Girls mature physically and socially earlier than boys, God’s way of bettering the survival odds for female children. This accelerated maturation coupled with the intrinsically feminine culture of public education, where the ideal student is a little woman, accounts for the scholastic dominance of girls in the early grades.
But as puberty strikes the old order abruptly changes. Boys forge ahead physically and intellectually, while girls sometimes feel as though their very selves are dissolving. Many crash into a miserable pit of self-doubt, a slavish boy craziness, a semi-hysteria not exactly conducive to academic achievement. Also, at least until the recent past, the middle and high school curriculum begins to involve some serious math and science. Having stoically endured years of a demasculinizing system, boys start to come into their own at last.
But not if Big Sister can help it. That pubescent female “crash” has become a call to arms for feminists and their agents throughout the educational bureaucracy. Such books as Mary Pipher’s Reviving Ophelia, Colette Dowling’s The Cinderella Complex, and Karen Blaker’s Born to Please, and such powerful policymakers as Donna Shalala and Ruth Bader Ginsburg argue that this slough of female despond is a crisis calling for full scale revision of all our institutions, assumptions, values, customs, norms, and methods, not least of which are our methods of teaching mathematics, which feminists correctly perceive as a fortress of male excellence. Whenever you hear loud demands for “inclusion” in “unfairly exclusive” fields, you know you arc in the presence of those who have been utterly inessential to the establishment or painstaking construction of those fields.
But deconstruction of them—now that’s another matter! Having tried for years with little success to boost girls’ achievement and interest in math, the educrats have finally concluded that the best way to close the gap is to cripple boys, by making girls’ “learning style” mandatory for all. Mathematics, so chivalrously called the queen of the sciences, is being neutered into “math appreciation.”
A major explicit goal of the National Council of Teachers of Mathematics (NCTM) is elimination of the “gender and non-Asian minority gaps” that widen as the math curriculum advances. Recent assessments, such as a 1996 study of fourth-, eighth-, and twelfth-graders in California, show that while overall performance is at a standstill or sliding backward, boys and girls have begun to do equally badly in math. The NCTM’s 258-page “Curriculum and Evaluation Standards for School Mathematics,” which has been undergoing implementation since its publication in 1989, makes the tactics of this crippling strategy clear.
Verbalization and visualization of problem solving. Real mathematical thinking may be preverbal or post-verbal or subverbal or supraverbal, but in any case it is definitely not “word processing.” Teachers now require pupils to write out in words how they get their answers. The parents’ group Honest Open Logical Debate (HOLD) reports that “teachers in middle and high school are actively discouraging the use of mathematical symbolism and penalizing students who write correct but short mathematical arguments using such notation.” This is equivalent to penalizing those with any genuine mathematical gift, while rewarding those without, especially girls, who studies have shown process math better verbally than abstractly, i.e., directly. Similarly, using pictures instead of numbers also sidesteps the basic abstraction of mathematics.
A parent named Charles L. Beavers recently confronted an educrat named Ruth Parker who came before her school district with a “New New Math” trick called the “Turkey Problem.” Briefly, the problem could be, and in the past would have been, solved by establishing that a ratio between the known amount and fraction equals the ratio between the unknown amount (x) and fraction and then solving for X. This method. Beavers pointed out, always works, no matter what the amounts and fractions involved. Parker’s solution, which diagrammed the problem as nine little circles which the student then divides up physically into a jumble of half-circles and quarter-circles ultimately adding up to x, “works, graphically, for one carefully chosen problem” only. Parker refused to discuss Beavers’ observation, suggesting he get input from schoolchildren if he were “curious.”
“The problem with the ratio method, and standard methods in general, is not that they don’t work,” comments Beavers. “Indeed, they have immense mathematical power. The problem is that too few people, including many elementary teachers who explain them to our children, understand the simple mathematical manipulations behind the methods.” He is too kind. If fools have been sent to teach math to our children, they have been sent knowingly and with malice.
