kitchen table math, the sequel: 9/6/15 - 9/13/15

Wednesday, September 9, 2015

Terrific comments on Willingham's "Teachers Aren't Dumb"

As a parent whose children just graduated from elementary school, I whole heartedly agree. Some of my kids' teachers were wonderful writers, but a lot of them seemed to have a middling grasp of basic grammar. Once, a teacher corrected my son's proper use of "all together" as in "My family was all together" to read "My family was altogether." That was altogether unfortunate! No wonder the kids can't spell.


I could not agree with Mr. Willingham more. I would only add that there is a huge ideological hurdle to surmount that dwarfs the one requiring an overhaul of the teaching of the teachers. It is ideological. There is a mass of thought that children will learn to read when they are ready, instead of learning because they are given the tools and taught. There is a revolt against "drilling". It's true in math, science, and all the literary arts: reading, writing, spelling.

Many, many children today are labeled learning disabled when they are only curriculum disabled. There is no artist, athlete, farmer, architect, doctor or nurse that didn't have to practice, didn't have to memorize information so that it might be accessed instantaneously without thought when needed. But somehow asking teachers to cause children to practice and children to do so is perceived as destructive, uncreative. Even coders practice, fail and try again. It's called a learning curve


My daughter transferred to a university that has a fast-track program to certify STEM majors as teachers. In her 2nd day of her introduction to teaching class, the lecturer, a former geneticist, said "We don't believe in the scientific method." She said there are no truths. This is part of the discredited pedagogy they are pushing: that teachers are the "guide on the side" and are hardly even allowed to tell students things. Students are expected to come up with complex rules themselves.

As someone who has been teaching math and Computer Science at the college level for 20 years, this makes my skin crawl. Actually I wouldn't know how bad this method of teaching is unless they had already tried to practice it on my daughter. Perhaps there is some good way to do this, but how it ends up in the hands of young unskilled, poorly educated, teachers is that they don't tell the students anything and the students flounder, feel lost, get discouraged, and doubt themselves. It makes me crazy.

Teachers Aren't Dumb by Daniel Willingham 9/8/2015

Tuesday, September 8, 2015

Just world

For quite a while now, I've been fascinated by the degree to which a sense justice comes built in (not just in people but in "non-human" animals as well):
When responding to ownership violations, children can focus on the victim’s needs, the perpetrator’s punishment, or both. Recent studies show that 3- and 5-year olds are equally likely to respond to second- and third party violations, and 3-year-olds return objects to their rightful owners. Children’s interventions are consistent with justice for victims.


Together, these results suggest that although children intervene in loss events experienced by them- selves and others, their interventions are a general re- sponse to any unpermitted loss of property rather than punishment of theft.

Young children remedy second- and third-party ownership violations
Julia W. Van de Vondervoort and J. Kiley Hamlin
Trends in Cognitive Sciences | September 2015, Vol. 19, No. 9
A "second-party" violation means that the child himself or herself was the victim; a third-party violation means that a puppet was the victim.

In either case, your basic 3-year old's attitude, with which I completely agree, is: Give it back.

I wonder at what age children start to feel that justice requires punishment? (Or perhaps children at this age innately feel that punishment relates to a different set of wrongs?)

I'm pretty sure I've come across a fair amount of research showing that a desire to see wrongdoing punished is built-in, too.

Monday, September 7, 2015

Aloha from guillotine-deadline land

This weekend's events:

I just got the answer to this problem right:
Ten out of every 1,000 women have breast cancer. Of these 10 women with breast cancer, 9 test positive. Of the 990 women without cancer, about 89 nevertheless test positive. A woman tests positive and wants to know whether she has breast cancer for sure, or at least what the chances are. What is the best answer?
I realize most ktm readers can do this in their sleep, but I had to reason it through ... and I did!

That really makes me happy.

Which brings me to yesterday's challenge: I wrote a proof!

On purpose!

I had been talking to friends about index funds, the stock market, and the ever-terrifying Federal Reserve...and pretty soon I found myself utterly confused.

My question was whether Ed and I needed to get the 401(k) out of an index fund and into cash while the stock market is losing its mind.

Both of my friends seemed to think that something called "dollar cost averaging," which I had never heard of, meant that you don't actually lose more money when the stock market declines because your dollar cost average now goes down as you buy more shares with each new deposit into the 401(k).

One said she sees stock market declines as opportunities to buy more stock at a discount. She doesn't seem to worry about stock market "corrections" at all.

Neither of my friends was making an argument about timing the market. Both seemed to be saying that when the market falls, your dollar cost average falls, too, so you come out OK regardless of whether the market has hit bottom or not.

I was so flummoxed that I pulled up an Excel sheet and did three hypotheticals comparing two investors starting with the same amount of money distributed between the market and savings. In each one the investor who stayed in the index fund as it sank, or who put more money into the fund from savings as it sank, ended up worse off.

Then I wrote a proof!

That was a moment.

Regardless of whether my proof is correct or incorrect, I had just had a real-life experience of the incredible power of mathematical proof. I was thinking about all those people asking when students will ever use algebra in 'real life' -- I just used mathematical proof in real life.

Several years ago, I read a book which explained that a loss is a loss is a loss: money you've lost in the stock market today doesn't come back tomorrow. That made sense to me, but now I find that, apparently, few people believe it.

And it is a hard idea to hold on to, because intuitively it feels like money "comes back" when the stock market rises again.

Intuitively, it feels like you lose the money only when you sell after the loss, not when you hold.

Now I can look at my proof and know that money lost is money lost. You can sell, you can hold. Either way, that money is gone.

What to do about it--if anything--is another question, of course.