The Doric Column
January 26, 1999
"Dad, can we practice math now?"
My daughter's importunings came as I was engaged in writing an earlier column. As in other matters in life, she would not be denied. And why should she be? There she was, holding the old clipboard with a yellow legal tablet in its jaw, ready to go.
Gina is 8.3 years old and in second grade. She has marvelous verbal skills which she exercises with amazing virtuosity to make a point, to describe an experience, or to demolish her older brother during a dispute. She has honed her verbal skills the old fashioned way, by reading.
But Gina is struggling a bit on the quantitative side. Her parents are not too concerned. The developmental course of a child, after all, is perhaps not unlike that of sailing uncharted seas, with unpredictable patterns of dead water and spectacular surges. The nonlinear dynamics characteristic of chaos theory could just as well have grown out of observing kids develop and plotting their progress.
We help Gina with her homework. We see to it that she gets some extra help during the summer through a math program offered by the St. Paul School System. And we give her lots of encouragement.
By the time Gina approached me for help, the yellow pad showed evidence of exercises in simple addition she had already undertaken. The results were mixed.
Gina really brightens up when she calculates a problem correctly. An incorrect answer, however, when brought to her notice, yields what I have diagnosed as the "drooping sunflower syndrome." The same droop also occurs when I, in my deep-seated male need to be "right," interrupt her when she's reading to correct a mispronounced word.
On this, I'm in something of a quandary. Is it better to correct on the spot and immediately shower her with bright beams of encouragement? Or is it better to listen and allow her to arrive at the correct pronunciation later on, perhaps in a more neutral setting than beneath the thunderheads of parental power?
But back to math.
"Gina, do you like math?" I asked out of the blue.
Her answer, which I allowed her to key in directly, is:
"yes becuse the probloms are fun to do at home"
Since she had enlisted me in this matter, I take some satisfaction with her answer. Besides, if math isn't "fun" at some level, especially early on, it won't be learned. And let's face it, math is more important today than at any time since the Babylonians baked trigonometrical problems on clay tablets six millennia ago.
"What's one plus one?" her brother, age 12.5 years, asked mischievously.
"That's easy. Two." she responded innocently.
"What's three minus four?" he asked again, pushing one of her buttons (and he knows where they are).
"Let's see, three minus four." She started working her digital calculator--her fingers--rapidly running out. "Zero."
After scolding her brother, I tried to explain. But the concept of negativity has not been formed in her little brain. Strike that. The concept of mathematical negativity has not yet been formed. The use of negativity in general, so critical to the child's emerging need to be a free agent in human affairs, is second nature to her.
No problems on that front.
Neither of Gina's parents has anything special in the way of abstract, quantitative reasoning to bring to the table for her benefit. Of her seven uncles and one aunt, half deal with numbers a lot in their work: two are in engineering (males), one is in management (male), and one is in accounting and finance (female). The rest are mainly right brain folks, interested in the arts, or they are bicameral. None is mathematically disabled.
Gina loves stories. I thought I would tell her the story of Hypatia of Alexandria (370-415 AD.), the mathematical genius, leaving out the part about how Hypatia met her end at the hands of an angry mob. Girls need mathematical role models of their own gender. And just maybe, given the current trends in college enrollment and gender action programs, math and engineering won't be the boys clubs they are today when Gina goes to college (e.g. See "Colleges in the U.S. Are Beginning to Ask, 'Where Have All the Men Gone?'" New York Times , Dec. 6, 1998).
"Have I ever told you about Hypatia?" I asked Gina.
"Well, no. I don't think so."
I took the story from a book Gina and I checked out together from our neighborhood library: Math Equals: Biographies of Women Mathematicians + Related Activities by Teri Perl (1978).
I asked Gina to do the reading, resisting the powerful impulse to correct her when she mispronounced a word:
"'Much of Hypatia's life is clouded in legend. We know she was the daughter of a mathematician. Her father was Theon, a noted mathematician and astronomer. It is thought that she never married. She was probably educated by her father. Some accounts tell that her father guided every aspect of her education. In order to develop this most 'perfect human being' he supervised the improvement of her body as well as her mind.
