Gyroscopic Investing

Someone found one of my old math papers.

A TYPICAL American school day finds some six million high school students and two million college freshmen struggling with algebra. In both high school and college, all too many students are expected to fail. Why do we subject American students to this ordeal? I’ve found myself moving toward the strong view that we shouldn’t.

My question extends beyond algebra and applies more broadly to the usual mathematics sequence, from geometry through calculus. State regents and legislators — and much of the public — take it as self-evident that every young person should be made to master polynomial functions and parametric equations.

There are many defenses of algebra and the virtue of learning it. Most of them sound reasonable on first hearing; many of them I once accepted. But the more I examine them, the clearer it seems that they are largely or wholly wrong — unsupported by research or evidence, or based on wishful logic. (I’m not talking about quantitative skills, critical for informed citizenship and personal finance, but a very different ballgame.)

Read the rest here...
http://www.nytimes.com/2012/07/29/opini ... ry.html?hp

Where was this guy 30 years ago when I was bleeding my way through algebra?

Ad Orientem wrote:
Someone found one of my old math papers.

A TYPICAL American school day finds some six million high school students and two million college freshmen struggling with algebra. In both high school and college, all too many students are expected to fail. Why do we subject American students to this ordeal? I’ve found myself moving toward the strong view that we shouldn’t.

My question extends beyond algebra and applies more broadly to the usual mathematics sequence, from geometry through calculus. State regents and legislators — and much of the public — take it as self-evident that every young person should be made to master polynomial functions and parametric equations.

There are many defenses of algebra and the virtue of learning it. Most of them sound reasonable on first hearing; many of them I once accepted. But the more I examine them, the clearer it seems that they are largely or wholly wrong — unsupported by research or evidence, or based on wishful logic. (I’m not talking about quantitative skills, critical for informed citizenship and personal finance, but a very different ballgame.)

Read the rest here...
http://www.nytimes.com/2012/07/29/opini ... ry.html?hp

Where was this guy 30 years ago when I was bleeding my way through algebra?

I was a math major in college, and I love math, but I agree with you completely.  There is no reason to make everyone learn this stuff. 

I do think people benefit from exposure to various subjects, so that they can figure out what their talents are, though.  I'm just not sure where the line between exposure and torture lies. 

Clive wrote:

I was a math major in college, and I love math

One of those that confuses Halloween with Christmas then? (Oct 31 = Dec 25)

It's like they say, "There are only 10 types of people in the world:  those who understand binary, and those who don't."

I'd get it if they were talking about partial differential equations, but basic algebra?  How is somebody supposed to tackle subjects like probability, statistics, physics, or trigonometry without this simple foundation?  The implication is that students are too delicate to ever be forced to confront these sorts of subjects.  Not good.

Even basic financial tasks are awkward without algebra.  I don't think we need people to get any worse with money than they already tend to be.  Without algebra, how are you supposed to understand chemistry?  Perform simple unit conversion?  And God help you if you ever want to understand the bond market.

The author's position is that the high failure rates indicate that there is some deep reason that many humans cannot grasp algebra.  But are people really that different? isn't it more likely that we currently just suck at teaching algebra?

For more perspective on algebra, I give you Salman Khan, someone who doesn't suck at teaching algebra:
http://www.khanacademy.org/math/algebra ... -algebra?k

Lone Wolf wrote: I'd get it if they were talking about partial differential equations, but basic algebra?  How is somebody supposed to tackle subjects like probability, statistics, physics, or trigonometry without this simple foundation?  The implication is that students are too delicate to ever be forced to confront these sorts of subjects.  Not good.

Even basic financial tasks are awkward without algebra.  I don't think we need people to get any worse with money than they already tend to be.  Without algebra, how are you supposed to understand chemistry?  Perform simple unit conversion?  And God help you if you ever want to understand the bond market.

The author's position is that the high failure rates indicate that there is some deep reason that many humans cannot grasp algebra.  But are people really that different? isn't it more likely that we currently just suck at teaching algebra?

For more perspective on algebra, I give you Salman Khan, someone who doesn't suck at teaching algebra:
http://www.khanacademy.org/math/algebra ... -algebra?k

I view math in general as basically increasingly complex logic problems.

Most people don't understand logic well--i.e., they don't understand the difference between a good argument and a poor one, and thus it would make sense that they also wouldn't understand math of even moderate complexity.

I admit that I didn't like math classes, but disciplining the mind to follow the unforgiving logic that the right answer to a math problem requires has application in many other areas of thought.

In general, I think that people don't like to think too hard about much of anything, and math is just one of these things that people don't like to think about.  Heavy thinking is kind of like lifting weights.  It's unpleasant, but it does lead to increased strength.

One possible factor contributing to the relatively high failure rate in math courses is that the objective nature of math makes it a little bit harder to inflate grades in that area. I'm not saying it doesn't happen, just that it's a bit harder to get away with.

Some teachers assign partial credit for long, complicated math problems, but ultimately you either arrive at the correct answer or you don't. If most of the students in the class are arriving at the wrong answers on most of their math problems, how is the teacher going to justify giving most of them As and Bs?

