Small towns, businesses, and ambitions; obscure books;Jedi barbers;midlist writer craziness;pepper soup, and why you can't nice guy your way into a date with the Luck Fairy. And nothing about math.

Longtime readers, or insomniacs who like to read a lot of back posts, know about my "seven observations" posts, where I list seven things I've been thinking about and then riff on them till I've produced something that may be converging toward coherent.  I guess newcomers and anyone who wandered in by accident are about to find out.  In general if the title is  a seemingly random list of stuff that doesn't appear to add up to anything coherent, probably it will be one of those posts. If the content is, it's really one of those posts.

Okay, let's go with that list:

1.     Officially the US Small Business Administration  says that to be a small business, "the business must have no more than 500 employees for most manufacturing and mining industries, and no more than $7 million in average annual receipts for most nonmanufacturing industries."  So with the possible exceptions of J.K. Rowling and a handful of others, and maybe some publisher-packager boiler rooms, pretty much all fiction in the United States is produced by small businesses, at least as those nosy government types define it.

2.   It's an old number and almost certainly is lower now, but back in 2006, when paper books were really pretty much all there was, Publisher's Weekly reported that the average book in America sold just under 3,000 copies over its whole lifetime. A common rough-and-ready rule is that most book copies will average about 3 readers before ending up in the trash, a book hoarder's stash, or an MFA art student's collage. We talk all the time about our "communities of readers", which means people who have read the same work and might talk about it together.  So figure each published paper book creates a community of fewer than 10,000. This also fits with the marketing concept of "base", the number of people who buy most of the work of a given author based on the name alone. Not all publishers calculate base and many try to keep it secret, but a typical number for a traditionally published mid-list writer (5 or more books out, no best-sellers, still getting offers but not increases in advances for the next book) might be around 10,000. So those "communities of readers" tend, from two different measures, to be about 10,000 people or so.

3.   The Office of Management and Budget, because so many policy decisions are made based on its data, has put a lot of effort into categorization of villages, cities, towns,etc.  North American geography is pretty odd by the standards of the rest of the world, but OMB's criteria break down into big, middle, and small cities, the latter being 50,000 people and up, with every county from which more than 25% of the population commutes into the central area being counted as part of the city; "micropolitan counties," which are counties with at least one town larger than 10,000* where more than 75% of workers stay in-county; and "non-metro," which are counties that have only "small towns," defined as towns with less than 10,000 people.

4.   Combine all those definitions and here's a reality: nearly all fiction writers out there, including the successful ones, are small businesspeople working for a community that isn't much bigger than a small town.

5.    I have always observed that the best and worst businesses I've dealt with, in a lifetime as a worker, customer, consultant, and service provider of many kinds, are small town small businesses. The good ones are better than any bigger business you might find in a larger city, but the bad ones are awful in ways no other business could dream of being.

6.   In my experience the reasons why some of them are the best, and the reasons why some of them are the worst, are very often the same reasons. A small-town shoe repair business is totally controlled by the owner, and if he really loves fixing shoes and takes pride in it, everything about the store will be devoted to fixing your shoes better than they've ever been fixed; but if it's the business he hates but inherited from his father, and he wishes to god he never had to see another fucking goddam shoe or talk to another spoiled customer who thinks he knows what he wants fucking ever again, and goddam it the business isn't making enough money and people are always acting like he owes them all kinds of things when all he does is write down the order and ship them to Taiwan for somebody there to fix ... well, your feet are not going to be happy.  I love diner food and my favorite diners are mostly in dots on the map; so are most of the places that appeared to be trying to poison me, once the stone-cold food finally arrived in the greasy paws of the apparently tubercular and suicidal waiter.

7.   So, I found myself thinking, what's it mean for literature that it is being produced by small business people working for small communities?

That was sort of seven, anyway.

Here goes on what it means .... and no promises I'll find anything or you'll agree with me if I do.

§

"Willy was a salesman. And for a salesman, there’s no rock bottom to the life. He don’t put a bolt to a nut, he don’t tell you the law or give you medicine. He’s a man way out there in the blue riding on a smile and a shoeshine. And when they start not smiling back—that’s an earthquake. And then you get yourself a couple spots on your hat and you're finished. Nobody dast blame this man. A salesman is got to dream boy, it comes with the territory." -- Arthur Miller, Deathof a Salesman. One of a dozen candidates for the great American play. If you didn't read it in school, go back and kick somebody. Then read it, or better yet, see it. 

Ever seen what happens when somebody on Yelp! says the pizza was greasy and arrived cold at Honest Fred's New and Used Pizza in Resume Speed, West Dakota? Depending on Honest Fred's personality, you may see abject grovelling and a promise to pave the customer's driveway in pizza for life if he will please-please-please just come back and give them another chance; or an immediate bombardment of testimonials extorted from friends and relatives of Honest Fred, ("I have been the only dentist in Resume Speed for thirty years and I do not see more than one broken tooth per year I can attribute to Fred's pizza") or outright sockpuppetry ("Honest Fred's Pizza is like a vision of the divine, an anonymous archbishop"); or of course Honest Fred absolutely losing it ("I remember you! You were the customer with the ugly wife and the foul-mouthed nose-picking children who undertipped my daughter and left stains on the chairs, and you better take that down or else!")

Ever notice what happens when non-bestselling writers (and even some at the low end of bestselling) get bad reviews, or when someone says something that might cause somebody not to buy their books?

Well, yes, that.