"'Exercises of all kinds were a regular part of each day. The rigorous training apparently achieved its objective: her beauty and talents were legendary. She was one of the university's most popular lecturers. Students came from Europe, Asia, and Africa to hear her lectures on the works of Diophantus and others. She was greatly admired as a magnificent teacher and human being, almost an oracle.'"
"Dad, can I stop reading now?" Gina inquired abruptly.
"Of course, if you want to," I answered. "Just remember that Hypatia was very good in math because she worked hard at it. And her dad helped her, too, just like I help you."
A voice echoed in my conscience, the voice of Senator Lloyd Bentsen delivering a message to Senator Dan Quayle during a debate in 1988: "I knew Theon. Theon was a friend of mine. And you're no Theon."
It's true. I'm no Theon. I was doing all right until my freshman year in high school. Then I was introduced to algebra by a gentle and kindly man, Mr. Anderson, who didn't understand that instruction in the absence of discipline is like dog paddling upriver. There's a great commotion, but you don't get anywhere.
Many years later, as a graduate student, I was reduced to asking a boyhood friend to assist me with the quadratic equations required for my economics class, which was about macroeconomic modeling. He was more than willing, and I learned how to do them. Soon my son will ask me to help him with his algebra and I will be forced to resuscitate those synaptic fields.
To supply some cover for my fear of math, I took a course on the history of Babylonian mathematics from Alan Shapiro, a University professor in the history of science and technology. The Babylonians invented quadratic equations. They are also responsible for dividing the day into 24 hours, each hour into 60 minutes, and each minute into 60 seconds. So blame them if there aren't enough minutes in the day.
But for all their wonderful mathematics, like many ancient cultures they did not provide for the education of women. And that was my immediate focus.
Girls have been slower than boys to immerse themselves in the world of computers. That's not all bad, mind you. There's no persuasive evidence that such immersion is beneficial in the long run, especially if it's total.
A few years ago there was a great hubbub about the fact that only about a third of people using the Internet were female. The gap has closed dramatically since then. Today nearly as many XXs use the Internet as XYs, chromosomally speaking. That "Gender Gap" has practically vanished.
Gina is quite comfortable on the computer. Doug Englebart's invention of the graphic user interface and the computer mouse have served to help develop her spatial reasoning skills. She has her own folder on the hard drive. She's big on art programs and the jigsaw puzzle. She prepares and mails bluemountain.com personalized cards over the Web, and she's been to barbie.com. Her favorite CD-ROMs are "Winnie the Pooh and the Honey Tree," "Arthur's Teacher Trouble," and "The American Girl," which was developed by The Learning Company and its co-founder, Teri Perl.
The digerati are mostly XYs, but the first computer programmer, the first person to develop computer language, was a double XXer, a woman. You would never know it by scanning the shop floor of the average software firm or cruising a computer expo, but, to paraphrase H. L. Mencken, facts are no less facts because they are unexpected. Whenever I see Gina at the computer or at the clipboard, I am reminded of this fact.
The Earth Mother of computer code, beginning with the punch card and proceeding to Java, the current programming rage, was the daughter of one of the greatest dreamers who ever lived, a man who didn't give a hoot about math or science and deplored what technology was doing to the emerging working class.
Fortunately, her mother did care about the abstract mental stuff. Her mother was Annabella Milbanke, a "cool rationalist with a strong interest in mathematics." Her father was George Gordon Lord Byron, the great romantic poet. She was Ada Byron Lovelace.
Ada Byron was born in London in 1815. A few months later, Lord Byron, in the proper spirit of the romantic, abandoned the humdrum of family life and never saw his daughter again, dying in Greece in 1824 when she was eight years old. By then, Ada was already showing a "mechanical ingenuity" that was hardly encouraged in young girls at that time, and not enough in this.
