ONE THING WE KNOW FOR SURE:

THE EDUCATION ESTABLISHMENT

HATES MATH

I just heard it on the radio, a young boy complaining about how pathetically incompetent US kids are at math. Compared to kids from around the world, Americans are in the bottom 25%. Could it be that bad? Is our Education Establishment that gifted at non-teaching?

So what was the boy’s proposed solution? You should buy a franchise for something called Mathnasium and teach the kids in your community how to do arithmetic. Because, as you know, the public schools can’t manage this feat. I’ve got nothing for or against Mathnasium. But here’s the bigger point: a remedial operation like this should NEVER be necessary. If public schools do a proper job, kids learn math and don’t need any outside help. I said IF. Here’s how one pundit summed up our dilemma: “Tests showed U.S. fourth-graders performing poorly, middle school students worse, and high school students are unable to compete....Chances are, even if your school compares well in SAT scores, it will still be a lightweight on an international scale.” Well, you don’t need to be Einstein to conclude that our public schools don’t have a clue about teaching arithmetic. Their greatest gift is selecting the worst methods and then claiming they are “research-based.” Since about 1990, public schools push something called Reform Math. But private and parochial schools don’t use this rubbish. Especially homeschoolers don’t. These are very picky consumers and squabble among themselves over the merits of Singapore Math, Saxon Math, Math Mammoth, MathUSee, and other ingenious programs that actually teach math, which has to be a miracle because our Education Establishment can’t pull it off.  Why not? Here’s my guess: they don’t want to. They’re collectivists at heart and believe in leveling, which quickly leads to dumbing-down. I’ll explain how this darkness works. But first a light moment. Here’s how one wit summed up the last 60 years:

Teaching Math in the 1950s (Traditional): A logger sells a load for $100. His production cost is 4/5 of the price. How much is his profit? Teaching Math in the 1970s (New Math): A logger trades a set “L” (of lumber) for a set “M” (of money). The cardinality of set “M” is 100. The cardinality of subset “C” (his cost) is 20 less than “M”. What is the cardinality of set “P” (his profit)? Teaching Math in the 1990s (Reform Math): A logger sells a load for $100. Her production is $80 and her profit is $20. Your assignment: underline the number 20.

My take is that New Math and Reform Math are the same long-running gimmick. Mix simple stuff with complex stuff and thereby create an impossible brew, counterintuitive, impossible to master, and virtually guaranteeing bad math scores. This brew--often called “fuzzy math”--is packaged into various curricula and textbooks, with clever names, pretty graphics, and fancy printing, all of which is lipstick on a large rat. The so-called experts claim they are teaching concepts and understanding, which sounds impressive. But the kids never master simple arithmetic because basic, common-sense content and memorization are summarily omitted. New Math and Reform Math are based on the same false premise, that children need to study abstract concepts before they can do practical applications. Exactly backward.  Here is another image that might help some readers understand what our non-teachers are doing nowadays. Suppose you need to learn archery. And I teach you archery by explaining the history and concept of sports, of muscular activity, of competition, the need for eye-hand coordination, the need for being in shape. And every week I toss in some aspect of archery--”look, this is an arrow,” and next week, “this is a bow.” Meanwhile you’re learning about football, baseball, basketball, and the concepts that each of these games is built on. What does it all mean? Other than that your teacher is crazy. It means you won’t learn archery for many months. And your grasp of archery will be muddled in with bowling, softball, hockey and skiing. But we all know there are only a few essential skills in archery: holding the bow, drawing the bow, aiming at a target. You have to focus on the basic skills and practice them with respect. You need to isolate them and master them.   Learning arithmetic is exactly the same. You don’t need to know the history of math to learn how to add 12 + 13. But the National Council of Teachers of Mathematics (NCTM) wants to pretend that the best way to learn arithmetic is the study of algebra, geometry, pre-trig, set theory, and whatever else the cat drags in.

I recently reviewed two books on Amazon, both published around 1965, that were intended to explain New Math to parents and kids. These books are dense, unfriendly, chaotic, inappropriate, impossible to understand without repeated readings--exactly like New Math itself. Here’s the good part. The country saw all these flaws immediately, and put New Math (and these two books) in the dumpster, where they belonged.  Never forget how dreadful New Math was. That dreadfulness tells us so much. The best and brightest professors worked on this thing for a long time. They are incompetent or they are criminals. Either way, you know this well is poisoned.  I can’t imagine that any human sincerely trying to teach arithmetic to children would devise New Math. I don’t know how you could conclude that it’s anything but a vicious hoax. (Conceptually, I would suggest that New Math is like Whole Word, which at that time was preventing millions of children from becoming fluent readers. Note that both gimmicks promised fluency but delivered disability.)

