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36: The Assault on Math
A companion to "30: The War Against Reading"
Background:
My focus for years was on reading
and on explaining why this country has 50,000,000 functional illiterates.
Many people cling to the notion that this catastrophe
was accidental. Isn't that hard to believe?
So many tens of millions of victims? Over so many decades?
Isn't it more logical to suspect that
our top educators embraced an ideology of leveling?
Which brings us to...
 
The Assault on Math

A METHOD TO THEIR MAYHEM

Only in the last year have I realized that the tactics devised to sabotage reading had an exact parallel in the techniques used to undermine mathematics. A disturbing thought. You have to grapple with the vision of our Education Establishment working across a wide front to ensure that students won’t learn very much in any discipline.
 
How do they go about this? First, the experts announce that the old approaches are hopelessly inadequate. That was basically the attack launched against “dear old phonics” back in the 1930s. The second thing they say is that they have analyzed the subject More Profoundly Than Anyone Before in History and have come up with a Higher, Purer Pedagogy. For example, the best way to learn English words is to memorize their shapes (which is in fact the worst way). So the educators claim intellectual advances; but in practice, as history abundantly shows, most children are carried steadily backward.

Similarly, in the 1960s our elite educators rethought math instruction and came up with something called New Math. The old ways, they said, were tired and inadequate. Only New Math could prepare children for the demands of the space age. In practice, however, New Math rendered children mathematically stunted, just as Whole Word rendered them illiterate.

New Math’s basic gimmick was to stir in college-level terms and perspectives, and to claim that little children would become skilled at math by working with these sophisticated approaches. Simultaneously, educators reduced the emphasis on basics, so that children didn’t master multiplication or even subtraction. The main results were heightened confusion, tearful frustration, and lower math scores.

New Math was properly ridiculed and soon discarded. However, the top educators were not defeated; they were regrouping. Around 1985 they came up with a dozen new math programs, the official title for which is Reform Math. However, these have all been collectively and sarcastically titled New New Math. To a remarkable degree, the new programs use the same tricks already mentioned plus some new ones: children should discover even the simplest things for themselves (that's the essence of constructivism); they should work in groups (cooperative learning); and they must use the calculator a lot. The result is that each child is carefully wrapped in six layers of separation from ordinary arithmetic competence.
 
The best-known Reform Math programs are TERC, Everyday Mathematics, Connected Math, Chicago Math, and MathLand. MathLand became so notorious that it is no longer published. Score one for common sense. My  impression is that all of these programs are worthless and dangerous. 

Why so many similar programs? I suspect the Education Establishment wanted to divide and confuse the public. One of the strategies our faux-educators use is to swamp the intellectual landscape with a thousand puzzling details, and to make communities argue over each one, so that parents finally give up and stop caring that their kids can’t count!

 
So let me start fresh by pointing out the obvious: the best way to teach EVERYTHING is to begin with small, simple stuff that young children can pleasurably learn and master (e.g., 1 + 2 = 3). Then you build upward from that foundation toward somewhat more difficult items (e.g., 2 x 3 = 6). And so on. You don't start with big, vague, sweeping, or complicated things. You don't "spiral" on to new material until all the students have mastered the previous lessons. Momentum is the goal. Confidence is perhaps the single most important ingredient for success.

Notice that our educators do everything the wrong way. They start with complex stuff and utterly destroy confidence. This is the detail to stay focused on. It tells you the people responsible for New New Math are not sincerely trying to teach math.
 

 
Let us suppose that the aforementioned sophisticated perspectives do have their place in a student’s education. Okay, fine. But surely the fifth and sixth grades are time enough to mention ideas that previously were never taught until late high school or college. But these maniac educators (both in New Math and Reform Math) want to drop big concepts on the heads of six-year-olds who can’t even add! Furthermore, thanks to the dictates of Constructivism (see #34), students must figure out everything for themselves. The resulting pedagogy is preposterous. It’s as though I want to teach you to drive by taking you out on a salt flat, tell you to accelerate the car up to 200 mph, and then begin explaining how to handle turns and control skids. The only sensible response is: ARE YOU INSANE???? I DON’T KNOW HOW TO STEER YET.

