Digging out the proof that is stuck in the pudding May 24, 2012
Posted by mareserinitatis in education, gifted, homeschooling, math, older son, teaching.Tags: CLEP, economics, geometry, math, older son, proofs
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Since the older boy was kicked out of school, I’d say he’s been doing more academically than before when he was in school. After he passed his GED in March, I asked him what he wanted to do until summer. He had the choice of getting a job or studying for a CLEP exam. He usually spends a good chunk of the summer with relatives, so he decided to wait on looking for a job and instead aimed to finish another CLEP. He chose to study macroeconomics. To do this, he got up nearly every morning and spent 3 hours at the university library (where he has no internet access), read through the entire textbook, and worked through the study guide. He passed the test on Monday, and we’re all very proud of him for his hard work. (He, however, was disappointed that he didn’t get a higher score and now wants to spend some time going through the text again to figure out the parts he got wrong.)
In addition, we began talking about college things, and I told him that he should take the PSAT in the fall because doing so would automatically enter him into the National Merit Scholarship Program. This is a scary topic because it requires that he go back and do something he hates: math. However, he keeps telling me he really wants to go to college, so he was willing to go back and do some. Of course, saying it and doing it are two different things.
He’d finished algebra 1 two years ago and last year, he’d made an attempt to jump into college algebra. He made it a good chunk of the way and then started having some real difficulties. Therefore, I decided to take a step back and see if he could get geometry done before summer. It turns out that he was better off than I thought because he did the initial evaluation and tested out of about 2/3 of the topics. In the past month, he finished off all the rest except for a handful, all of which had to do with proofs. (Apparently, he is serious about the PSAT.)
I have to admit that this is different than when I took geometry. My geometry class was entirely proofs. It was one of my favorite classes because, to me, doing a proof is a completely different animal than solving an open-ended problem. You know where you’re starting and finishing. All you have to do is find the path between here and there. Usually it was extremely obvious, so I was able to write out my proofs for class and often have time left over to read. I remember being very confused why other people thought the class was hard. Later on, when I took physics in high school, it felt like the same thing. You’re trying to find out a quantity using a bunch of other quantities and formulas. Easy peasy…
I sat down to help the older boy yesterday, and I have to admit I got frustrated pretty quickly. I read the problem, saw what was supposed to happen, and knew immediately the steps in the proof.
Problem was the older boy didn’t.
This really threw me for a loop. I mean, the kid’s obviously smarter than me (and just as obviously less wise and experienced). It really stunned me that there were a couple points where he was struggling to figure out what to do next. He was getting frustrated, though, so I walked him through a few of them, explained the reasoning, and tried to talk to him about how I viewed the problem (which is hard to do when you think in terms of vague notions of going places on diagrams).
It got me wondering, though, if this is why he doesn’t like math. Is it that hard for him to see the end goal? Is the process of finding logical steps difficult? And why is it so easy for me to formulate these things and difficult to him? Do our brains work differently? The whole thing left me with a lot of questions, and I’m still very perplexed.
By the end of the session, he seemed to have it down and was making good progress. I was able to back off and just let him work, and he even found some of his errors when he got things wrong. The best part was, however, at the end when he turned to look at me, grinned, and said that it was actually kind of fun. Mission accomplished.
Linkety Link January 3, 2011
Posted by mareserinitatis in links.Tags: aliens, economics, iphones, quadrantids, writing
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Being Brilliant versus Writing Well: In the vast world of academic Computer Science publishing, I am about to tell you the greatest secret of all: You can make up for lack of genius by being a good writer.
Frautech doesn’t believe in rational consumers.
We should find aliens any day now.
iPhones in Space: after this, I want an iphone even more.
And speaking of space, don’t miss the Quadrantids. (I probably will, though, because the temps are below zero and it’s just too cold to go outside right now.)
The science education mantra September 28, 2010
Posted by mareserinitatis in career, education, societal commentary.Tags: economics, science education
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I can’t help but wonder why there is this huge cry to improve science education, but yet another article came out saying that the US is falling behind.
Although U.S. school achievement scores have stagnated, harming the economy as employers look elsewhere for competent workers, the report says that other nations have made gains.
If U.S. students matched Finland’s, for example, analysis suggests the U.S. economy would grow 9%-16%.