The next development is revealing. The mad scientists who created New Math went back to their laboratories for a decade and, instead of coming up with a single program as before, concocted a DOZEN programs (during 1980's). The strategy would seem to be: divide and confuse. Note: all programs were bad. The experts seem to have learned nothing about teaching math but a lot about overwhelming and bamboozling the public. Collectively, these dozen programs were called Reform Math. Students didn't like them. Parents didn't like them. Most teachers didn't like them. Typically, a community would waste years figuring out how much they disliked a program; evaluating other programs; selecting the new program; only to find that that everyone hated it, too. Some of the infamous names are MathLand, Connected Math, TERC, Chicago Math, Everyday Math, Core-Plus, Constructivist Math, and many more. Parents saw the continuity with New Math and derisively called the new curricula “New New Math.”    Wikipedia rather cutely explains, “Traditional mathematics focuses on teaching algorithms that will lead to the correct answer.” How quaint.  These new programs, on the other hand, emphasize all the bad ideas now ruining the teaching of most subjects. For example: Cooperative Learning makes kids work in teams so they never learn to think for themselves. Constructivism requires that children invent methods for themselves, so they never learn to do anything automatically, such that 30 years later, every restaurant check is a new challenge. Self-Esteem is stressed, so even if kids don’t know anything, the teachers say that they do. One spectacularly destructive component is called Spiraling which requires that teachers jump from topic to topic without requiring that students master any of them. Are there any good ideas? Don’t bet on it.

What grounds, you might protest, do I have for such cynicism? Again, I have two words for you: New Math. This thing was rotten at its core. That's not my verdict. Everyone saw it. Years later, when the professors came back with the first wave of Reform Math, it was essentially the same old goulash. Even that is not my verdict. You can find on the web many disgruntled reports from smart people trying to make sense of one program or another. My contribution, if any, is simply to call attention to the epic sweep, the inexhaustible dim-wittedness, of all these pedagogical efforts for the past half-century. These so-called experts purvey bad to the degree they can get away with bad.   In fact, a tiny little anecdote in a small book written in 1953 shows us how long the anti-math plot has been in play. The book is titled “Retreat from Learning: Why Teachers Can’t Teach. The author is a young woman who taught in tough Brooklyn schools for several years before giving up; her name is Joan Dunn.   She writes: “...educators are still undecided about the best way to teach the alphabet. They go through agonies because two and two equal four and a way must be found to teach that disturbing fact without mentioning numbers. The poor grade-school teacher finds herself emptying gallons of water into pint containers because some educational theorist (who probably has not taught in 30 years) has decided that her little charges might be permanently scarred if exposed to the brutal fact that 2 + 2 equals 4.”   I have to say I love the wit and wisdom of Joan Dunn. You see, this is many years before New Math was set loose upon the country. Clearly, however, all the counterproductive ideas were brewing in this Brooklyn public school by 1950. The so-called educators simply don’t want to teach basic arithmetic. Joan Dunn couldn't anticipate where all this nuttiness would go; but she glimpses the essence. The educators are SQUIRMING to find a way--any pretext whatsoever--to avoid teaching arithmetic. And that is what we are still seeing today.

Now Reform Math seems to be morphing into Common Core Standards (and other names). These newer versions of Reform Math remain, I believe, perverse top to bottom. But that’s not the extent of the sin. To protect the foolishness, these programs present themselves to us in a whirlwind of numbing verbiage, technical mumbo-jumbo, and pseudoscientific pretension. Let’s go to the National Council of Teachers of Math website and read their breathless “Curriculum Focal Points”: “Children develop strategies for adding and subtracting whole numbers on the basis of their earlier work with small numbers. They use a variety of models, including discrete objects, length-based models (e.g., lengths of connecting cubes), and number lines, to model “part-whole,” “adding to,” “taking away from,” and “comparing” situations to develop an understanding of the meanings of addition and subtraction and strategies to solve such arithmetic problems. Children understand the connections between counting and the operations of addition and subtraction (e.g., adding two is the same as “counting on” two). They use properties of addition (commutativity and associativity) to add whole numbers, and they create and use increasingly sophisticated strategies based on these properties (e.g., “making tens”) to solve addition and subtraction problems involving basic facts. By comparing a variety of solution strategies, children relate addition and subtraction as inverse operations." And that, my friends, is what they do to first graders.

Can you stand more? “Students understand the meanings of multiplication and division of whole numbers through the use of representations (e.g., equal-sized groups, arrays, area models, and equal “jumps” on number lines for multiplication, and successive subtraction, partitioning, and sharing for division). They use properties of addition and multiplication (e.g., commutativity, associativity, and the distributive property) to multiply whole numbers and apply increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving basic facts. By comparing a variety of solution  strategies, students relate multiplication and division as inverse operations.“ That’s your third graders, cannon fodder for somebody’s wicked theories. I believe this language is deceitful and counterproductive, but profoundly illuminating. People who write like this are hostile to children, parents and arithmetic itself.  I do not believe that most children can do the things described in this paragraph. Can eight-year-olds “apply increasingly sophisticated strategies based on these properties to solve multiplication and division problems?” How many strategies are there?? What if kids simply learned to do one strategy really well? That’s what teachers push if they actually want children to master arithmetic. But the one best way is the first thing killed off in many of these programs. Killed off and never mentioned.

