I have been baffled by the recent avalanche of reform math materials making their way through public schools lately. I knew about the concept when my oldest son was in elementary school in California, and I went through California "Math Wars" until in ended in 1999, with a set of standards most scholars agreed were world class. I thought it was the same story in other states. Wrong, my dear Watson! Reform math resurfaced as Connected Math Project(CMP) in Oregon, and then again, in Washington, where I live.
My first introduction to CMP/CMP2 was about 2 years ago, when my daughter was taking it in the International School of Beaverton. I was already alerted to it by others in the Beaverton Math group, but nothing got me like dealing with it on a daily basis. After a few months, I was convinced that it was the modern equivalent of the Aesop's fable about the "stone soup". Let me explain:
* I would start with a chapter on CMP, which was supposed to be strong on explaining concepts, but irony of ironies - I could not find many good explanations of concepts that made sense to my "cursed" logical mind. So I decided to start with the base of Heymath! and had my daughter go through the many excellent animations of concepts. Voila! She would come out with a great intuitive grasp of the concepts. This was especially true for geometric concepts.
* I would look for examples of solved problems in CMP books, so that she can learn standard ways to solve them. Again, no go. So, I added a dash of examples from my old Glencoe California text books, that had worked out examples on the concepts. She had no trouble figuring out how to solve the problems after that. That took care of the examples issue.
* Then I noticed CMP was weak on skill building, since there were too few exercises that honed in a specific concept. So we added a healthy serving of Kumon exercises, and that took care of her skill building.
Pretty soon, we were sold on the concept of discovery based learning. We "discovered" that we could build an excellent math program with right proportions of Heymath, Glencoe, and Kumon, and did not need the CMP2 books at all. So we threw it out of the "stone soup".
We still keep our "recipe" handy for home schooling :-)
Monday, June 23, 2008
Tuesday, June 10, 2008
Of Social and Economic justice
Social justice keeps coming up as a topic whenever I hear about ed schools. My son's middle school English teacher kept bringing it up as a topic whenever I talked to her. At that time, I was quite naive to what was behind her assertions. Since then, I have read up enough to understand what the ideological underpinnings are. As I understand them, they go all the way back to the early 1900's. A lot has happened since then, and I think those ideas may be as outdated as buggywhips. Let me attempt to explain why I think so:
Social justice cannot exist in a vacuum. For lasting social justice, economic justice must come first. When I was a kid growing up in India, the prime minister, Nehru, was impressed by the quick rise of the Soviet Union, and decided that India should be socialist too. But with a majority of the population under poverty line, there wasn't much that could be done with meagre resources. The running joke at that time was that India could not afford a socialistic system, because the only thing we had plenty enough to share, was poverty. But the government went ahead anyway. Three decades later, rampant corruption and incompetence accelerated the "redistribution of poverty", had only succeeded in making more people poor while the rich got richer. It wasn't until 1991 that government owned enterprises were sold, and free market reforms allowed competition in all areas (including education).
Now the question comes - how does one achieve economic justice? What is economic justice, anyway? Very simply put, economic justice links income to productivity. In other words, if someone works more efficiently, they should earn more. In the US, since the 1970's, this has been going in reverse. All the improvements in technology have made the American worker more productive than ever, but the compensation has gone down in real terms. Why is that? One big component has been the relatively stagnant number of people working in wealth creating professions like engineering, science and mathematics. The only new job creating branch of mathematics to come out in the last century, computer programming, has employed millions in high paying jobs worldwide, but still is viewed as a profession of social outcasts in this country. So, I will assert that there can be no social justice, while the culture actively banishes the professions that create economic justice. If you take this to an extreme, you will see why Prof. Yunus, an Economics Professor from Bangladesh, received his Nobel Peace Prize (and not the Nobel prize for Economics). Yunus, it turns out, created the concept of microfinance. He created a bank that would loan as little as $10 to women who worked at home weaving rugs and baskets. Who in turn would sell their wares at the local market, and pay back the loan. There was no collateral required, just trust. The concept became so wildly successful that other countries in Asia nad Africa are implementing it. In their recognition letter to Dr. Yunus, the Nobel Committee noted :"Lasting peace can not be achieved unless large population groups find ways in which to break out of poverty." In other words, social injustice (leading to conflicts around the globe) cannot be rooted out without removing economic injustice i.e., eradication of poverty.
