Is it possible that by attempting to eradicate a non-critical advantage in math, that we are distilling math and engineering education for both boys and girls?
Bertrand Russell once said: “Mathematics is the field where we don’t know what we are talking about.” This reveals the nature of mathematics – which is distinct from the machinery called arithmetic (which is taught in elementary school). Mathematics is an abstract discipline, relying on internal visualization and abstract focus.
Recent research has shown that women have more neurons that travel between the brain’s hemispheres and men have more neurons that travel along the hemispheres.1 Some suggest this enables a woman’s communication and multi-tasking skills (I rarely see published articles that object to these abilities in women), and men have a greater ability to focus and single task (I usually see published articles that object to these abilities of men).
Men created the language of math through visualization and abstraction. In addition to the aforementioned biological differences, there is social research to indicate that the top one percent in math will always be male dominated.2
And it is this one percent that gives rise to the thirty point difference in math SAT scores.
But does this gender difference at that top level matter? Are current interventions failing because they are inordinately focused on a percentage that has little relevance (except to feminist ego)?
The top one percent in mathematical ability does not drive science, engineering and technology; they populate math departments. The top twenty-percent in math drives civilization and women are capable of thriving and excelling at that level. I contend that women drop out in greater numbers from engineering than they normally would have if, instead, they were not given false assurance through current “Girl Engineer” programs; or if the pedagogy had been properly constructed to draw them into the top twenty, ten or five percent; or if we did not create artificial silos between the sub-disciplines of math to enable assessment strategies. I believe that if proposed redresses are premised on “misogyny,” the fix will fail. Mathematicians and engineers do not have a problem with women, today. It is politically correct interventions that have a problem with the nature of math and engineering.
In part, I believe that the very thing that will inhibit women from advancing in engineering is society’s diminishing respect for aspects of the masculine mind and a feminism that has migrated from a focus on social equality and now insists on biological equality.
Men dissect; and this is a reflection of the very masculinity that current popular discourse disparages. Popular media views men as cold for their desire to “conquer” and “dominate” the observable world. The popular discourse prefers a holistic understanding of the world. And it has dulled the distinction between magic and beauty, undermining one aspect of the masculine brain.
When I see a rainbow, I want to slice it open, analyze it and understand it from a perspective grounded in mathematical physics. I want to dissect it as if it were an object (e.g. Why are the colors reversed in the internal secondary rainbow in a double rainbow?). Contemporary talk-show culture paints this as if I am objectifying the rainbow, and that I should simply relax and appreciate its spiritual magic: I have been told as such and by women (“Can’t you just enjoy the beauty of a rainbow?”). I claim, however, that my curiosity is my way of trying to understand the physical world that surrounds me. Magical mysticism is lazy; beauty reveals itself through cold understanding.
The top one percent in math is male dominated because of the male brain, and this will likely never change. The few women in the top one percent think like men. Sophie Germain (April 1, 1776 – June 27, 1831) admitted to dressing like a man to attend the French Academy to make her contributions to engineering. A feminist would suggest she did this to circumvent the patriarchy. I suggest she blossomed in male culture. When a man suggests that to succeed in math, a woman should think like a man, he is rebuked. But what is wrong with thinking like a man? I have no objection when the media insists that my compassion derives from my feminine nature. I take that in stride. So what is the problem with accepting that math/focus/abstraction derive from masculinity? When did it become an insult to think like a man?
The top twenty percent of men and women can excel in mathematical applications in science and engineering but academic feminists and policy makers have become fixated on the top one percent. Google “math, boys, girls, scores” and see hundreds of funded research papers that purport to explain a thirty point difference in math scores. Does this difference really matter considering that those thirty points are attributed to the top one percent? Whenever women excel over men in any discipline, their virtues are extolled in the media. When men excel over women, the media paints this as a bad problem that must be fixed — and now we are “fixing” engineering by simplifying math.
The institutions driving change in mathematics education are reducing mathematics down to machinery and algorithm in an attempt to close a slight gender gap. In the process, they are making math boring and this will have ramifications in later years. They are meeting with some partial success. Girls excel at the machinery of calculations: division, subtraction, algorithms, numerical methods, integration and so on – what we know as arithmetic. But then the abstract nature of math reveals itself as essential as their studies advance. Then, in reaction, women start to drop out of engineering when they see a false advantage evaporate. Society blames misogyny for this.