Because the actual customer base is so small, there's a real fear that having a bad word or phrase attached to the author -- whether it's "historically inaccurate," "racist," "ungrammatical", "made me feel dirty to read," or "no, just no"** — might be enough to put an end to a career, the way that a bad Yelp! review might make just enough cars passing by on the interstate decide to go ten miles on to the nearest Pizza Hut.  There can be an overwhelming feeling of "it's their opinion but it's my living," and people seldom behave well when they feel powerless. Hence the wise advice from writer-friends who have not gotten slammed lately: ignore all reviews, learn to read any review as just an abstract bit of marketing data, or don't read them at all. Take nothing personally.

Of course the same writers who give that advice will need it again themselves, probably.  When the heart is pounding with, "What if a school board bans my book because one anonymous person said I was anti-Jesus or anti-gay or both?" it's pretty hard to remember: one reader's opinion, read by almost no one (even if it's in a major review outlet; the vast bulk of people who read for pleasure seldom or never read reviews).

Pretty much every "How to Be A Real Live Writer Like Me" website, book, seminar, etc. outside there will tell you it's important to grow a thick skin, or just not read reviews, or work on either not caring or not knowing about the bad things people are saying about your work.  Most of them, though, don't mention the real reason: because way down there in the existential am-I-gonna-make-it level, anything bad said about us or our work out in public scares the living piss out of all of us.

You can be bitter about it like James Thurber was in "A Very ProperGander." You can try to shrug it off like most of us do, more and less successfully.  You can lose your shit all over the Intarwebz and go after your critics like a raving nut, which we almost all hope not to do.*** But that feeling that one fast-spreading ugly word about you can be the end of the world never goes away.

§

All my life I'm looking for the magic
 I've been looking for the magic

-- Dwight Twilley. NOT a great song. You don't have to read, see, or listen to it, as far as I'm concerned. Though I'm sure Dwight Twilley would forgive you if you did.

Is there any of you out there who has ever really liked a really obscure writer?**** And have you ever noticed that there was something you thought was pretty wonderful that no one else, or almost no one else, seemed to love like you did?

I think that's the common experience of readers everywhere.  There's only so much literary attention to go around, what there is seems to be rather like a Zipf distribution; for every Harry Potter there are ten squidzillion other boy magician stories (my favoriteis Zilpha Keatley Snyder's Black and Blue Magic,  which isn't even her best book, but I'm not much of a boy-and-magic kind of person).  Ben-Hur and Quo Vadis and even Rosemary Sutcliff's Aquila family YAs stay in print forever and shape a million kids' vision of ancient Rome; ForFreedom and for Gaul gathers dust on a few obscure school library shelves, and George Finkel's Watchfiresto the North (Twilight Province in the UK)  is something you pretty much have to go to a rare book dealer for, but I can testify that they absolutely fired my 13-year old imagination (which was going through a serious Roman kick) every bit as much as their more famous cousins.   I've had an amazingly fine time of a sea adventure with Stephen Sheppard's For All the Tea in China,  as much fun as anything Sabatini or C.S. Forester or dare-I-say-it Patrick O'Brien ever wrote. I've spent memorable and pleasant evenings reading a fine cozy mystery (and I usually hate cozies), AllEmergencies, Ring Super and a quirky little crime novel, Jen Sacks's Nice, either of which would fully deserve the kind of attention that Lawrence Block gets for Bernie Rhodenbarr or Elaine Viets for her "Dead End job" mysteries.  Just this evening, as my spouse was looking for something historical and romantic, I handed her a copy of Ciji Ware's Wicked Company, which is describable as "theatre history fiction"***** and which I would figure any Diana Gabaldon fan would gobble up, but it's not even Ciji Ware's best known book by a long stretch.

Now, aside from causing some of you to check off a list of obscure books you've never heard of but think sound kind of interesting, the point of that exercise is this: every year there are some pretty damned fabulous books that roll out the publisher doors and sink without a trace. And equally truly, every year there are some books that for no better reason, and with no more publicity, break out and burst onto the best seller lists—all of us in the business know something of the history of The Hunt for Red October, 'Salem's Lot, The Godfather, Forever Amber, Gone With the Wind, To Kill a Mockingbird, and all the rest, because after all hardly anyone starts out as a best-seller, but we all have dreams and we like to know it happened before and could happen again.  Somehow, one costume drama breaks out and takes over the bookshelves for  a decade; one  vampire novel (at a time when the genre was thought to be dead and staked) comes bursting out; one "desk jockey intelligence analyst has to become a field agent" thriller storms through the best-seller lists.

          And this breeds a slightly pathetic belief in magic among us small business owners serving small communities, because that's the very natural response to having your life depend on something unpredictable and just outside your control.  The Jaycees decide to rent your back room for their first-Tuesday breakfast meeting, five of them fall in love with your  Farmer's Scramble, and suddenly your restaurant is thriving.  You get the Ace franchise for a hardware store and open up the month before a major construction project starts five miles up the road, and then a hailstorm hits the county, and suddenly you can't keep basic tools and materials in stock; by the time the rush is over, you're the hardware store for a fifty mile radius.  Your Just Like Home Made jams take first prize at the county fair, and you hand out a ton of samples, and three prominent local Ladies Who Lunch start talking them up ... any of that can happen.

Or your first week open, a new teenage employee posts a selfie of himself venting his nose into your pies; or the local Wal-Mart expands its hardware section the week before you open and beats you with prices you can't match; or you staked it all on your brilliant huckleberry jam and the guest judge is allergic to huckleberries.