So maybe the failure isn't mainly in math. Maybe the failure is in all sorts of other subjects, too--those failures just happen to be masked more by grade inflation due to the fuzzy/subjective nature of their subject matter?

Tortoise wrote: One possible factor contributing to the relatively high failure rate in math courses is that the objective nature of math makes it a little bit harder to inflate grades in that area. I'm not saying it doesn't happen, just that it's a bit harder to get away with.

Some teachers assign partial credit for long, complicated math problems, but ultimately you either arrive at the correct answer or you don't. If most of the students in the class are arriving at the wrong answers on most of their math problems, how is the teacher going to justify giving most of them As and Bs?

So maybe the failure isn't mainly in math. Maybe the failure is in all sorts of other subjects, too--those failures just happen to be masked more by grade inflation due to the fuzzy/subjective nature of their subject matter?

We live in an age of much fuzzy thinking.

I'm with Lone Wolf.  I don't think the problem with US schools is that we're teaching too much math.  We're just not good at teaching it.

Like I saw pointed out on another blog, I'm an engineering major with a math minor, and even I didn't "get" differential equations until I took control systems and heat transfer, where I learned how all the numbers and variables apply to real-life systems and objects.

Not everyone is good at memorizing equations. (I'm certainly not). But lots of people can be good at math if teachers knew how to teach it.

I'm all for the basics such as history, algebra, etc, it's pretty amazing that there isn't a greater emphasis on personal finance and basic economics. 

Personal finance, impacts EVERYONE on the planet from the time they're on their own financially until they die. 

It's hugely important and most HS grads might take 1 semester of basic personal finance and possibly 1-2 more throughout college.

clacy wrote: I'm all for the basics such as history, algebra, etc, it's pretty amazing that there isn't a greater emphasis on personal finance and basic economics. 

Personal finance, impacts EVERYONE on the planet from the time they're on their own financially until they die. 

It's hugely important and most HS grads might take 1 semester of basic personal finance and possibly 1-2 more throughout college.

Completely agree.  High school classes in chemistry, biology, history, are important for the select few who go on to a professional degree.  For everyone else, personal finance should be their most important class.  Yet, very little of it is taught in high school (or college for that matter). Even though I have an MBA, the only really useful finance class I took was, weirdly, engineering economics.  They cover everything regarding time value of money. 

Everyone should take algebra.

Geometry is questionable.

Trigonometry is only useful if you intend to take calculus or go further in more advance math.

Calculus is only useful if you intend to go deeper into science or engineering.

Formulas, periodic tables, or anything else for that matter should never be a forced memorization. It makes the subject become harder than it needs to be. If memorization ability is a skill that educators decide to test for, then memorizing state capitols would have just as much benefit as math formulas and wouldn't sour students against math.

In an age of cell phones and Google, I find it perplexing why anyone needs to memorize anything.

1) Learn key, core concepts
2) Learn where to search for things
3) Learn how to search for things

If anything, we should be giving classes on how to use Google effectively and making that mandatory. It's more useful than geometry. In any real life, non-artificial classroom environment, people can use Google to find stuff. However, if you don't understand the core concept, you won't know what to Google for or how to parse the information you find and apply it to your immediate problem.

I think mental math is an important way to develop synapses in the brain and increases cognitive ability. However, calculators are on every cell phone. If forcing mental math use is discouraging students away from math concepts, it needs to removed from the curriculum.

Most things taught in US schools these days are garbage. If schools were doing a good job teaching math and science, we wouldn't be importing half of our math/science graduate students from China and India. If schools were doing a good job teaching basic economics/finance/math concepts, we wouldn't be in a fiscal crisis. If schools taught history / social studies well, the government would not be the huge, bloated, unconstitutional disaster it is today. But maybe that's the point?

clacy wrote: I'm all for the basics such as history, algebra, etc, it's pretty amazing that there isn't a greater emphasis on personal finance and basic economics. 

That's true.  Virtually everybody must perform basic financial tasks.  I actually had no personal finance classes of any kind in school.  Fortunately, my parents did great work here.  It was common for us to talk about financial concepts, the wise use of money, and all of the stupid mistakes that people tend to make.  They made sure that I had my own checking account as early as possible and that I knew what I was doing maintaining the books for my weekend/summer lawn care business.

I guess that nothing beats practical experience, regardless of subject matter.

TripleB wrote: Trigonometry is only useful if you intend to take calculus or go further in more advance math.

I actually think trig is one of the more practical post-algebra topics.  I don't think that you can start with physics if you don't have basic trig down pretty much cold.  Any time that you need to model the real world (or at least the real world as viewed through the prism of Newtonian physics), it's largely based in trig.

This definitely extends to most types of physical engineering (such as civil or mechanical engineering) and pretty much any work on video game graphics, physics, or advanced modeling.  Architecture is another area that definitely requires trig.  Even electrical engineering's going to depend on some trig.

I agree that there are a lot of practical jobs you can do without knowing trigonometry.  My concern is how many areas of study that you can't even start with if you haven't got trig.  Newtonian physics, for example, is so fundamental that I'd hate to see anyone missing out on that sort of thing.