% of respondents
more than 50% of budget :: 7% of respondents
don't know :: 3% of respondents

I marked the correct answer in bold, but it doesn't go quite far enough. The budget for CPB is about 1/100 of 1%, which sounds tiny. It's $420 million in actual money, which sounds like real money to a broke-ass math teacher like me, but in terms of the news and entertainment field, it's pretty damn puny. When the financial crisis hit in 2008, NBC Universal asked the NBC News organization to cut $500 million out of their budget, more than the entire budget for CPB.

So we have 27% who have a rough idea (less than 1% can mean waaaaay less than 1%), 3% who don't know and KNOW they don't know and 70% who don't know, but that doesn't stop them from guessing.

Wildly.

And when we have 7% thinking its more than half the national budget and another 9% thinking it's on par with the defense budget, words fail me.

Let's look at similar numbers for the food stamps program.

Less than 1% of budget :: 6% of respondents
1% to 5% of budget :: 40% of respondents (most popular answer and correct answer)
6% to 10% of budget :: 16% of respondents (median)
11% to 20% of budget :: 13% of respondents
21% to 30% of budget :: 4% of respondents
31% to 50% of budget :: 9% of respondents
more than 50% of budget :: 10% of respondents
don't know :: 2% of respondents

Well, let me polish this turd for a little bit. It's something of an accomplishment that 40% got the right answer, but the right answer is about 1%, so even a passel of people in there could be overestimating the budget by a factor of two or even a factor of five.

But then there's the bad news. One in every ten people think half the federal budget is food stamps. Even worse, two in every nine think the food stamp budget is on a par with Social Security or the defense budget.

I'm not sure how much we are spending currently on sterilizing the stupid, but clearly it's not enough.

The most useless poem in the world, English division.

I before e
Except after c
Or sounded like "A"
As in neighbor or weigh.

So now we know how to spell words in English! Done and done!

What's for lunch?

Hmmm... not so fast.

Of all the rules I learned in school, this one ranks as one of the most useless. I also remember the rules about "silent e", and the poem

When two vowels go walking
The first one USUALLY does the talking.

At least this poem admits there are no hard and fast rules, though it ruins the meter.

If "silent e" always worked, there would rhyme with here and are would rhyme with bare. If the two vowels rule was any good, bear and ear would rhyme.

To any adults learning English as a second language, you have my deepest heartfelt apologies, but I'm in no position to change it. It is what it is.

Back to "i before e". The extra line about neighbor and weigh makes it better, but not perfect. Weight rhymes with eight. So far so good. So how about height?

Oh, you already know the answer.

Short list of e before i with no c and not sounding like "a": protein, feisty, seize, height, foreign.

I'm sure there are more, and I'm sure they will bite me in the ass when I'm playing Scrabble.

Of course, in German there are rules and ZOSE RULES VILL BE FOLLOWED MITOUT EXCEPTION!

E before i sounds like the long "I" in English, as in Einstein and Heidi.

I before e sounds like the long "E" in English, as in Riemann.

I tease the Germans, but seriously, every language has pronunciation rules that make sense once you learn them.

Except for us. And the French.

Think about how people sneer at the French. You can be pretty sure they feel the same about us, but they do it behind our backs.

And don't think we haven't earned it.

Mastery and Memory

Working at the polls last week, I was talking to a fellow old person. Since she was female, it would be impolitic of me to say she's even older than I am, but it would not be false. The topic was young people today, a favorite topic of old people everywhere.

The reason I think my co-worker last week is my elder is because she said when she got vocabulary words wrong, she had to write them 100 times. That sounds more like torture than teaching to me. I think the standard in my day was ten or maybe twenty repeats of each misspelled word.

While I am not against computers and calculators as teaching aids, a lot of kids don't put much effort into committing things to memory. After all, why learn to spell when there is spell check? Why learn basic math when there is a calculator handy?

When I was a lad, I was good at spelling, though you might not believe me when you see the many typos in my blog. My common fault is that I'm a weak typist and lazy editor. On a test this week, my right thumb got ahead of my left hand and I typed "an done" instead of "and one". A spell checker isn't much use when you incorrectly spell the word you wanted but correctly spell something that makes no sense.

This is a significant problem in early education these days. The question "When will I use this?" often expects a specific answer of when the exact skill being demonstrated will be used in a real life situation. Sometimes, the skill the student is actually learning is how to learn.

