Last week I purchased a burger at Burger King for $1.58. The counter girl took my $ 2 and I was digging for my change when I pulled 8 cents from my pocket and gave it to her. She stood there, holding the nickel and 3 pennies, while looking at the screen on her register. I sensed her discomfort and tried to tell her to just give me two quarters , but she hailed the manager for help. While he tried to explain the transaction to her, she stood there and cried. Why do I tell you this? Because of the evolution in teaching math since the 1950s:
1. Teaching Math In 1950s
A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price. What is his profit ?
2. Teaching Math In 1960s
A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price, or $80. What is his profit?
3. Teaching Math In 1970s
A logger sells a truckload of lumber for $100. His cost of production is $80. Did he make a profit?
4. Teaching Math In 1980s
A logger sells a truckload of lumber for $100. His cost of production is $80 and his profit is $20. Your assignment: Underline the number 20.
5. Teaching Math In 1990s
A logger cuts down a beautiful forest because he is selfish and inconsiderate and cares nothing for the habitat of animals or the preservation of our woodlands. He does this so he can make a profit of $20. What do you think of this way of making a living? Topic for class participation after answering the question: How did the birds and squirrels feel as the logger cut down their homes? (There are no wrong answers, and if you feel like crying, it's ok. )
6. Teaching Math In 2009
Un hachero vende una carretada de maderapara $100. El costo de la producciones es $80. Cuanto dinero ha hecho?
7. Teaching Math In 2010
Who cares, just steal the lumber from your rich neighbor's property. He won't have a gun to stop you, and the President says it's OK anyway cuz its redistributing the wealth.
Monday, August 23, 2010
Math Education...
Via my brother Mark:
Russian Minorities in Estonia...
Regular readers know that I have visited both Estonia and Russia many times, and that I have friends there. Many of my friends are ethnic Russians; some are ethnic Estonians. The history of Estonia is very complicated; the country has been independent twice, for a total of well under a hundred years. The rest of the time it has been ruled by another country. Most recently that was the Soviet Union, which was dominated by Russians. The history of the Soviet domination of Estonia is not pretty – many Estonians suffered greatly under Soviet rule (including many who were outright killed). In addition, the Soviets actively suppressed the Estonian culture and language, trying to force the integration of Estonians into the Soviet Union. So naturally once Estonia gained its independence from the Soviet Union (in 1991), there was a great deal of tension between the ethnic Russian and Estonia communities. That tension continues to this day.
It's easy to understand this tension in the abstract. The history is clear. The Estonians have good reason to be angry and resentful about their treatment at Soviet (mainly Russian) hands. It's much harder to analyze in the concrete sense of people that you know.
Many ethnic Russians whom I know bear no ill will toward Estonians. They think of the historical treatment of Estonians as history, and not something they bear any personal responsibility for. At the same time, many of them would like to continue using their language and to be free to become citizens.
Many ethnic Estonians whom I know bear no ill will toward Russians. They think of the historical treatment of Estonians as history, and not something they've been personally subjected to. At the same time, most of them support their government's efforts to enforce Estonian as the country's language – and in particular to require fluency as a prerequisite for citizenship.
I don't see any easy answers out of this. I can easily place myself in the position of any of the people I know, and think about it from their perspective. History has dealt the people of Estonia a tough hand in current times, and I suspect the only “solution” is to let a lot of time go by. Decades, probably, before these tensions fully subside...
It's easy to understand this tension in the abstract. The history is clear. The Estonians have good reason to be angry and resentful about their treatment at Soviet (mainly Russian) hands. It's much harder to analyze in the concrete sense of people that you know.
Many ethnic Russians whom I know bear no ill will toward Estonians. They think of the historical treatment of Estonians as history, and not something they bear any personal responsibility for. At the same time, many of them would like to continue using their language and to be free to become citizens.
Many ethnic Estonians whom I know bear no ill will toward Russians. They think of the historical treatment of Estonians as history, and not something they've been personally subjected to. At the same time, most of them support their government's efforts to enforce Estonian as the country's language – and in particular to require fluency as a prerequisite for citizenship.
I don't see any easy answers out of this. I can easily place myself in the position of any of the people I know, and think about it from their perspective. History has dealt the people of Estonia a tough hand in current times, and I suspect the only “solution” is to let a lot of time go by. Decades, probably, before these tensions fully subside...
Imaging Molecules...
Morning Walk, on the Morning After...
A nearly perfect full moon was low in the southern sky, bright enough to show colors nearby and to see the mountains to our north clearly. Most of the stars were washed out by its glow, but in the northeast Orion was visible – for the first time this year (at 3:30 am), all of it was above the horizon.
The dogs this morning didn't seem to smell anything in particular. Race was bouncing around at the end of his leash, looking for pine cones to catch. The three field spaniels were all tugging strongly, each trying to pull me in a different direction. The vector sum of the force on the least this morning was less than a half-dog (where one dog is the force that an average field spaniel can exert); it was easy to hold them all still. But when I tried to walk anywhere, the dogs opposing my motion seemed to redouble their efforts, and the vector sum rose to over a dog, maybe close to two dogs. It made walking challenging!
The morning after what, you ask? Why, the morning after a (for me) vast expenditure of physical effort. My mother-in-law (Kate) is coming to visit with us on Friday, as she does on most years. We have a spare bedroom that she stays in while she's visiting – these days, she's the only one who uses it. The rest of the time that room is stuffed to the gills with stored things – everything from Christmas decorations to slide rules. So to get ready for her visit, I have to move all that stuff into our living room, where I pile it all the way to the ceiling in one corner. Then I set up her bed and generally make the room livable. So yesterday I did all this moving – I'm guessing about 3,000 pounds of stuff. And this morning I'm feeling it...
The dogs this morning didn't seem to smell anything in particular. Race was bouncing around at the end of his leash, looking for pine cones to catch. The three field spaniels were all tugging strongly, each trying to pull me in a different direction. The vector sum of the force on the least this morning was less than a half-dog (where one dog is the force that an average field spaniel can exert); it was easy to hold them all still. But when I tried to walk anywhere, the dogs opposing my motion seemed to redouble their efforts, and the vector sum rose to over a dog, maybe close to two dogs. It made walking challenging!
The morning after what, you ask? Why, the morning after a (for me) vast expenditure of physical effort. My mother-in-law (Kate) is coming to visit with us on Friday, as she does on most years. We have a spare bedroom that she stays in while she's visiting – these days, she's the only one who uses it. The rest of the time that room is stuffed to the gills with stored things – everything from Christmas decorations to slide rules. So to get ready for her visit, I have to move all that stuff into our living room, where I pile it all the way to the ceiling in one corner. Then I set up her bed and generally make the room livable. So yesterday I did all this moving – I'm guessing about 3,000 pounds of stuff. And this morning I'm feeling it...