“The real point is that we have to have a well-educated workforce to create opportunities for young people,” says Charles Vest, head of the National Academy of Engineering, a report sponsor. “Otherwise, we don’t have a chance.”
I’m a bit perturbed by Vest’s comment. Having a well-educated workforce means that you have a well-educated workforce. It does not mean that workforce has sufficient job opportunities. It does not mean that this workforce will have anything to do once they get out of college. I think the emphasis should be the other way: how can we create opportunities for a well-educated workforce, particularly one that is more expensive than nearly any other group of workers in the world? It takes very little to price oneself out of the job market in technical areas in the US.
I also fail to see how pumping out more science grads will cause our economy to grow when, as mentioned later on in the article, there are three times more science and engineering college graduates than job openings each year.
How is oversaturating an already saturated market going to help especially when older engineers are being scrapped for younger, and younger for their cheaper overseas counterparts? Scientists cannot find jobs in their fields, and the competition for science positions is extremely fierce.
And, of course, there’s this zinger: China has replaced the United States as the world’s top high-technology exporter. Is it possible this has nothing to do with educational level and is due instead to the fact that businesses are going to find ways to minimize their costs, which is often accomplished by outsourcing? Businesses are profit-driven, and they will take a hit in quality if it means production is cheaper.
This whole argument about improving science education in order to bring economic improvement is very much like having a wound on the bottom of the arm and then putting a bandaid on the top of the arm because that’s the part that’s the easiest to see. It simply doesn’t accomplish anything.
I also blog at Engineer Blogs, home away from home to some of the best engineering blogs.
And on the 8th day, God created capitalism… January 5, 2011
Posted by mareserinitatis in education, societal commentary.Tags: capitalism, economics, education, gas
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I have a radio alarm clock because I like waking to music. This morning, however, I think I would have preferred the agonizingly high-pitched digital screech to the airwaves.
The DJs were discussing gas prices and playing the opinions of a few people who called in.
This was, quite unfortunately, a confirmation of something I’d realized a few days ago: the majority of high school graduates have not taken an economics course.
While I am not one who agrees with the notion of true laissez fair capitalism, I do think having economics in one’s education is probably even more important than history. With few exceptions, everyone in this economy participates in the market. Nearly everyone has the opportunity to elect politicians who will determine the course of the market and corresponding government oversight.
I find it disturbing that people are making these decisions on vague notions, some of which are totally false, rather than having been exposed to the fundamentals of economics, how the economy supposedly works, and the historic shortfalls of our economic system. So many people believe in the notion of the Invisible Hand without even knowing what it is and the implications of a truly unrestricted market (unless, you know, you’re Michelle Bachmann).
Let’s look at a couple examples from the radio this morning: “I don’t know why they’re charging higher prices for gas now when everyone needs it. It’s not like Walmart starts jacking up their prices right before Christmas.”
Actually, that’s probably false. What everyone sees in ads are called “loss leaders”. Most retailers are actually raising their price while luring in customers with specific items listed as close to cost (or even sometimes below, hence the ‘loss’) as the retailer feels they can afford. Their hope is that the increase in prices on other items will compensate for the losses on the sale items. While it looks like prices are going down, overall, they probably are not. Either way, at Christmas, demand for some items will increase which, according to the law of supply and demand, means that prices will be greater for those items. (Anyone remember the Tickle Me Elmo debacle?) Same thing goes with gas: when demand is increased or supply is low, you will see a rise in prices.
Two other comments that were played were along the lines of, “Why don’t the politicians do something about this?” and, “I bet crude oil prices are lower now than they were when prices were high a couple years ago.”
The answer to the first is this: this is how the markets operate. Decrease in supply or increase in demand will raise prices. (If you want to delve into it a bit more deeply, you can read this.) Politicians really don’t have much control over it. And crude prices are, in fact, around the same price as a couple years ago. This is not the result of a conspiracy on the part of gasoline retailers; this is a response to the overall demand for crude increasing and driving prices up.
We have a whole nation full of people who don’t understand why prices are going up, that there isn’t much that can be done (or that things that may be done are going to have other consequences later), and that all of this could be a giant conspiracy. And yet how many of those same people are also insisting that capitalism is fundamentally guaranteed in the Constitution or some sort of religious-moral imperative?