So the small businessperson gets out there and tries to make things happen, by means rational and not, and because so much is out of control, can become obsessed with almost any aspect of the business. Maybe just the right sign, maybe working just the right contact, maybe ... in a way not too different from obsessed loser guys trying to attract the pretty girl about which they know nothing, they're looking for that one thing to let her see I'm a Nice Guy.

Her? Her who?

Let's just call her the Luck Fairy.

Ever seen a writer go berserk about awards? or about review copies? or promotional contests or newsletters or business cards or tweets or ...

Somewhere out there, there's the magic. Something will make it happen. Ten books ... twenty books ... in the case of one guy I know******, 31 books .... the next one, though, that's gonna turn it around, because it'll have the magic. You'll figure out a way to charm the right delivery drivers, the way Jacqueline Susann did with Valley of the Dolls. You'll tell a bunch of great stories to a publishing exec and your book will be bought without an outline, like Mario Puzo did for The Godfather. You'll die and your mother will lay siege to every press in America to get your masterwork published (I don't think that was John Kennedy Toole's conscious strategy, actually). The president of the United States will mention that he really likes this obscure series of books about a spy named James Bond ...

So you chase awards, or worry about whether they're fair; and you try to get celebrities photographed holding your book; and you go to conventions and bomb the hell out of the freebie table with clever bookmarks; and one way or another, you do the dance of trying to attract the Luck Fairy, like the invisible Nice Guy soaked with flop sweat waiting for  a chance to talk to her. 

Because ... if you court the Luck Fairy and she spurns you, at least you tried. Heck, you were a nice guy. It wasn't fair. She didn't give you a chance.

Whereas, if you just leave it up to her, your fate is in the hands of the most capricious and indifferent power there is. Because nobody really knows what  the Luck Fairy wants.

§

Another thing about small town small business people: they either really know their market or their market really doesn't have much choice, and either way can work, and either way can be a sudden catastrophe.  If, as a barber, you know every head in town, and what would look best on it and what the most important people in that person's life like and what the insecurities are, your continuing attention means they'll be back, always, over and over. But if you're the only barber in town, maybe everyone's in a mullet, because you really know how to cut mullets, and that works too, for a while.

When a new barber comes to town, if you're the one who knows the local market, you're basically okay. Some people will go to the new barber, but mostly your customers will stick with you.  The new barber will take a while to win customers over, even if he's very good, and by that time you'll have retired or upped your game. You can even afford to be friendly with the new guy; there's enough hair for all of you, and you can find ways to split the market profitably, and even perhaps expand it. Maybe he knows how to sell speciality dyes and shampoos that you don't have much experience with, and he'll share his expertise, and you'll share your local knowledge, and soon the town will have two good thriving barbers.

On the other hand, if you're the mullet specialist, you're through. And you're likely to think, for the rest of your life, that everything was fine back when you were the Old Republic's One True Jedi Barber, until a Sith Barber came in and stole all the business.

Which, again, is part of why there's such a polar response to the next generation of writers among the not-quite-has-beens-cause-we-never-was writers.  Either you figure you're good at what you do (correctly or not) and you can still find a niche, or you think the new lot are ruining it for everyone (even if, or especially if, you were pretty good but fashions are just changing).

§

One of my first employers -- I swept out his shop when I was in high school -- was a jewelry store owner who taught me a marketing secret I still treasure.  "There are two mistakes you can make with your market. One is to ignore it. The other is to suck up to it."

This was how he explained that he always listened very carefully to what people were asking him for, but if they were asking for something that was going to look wrong on them -- or saddle them with too much debt -- or in general cause them to regret their purchase eventually, he'd politely tell them it was a bad idea.

More than once, I've been saved by a waiter who said, "Um, that's on the menu, and I'll serve it if you want, but ...."  Years later I sold credit card services to a restaurant owner who asked experienced waiters if they'd ever said anything like that to a customer. "If they say they have, it's a big thing in their favor," she said. "Naturally I tell them that if we've got anything like that on the menu I want to hear about it. But while I'm deciding whether to keep it, change it, or replace it, I want my waiters to be looking out for the customer experience. If I decide they're wrong, I might tell them to say, 'Well, I just don't like ...' or 'It's very different from ... ' so that they don't have to directly recommend something they don't like.  But if you make someone sell something that they think sucks, they won't sell it well, and the customer will be primed to hate it, and that does no one any good."

That's a small obsession of mine that I'll re-echo here: the worst thing that can happen to a book, often, is to be sold as some other book. That's why in my early career, when people were sticking that "next Heinlein" label on me (and several other writers, since Heinlein had just recently died) , I gritted my teeth a lot********.  Because, honestly, people who opened up my books were not going to find a Heinlein novel inside, and if that was what they were looking for, they would start off disappointed.  It's also why I really detest having a cover that is aimed to sell well but not to sell my book; reader expectations are set by that cover and if they're not expecting what they get, they react like the legendary man eating in a French restaurant for the first time, who discovered snails in his escargot.

For the most part, small stores will never be Wal-Mart, two-chair barber shops won't become Great Clips, your little Mexican restaurant is not going to boom into Taco Bell. And you won't be happy unless you can love that fact, unless you'd rather be who you are and do what you do than be really, really big. (Being happy after becoming really, really big is not anything I know jack about. Note to Luck Fairy: I would be happy to find out).  It's nothing to do with lack of ambition; plenty of splendid writers were economically marginal their whole lives, and are now remembered only by a few of us, despite their own best efforts. It's just that some of us don't have the knack or luck or whatever for big success; we're not "too different" or  "too bold" or "too ahead of our time," we just didn't find a wide enough readership to be big. Nor were we too honest to sell out; most big-selling writers do things that annoy their most devoted fans from time to time, just because that's the way of writing, you can't please every reader all the time even if you try, and trying is to do so is hard work to no purpose.