Through her persistent correspondence, she came to know and work with Charles Babbage, inventor of the "Analytical Engine." Babbage's machine was a precursor to the modern computer. Author Teri Perl described how Lovelace compared the engine to the Jacquard loom, which also used punch cards:
"As in modern punch cards, the patterns of holes correspond to mathematical symbols. In Lady Lovelace's words, 'We may say most aptly that the Analytical Engine weaves algebraic patterns just as the Jacquard loom weaves flowers and leaves.'"
Thus Ada Byron Lovelace joined metaphorically the symbols of both the Industrial Age and the Information Age: the loom, the target of the Luddites; and the computer, the target of the Y2K bug.
Lady Lovelace also predicted computer music: "Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expressions and adaptations, the engine might compose elaborate and scientific pieces of any degree of complexity or extent."
Ada Byron Lovelace died young, at 36, the same age as her father when he died in Greece. But not before conspiring with Babbage to try to develop an "infallible system" to beat the odds on horse betting, a attempt that left them both in debt and scandal-ridden. Game theory went to the heart of her heart as well as her mathematics.
"As the first expositor of computer language and programming more than a century ago," Perl wrote two decades ago, "she is now beginning to receive a more appropriate place in the history of mathematics and science."
Gina is fortunate to be studying math at a time when public awareness of gender stereotypes is high and resources have been marshaled to address the problem.
The American Association of University Women (AAUW) is leading the effort. It followed up its 1992 report, "How Schools Shortchange Girls," last year with "Gender Gaps: Where Schools Still Fail Our Children."
Some of the recent report's key findings are listed on the Minnesota chapter AAUW Web site:
Science tells us that, generally speaking, boys have a slight edge over girls in math ability. "Enriched" schooling for girls doesn't seem to alter that edge among mathematically gifted children ages 5.5 to 8 years old (Science, "Girls + Boys + Math," March 6, 1998).
"Single-sex education," both in terms of schools and classes, has been growing despite the lack of evidence that it improves the picture for girls. One of the more visible schools for girls is the Girls' Middle School, a private school for sixth through eighth grade in Mountain View, California, in the heart of Silicon Valley. The school's focus, naturally, is on technology. Its mission is to help girls become tech savvy with the hope that they will take on technology leadership roles. The popular Web site Girl Tech also aims to encourage girls to aspire to leadership in science, technology, and math, but uses cyberspace rather than schoolspace.
The AAUW is concerned enough about "computer-shy girls" that it has commissioned a group of educators, researchers and software developers to look at the problem and make recommendations. In its account, the New York Times quoted AAUW executive director Janice Weinman as saying that, despite the progress girls have made in mathematics and science, "the area in which there appears to be a new boys club, so to speak, is technology." ("New Efforts Seek to Help Girls With Computer Education," July 8, 1998.)
MIT sociologist Sherry Turkle and former FCC commissioner Patricia Diaz Dennis have been recruited to lead the effort. Turkle has studied how girls and boys use computers in different ways and have different approaches to programming. In brief, boys tend to take a reductionist approach. Girls tend to take a free association approach. This conclusion will not come as a huge surprise to vigilant parents.
Even though Turkle is impressed how comfortable the current generation of kids is with "digital objects and virtual space," the challenge ahead, in a cyber era, is a familiar one: How can parents and educators impart critical reading skills to children? Reading has no equal when it comes to honing critical skills. ("An Ethnologist in Cyberspace," Scientific American , April 1998).
Which brings me back to Gina. We tackle math together on a now-and-then basis, but her "WEB" is mandatory. On that, she won't be denied. No evening is allowed to pass without addressing it.
Gina's WEB has nothing to do with computers or computer networks. It is a free association of a seemingly infinite variety of stories and books and book chapters that she selects from the school library and reads aloud in the presence of a parent. Upon its completion, each selection is duly recorded in a spiral notebook, dated and initialed by the parental overseer. The list constitutes her WEB, the "Wonderfully Exciting Books" program established by the St. Paul Schools.
It is a Jacquard loom at work in cerebral space weaving a mental fabric of exquisite patterns and gossamer dreams.
--William Hoffman firstname.lastname@example.org
Hypatia of Alexandria