Division is the most powerful arithmetic operation. It makes comparisons. When the numerator and denominator have the same units, the comparison makes a dimensionless number, the only kind that the universe cares about. Long division, however, is something else entirely. In my post “Dump algebra,” many commentators objected to my loathing of long division. But long division is not division! Long division is just one way to do the computation, and is far from the most useful way.
On America’s first subway, Boston’s Green line, the middle doors stopped opening. When I asked the driver to open the doors, he said that he couldn’t: now all boarding and deboarding at the above-ground stops is through the narrow front door by the fare box. Ah, the MBTA: making up for the 23 percent fare hikes on July 1 with improved service!
Me: ”The new policy slows the ride for everyone. Now passengers cannot board and pay their fares until all the deboarding passengers have left.”
Driver, shrugging: ”It’s the new policy. I just do what my boss tells me to do. I don’t question.”
Me: ”We could use some questioning.”
Driver: ”Questioning isn’t part of my job. I just wait for my pay day.” Read More »
Fellow blogger Daniel Hamermesh recently explained the virtues of exchange as a painter helped him break into his Berlin apartment. My exchange example is not as glamorous. Shopping at the local co-op in Cambridge, I heard over the public-address system, “If you are the owner of a gray Subaru Outback, you are being towed!” I leaped over a low chain and made a break for the parking lot, as a mother nearby offered to watch my daughters (ages 1 and 4). The Subaru was hooked up and about to be hoisted onto the tow truck. In view of my timely arrival, the tow-truck operator offered two options: Pick up the car later that day in Somerville for $200, or pay $50 (cash) and he’d unhook the car now. An offer I couldn’t refuse. Everybody gained, yet I am still furious!
Being a good teacher, I like to think, requires a curious and freethinking mind. A supporting example is Andrew Hacker, described by a former Cornell colleague as “the most gifted classroom lecturer in my entire experience of 50 years of teaching.” His book Higher Education?: How Colleges Are Wasting Our Money and Failing Our Kids—and What We Can Do About It, co-authored with Claudia Dreifus, convinced me that tenure is harmful. His latest broadside, “Is Algebra Necessary?”, in last Sunday’s New York Times, is as provocative.
He argues that we should stop requiring algebra in schools. Despite the vitriol in several hundred comments (“We read them so you don’t have to.”), he is right. Read More »
As a country, we are often at war. If it’s not against Germany, England, terrorism, or Grenada, it’s the war on poverty (that’s gone so well), the war on cancer (ditto), and, of particular interest to me, the Math Wars, which have been raging for decades. On one side, the traditionalists insist on drilling and back to basics, “on behalf of sanity and quality in math education.” On the other side, the reformers insist on conceptual understanding using computers and calculators, to “promot[e] the rational reform of mathematics education.”
Both are half-right and half-crazy. As the reformers say, students need to understand what the mathematics means. Students whose word problem for “6 x 3 = 18″ is of the form “There were 6 ducks, and 3 more showed up, so 6 times 3 is 18,” understand little. (See “Children Learning Multiplication, Part 1,” in the articles by Professor Thomas C. O’Brien.) As the traditionalists say, using computers for everything leads to needing a calculator to compute what 6.5 x 10 is.
However, there’s a tool to combine the merits of both sides: the Quick, Approximate, Mental Arithmetic (QAMA) calculator. Read More »
One midnight, fed up from revising our dissertations all day, a friend and I drove the 10 minutes from Caltech into Chinatown to dine at Full House Seafood, open until 2 AM. (My Ph.D. adviser once asked why graduate students all seem to live on Guam time.) The restaurant was lively and crowded but not packed, and we quickly got a table. While waiting to give our order, I noticed an African-American man sitting on the chairs near the front counter. Even though several tables were free, the waiters did not offer him a table. Other customers came in, and were seated. As our dumplings arrived and got eaten, and then the spicy tofu, the man still sat on the small chairs. Read More »
I owe my favorite local bookstore, the Harvard Bookstore, for making another day for me. Wandering the tall, packed shelves on a warm and breezy evening, I ran across Schaum’s Outline of Principles of Economics. One subtitle on the cover: “964 fully solved problems.” The problems include, for example (from page 50): “True of false: As used in economics, the word demand is synonymous with need,” or “True or false: A surplus exists when the market price is above the equilibrium price.”
I didn’t long much for either answer.
Instead, as the U.S. mortgage market has, as James Kunstler predicted on October 10, 2005, imploded “like a death star” and dragged “every tradable instrument known to man into the quantum vacuum of finance that it create[d],” as euros flee from Greece, and as bank loans dry up in Spain, I wished that the 964 fully solved problems included one or two of the real problems.
Since putting email back in its corral, I’ve turned some recovered time to reading actual books in print — the latest being Retirement Heist: How Companies Plunder and Profit from the Nest Eggs of American Workers by Ellen E. Schultz. If a nation of sheep shall beget a government of wolves, then the lesson from Retirement Heist is that today the shears are sharpened with numbers.
Retirement Heist is, as one blurb describes, a “meticulously researched and gripping as a crime thriller.” Each chapter explains, with detailed research data and outrage-generating examples, yet another method corporations use to steal retirement benefits and mask the theft behind accounting shenanigans. It is one of the few books (since Cadillac Desert) to describe outrageous behavior so well that I threw it across the room. Read More »