 §

Old joke: a man new to town goes into a local diner and asks what's good.  Everyone, the waiters and customers, immediately says "Always order the soup of the day here, it's the only place with good soup in town." So of course he does. But on the first bite he finds himself gagging and grabbing for his water glass; there's so much pepper that he feels like he's just annoyed a policeman.  The waiters summon the cook who comes out and says, "Sir, I hear you don't like the soup. I'm really sorry. Wasn't there enough pepper?"

Notice that the diner's fortunes would not be improved by reducing the pepper; it's what everyone comes there for. You've got to be willing to lose some customers because you don't make what they want. You probably should name your place House of Plenty Pepper, and label all the soups "... with super pepper!", and in general let people know that's what you sell. You definitely shouldn't let your advertising people talk you into selling them as "mild and creamy"  just because they hear that mild and creamy is in this year. But, dammit, if you make awesome pepper soup, make it, and do your damnedest to let all the pepper soup lovers know that's what you make.

§

Well, that's quite enough of that. I don't seem to have reached a conclusion. And I don't know that I've said anything very interesting to anyone but me. But there it is.

Was there enough pepper? I hear the Luck Fairy really likes pepper.

 §
*the "micropolis," a word I've got to use in a story one of these days
**to quote from some of my own 1-stars
*** but understand painfully well when one of our friends does
****That guy in the back who just said, "Yeah, you" -- thanks, I think
*****I used it sometimes as a text when I taught theatre history; not only does it give a very accurate picture of 18th century London theatre, students actually read it
****** for radio call-in self-help, or an advice column, this would be phrased as "I have this old friend ..."
*******  And I've heard from several of the others that they did too. For a while there in the 90s it was Gritfest among youngish white male SF writers

Why is school so popular and learning so not?

This is an outtake of sorts from Singapore Math Figured Out for Parents.  Sometimes I whack out a passage in white heat, when an idea seems important, intending to come back and turn it into something that fits the tone of the work.  This is one such passage.

But I don't think the ideas in it will make it into the finished book; they are my ideas, it will be my book, but I doubt that ultimately they will belong together.  I kind of think they won't. Certainly if I decide this point is vital to the book, I'll have to put it in more temperate language. So when I hit that point in the outline and re-read the text from months ago, I thought, yeah, out with it. That's why I have an outtake bin, and that's why the outtake bin is usually just Text Purgatory before being sent on to Bit Heaven.

But when I went to cut it, I thought, no, I don't want to lose these entirely.  So here's a small random slice of the kind of thoughts that lure me down rabbit holes, as I keep trying to pursue that question about what the best way to teach math should be.

§

In terms of performance and readiness, the Singapore Math approach beats all the things you are likely to have encountered in the great majority of American schools, from the strictest math-facts-drilling Sister Mary Knucklewhacker to the loosest hippie-ish "I'm Bruce, I'm like, your guide to math discovery. Let's just look at these numbers and feel positive today, 'cause numbers are, like, the cosmic dance of love and harmony. There's even a thing called a harmonic function."

My guess is that although Singapore Math is very worth talking about, since the main point of American educational debate is to secure funding and ongoing employment for the academic partisans of the approach the speaker champions, it is quite likely that conservative politicians will go on running for school board on a platform of "make them learn shop and retail arithmetic so Grandpa will know what they're doing," and liberal politicians will persist in the "trust the educators (who mostly aren't very good at math) to care for your children." And neither of those positions will have much to do with Singapore Math, but its fate in our schools is apt to be decided by that pseudo-debate anyway.

What if we thought about what really matters in the math education debate, in the very long run?

The real problems are two.  One is that Americans don't know enough math to know what math is actually good for. We can only fix that problem over generations, as each generation gets a bit better clue than its parents and demands somewhat better math instruction than they themselves received. 

The more serious, nearly ineradicable problem, is that as a culture we like school a lot but we're not very comfortable with learning. 

Think how well school fits with our values and how badly learning does.

School strives to treat everyone equally; learning makes people unequal because they learn different things (by choice or chance), at different speeds, and in different quantities. 

School provides comforting routines -- you can count on kids making hand-tracing turkeys for Thanksgiving, they're probably reading at least some of the same stories that you did when you were a kid, the cliques are mostly the same, everyone still complains about school lunch, and although the person occupying the niche changes, the class clown, popular girl, all-round achiever, cheerful jock, bleak-spirited artist, and so forth are eternal. Learning introduces your kids to things you never heard of, suggests constant reappraisal of the received material in light of new knowledge, and very often even suggests that there are new people to be and new ways to be them.

School gets people ready for slots in society; learning equips people to climb out of them. 

School, whether it intends to teach tolerance or chauvinism, orthodoxy or radicalism, is built around students repeating back what they're told, and evaluates them on the quality of that nth-generation copy; learning is about acquiring the authority that comes from one's own well-prepared mind. 

Ultimately, school is a comfy place of routines and fitting in; learning is demanding and frustrating and may or may not ever pay off, and when it does pay off, it might very well decide to pay the neighbor and not you, if they made better choices or just did a better job of learning.

No wonder most people, in their hearts, prefer school.