Social justice cannot exist in a vacuum. For lasting social justice, economic justice must come first. When I was a kid growing up in India, the prime minister, Nehru, was impressed by the quick rise of the Soviet Union, and decided that India should be socialist too. But with a majority of the population under poverty line, there wasn't much that could be done with meagre resources. The running joke at that time was that India could not afford a socialistic system, because the only thing we had plenty enough to share, was poverty. But the government went ahead anyway. Three decades later, rampant corruption and incompetence accelerated the "redistribution of poverty", had only succeeded in making more people poor while the rich got richer. It wasn't until 1991 that government owned enterprises were sold, and free market reforms allowed competition in all areas (including education).
Now the question comes - how does one achieve economic justice? What is economic justice, anyway? Very simply put, economic justice links income to productivity. In other words, if someone works more efficiently, they should earn more. In the US, since the 1970's, this has been going in reverse. All the improvements in technology have made the American worker more productive than ever, but the compensation has gone down in real terms. Why is that? One big component has been the relatively stagnant number of people working in wealth creating professions like engineering, science and mathematics. The only new job creating branch of mathematics to come out in the last century, computer programming, has employed millions in high paying jobs worldwide, but still is viewed as a profession of social outcasts in this country. So, I will assert that there can be no social justice, while the culture actively banishes the professions that create economic justice. If you take this to an extreme, you will see why Prof. Yunus, an Economics Professor from Bangladesh, received his Nobel Peace Prize (and not the Nobel prize for Economics). Yunus, it turns out, created the concept of microfinance. He created a bank that would loan as little as $10 to women who worked at home weaving rugs and baskets. Who in turn would sell their wares at the local market, and pay back the loan. There was no collateral required, just trust. The concept became so wildly successful that other countries in Asia nad Africa are implementing it. In their recognition letter to Dr. Yunus, the Nobel Committee noted :"Lasting peace can not be achieved unless large population groups find ways in which to break out of poverty." In other words, social injustice (leading to conflicts around the globe) cannot be rooted out without removing economic injustice i.e., eradication of poverty.
Monday, June 9, 2008
I received an email from a friend about a kid in Canada, who is writing a play about a company trying to capture all the kid's calculating ability in their calculators, and then sell it back to them for profit. My reaction to that was, "Hey, where have you been? It has been happening in the US for the last two decades, under the name of reform math curricula." A calculator could pretty much automate anything anyone could do mentally since the 1970s, and it did not take very long for them to be sold as a substitute for human's ability to figure, rather than an aid or a tool.
But we have come a long way since then.
Consider this:
When I joined Intel in 1982:
They had just announced the IBM PC with 4.77MHz processor with less than 30,000 transistors
The typical DRAM memory chip density was 64 kbit
No hard disk, but 256 kB floppy drives
Large enough to fit on an average sized desk
When I left Intel in 2006:
A high end laptop had 2 cores running at 2.2 GHz - Almost 1000x (100,000%) of the throughput
The DRAM memory chip was 1Gbit, which is 13,000x (1,300,000%) in density
Typical hard disk size was 100 GB, which is 4,000x (400,000%) in size
All this in a size and weight that was low enough to fit in a backpack.
Never in the history of humankind has there been such an exponential increase in any capability in such a short time. All this started in a small area called the Silicon Valley right here in the US of A.