My strongest memories of grade school are drills learning how to diagram a sentence or knowing the homonyms backwards and forwards. I almost never make a mistake about there, their and they're or yore, your and you're. I am a fully deputized member of the apostrophe police to this day. There was no such thing as spell check in my youth, and it still won't stop someone from typing loose when lose is correct. That is the nightmare of English spelling. If there was a shred of consistency, lose should rhyme with close and loose should rhyme with choose.

Sorry, kid, no consistency here. Learn how to spell or look like an idiot. It's sink or swim in this pool.

A major difference between language and mathematics is how important the foundation is. A good writer doesn't have to be a good speller if that writer can find a good editor. Shakespeare was famously bad at spelling, but brilliant at rhythm, remarkably insightful as a student of human nature and if he isn't the best coiner of new words ever in any language, I have no idea who is. (Examples: Give me precise synonyms for "assassinate" and "apostrophe". I haven't a clue how people expressed those ideas succinctly before Shakespeare made those words up, among dozens and dozens more.) James Thurber, who wrote some great and funny essays about grammar, freely admitted his first drafts were terrifyingly clumsy.

You won't get to be good at math if you can't do arithmetic. I have a lot of students who don't know if 3/4 should be .75 or 1.333... I tell them that if the top number (numerator) is less than the bottom number (denominator), the decimal should be less than 1. It goes in one ear and out the other.

It's pretty well established that children need to learn language early, probably before the age of five, or they will not understand grammar rules, synonyms and context. I have a hypothesis which I haven't seen tested that committing stuff to memory helps you commit more stuff to memory, like exercise makes you stronger in the long run. The other important component of a good memory is the relational end of it, when you can access a memory from multiple directions. I'm not sure exactly why some people are better at that than others. I know I've had times in my life when my relational database failed me spectacularly, but I haven't been able to come up with a testable hypothesis for why it happened and the best way to avoid it in the future.

I'll be blunt here. I sit on top of a mighty mountain of mathematical knowledge and most of my students are barely in the foothills on a cloudy day, completely unaware of the mountains they have yet to climb, or more likely never will climb. How do I teach mastery to them? I can teach them a few cute tricks they may have never seen and maybe, like me, they'll decide they want to see more. I can give them some vocabulary and grammatical rules, but will they have even a vestige of mathematical insight?

When you see it work, when you have a thorny problem and you see the path home, it's like heaven. Those who haven't done it may not believe me, but it's prettier than Indira Varma when the solution to a hard math problem falls into place. It really helps to have a memory that makes getting to the end of a mathematical idea no harder than finding your way to your childhood home from a few miles away. I am convinced you get that memory from exercising it again and again when you are young. I worry that we have a generation where that kind of exercise is getting rarer and rarer.

Some articles about math education.

The standard view is that American kids aren't as good at math as kids in other countries and are learning less than we did "back in the day", but from my own experience I can say that our educational system currently expects more people to know more math than at any time in history. AP Calculus was pretty rare in my era, and expecting high school students to get through statistics or a beginning programming class was absolutely unheard of back before 1973 when the integrated circuit started the computer revolution. When I teach linear algebra at Berkeley City College, I can expect a lot of kids from Berkeley High School sitting in on what is still viewed as a sophomore level college class. Some material has been "dumbed down" without question, most notably reducing the emphasis on proof in geometry. As someone who was actually pretty good at it, I'm not exactly sure when we should ask students to sink or swim with the concepts of proof, but I think it's probably not something we should force on all kids at the age of sixteen with the threat of not graduating high school.

Friends send me links to articles about math and math education. My friend Ken sent me an interesting article from the New York Times quite a while back about the correlation between mathematical success in school and an early talent for estimation. As the article states, the skill of looking quickly at a picture and deciding if there are more blue dots or red dots is math brought down to the level where the test could be administered to lab rats, but people who show an early skill at this tend to do better in math than people who don't.

My friend Art sent a link to a paper done by some researchers from his alma mater Texas A&M that states American students somewhere in their early education are not grasping the concept of the equal sign as well as students from other countries. If the problem is stated as 3 + 4 + 2 = (____) + 2 for example, many students will add all the numbers from the left side and put a 9 in the blank, when the correct thing to do is just add the 3 and 4 to put 7 in the blank. I see things like this in my classes that appear to me to be about reading comprehension, especially on tests. If the instructions say "round to the nearest tenth of a percent", I will invariably have some students ask "Do you mean to the nearest tenth?" It's almost as if they run out of gas before they get to the end of the sentence.