Traditionalist Marianne M. Jennings laments in her critique of the new algebra curriculum [Wall Street Journal, December 17, 1996) that current textbooks “have all but eliminated numbers. . . . By taking the math out of math, educators have stripped the discipline of its beauty.” While it may be true that most of us “innumerate” masses will never revel in the sheer joy of number theory or bask in the reflected glory of Format’s elusive Final Theorem, that beauty is the heart of the mathematical enterprise. Never to glimpse it is to live in a kind of twilight; to be taught not to look for it is a crime against human nature.
Use of manipulatives. These are basically toys of various kinds—counters, cubes, sticks, marbles, grids, and so on. Even the NCTM admits in its Standards that manipulation of manipulatives is incapable of proving any mathematical proposition, yet it advocates such a hands-on approach well into the fifth grade.
This approach is closely related to verbalization/visualization in that it is innumerate, anti-theoretical, anti-conceptual, and anti-abstract. Remember the multiplication principle, or basic set theory? To determine the total possible number of sets of certain variables, one multiplied the quantity of the first group of variables and the quantity of each other group. But not any more. Now students are instructed to make an “organized list.” This means writing down, line after line, all the possible combinations of variables, after which you add them all up. This chore may then be followed by the manipulative exercise of coloring and cutting and pasting little paper representations of your sets, which are not of course called “sets.” Math is now a lot of dull busywork.
William G. Quirk, a Connecticut software consultant and former university math teacher, has battled the math establishment for years on these issues. He has posted what he calls “The Truth About the NCTM Standards” on the Internet and has this to say about manipulatives: “Prolonged reliance on concrete ‘pacifiers’ interferes with the most important social reason for studying math, the development of the average citizen’s ability to think abstractly.” It does indeed. Are we beginning to get the idea that the average citizen’s ability to think abstractly is not something ardently desired by those in positions of authority?
Repetition. The same ground is covered in grade after grade, especially in elementary school. The “organized list” business, for instance, has been handed my children in both second and fourth grade, without any conceptual difference between the presentations. My fourth-grader, by no means a math whiz (possibly thanks to the new mathless math), was instantly able, however, to grasp real set theory, remember it, and apply it; so the rationale that “kids aren’t ready for it” is not supportable.
Guess and check. Otherwise known as trial and error, this “strategy” says brightly (actual example): “Sometimes you can solve a problem by identifying two conditions. You can guess at an answer that satisfies Condition 1. Then you can check to see whether your guess also satisfies Condition 2.” Sometimes students can stumble upon the solution, too, if they recognize it as such. How many diagonals can be drawn inside a four-sided figure? Guess. Four? Okay, draw them. No, only two. What about a pentagon? Five? Three? Yes, five. A hexagon? Six! No, nine. And so on. Guess, then draw the tiny lines. The teacher told my fourth-grader, “There’s a formula for this, but I don’t remember what it is, and you don’t need to know it.”
“Everyday problems” or “real-world” math. The New New Math argues that math instruction must be related to everyday life and practical solutions. They call this a switch from “skills orientation” to “meaning orientation.” Arithmetic does of course help children tell time, make change, count their Halloween candy, and so forth. But as William Quirk points out, “Most math has no ‘everyday’ application.” Mathematics is an abstraction that exists solely as a result of human mentation. “Who will build those bridges in the 21st century?” asks Quirk. “Right now, it looks like the Asians.”
Teamwork vs. individual effort. Used sparingly, the team approach can be an exhilarating change of pace within the school day as well as a valid means of arriving at new knowledge. In the context of the New New Math, though, it is just another means of devaluing the concept of a teacher teaching objective facts and skills to students who need to pay attention and learn, memorize and practice them in order to get—yes—the correct answer. The theory behind having teams of ignorant students wrack their empty little brains to arrive at estimated approximate solutions is called “constructivism” or “discovery” learning. Needless to say, since the teacher is no longer conveying a body of knowledge but presiding over a vague “discovery process,” the testing of these “discoveries” is necessarily problematic and to be avoided.