Now comes the shocker. The ability to take economic advantage of this explosion in the number of transistors has fled this country. What discipline takes advantage of such an exponential rise in the number of transistors? It is the newest branch of mathematics - computer programming. The graduates of computer science make $60,000 right out of school, and easily double their income within a decade. And if we look around and ask if we are preparing enough kids to be excited about these high paying careers in computer programming, the answer comes back negative. The number of computer science graduates has remained flat at around 60,000 per year, or gone down slightly in the last two decades. India now produces 10 times the number of programmers per year, and the number is expected to double in the next decade. Just one institute in India, the NIIT (National Institute of Information Technology) trains 500,000 programmers per year. I am happy that this is helping a lot of Indian people escape poverty, but this is way lopsided in one direction. We could have done better training our kids to take the high paying jobs. But with the jock culture that is pervasive, I get the feeling we are just training our kids to be used car salespeople (like we need more of them).
Next time you go to your friendly neighborhood public school, ask them what computer science courses they offer. If you get blank stares, don't be surprised. I already warned you.
But we have come a long way since then.
Consider this:
When I joined Intel in 1982:
They had just announced the IBM PC with 4.77MHz processor with less than 30,000 transistors
The typical DRAM memory chip density was 64 kbit
No hard disk, but 256 kB floppy drives
Large enough to fit on an average sized desk
When I left Intel in 2006:
A high end laptop had 2 cores running at 2.2 GHz - Almost 1000x (100,000%) of the throughput
The DRAM memory chip was 1Gbit, which is 13,000x (1,300,000%) in density
Typical hard disk size was 100 GB, which is 4,000x (400,000%) in size
All this in a size and weight that was low enough to fit in a backpack.
Never in the history of humankind has there been such an exponential increase in any capability in such a short time. All this started in a small area called the Silicon Valley right here in the US of A.
Now comes the shocker. The ability to take economic advantage of this explosion in the number of transistors has fled this country. What discipline takes advantage of such an exponential rise in the number of transistors? It is the newest branch of mathematics - computer programming. The graduates of computer science make $60,000 right out of school, and easily double their income within a decade. And if we look around and ask if we are preparing enough kids to be excited about these high paying careers in computer programming, the answer comes back negative. The number of computer science graduates has remained flat at around 60,000 per year, or gone down slightly in the last two decades. India now produces 10 times the number of programmers per year, and the number is expected to double in the next decade. Just one institute in India, the NIIT (National Institute of Information Technology) trains 500,000 programmers per year. I am happy that this is helping a lot of Indian people escape poverty, but this is way lopsided in one direction. We could have done better training our kids to take the high paying jobs. But with the jock culture that is pervasive, I get the feeling we are just training our kids to be used car salespeople (like we need more of them).
Next time you go to your friendly neighborhood public school, ask them what computer science courses they offer. If you get blank stares, don't be surprised. I already warned you.
Sunday, June 1, 2008
Of soccer, baseball, and chess parents
My family moved to Oregon in the year 2002. My wife and I had 3 kids in tow, one in high school, and two in elementary school. Education and extra curricular activities, of course, were high on our list. We had done our homework, calling the school districts, having phone meetings, from California, the whole works. We even made the decision to buy our home based on the schools, as most parents do. Besides academics, our kids were active in soccer and chess, so we found a school with a chess club close by. The club had many parents who were very involved. As a matter of fact, all chess lessons were taught by parents in the evening. Many parents attended the classes along with their kids, so they could learn. I had not paid much attention to the demographics of the club, but it appeared to me that more and more members were coming from immigrant families. As time went by, one thing led to another, and I led the start up of a new statewide organization in Oregon to promote chess competitions, called the Oregon Scholastic Chess Federation. And again, in our first two state championships, I saw more and more immigrant families bringing their children to the state championships.
In parallel, my wife and I did our duty as soccer parents also. My wife and I signed up as volunteer coaches, and did our duty as soccer parents. Again, there were a disproportionate number of immigrant's kids in our soccer teams, albeit not as lopsided in chess. Then my son, then a fifth grader, expressed an interest in joining a baseball team. I had no clue about baseball, but I had played enough cricket in my life to understand his interest. We signed him up for a team. I had not paid attention earlier in the season, but as time went on, I saw hardly any immigrant's children on the team.