And no wonder it's very hard to keep the school from blocking or damaging the learning.  To learn some things, intensive drill and memorization is needed, and that breeds a sullen lack of enthusiasm in an environment that likes pep rallies and group singing. To learn other, different but equally important things, quiet isolated reflection and intense concentration is needed, and school is above all else a social place. The graceful and always varying cycle of observation-analysis-synthesis-deconstruction-reobservation falls afoul of the orderly locksteps of read-regurgitate-forget, plagiarize-write-collect-credits, or question in, answer out, like a couple of champion rollerskate waltzers on a floor full of people doing the Electric Slide. School's necessary drive to hammer a few testable round pegs into high-scoring square holes -- the endless game of "all you need to know for the test is" becoming "all you will ever know" becoming "all you will know for about a week" -- distorts and warps the processes people learn by.

Some people who love learning anyway bend school to their purpose; that, I think, is what can be done with Singapore Math. A few people who love learning and can't stand school just go somewhere and learn, and God love'em for that, they're the best hope our miserable species has. But the great majority, who would rather not learn, likes school just fine. It's a great place to not learn.

Sort of a progress report on Singapore Math Figured Out for Parents, and a whole lot about why I think it's important.

The work on Singapore Math Figured Out for Parents, which is my book about exactly that, is proceeding very nicely, and I thought I'd give a bit of progress report here. For those of you who like the social commentary essays or want me to talk about my science fiction writing, all things in time—I'm trying to maintain a rotation. I'm not a brand. I'm trying not to become one. I'm probably going to be something other than a brand, and when I become that, I'll pretend I became it on purpose.

Meanwhile, in my non-brandish kind of way:

Quick catch-up on what this is about: the Singapore Math system was developed in that nation in the 1980s, and has undergone continual development and improvement since that time. In the international math achievement rankings, the top 5-6 nations for the last few years have consistently been places that adopted Singapore Math a decade or more previously (as you might expect, students who start out in Singapore Math reap more benefit than those who have to cross over when they're older). Almost entirely because of those international statistics, many high-achievement-oriented charter schools in the United States have tried to adopt Singapore Math in the last few years, with varying degrees of success. Some mostly-affluent public school districts are in the early process of adoption, and a few of the charter systems that are dedicated to raising student achievement in low income students and/or students of color are exploring it as well.

Even if your kid's school is not going to Singapore Math directly, it's going to get closer to it. The incoming Common Core math standards have borrowed some material from Singapore Math. Furthermore, the necessity of teaching to the test in the present climate of No Child Left Behind plus Common Core standards has caused the main Singapore Math publisher in the United States to bring out a line of Singapore Math books which are "aligned with the standards." *

Singapore Math is better math for elementary students, but it can't be adopted by just handing the teachers copies of the new textbooks and telling them to stay a chapter ahead. That's the main thing I'll be talking about later on in this piece—why it's better and why it's also hard to implement. For some parents trying to help kids with homework, it is somewhere between terrifying, confusing, and enraging.

Hence my project: a book that figures out this Singapore Math thing for parents. By figuring out, I mean several different things:

•figuring out why your kid's school is changing to Singapore Math, or might, or should

•figuring out how Singapore Math is going to make your kid much more math-proficient; there's a reason it works, and a reason it works better than approaches you may be more familiar with

•figuring out why they do that**

•figuring out how to help your kid with homework

and

•figuring out whether your kid is actually getting the benefits of Singapore Math, or just being pushed through a different set of worksheets.***

One way to my conclusion: reading and theory. Lately I've been polishing and clarifying that first part, about how Singapore Math is the better way to teach math. Since to write it, I have to understand it myself, much of my recent reading has been in understanding the deep reasoning that underlies Singapore Math, and the fundamental problems with the alternatives.

The tradition of arguing about how kids ought to learn math goes back at least to Reverend Thomas Vowler Short in 1840, accelerating into a full-blown uproar by the turn of the twentieth century. **** So lately my research reading has been devoted to getting caught up enough to say something reasonably intelligent (or at least excusably not-stupid) in the long-running discussion about how people in general and kids in particular ought to learn mathematics. I've read a great number of highly influential books that only experts have ever heard of—sometimes feel like I'm reading the secret history of elementary school.

Where it has all led me is to a much deeper conviction that:

• the Singapore Mathematics methods are flat-out the best system ever devised for teaching mathematics to students whose abilities are in the range from about one standard deviation below to about two standard deviations above average, which embraces about 80% of all math students.

•Singapore Math is better for a reason that is subtle, complex, and, to use a scary word, deep—not as in "deep philosophy" but as in "deeply embedded."

Another way to my conclusion: practical experience. In the last few months, this has also been confirmed by personal experience. My wife is a reading and math intervention specialist; she helps kids who are having reading or math problems get back on track before they fall too far behind. She has a tutoring business on the side which is usually booked up with a waiting list, and since my math background goes a good deal further than hers, and she gets occasional calls from parents who are mainly worried about math, she started working me in to cover math tutoring on more advanced subjects, as another pair of eyes while she was administering diagnostics, and in general to help out on math interventions.

