Math in the real world

Excerpt from:
Multiple Numeric Competencies: When a Number Is Not Just a Number
by Ellen Peters & Par Bjalkebring
Journal of Personality and Social Psychology
May 2015, Vol. 108, No. 5, 802–822

Jeff is a friend of one of the authors and a highly skilled carpenter who claims he is “no good at math.” He excels, however, at estimating the angles, lengths, and areas that are critical to his craft. Ruth, a smart and personable woman in her 70s, broke down crying while attempting to answer questions about numeric data in a Medicare insurance choice experiment. She explained through tears that she was “not a numbers person” and that her husband always did such tasks for them until his death 2 years prior. Numbers were fraught with emotion for her. Individuals like Jeff and Ruth are common. Although students often ask why they should learn math and whether it will ever be useful, Jeff and Ruth provide examples of the importance of everyday math, belief in one’s numeric ability, and (in Jeff’s case) how compensatory numeric skills might exist.

Making good choices in life often involves understanding and using numeric information (Hibbard, Peters, Slovic, Finucane, & Tusler, 2001; Thaler & Sunstein, 2003; Woloshin, Schwarz, & Welch, 2004). Choosing the best health insurance involves calculating likely annual costs from monthly premiums, deductibles, and office and pharmacy copayments. Making an informed decision about a medical treatment or screening option requires understanding risk and benefit information (including their probabilistic nature). Such numeric data are provided to facilitate informed choices, but numbers can be confusing and difficult for even the most motivated and skilled individuals, and these issues are exacerbated among the less numerate. In the present article, we explore the value of explicitly considering multiple measures of numeric competence—objective numeracy, subjective numeracy, and the mapping of symbolic numbers. We review their likely interrelations, test their possible dissociable roles in evaluations and decision processes, and consider future directions in personality and social-psychological processes.

I find the image of a woman in her 70s crying over math profoundly sad.

I guess that's what I was trying to say about my years reteaching math at home--about not getting what I wanted, but getting what I needed instead. (scroll down to end of post)

After all the crying shouting over math around here during the middle years, I'm pretty sure I managed to raise a child who does not, at this point, define himself as "no good at math."

It wasn't easy.

But it was definitely fun.

Books are better

On NPR this morning:

The book also has fans from other unexpected quarters. David Gelernter, a professor of computer science at Yale, pioneered advances like "parallel computation," yet he admires the brilliant design of the codex. "It's an inspiration of the very first order. ... It's made to fit human hands and human eyes and human laps in the way that computers are not," he says, wondering aloud why some are in such a rush to discard a technology that has endured for centuries. "It's not as if books have lost an argument. The problem is there hasn't been an argument. Technology always gets a free pass. ... [People] take it for granted that if the technology is new it must be better."

~~~~~~~~~~~~~~

As far as I can tell, the reason inferior technology wins inside schools isn't that "people" take it for granted. 

The reason is that tech companies sell to schools who force iPads and Chromebooks on families and taxpayers.

That's certainly been my experience here.

Art Garfunkel, thinking in proportions

In the Telegraph:

[Art Garfunkel] also does a lot of mathematics, having read it as a student at Columbia. “I’m precise. I think in proportions. I play games with numbers and I proportionalise. I imagine we have now done 1/8th of our interview.” I check my watch.

He even took a job as a maths teacher at one point, in the Seventies, despite being a world famous pop star.

“I’d just got married and moved to Connecticut, and there was a nearby preparatory school and so I taught math there. It was a weird stage of my life, to leave Simon & Garfunkel at the height of our success and become a math teacher. I would talk them through a math problem and ask if anyone had any questions and they would say: “What were the Beatles like?”

[snip]

When he drifts off back to the lifts, singing to himself again, I check my watch. Turns out his mental clock, when he guessed how far we were through the interview, was exactly right.

Art Garfunkel on Paul Simon: 'I created a monster'
By Nigel Farndale | 10:25PM BST 24 May 2015

How to Google stuff when you don't know anything

I've been joking with some of my friends about how exactly you would Google stuff when you don't know anything about the subject you're Googling.

Take history.

How do you Google history when you don't know any history?

What is your question?

"Did something bad happen one hundred years ago that I should know about?"

Robert Shiller has a really bad idea

In the Times today:

Most people complete the majority of their formal education by their early 20s and expect to draw on it for the better part of a century. But a computer can learn in seconds most of the factual information that people get in high school and college, and there will be a great many generations of new computers and robots, improving at an exponential rate, before one long human lifetime has passed.

Two strains of thought seem to dominate the effort to deal with this problem. The first is that we teachers should define and provide to our students a certain kind of general, flexible, insight-bearing human learning that, we hope, cannot be replaced by computers. The second is that we need to make education more business-oriented, teaching about the real world and enabling a creative entrepreneurial process that, presumably, computers cannot duplicate. These two ideas are not necessarily in conflict.

What to Learn in College to Stay One Step Ahead of Computers by Robert J. Shiller | May 22, 2015

Number 1: General, flexible, insight-bearing human learning in the sense of "critical thinking" does not exist, and you would know this if you troubled yourself to dip into the relevant research in cognitive science before writing an op-ed for the New York Times.

Number 2: We already know what type of education produces general-flexible-insight-bearing-human-learning, and that is liberal education, precisely the kind of education Shiller is argues we should abandon because computers. Liberal education gives students a broad foundation in history, literature, science, math, and the social sciences, which they can then draw upon for a lifetime. I am living proof. I'm still using my Wellesley/Dartmouth education in psychology to write books about the brain. I learned nothing about the brain in college, but I can write about the brain today because I learned some fundamentals of biology, math, and psychology.

Number 3: New computers and robots don't invent themselves. If students don't study computer science in college and graduate school, there aren't going to be any new generations of computers and robots.

Speaking of which, Ed attended the Masters graduation ceremony at NYU last week. Every student receiving a degree in math was Asian, and all seemed to be Asian-Asian, not Asian American. Same with computer science.

Number 4: Business-oriented...real world...creative entrepreneurial process.... This is exactly what public schools have now moved on to. (In my district, Common Core has been swallowed whole by Tony Wagner, and I see the same process elsewhere.)

Why spend another four years, not to mention many thousands of dollars in tuition, room, and board, doing more of the same in college? Surely 13 years of pretend entrepreneurialism is sufficient.

Which reminds me.

C. took a marketing course this semester.

I was excited. I wanted to learn what there is to learn about marketing, too, and I figured I would.

Nope.

The course had no textbook, just case studies, which I never did manage to get my hands on. The class seems to have learned something about loss aversion, and also something about not dissing your initial contact at a hospital you're trying to sell major medical equipment to. Beyond that, nothing seems to have made much of an impression (which is not true with C.'s traditional liberal arts courses in history and literature).

As their final assignment for the course, students did a group project. C's group did theirs on tampons. (He was the only male in the group. So: tampons.)

The course did afford me one moment of joy.

C. came home and reported that the professor had given the class a marketing algorithm.

(Did I ever tell you that I taught C. to remember "algorithm" by having him recall "Al Gore has no rhythm"?)

The marketing class was mostly girls, and not one of them was having anything to do with the  algorithm. Not one. They wouldn't touch an algorithm with a 10-foot pole.

Not C.! Not only did C. deploy the algorithm--and with some alacrity, too--he was mildly scandalized by the fact that the rest of the class did not.

Also gratifying: C. seemed to have a pretty clear perception that There but for the grace of God go I. Sometimes having a mother who spends four years of her life reteaching the entire math curriculum at home comes in handy.

I've been savoring the moment ever since. My years of afterschooling didn't achieve what I wanted them to, but they did do what I needed them to. C. didn't make it to calculus (that's another whole story), but he is today a young adult who is on reasonably good terms with mathematics, and who will be able and willing to learn whatever math he needs to learn as an adult.


Other famous people with really bad ideas:
Kofi Annan
David Brooks
The Daily
Barry Eichengreen
Reed Hastings
President Obama
Larry Summers