I am in awe of mathematicians, for they evince one aspect of masculinity in its cold detachment from reality and its embrace of abstraction. I am not in that top one percent: and I am fine with that. But I find those men as inspiring as chess players (there are also papers that try to explain the disparity in chess, too; none of which make any sense). There is an anecdote from the life of Linus Pauling; He was delivering a guest lecture and after scrawling theoretical mathematics all over three blackboards, a student raised his hand and pointed out that 7 times 8 had been multiplied wrong in one of the earlier steps. Pauling just waved away the fact that the numerical conclusion was obviously not accurate. Pauling’s answer was, “Oh, that error, yes; it does not matter; numbers are just placeholders for the concept.”
The solution in engineering is to raise expectations. Instead, we are doing the opposite. We are lowering the bar on math by eliminating the abstraction; and we have practically deleted physics from the elementary school curriculum. And we are doing this to eradicate a gap in math that stems from the top one percent. We are no longer inspiring and challenging our better students. The goal should not be to ensure that girls score as well as boys at that distal end – let nature take its course, there, without interventions. The goal should be to create interventions that retain more girls in the top ten or twenty percent while continuing to inspire the boys. And this could be done with interactive technologies if feminism relaxed the stranglehold of its obsession on the top one percent.
Society today condemns the very masculinity that created mathematics. The Asian countries, less riddled with politically toxic academic and common feminism, are out-performing the world in math, while the more feminist countries are failing in math. One does not have to embrace the misogyny of eastern culture; but by the same token, the west has embraced a misandry.
Today, we are reducing math to word games. Common Core Math in the U.S. is a perfect example of this: it is reducing math to verbal skills. In the future, girls will soon excel over boys in math (which, of course, will not really be math: just exaggerated arithmetic). But then girls will get to college and confront the wall of abstraction without teachers who can inspire them with a detached (and, yes) masculine perspective. Naturally, the politically correct will blame male custodians or male bus drivers or a campus rape culture or maybe they will turn on male fruit flies down in the biology labs, and blame them. Many more boys will never get to college: they will fail out of it, never having learned the abstract underpinnings of math. (The new SAT will actually reduce the number of math questions and increase the number of verbal questions.) But I suppose that will make the politically correct happy, for then there will be total equality: NO men in the top ten percent and NO women in the top ten percent. Feminists will get what they wanted: a country of total math and engineering equality: zero = zero. Meanwhile, China, and its excess of two hundred million men will dominate technology.
AN ANECDOTAL ASIDE:
Engineering has two aspects: SYNTHETIC and ANALYTIC.
Synthetic goes by the name ENGINEERING DESIGN.
Analytic goes by the name APPLIED MATH AND ENGINEERING SCIENCE.
Today elementary schools are trying to teach engineering. But in
reality, they are teaching Engineering Design, only: build Lego Robots,
toothpick bridges, etc.; and then write reports and project plans. The
girls excel. The boys don’t. This is because “design” hinges on
collaboration and communication: verbal and communication skills.Analytic goes by the name APPLIED MATH AND ENGINEERING SCIENCE.
However, future engineering will derive from APPLIED MATH AND ENGINEERING SCIENCE. We need the math to create new microscopic machines and quantum computing and robotics. And the girls have been deluded into thinking that engineering is about communication and not math. It is not that girls cannot do this, but that policy makers do not know what engineering is really about. They think they are inspiring girls; but they are inspiring with only half the picture. And when the girls fail, feminists will blame misogyny and male exclusion practices.
Some men have excluded women from engineering; but that type of misogyny is now nearly non-existent and not enough to warrant interventions. Contrary to what some think, men do not exclude women from engineering; men seek a place to call their own (a distinction between cause and effect). Today, spaces for men are vanishing while spaces for women continue to blossom. Rather than interpret male resistance to female engineers as a negative view of women, why not consider it a self-indulgent desire for a male space? Then, upon recognizing that, and curtailing the negative stereotypes of male spaces, maybe men will be more inviting to women in engineering. What do feminists want anyway: to change men and destroy all male space (even disallowing sixth grade boys to pee in their own bathrooms), or to understand the issue and help women? These days, it appears to be the former. Consider the discipline of dynamics.