One wonderfully grotesque theme that runs through all these programs is that the educators refuse to teach the standard ways of doing anything. The multiplication you probably know, the long division you learned in school, these are taboos, the math that dare not speak its name. Instead, little children must learn awkward and confusing “algorithms” that their parents will not be able to understand. The “lattice method,” for example, surely qualifies as child abuse (or torture, as the New York Times uses that term). A leading math educator actually said: "Everyone needs at least two ways to add, subtract, multiply and divide efficiently and accurately." To which the correct answer is, “Nonsense!” Think of all the time that will be wasted trying to achieve this double and triple proficiency, and all the mental confusion that will dog “everyone” forever.
 
In essence, New Math, New New Math and Reform Math might best be called Mediocre Math, whereby all children are collected at the same low level and kept there forever. What could be fairer?
 

Crawl. Walk. Run. Dance or Ski.
That’s the natural order in learning things.
A lot of the weirdness introduced into education in the last 100 years
has an odd common denominator:
jumping ahead a step or three
so that children are thoroughly discombobulated.
They’ll dance some day, the argument goes, so let’s drag them
out of that crib and put them in a ballroom.
Even worse, you don't get the feeling that the
goal is really dancing.
No, the goal seems to be to make sure that everybody
is so confused and unhappy,
they lose interest in dancing altogether.  
Anyway, that's what happens all too much.
 
 
 
 
 
Here’s my suggestion for the one best way
to understand the math mayhem:
a video on YouTube by M. J. McDermott.
Takes 15 minutes; but then you’ll know.

 
For an article that tries, in only 900 words,
to cover the whole pseudo-educational scene,
please check my:
Educators Best Understood as “Ignorance Engineers.”
 

 
Which math programs are best??
The names I hear praised most often are
Singapore Math and Saxon Math.
(JULY, 2010: I've recently discovered
a lot of enthusiasm among homeschooling families  
for Math Mammoth and MathUSee.) 
 

"If you have a child in a school,

and they are using one of these programs,

you need to seriously consider an alternative--

 Cognitive Tutor Algebra          College Preparatory Mathematics
 Connected Mathematics Program        Core-Plus Mathematics Project (CMIC)
 Discovering Math        Everyday Mathematics
 Growing With Mathematics         Interactive Mathematics Program
 Investigations Math              MathLand
 Middle-school Mathematics through Applications Project
 Number Power               Trailblazers
 The University of Chicago School Mathematics Project..."
 
Advice found on FUZZYMATH, a site within Squidoo.com
 
Marva Collins
also consults on math instruction. Here's a 2-page pdf
that will suggest how real educators approach the teaching of math.
RELATED ARTICLES ON THIS SITE:
"34: The Con in Constructivism"
is related because the central gimmick
in much Reform Math is, in fact, Constructivism--
i.e., students must re-invent everything for themselves.
 
"53: The Education Establishment Hates Math"
is more analysis of same issues. 

 

 
The essential foolishness of Reform Math is to keep everything abstract, difficult and remote from real life. I often suspect the answer, for younger children, is to stick entirely with the most practical and fun of objects--coins, dominos, dice, cards, and bingo. Children can begin by learning the combinations possible with pennies, nickels, dimes, and quarters. We're doing this every day, all of our lives. So that's a very useful place to start.
 
As discussed in "28: Tips...", a good way to help children grasp multiplication is by using a chess board or tile floor. Consider an area 3 squares by 5 squares. That's the same as adding three rows of five, or five rows of three. A child can stare at the tiles, and count them, over and over, until the shift from addition to multiplication seems obvious.      
 

POSTSCRIPT: A TALE OF TWO LETTERS

My article about "Ignorance Engineers"
roused one expert to complain: 


“Dear Mr. Price,

I happened upon your article about “Ignorance Engineers” today. I was amazed to see how effortlessly you dismissed MathX [let us call it] along with other contemporary elementary school mathematics curricula.