It raises a question relevant to all education, not just math education. Most people who teach a subject decided to do this job because they are good at the subject, and with disciplines like math, music and athletics, innate talent means some people will be better than others even though they put in about the same amount of time in study or practice. It can be hard for the innately talented to get ideas across to people who don't have the same gifts, much in the same way as it would be for a person without colorblindness to explain green to someone who can't tell green from blue.

The struggle continues.

I believe in education, despite massive evidence to the contrary.

Over on the Huffington Thing, as my blogging hero Princess Sparkle Pony calls it, there's an opinion piece railing against VitaminWater, which is currently being sued over misleading advertising. I know next to nothing about the stuff, so I decided to snoop around the Interwebs for a while.

It is bottled by a company called Glaceau, now owned by Coca-Cola. The advertising includes a lot of basketball players (Steve Nash, Kobe Bryant and others) and a few years ago had ads featuring the rapper 50 Cent, who is known for his physique as well as his rhyming skills. Besides vitamins and water, it also has plenty of sugar, though only about half as much as Coke, so it could be seen as baby steps towards a healthier lifestyle.

I found this article over at ScienceLine written by Christopher Intagliata, a website maintained by New York University with the stated purpose of science more accessible. The major point made is that several of the vitamins in VitaminWater are completely pointless in a fat-free drink because they are fat soluble instead of water soluble. For example, putting Vitamin D in milk makes some sense because milk has fat content and D is one of the fat soluble vitamins, along with A, E and K. So unless you are drinking VitaminWater to wash down a burger or potato chips (not a recommended meal, by the way), many of the vitamins in the drink for which you paid good money are going to take the quick trip through your body and into your municipal sewer system without stopping over in any of the places in your body where it might have had some nutritional value.

So far, so good. Useful scientific information without a lot of difficult jargon.

Then I read the comments.

Where's teh stupid? You're soaking in it. People love to drink it or somebody told them it gives you cancer. Not one comment in fifty deals with water soluble vs. fat soluble. Just when you think you've read the stupidest comment possible, along comes another comment even more deeply stupid.

In the words of my professor Victor Manjarrez, we don't deserve to survive as a species.

N.C.A.A.: No Care for Athletes Absolutely

At Laney College, the football program has expanded from sixty players to one hundred players in the past few years, a time that has seen major cutbacks in classes across the board and an act of blatant theft by management against the part-time professors by taking $400,000 owed to about 600 workers and using it for Odin knows what.

It's galling to see this increase in funding for sports when budgets are getting slashed for teachers and facilities, but that is not the worst of it. In the past, only student-athletes who wanted to go to certain schools were forced to pass Introduction to Statistics. For example, all the state schools in California required that, both in the state schools, where Fresno State, San Jose State and San Diego State have programs that have sent a few players to the NFL, and the University of California schools, where Cal and UCLA have several alum who turned pro and UC Davis is starting to see some success along those lines. What this meant for me in the past was I had some students from the football team in my classes and most of them were serious about passing the class, as well as having a reasonable shot at passing. Those whose math skills weren't strong enough did not have to attend.

In steps the NCAA. They now require statistics for all student-athletes. This summer, this meant fourteen football players trying to pass a six week summer session course. The six week courses cram the same amount of material designed to be taught in a full semester into classes taught four days a week. It requires commitment and punishes people who have weak math skills. There's very little time for extra studying to catch up. The vast majority of the football players weren't ready and the attendance record was very bad. Worse than that, many were caught cheating on tests and got zero when that happened.

I don't think of statistics as a "hard" class. Technology has changed the nature of the course completely in the last fifty years. Back in the sixties, John Tukey came up with some very clever workarounds to avoid having to find the standard deviation for sets of data with many entries. Over the past few years, I practiced several times taking the average and standard deviation of sets of 40 numbers, and without a calculator or spreadsheet it took me between an hour and an hour and a half to find those values, and I sometimes got the answers wrong. With a cheap calculator, it takes less than five minutes and maybe a minute to double check that I input the numbers correctly. If the numbers come from some website, it takes less than a minute with Excel and I don't have to double check for entry mistakes.

Even with technology making the class easier, the class takes someone to be fluent with numbers and a lot of students leave high school without that fluency. Many people who whine about our educational system are equally incompetent with numbers, but that is equal parts problems with education in the past and people long out of school letting their brains go to seed.

I don't expect the NCAA to rescind this silly policy, and Laney gets publicity by having a good football team, so both the factors helping to make my life a living hell probably aren't going away. I just wanted to vent a little bit.

Good thing I have a blog.