Naturally enough, since I've been spending months understanding what's up with Singapore Math, I reached for that toolbox, and I've been delighted with the results. I'm a reasonably good tutor—I know the math, I know the educational theory, I get along with children, I have a large bag of tricks for getting the math and the kid onto better terms with each other. But with the Singapore Math concepts and approaches, I'm a much better tutor, and kids who once seemed hopelessly blocked are moving ahead fast enough to eventually catch up with and pass their classmates. (It's also a major kick to hear them say, "I like math," sometimes in a tone of astonishment, or, to quote one of them directly, "It's math but it's actually kind of cool.") I've said for many years that the ability to use math well is a basic human gift like poetry, dance, music, storytelling, drawing, dressing well, making small talk, coding, or cooking, something kids should be able to do competently and confidently, and appreciate intelligently, by the time they grow up.

In the short run, I'm taking on much more tutoring work. As I coach more kids through their personal math walls, I learn vastly more about how Singapore Math works at the level where ultimately any system of math instruction has to work: in the mind of the individual kid. I'll end up with a better book because of that.

But in the longer run, here's what I've really learned between the reading and the tutoring experience: Singapore Math is the one system of math instruction that really understands and uses the deep relationship between procedural proficiency and conceptual understanding.

The meeting of theory and practice: why Singapore Math is really better.

Quick definitions: procedural proficiency is the ability to execute an algorithm quickly and accurately; it's quite literally know-how. If you can do a long division of a 4-digit number into a 9-digit number, keeping the decimal point where it belongs, out to 6 digits of accuracy, in less than 2 minutes, you are more procedurally proficient at long division than about 95% of American adults (and about as procedurally proficient as a run-of-the-mill Japanese adult, or a top-of-the-first-quartile Singaporean). There are several components to procedural proficiency: knowing which algorithm goes with which problem, remembering all the steps correctly, and executing each step quickly and accurately. If you know how to hand-extract an nth root, you're more procedurally proficient than someone who only knows how to hand-extract a square root. If you know four ways to find the roots of a quadratic equation in one variable******, you're more procedurally proficient than the guy who only knows the quadratic formula. If you know the inside-out pattern for multiplying two-digit numbers, but you sometimes reverse the inside and outside products, you are less procedurally proficient than the person who never does. If you've got multi-digit lattice multiplication down cold but have to stop and count out any time there's an eight or a seven, you're less proficient than the person who knows the whole multiplication table.

For our purposes here, procedural proficiency applies to any procedure and any problem. Whether a student is doing division of whole numbers by counter-rectangles (a method which especially irritates some parents) or by short division (most parents don't even know there's such a thing nowadays), if he's doing it quickly and reliably, he's procedurally proficient at it. If a student always checks to see whether the coefficients of x¹ add up to zero and uses the trivial ±√c/a when they do, that's a procedurally proficient decision even if he doesn't know the quadratic formula.

Conceptual understanding is being able to make a simple mathematical argument about why an algorithm works, why a thing is true, or in general, "why." If, off the top of your head and without having to think about it, you can quickly and clearly explain why, to divide a fraction by a fraction, you invert the divisor and multiply, you've got conceptual understanding. If you can prove the Pythagorean theorem or that there's an infinite number of primes, you have conceptual understanding of those ideas, no matter how slowly you use the Pythagorean algorithm to find the diagonal of a rectangle or how difficult you find it to do a simple factorization.

Traditional methods: going really fast till you sock into that wall. Those two concepts are the heart and soul of why teaching mathematics has been such a thorny problem, ever since Reverend Short first made a good guess on the subject. Young kids love patterns, rhythms, repetition, and so forth and learn them very easily (consider clapping games, nursery rhymes, songs like "B-I-N-G-O," games like hopscotch and jacks, just to start with, or just wait till you're on a city bus next to a little kid who has a favorite commercial jingle s/he sings over and over).

So the traditional method of instruction, learning highly patterned algorithms (write this here, put that there, cross that out and write the next highest, etc.) produces very quick, easy procedural proficiency. Nearly every adult who has math trouble (which is, truthfully, most Americans) will tell you sadly that they "loved math" or "were good at math" up till ... and that up till is almost always some point where the fading memory of a maturing brain was no longer able to keep all the patterns straight, or the patterns became too complex (think how much more complicated long division is than two-digit addition), or there just wasn't any reliable pattern any more. Usually the same people will tell you they loved math but hated word problems, which is something like loving playing scales on the clarinet but hating music, or loving counting out the box step but hating to go dancing.

Mary Boole seems to have been the first person to figure out and articulate clearly that if kids learn it algorithms exclusively as aconceptual patterns for manipulating meaningless symbols, they will inevitably hit some wall later. When that happens, if they don't have the tool of referring to the underlying principles and concepts, they're done; they can go no further. Some few kids are lucky enough that they acquired concepts all along (very often on their own, by simply enjoying playing with numbers); those are the ones we think are "naturally good at math." Other kids, driven by one kind of necessity or another (wrath of parents, lure of a career, etc.) begin belated and partial conceptual learning, and get enough of it to go on for a while, at least until they hit the limits of their conceptual learning skills. And the great majority just declare themselves "not good at math" and give up, spending the rest of their lives evading situations that math could make easier.*******

Now, a good math teacher in the early grades has always been able to point out concepts as the students progressed. A stack of blocks, by not getting any taller or shorter when blocks are moved around within it, beautifully illustrates the commutative and associative principles (whether they're called by that name or not). The number of tiles on the floor doesn't change whether you stand on the west or the north side, and that can teach the commutative principle for multiplication. But there have also always been too many teachers out there who just wanted to get done with the worksheet, and whose answer to "Why?" was "Because you don't want to stay in from recess."