Perhaps the most disturbing statement in the NCTM’s entire document is this: “Students might like mathematics but not display the kinds of attitudes and thoughts identified by this standard. For example, students might like mathematics yet believe that problem solving is always finding one correct answer using the right way. . . . Although such students have a positive attitude toward mathematics, they are not exhibiting the essential aspects of what we have termed mathematical disposition.”
Most students who “like mathematics” do so precisely because it offers a “right way” to arrive elegantly at the “correct answer.” The NCTM seems to be implying that such students are in need of “disposition” modification. And it seems to be imposing just that upon our hapless young.
Forget memorization. The NCTM Standards call for a curriculum focused “on the development of understanding, not on the rote memorization of formulas.” Here is proof positive these folk do not know what thinking is. The content of human memory is what “thought” operates upon: no content, no operation. It’s like trying to open a computer file without an application program. Without stored knowledge of facts, sense cannot be made of past or current experience: there is literally nothing for “understanding” to build with. To downplay memory is to disable the brain itself. According to Jack Youngblood, a teacher who advocates the Kumon method to undo the damage of public school math, “You can’t teach ‘concepts’ without teaching math.”
Use of calculators. Astonishingly, the NCTM Standards declare, “There is no evidence to suggest that the availability of calculators makes students dependent on them for simple calculations.” Do math educators never witness the agonies of young cashiers when the register goes down? The Council promotes calculators in the classroom and proclaims they have transformed the way math is understood; they have freed humanity from the need to compute; we can now forget about number facts and concentrate on “meaning.” Meanwhile, even with calculators, American students trail the industrialized world in math, and they not only can’t do sums but don’t know what they “mean,” either.
G.D. Chakerian and Kurt Kreith have compared the “constructivist,” “meaning- oriented,” “discovery” approach to the Pythagorean theorem with the traditional, “skills-oriented” approach and have sorrowfully observed: “Experiments performed under the tutelage of unskilled guides can lead students into a chaotic jungle, one in which their minds become entangled in an underbrush of mismatched concepts to which they, their parents, and their future teachers will be hard pressed to bring order.”
The minds damaged most by being dragged into this “underbrush of mismatched concepts” are those of boys. What is happening today in American education is truly a bias crime if ever there was one, perpetrated with mindless ingratitude. Who, after all, has generously granted inexperienced women entry to the professions they founded? Who have been the caring, demanding mentors to tens and hundreds of thousands of women over the centuries? Fathers in particular are so notorious in this booster role that literature and literary history are replete with them; behind virtually every high-achieving woman is a doting dad.
Who, conversely, are those brassy young singles out trolling for your husband in the workplace, with no regard for your happiness or your children’s welfare? (“Feminists think men are jerks,” someone noted, “and they all want one.”) Whose heavy favoritism toward their sons drives their daughters to speechless rage and lifelong depression, and whose negative criticism drives their daughters to anorexia and bulimia, according the Journal of Abnormal Psychology? Who are all those teachers supposedly turning a deaf ear to girls’ contributions in class? Who is most threatened by the dynamic new woman in the office or graduate department and wills her to fail? And who are all those math idiots who voted Bill Clinton into the White House?
It is less the hostility of men than women’s own marked preference for males over females that blights their own lives and the lives of girls. Mothers prefer sons, daughters prefer fathers, and, as Gregory Corso observed in his poem “Friend,” “The majority of friends are male / Girls always prefer male friends.” As for the cause of the aforementioned pubescent “crash,” in which “Ophelia” goes mad and drowns her Self, in the absence of common sense one might turn to Tolstoy, who described the phenomenon so beautifully in War and Peace: it is the green sickness that gets Natasha in its vise and makes her hysterical and almost ruins her, all because Prince Andrei does not marry her in time.
Tragically, teenage girls today may not marry even if they suffer the green sickness unto death; they are considered too young by modern social standards for that most simple and humane of cures. And so they will continue to drown. But now, at least, they can take everyone else down with them, because surveys for the first time show that more young men than any other demographic sector report themselves “depressed.”