I believe that “ignorance engineering” is a good name for what I see you doing--lumping different curricula together and dismissing them as valueless without any evidence of critical examination. The “evidence” you offer for the failure of recent NSF-sponsored elementary school mathematics curricula-- M.J. McDermott’s poorly thought through and weakly argued video segment—invites people to unreflectively accept slander and innuendo given by authority figures as considered evidence.

I certainly would never argue that MathX (or any other mathematics series) is “the best” mathematics curriculum for every teacher and every student in every circumstance. Nor would I argue that I should choose the curriculum for any parent, teacher, or school. I also wouldn’t argue that MathX teaches mathematics in the only possible way.

But I would argue that, properly implemented, MathX gives children from all backgrounds a good shot at a sound understanding of mathematics and a defensible set of mathematical proficiencies that they will retain for a long time to come. There is plenty of evidence that the curriculum works as well or better than other math curricula. There is precious little information on the success of so-called “traditional” methods of teaching mathematics.

Sincerely yours,
XX"
[The writer is actually a BIG SHOT at one of the major programs.
His attack on me and MacDermott is fairly spirited,
but I felt his defense of MathX, his own program, was weak.
Deep down, he doesn't seem to believe in it much more than I do.]   

Here is my answer to the expert:

"Dear XX,
 
I'm honored that you took the time to write. However, I'm satisfied that McDermott et al are correct.

Your letter prompted me to browse the net for more input. You people have inspired a lot of hostility! It's tough to say which of the New New Math programs is most disliked...All of them seem to use the New Math tactic of stirring in advanced concepts that will confuse younger children, while making sure that no basics are mastered. Additionally, they toss in constructivism, cooperative learning, and fuzziness to create instruction that is not very helpful. There seems to me a lot of contempt for parents.

It's remarkable how parallel the New New Math situation is to Whole Word, where experts assure parents that the new ideas are good for children. But the children end up damaged. As the great Marva Collins said: “Our children and parents surrender themselves to those who are identified as protectors, but who actually destroy them.”
 
What I do not understand is motive. Look at it from my mystified point of view. All these credentialed people! All that grant money! But the best they can come up with is MathLand, TERC and Everyday Math??? The creators of New New Math programs would seem to be ideologues who think it's desirable that children be herded along in mediocrity (because it's fairer). Is this true? (My own credo is very different: I want all children to be pushed as far as each can go.)

I've been trying to imagine how this thing looks on the inside. I'm guessing that the people who stay in ed, and who hope to advance, all have the same opinions. They always think inside the box. But what if your dogmas invariably create mathematical illiteracy, as seems to me to be the case? Just as Whole Word always creates verbal illiteracy.

Here's another slant. Were you in business and paid only for success, I bet you would discard most of the ideas you are now promoting.

Funny thing is, I'm not even a teacher and not good at math, but I'm sure I could easily out-teach your program. Because I would start from a love for numbers and a love for children. Indeed, should your group become serious about teaching math, please consider me as a consultant. I'm very interested in the ergonomics of education.

Cordially,
Bruce Price"


As you might sense, writing back to my critic was the starting point for this whole article. So I'm endebted. No, he didn't answer, yet. And yes, I am totally fascinated by motives, and what it looks like on the "inside." If anybody knows, send a note. I'll share my suspicions that education is a TIGHTLY vetted field. People aren't promoted unless they have the right opinions. In short, everybody does think inside the box. Which wouldn't be so bad if their opinions led to better education.

ADDENDA

I: September, 2009--I've just read and reviewed "War Against the Schools' Academic Child Abuse" by Siegfried Engelmann. He's the founder of Direct Instruction and a tireless advocate for sensible education. Chapter 10 in this book is titled "Math Madness" (pages 106-125) and is a charming, and quite sweeping condemnation of all things Reform Math. If my article has made you curious, please continue on to this chapter. Obtain book on Amazon, where my review is.

II: April, 2010, I just reviewed (on Amazon) a book that was published in 1964 to explain New Math to parents and teachers. This review gives a good sense of how idiotic New Math was and argues that Reform Math evolved from New Math, which in turn had evolved from an earlier project intended to undercut the mastery of arithmetic. In short, the assault on math goes way back. 

 

© Bruce Deitrick Price 2009-2013