So essentially, the traditional style of teaching math has been shown, under all sorts of conditions, for a good hundred years and more, to produce early procedural proficiency but expose many students to a later conceptual block. You get more kids who can make change quickly but fewer who can go to engineering school. And when they hit the blocks, it's painful and frustrating and most of them come away hating math.

Reforms: don't go there, there's a wall; or here's a key, so why do you need a lock?

Naturally enough, reformers who wanted to fix the hitting the wall problem either tried to avoid the hitting, or tried to avoid the wall, i.e. most reform math movements involved either:
1.           simplifying and dumbing down math so that kids can learn a basic set of patterns and let it go at that (never a very good option and a disaster in the 21st century when so much of the better part of the job market requires math)

2.           teaching conceptual understanding as an alternative. That's what New Math, inquiry-based math, and several other systems try to do.

That second idea makes sense on the surface; if the reason little Sammy can't grasp fractions is that s/he only knows multiplication and division as procedures, teach them to him/her as concepts in the first place.

But as is well-known, in practice this leads to kids who can define the cardinality of a set but can't figure it out without resort to their fingers. Concept-heavy math education often fails to lead to procedural proficiency; worse yet, because the concepts are ungrounded in any experience, the students seem to know them only as names, and not to be able to apply them or see what they refer to. If we were producing calculus wizards who couldn't make change, we might live with that by automating change-making or training change-specialists; but the embarrassing truth for conceptualists has been that without a procedural base, people don't seem to acquire the concepts either.

So there's the dilemma: emphasize procedural proficiency and lose large parts of every cohort to frustration and despair when they don't have the conceptual basis to go on. Emphasize conceptual understanding and lose even larger parts of every cohort to learned helplessness and a propensity to name things but not be able to work with them.

Where Singapore Math is really a revolution. The mathematicians (Singapore has some superb ones) and the educational psychologists (ditto) looked at the problem something like this:

Procedural proficiency approaches are focused on manipulating symbols quickly and accurately. Conceptual understanding approaches are focused on connecting meanings accurately. But a student can only really know for sure that a procedure is accurate if s/he understands the concept behind it, and a concept isn't really understood till the student sees it happening.

In short, procedures are what concepts mean about, and concepts are the things that govern and allow us to remember procedures. It's a dialog.

Concepts are how we remember procedures. The last few decades of memory research have shown that memories are not recordings, but a set of cues from which we structure and rebuild a narrative, visualization, or other coherent thing we need to refer to. If you're truly procedurally proficient, you know that already; if your mind slips for a moment while doing long division, the concept that explains why you multiply and then subtract (and go back a step if the partial remainder is larger than the divisor) is there in your memory too, ready to activate if you do something in the wrong order or get stuck.

Also, procedural proficiency is essential before the next level of concept can be learned effectively. A student who can only add by counting forward has to do far too much work for a 7-year-old memory (which is highly accurate and retentive but works in tiny chunks) to be able to also grasp multiplication. There are only so many processors and registers available, and they have limited capacity; to grasp higher concepts, lower ones have to be automated. Let me give you three very fast analogies:

1)        You control where you point your eyes (high level concepts about your environment) but you usually leave depth of focus "automatic" and you have no choice at all about whether to see with your rods or cones. If you had to decide how to balance the signals coming in from your eyes, you couldn't see at all.

2)       If you've ever watched a young kid learning to play baseball, you know there's not much use telling him/her "The play's at first" until s/he knows that a "play" is "a situation into which you should throw the ball," and all that's useless until s/he can throw a ball somewhere reasonably close to first base. The concept of a "play" is meaningless until the kid is actually someone who can play the game as a player who can throw into a play.

3)       A college science instructor friend tells me that he has to coach students to read every formula and equation (many of them seem to think that stuff is just decoration and the meaning is in the words around it), and strongly urges them to solve each one for all the variables. If they can easily see that F=ma implies m=F/a and a=F/m, and keep all those in mind as they read on, he figures they'll probably make it, though not as easily as the students who didn't need to be told. If they don't see much relation between those three, or think of them as three separate facts, he suggests they change majors to "something words-only."

And there's the great thing with Singapore Math. There's a structured pathway from concept to procedure to higher concept to more complex procedure to even higher concept, on and on; the concepts are not just window-dressing and decor to keep the smart students from getting bored with algorithms. Nor are the algorithms mere passing examples of the to-be-admired concepts. It's understood that the ground for a concept has to be prepared with procedures that have become largely automatic—you can't have an a-ha! where everything clicks if the pieces of it can't move fast enough to click. And it's equally understood that the focus for a procedure has to be on implementing a concept; a kid who is chanting "four times nine equals thirty-six" needs to be thinking of what "times" and "equals" mean every time he chants it.

What great teachers have always done anyway, Singapore Math is built around.  So unlike any other system, Singapore Math doesn't try to "emphasize the really important thing, which is" {procedures, concepts}. It builds in that vital alternation, that you acquire the concept to help remember the procedure that will allow you to see the next concept that will enable you to remember/construct/apply the next procedure, over and over—like a person walking forward on two feet instead of spinning in a circle around a stationary foot, or a climber going hand over hand, not limited to the height of the first handhold.

And as a corollary, Singapore Math training materials make it clear that we acquire procedures by procedural methods (i.e. practice, including both repetition and variation, or to use the dreadfully old-fashioned words, drills and exercises). We acquire concepts by conceptual methods (inquiry, pattern-finding, reasoning, extrapolation, and so forth). And we join procedures to concepts, and concepts to procedures, and move on.

Contemplate that phrase, if you will. And we join procedures to concepts, and concepts to procedures, and move on.