Fast forward to yesterday, when I was at the Portland Chess Club, where my kids were playing in their monthly tournament. I bumped into a professor from U of O, who had driven his son all the way from Eugene to play. He and I were killing time, talking about our common experiences. It turns out he was an immigrant from Scandinavia. He brought up the observation that in all the chess events he has been to in Oregon, he sees more and more kids of immigrants. To a lesser extent, in Soccer. In Europe, of course, he was just used to seeing Europeans in both events. He wondered, where all the native born kids were. Surely, there are enough of them in the same economic brackets and similar leisure times. What do they do on the weekends?
His last remark took me back to my son's baseball years, where most kids came from middle to upper middle class families. The coach called his son "A-Rod", and drilled the team like an army drill master. He yelled and screamed at kids who did not perform up to his expectations, but I did not see any parents complain. When I thought he was being a little over the top, I would quietly bring it up with other parents, and they would say something like "oh, the kids need to know it is rough out there. He means well. Besides, it builds character." I thought, all this to make sure someone knows how to handle a fastball? Wouldn't it make more sense for his kid to take up an activity, like chess, that has been proven to build intelligence? After all, it has some immediate benefits like helping them do well in school. In many conversations I would strike with the parents about chess, they would either change the subject, or dismiss it summarily. I felt as though academic and intellectual achievement was either not valued, or was just plain taken for granted.
Back to the present, the professor and I parted with a shared understanding that there are some deep cultural divides that separate first generation immigrants from the rest of the population. When I came home, I saw the day's newspaper. I saw that the top two National Spelling Bee contestants were children of Indian immigrants. I said to myself - yes, the cultural divide is alive and well.
In parallel, my wife and I did our duty as soccer parents also. My wife and I signed up as volunteer coaches, and did our duty as soccer parents. Again, there were a disproportionate number of immigrant's kids in our soccer teams, albeit not as lopsided in chess. Then my son, then a fifth grader, expressed an interest in joining a baseball team. I had no clue about baseball, but I had played enough cricket in my life to understand his interest. We signed him up for a team. I had not paid attention earlier in the season, but as time went on, I saw hardly any immigrant's children on the team.
Fast forward to yesterday, when I was at the Portland Chess Club, where my kids were playing in their monthly tournament. I bumped into a professor from U of O, who had driven his son all the way from Eugene to play. He and I were killing time, talking about our common experiences. It turns out he was an immigrant from Scandinavia. He brought up the observation that in all the chess events he has been to in Oregon, he sees more and more kids of immigrants. To a lesser extent, in Soccer. In Europe, of course, he was just used to seeing Europeans in both events. He wondered, where all the native born kids were. Surely, there are enough of them in the same economic brackets and similar leisure times. What do they do on the weekends?
His last remark took me back to my son's baseball years, where most kids came from middle to upper middle class families. The coach called his son "A-Rod", and drilled the team like an army drill master. He yelled and screamed at kids who did not perform up to his expectations, but I did not see any parents complain. When I thought he was being a little over the top, I would quietly bring it up with other parents, and they would say something like "oh, the kids need to know it is rough out there. He means well. Besides, it builds character." I thought, all this to make sure someone knows how to handle a fastball? Wouldn't it make more sense for his kid to take up an activity, like chess, that has been proven to build intelligence? After all, it has some immediate benefits like helping them do well in school. In many conversations I would strike with the parents about chess, they would either change the subject, or dismiss it summarily. I felt as though academic and intellectual achievement was either not valued, or was just plain taken for granted.
Back to the present, the professor and I parted with a shared understanding that there are some deep cultural divides that separate first generation immigrants from the rest of the population. When I came home, I saw the day's newspaper. I saw that the top two National Spelling Bee contestants were children of Indian immigrants. I said to myself - yes, the cultural divide is alive and well.
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