Middle and High School … from a Montessori Point of View
With recent hopes of democracy and a new renaissance of the Islamic world, it’s perhaps appropriate to look back at the contributions that came from Muslim lands. This includes works in the fields of optics, ecology, engineering, algebra, mostly done in the years between 800 and 1250 A.D.. David Beillo has a wonderful slideshow in Scientific American.
Being a scientist is a state of mind. It’s really a way of looking at the world with wonder, curiosity, and logical rigor. Once you realize that, and get past the tedium of moving little bits of water from one place to the next, or peering through endless mathematical equations and lines of code, you’ll be a lot happier. At least that’s what I got out of Adam Rubin’s essay, “Experimental Error: Most Likely to Secede.”
His memories of growing up a scientist in middle school:
A scientist in middle school: Some of my classmates seem to have gotten large and confident very quickly. And the kids with the most friends are the ones who think science is lame. But I want friends. And I don’t think science is lame. Ah, the eternal question: WWDHD? (“What would Don Herbert do?”)1
Science questions explored: What is the difference between “weight” and “mass,” and why won’t you understand it no matter how many times it’s explained? What is static electricity, and why won’t you understand it no matter how many times it’s explained? What is a hypothesis, and why won’t you understand it no matter how many times it’s explained?
— Rubin (2011): Experimental Error: Most Likely to Secede
After going through the free-market part of the economic system simulation, the least wealthy people –the students who ended up with the least kilobucks— staged a socialist revolution.
Well the most wealthy students were not too happy with that, because the revolutionaries confiscated all their wealth, assigned them all jobs (to simulate a command socialist economy), and started paying everyone equally. One student, assigned to produce food, produced a chicken, a cookie, and a dead socialist. She got sent to jail.
Fortunately, for her at least, she was able to get hold of a phone that had been left lying around from the market part of the simulation, so she sent a simulated text to her fellow former oligarch to try to start the counter revolution. She got a return text:
It’s nice to see that our time spent talking about Egypt has not been wasted.
Evan Ratliff has an excellent article that ties well into our discussions of evolution. It’s on the breeding of foxes to make them want human companionship, much the same way wolves were domesticated.
… researchers … gathered up 130 foxes from fur farms. They then began breeding them with the goal of re-creating the evolution of wolves into dogs, a transformation that began more than 15,000 years ago.
— Ratliff (2011), in National Geographic, Taming the Wild
It worked remarkably well, and not just with foxes, but with rats and mink as well.
The scientist in charge, Dmitry Belyaev, was looking into something that Darwin observed in 1868: domesticated animals are smaller, with floppier ears and curlier tails, than their untamed ancestors.
In terms that we’ve studied, domesticated animals all have similar physical characteristics (phenotype) and Belyaev wanted to find the genotype. His theory is that there is:
… a collection of genes that conferred a propensity to tameness—a genotype that the foxes perhaps shared with any species that could be domesticated.
— Ratliff (2011), in National Geographic, Taming the Wild
Well, it’s really kilobucks and economic systems, but that does not have the same rhythm for a title. We’re reprising the market versus socialist economies simulation game, my student came up with last year for his IRP.
I though I’d also include a little lesson on the metric system as a subtext. Hence the creation of the kilobuck. I’ll also talk about the centidollar, decidollar, decadollar and hectadollar.
Using the actual U.S. wealth distribution data from Norton and Arieli (2011; pdf), I created a little addendum to our exercise on the distribution of wealth.
I started with the definition of wealth. Students tend to think you’re referring to annual income, so I gave the example of someone who does not have a job but owns a house; they have no income but some wealth in the value of the house. Alternately, someone who has $2 million in the bank, but owes $4 million, actually has negative wealth.
Then I drew a little stick figure diagram to represent the population of the United States. With ten figures, paired up, that gives five parts, aka quintiles.
Students were then presented with an empty bar graph and asked, “How much of the U.S.’s wealth is owned by the wealthiest 20% of the population?” Instead of asking in percentages (as are shown in the graph), I asked them to assume that the total wealth in the U.S. is $100 trillion.
The first suggestion was $35 trillion, which is shown below. Others offered different amounts, ranging up to $50 trillion. Someone even suggested $15 trillion, which is not possible, since that would mean that the wealthiest 20% have less than 20% of the total wealth of the country.
Once they got the idea, I showed them what the graph would look like in an idealized socialist country, where everyone had the same wealth.
Finally, I asked my students to fill in what they believed to be the actual case for the U.S. for all five quintiles. The results had to add up to $100 trillion. They gave me their numbers individually before we broke up our meeting, and I entered it in the U.S. distribution of wealth spreadsheet to produce a graph.
After lunch, I showed them the results.
For dramatic effect, I hid the last two bars at first. We talked over their numbers, then I showed them the equal distribution case (which they’d seen before), and finally the actual distribution.
The response was salutary; a moment of surprised silence and then whispers. What then followed was a nice, short discussion. I pointed out the pie charts showing the U.S. versus an equal distribution, versus Sweden and asked what they would do, if they were an autocratic monarch, or if they were the president to make the U.S.’s distribution more equal.
We talked about the government just taking private property, like the communists did. Then we talked about progressive taxation. We ended by talking about the estate tax, and meritocracy, which we’d touched on in the morning.
I thought the exercise worked very well. Not only did we get into an interesting economic issue, but got some practice with math and interpreting graphs too.
SPENT is an online game that challenges you to survive for a month while facing the choices of someone poor, living in the United States.
The choices are hard, but the game ties in well with the personal finance part of the curriculum, as well as the consideration of the wealth distribution.
Razib Kahn has a fascinating interview with Milford Wolpoff, one of the main scientists behind the research that argues that humans are not all part of a single family tree, descended from a single ancestor who moved out of Africa about 200,000 years ago.
This section focuses on the theory, and has a nice explanation of what mitochondrial DNA is (and why it’s important):
It gives an excellent perspective on how science works, and how scientists work (scientists are people too with all the problems that entails).
The entire thing is a bit dense, but it’s one of the better discussions I’ve seen describing the process of science in action, with little hints at all the challenges that arise from personality conflicts and competing theories.