How's it work in practice? Let me take an example I've now seen three times: some kids cling to very simple but time-consuming procedures like counting up to add, counting down to subtract, or counting by factors to multiply (e.g. to multiply 8X5 they tick off 5,10,15,20,25,30,35,40 under their breath as they pop up eight fingers in sequence). In each case, it turned out that one reason the kid did this was because s/he thought the construction caused the answer to be right—in other words, the equal sign did not express that 8X5, 5X8, 10X4, and 40 were all the same number. Rather, the equals sign was a command to "calculate now," and 8X5 would not be 40 until you calculated it.

I found that out by slowly walking them through their mental process, until I confirmed that for them, calculation was what made the result true, rather than a procedure for finding the truth.

The cure was then to demonstrate, in up to a dozen different ways, what = actually means—that 8X5 is not "how you make 40" but "another name for 40." Once they saw that, they also saw that 40 could be right without doing the calculation—and with a bit of salesmanship on my part, that it would be much easier to just know that when you needed it (just as it's easier to get a pizza if you know it's called a pizza, rather than to say, "I want you to make me a circle of dough and put cheese and a mixture of spiced crushed tomatoes on top of it, then heat the oven ..." every time).

Then, pushing them to remember every single time what the math facts meant, so that they would know when and where to use those automatic bits of knowledge, we worked out a mutually agreed on plan and timetable for memorization. They all did it faster than expected/required. And the next step was that we used their newfound procedural proficiency to start exploring the next concept up the ladder ... from which would flow more procedures, with which they would be able to understand more concepts.

One last thing: tutoring students almost always move on, as they catch up with regular students or as they become secure in running ahead of their classmates. The biggest thing they take with them from that dose of Singapore Math, I hear, is that once they have that model of how to learn math, they can apply it whether their teacher does so consciously or not. They have, in short, acquired the ability to learn mathematics—really learn real mathematics—whether the teacher is good or not. And if knowledge is power, that's the very source of power.

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* quick translation of that for those of you who don't read American educationese fluently: the order and timing of mathematical topics from Singapore Math has been partly copied into the new guidelines (Common Core) that many schools are adopting. (Feel free to insert several hours of reading up about politics of Common Core right here, if you insist. Go ahead, I can wait. I've done it myself. I'll even feel some sympathy for you after you're done). In general, the international version of Singapore Math far exceeds what Common Core asks for, so within the Common Core process, Singapore Math has been a force for higher standards and against dumbing-down. No Child Left Behind is a Bush administration holdover law that the Obama Administration has found useful as a tool against underperforming schools, and so has not given it up despite heavy pressure from their close political allies, the teacher's unions. NCLB is a system in which poor student performance on standardized tests makes schools liable to pressure and sanctions that can go as far as reallocating their funds or students to the point of closing them down. Many terrified school boards and school administrators therefore insist that any curriculum be "aligned with the standards" by which they mean an exhaustive list of "right here on this page is where we teach the third graders the material they'll need to correctly answer the type of question that a specific standard requires." Because Singapore Math is generally more advanced at comparable ages than the standard American math curriculum, most of the "alignment" consists of verifying that by the time students are tested on any topic, they'll already have been taught it; almost no material has had to be added, and little existing material has had to be moved earlier. This checklist/bookkeeping process seems to have produced little or no actual change from international Singapore math, but it's probably been very successful at selling new editions of the old textbooks.

** for many different values of that. In general, Singapore Math presents the material in an order and manner that has sound reasons in educational psychology, mathematical rigor, and preparation for more advanced work—often in all three. For obvious reasons, though, this isn't always explained in student textbooks, and sometimes even the teacher may not be clear on it, especially in the many places where Singapore Math is being thrown at them on the "stay a chapter ahead" basis. For most parents with kids in Singapore Math, there seems to be an occasional that, as in, "Well, she seems to be learning math, and I see why they have her do most of it, but what is that about?" Hence, a whole section of the book dedicated to thats.

*** subject for a future blog. I think most of us realize that a really good math teacher can use many of the not-very-good textbooks and materials on the market, and still really teach math to most or all of the kids in the room, by supplementing, emphasizing, or sometimes teaching against the materials. Unfortunately, underprepared, mathphobic, rigid, insecure, or otherwise weak math teachers can also use a great curriculum to baffle, confuse, frustrate, and turn off a whole roomful of kids. Some teachers who are being handed Singapore Math to teach are being thrown in over their heads, and it really doesn't matter whether they're in over their heads because they aren't getting enough support, didn't get enough preparation, never learned the underlying math, or just hate math. Whoever's fault that is, it's the kids who pay the price. So that section of the book will be about making sure that if your kids' school is wise enough to offer them Singapore Math, what they get is actually Singapore Math.

**** see, for example, the surprisingly modern-sounding arguments in Mary Boole's Lectures on the Logic of Arithmetic (1903) or John Dewey's The Psychology of Number (1895).

***** and you gosh-danged well should, too.

******* subject for another future blog after I do some more research: it is extremely well established that illiterate adults have an enormous number of tricks for not getting caught being unable to read (getting other people to fill out forms for them, sticking to restaurants and canned goods that have pictures of the food, listening to class discussion and repeating things other students have said, saying they forgot their glasses and asking someone to read the text to them, etc.) There are probably as many tricks, and as clever tricks, for innumerates, but they are probably used much more often. Unlike illiterates, however, I suspect that there are many, many more innumerates who just live with being cheated, pay too much, having to use trial and error, etc.