Throughout our lives, when we have math to do, we typically have to do it by ourselves. It is very handy to know the simplest approaches, to know them in a reflexive and automatic way. Everything in public schools and Reform Math takes you in the opposite direction. You know nothing automatically. You are trained to reach for a calculator but you don’t even know if an answer is close. You are told to come up with your own way to solve every problem, and make sure you can explain your answers. But can you calculate how much paint to buy to paint your house? The essence of successful education is to start at the very beginning, learn about and master the simplest things, and then steadily advance from the easy to the more difficult, over many years. Reform Math says, no, let’s not master anything, let’s learn 5th grade concepts that first year, and 3rd grade concepts and some college concepts too. The smarter kids, the ones who will go on to major in math, may find all this quite congenial. But that is irrelevent. This isn’t a gifted class. The ordinary kids will be destroyed. Little math will be learned. Which seems to be the goal of the ideologues in charge.

I’ve been wondering if the Education Establishment, should they become serious about their work, couldn’t simply take the best features from Saxon, Singapore, Math-U-See, Math Mammouth, Horizons, Switched-On, Schoolhouse, Abeka, et al. I even asked some of the people behind these programs: couldn’t you create something to save the public schools? Well, they were smart enough to say, look, our programs are for home use and the public schools present special problems. Still, I can’t help thinking that these people can provide the answers way before the National Council of Teachers of Math can.  I’ve been wondering if Bill Gates, if he wanted to help the public schools in the simplest, quickest way, couldn’t organize a team of America’s most gifted math teachers (elementary and middle school level only) to find the best programs, cull the best features, and create something called American Math, and give it to the country. Imagine a press conference where Bill Gates, Steve Jobs, and Michael Dell announce, “This is our gift to the American people. Our experts say this is the best, the easiest, the fastest. Everyone should start using it today. Arithmetic leads to higher math, and both lead to science and technology. We need every American to be skilled in these areas. Let’s get cracking!!!”   I don't mean to suggest that ideas need be stolen. They would be licensed where appropriate. American Math might be a joint publishing venture. Perhaps the final product could be sold cheap, say $10. There's still plenty of money to be made. Now, many of the Reform Math programs are quite expensive but don't work. That's stealing.

"36: The Assault On Math" is a complementary piece.   Both are aspects of "45: The Crusade Against Knowledge"

ADDENDA

Every state has its own Standards. Wretched prose such as: "Demonstrates conceptual understanding of rational numbers with respect to: whole numbers from 0 to 100 using place value, by applying the concepts of equivalency in composing or decomposing numbers; and in expanded notation using models, explanations, or other representations; and positive fractional numbers (benchmark fractions: a/2, a/3, or a/4, where a is a whole number greater than 0 and less than or equal to the denominator) as a part to whole relationship in area models where the denominator is equal to the number of parts in the whole using models, explanations, or other representations." First graders in Rhode Island are supposed to do all that.

I once asked a teacher (second grade, I think) what she would do if she wanted to introduce something challenging. She said, "Oh, I don't know. Base-8, I guess." This was a shock at the time. I now realize this base-6, base-8 stuff is very common. It was in New Math, and continues to haunt us. Offhand, I'd say there is absolutely, positively no reason a child needs to hear about such things. Oh, maybe in high school, after one can do a lot of arithmetic more or less automatically. Now, let me see if I have this straight. In base-8, what we now call 8 would be represented by "10." And what we now call 9 would be represented by "11." Make a kid do base-8 problems for a day or two, and you can pretty well guarantee schizophrenia. You can induce the level of confusion that Whole Word causes in reading, where the child doesn't know which way to read "was" and "saw." The child will see 9, 10, 11 and have no idea which amount is designated. 20, 21, etc. will present weird problems. Sick. Of all the counter-productive nonsense in Reform Math, this might be the worst.

FROM A VISITOR:

I highly recommend you check out John Mighton's math program at http://jumpmath.org.    He follows your recommended approach -- "The essence of successful education is to start at the very beginning, learn about and master the simplest things, and then steadily advance from the easy to the more difficult, over many years." -- to a T. I also recommend Mighton's book, The Myth of Ability: http://www.amazon.com/Myth-Ability-Nurturing-Mathematical-Talent/dp/0802777074. Byron ------------- Byron Davies, Ph.D. StarShine Academy