When I was in the fourth grade, boys learned to pee while standing. We often made a mess (boys are always in motion, fighting with the world, it seems), but the custodians were paid to clean the mess.
To understand dynamics (the study of motion), one must brutally sever an object from its surroundings. Then, one must replace all formally contacting objects with forces. This is the essence of Newton’s third law.
I remember, one time, this one kid peed out of the third floor window. That afternoon, the boys kept laughing in class and we all got in trouble because no one wanted to snitch.
This process is called the creation of “free body diagrams.” It is not holistic, it is not integral. It is brutal rupture of an object from its environment, enabling one to focus on it exclusively.
The boys would compete against each other as we aimed our streams, like rockets launching from a silo.
Then, after such isolation, one employs the discipline of differential equations to model the trajectory of an object. Naturally, it is not entirely accurate: it is only a model aimed at a prediction.
Often, we would joke with each other. Sometimes, we made fun of each other. Sometimes we deliberately aimed at each other. But eventually, we learned to pee while standing.
Then, one must solve the differential equations. In reality, one could inspect the terms and anticipate the motion, but today students drive blindly and relentlessly to get a number and overlook the beauty of the predictive quality of equations. We turn to computer programs that circumcise the complicated equations to obtain an answer (an answer that is often sterile and meaningless: just a number). Today, students turn to computer programs to get an answer in order to do well on a test. But in that process, a deeper understanding of the phenomena never emerges.
We boys learned to pee by watching each other and getting a little jealous of each other’s aim. Maybe, sometimes, we were jealous of that one kid’s parabolic fluid trajectory out the window.
You see, one does not need to solve every equation. In reality, one can inspect equations and deduce their “tendencies.” One could see, from looking at equations, that the “tendency” of an equation is to reveal a behavior. But engineers are losing the ability to “envision” the “tendency” of equations as we continue to sterilize math in order to check bubbles on an exam. Today, students are expected not to act until they know they have a direct hit on the computational solution and a numerical result.
The process of not solving the equations for complete solutions, but using them to extract information, is a critical aspect of engineering focus – and is being lost. In the past, one did this by sketching a solution on the back of an envelope, often in a sloppy way.
Lately, I have come to find out that in some schools, the boys are told not to pee while standing until they first learn to pee properly. This is humiliating for them; for they are indirectly told that the boy’s room is not for them alone (it’s bad enough there are so few male spaces; now even the men’s room does not belong to them). They are lectured on how to be boys and are expected to be boys on the terms of a custodial staff.
To help the girls, we are removing the detached abstraction of math and replacing it with a simplistic arithmetic of word games that are more suitable for girls and their communication skills.
Much worse, the very ability of boys to get down and dirty with math is being “fixed.” The walls of disciplines – strictly enforced for testing and evaluation (but not for learning) – discourage the ability and/or desire to question the legitimacy of physical models. Who would want to question a model if the teacher might incorrectly assume your question is one of ignorance and not insight?
So that is why I tell my son to pee while standing despite what the school says. For the goal is not the end. To pee while standing is irrelevant; the goal is to learn how to pee while standing (to learn how to do what men do, with other boys): the goal is a process, not an end. The goal is to aim, to miss, to reload, to aim better, to make the attempt at a solution, to splatter the floor, to abandon one method, to learn that the world will not end if there is urine on a wall, to reload, to pee out the window and watch the parabolic flow of fluid, to get a partial solution, to break a barrier and finally hit the target. And if the school has an issue with how boys learn, they can remind the custodians and teachers that they work for the students, not the other way around. It’s a toilet, not a boy.
Let the boys be boys, again. We have already ensured social interventions to respect a woman when she says “no”. Now it is time to back off from the endless vilification of men for a while and tell the feminists to take a step back from the continued vilification of things masculine. Let the boys have their recess, let them shoot things (and study trajectories of imagined bullets or urine), let them fling mud or footballs; yes, even let them be slightly aggressive. Otherwise, we should learn to speak Chinese.
References:
[1] Madhura Ingalhalikar, et. al. Sex differences in the structural connectome of the human brain, PNAS vol.111 no.2, 9/2013
[2] Benbow, et. al. Sex Differences in Mathematical Reasoning, American Psychological Society, Vol.11, No.6, 11/2000
Editor’s note: Feature image by DonkeyHotey
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