The Danger of Happiness

Here's a piece from the Atlantic about the dangers of the pursuit of happiness. If that's all we desire for our children and if we always strive to secure it for them, then paradoxically they often won't have it.

Aristotle knew this. Happiness shouldn't be a goal in itself. Rather we should pursue success. Learn to do a thing well and happiness might come as a consequence. But pursue the happiness itself and likely it will elude you.

Choose a task. Devote yourself to success within in. The sum of your successes is the value of your life. If you achieve some measure of happiness along the way, feel fortunate. But do not mistake that happiness for the purpose of your life. Your purpose is success.

Wasteland

I've poked around on YouTube recently in hopes that I would find a few proofs from geometry.

I was deeply disappointed. YouTube is a geometrical wasteland. Most of what's there is either wrong in one way or another or just plain trivial. Go on a hunt for, say, a proof of the special properties of parallelograms and all you're likely to find is demonstration after demonstration of how to find the area of a parallelogram. What a bore.

I mean to fix that. Tell me what you think.

It's Society, Stupid

A conviction has begun to grow in me over the last few years.

It has grown as I have become more confident of my abilities. I know my subject-matter. I know it well. Moreover I know how to teach. Many of my students leave my class with a deep knowledge of elementary geometry. This is rare today. The quality of geometry instruction in the U.S. is quite low. I am an exception. (Think that I am overly confident? That I praise myself too much? Engage me about elementary geometry. You'll find that I know it and know how to teach it. I have made that my sole study for four years.)

I do love geometry. I do love to teach it. But still, every semester, many of my students leave my class with little or nothing to show, and the fault isn't mine. Many students are superb, but more are quite poor. I fault the society around them.

Let me quote here a commentator on a recent New York Times article on teacher evaluation. She makes the point well.

My husband used to teach in a low-performing public school in Maryland. It nearly killed him - waking up at 5am, coming home at 6pm, working at home until almost midnight, and then grading papers and writing lab and lesson plans all weekend and during most of winter and summer breaks. He was a highly rated teacher (and deservedly so) but the fact is that much of his time, when not under observation, was devoted to keeping fights from breaking out in his classroom, taking phones and ipods away from kids who texted or listened to music during class, and disciplining students, since the school administration had informed teachers that sending kids to the principal for discipline was a failure of teaching and was unacceptable.


The same kids who routinely slept and fought in class would aggressively petition him at grading time, urging him to "drop a D on that b****" in lieu of a failing grade. And the administration implemented byzantine procedures for failing a student, including a requirement that the teacher successfully make contact with the parent several times to discuss the student's problems. In some cases, the student provided a false telephone number for the parent at registration time, so there was no reaching parent. In most other cases, the parent either was unreachable or did not respond. Nonetheless, the same students who would have failed if not for these procedures eagerly anticipated attending college, which they predicted would be easier than high school.


In his second year, after surviving a round of teacher firings, my husband quit mid-year and went back to practicing law, where he makes several times the salary for less than half the effort. All the evaluations in the world aren't going to fix this problem.

I attended a highly ranked public high school in an affluent part of the midwest. As good as my teachers were, I have no doubt that each of them would fail if reassigned to my husband's school.

This is exactly right. We have a bit of a problem with bad teachers. But it's dwarfed by the problem with bad students. Lazy students. Disrespectful students. Lackadaisical students. Students who care little (or none at all) about their education.

(Don't think that I mean all students. Of course I do not. I have many superb students. But I have more that exemplify these traits. Recall that I have said that we have one country but two cultures. One values education. One desires to learn. The other places not value on it, or in some cases is openly hostile to it.)

How did this come to be? Its cause is the wider society in which the school is embedded. Students bring the culture outside the classroom into the classroom, and that culture often thinks education worthless.

Student quality is a reflection of culture quality, and that has been in decline for decades now. But few will say this, because it requires that we look at ourselves and what we have let our culture become. We would rather blame our problems on others.

As I have said before, the problems of the classroom don't have their origin in the classroom and thus cannot be solved there. Culture must be restored. We must all begin to value education, and we must show that we do so everywhere - in our homes, in our media, in our places of business, in our churches, and everywhere that we congregate. Let us begin now.

The Khan Academy on Centroids

Here's a short little video from the Khan Academy on triangle centroids.

(Not know the Khan Academy? Not heard all the chatter about it? Try here.)

What you have here is typical of the sort of thing you find in the current crop of texts. What's called a proof is not really a proof at all. Lots is loaded in that is unproven. What's worse, it's not even noted that there are gaps in the proof. What's a perceptive student to think? That she's stupid because things that the speaker seems just to assume aren't obvious to her? Don't call something a proof if it's not. You do students a disservice.

Here are my objections in detail. Read them after you've watched the video.

1. It's never explained why the medians are concurrent, that is why they all come together at a common point. It will seem utterly mysterious to students why this is so. The concurrency proofs are some of the most beautiful in elementary Euclidean geometry. Why pass over them? Why not even mention that a proof is necessary? Inexcusable.

2. It's never explained why the coordinates of the centroid will be (a/3, b/3, c/3). Instead it's just assumed. This makes the "proof" circular. When one assumes these coordinates, one has in effect assumed that the centroid lies 2/3rds of the way from vertex to midpoint of opposite side.

3. It's never explained why the centroid represents the center of gravity of a physical triangle. This isn't really very hard. It begins with the claim that a median divides a triangle into subregions of equal area. Why isn't this done? Time? Ignorance? No matter the reason, again it seems inexcusable to me.

I expect that students (the perceptive ones, anyway) will come away with the impression to do mathematics, one must have little mathematical nuggets must rain down from heaven, unmotivated and unexplained. What a terrible impression.

Consumption and Creation

Consumption of technology is easy. Creation is hard.

To consume, all you have to do is learn the interface, whatever it is. How difficult is the Facebook interface really? The interface to the iPhone? These and all the rest are simple. Give a reasonably intelligent person a few hours and they'll have the basics down.

The point? Our task is not to teach students to consume technology. That they will do on their own. Rather our task (at least in part) is to teach them to create those technologies, and that's hard.

We need scientists, we need programmers, we need engineers. These are the creators of our technologies, and they must have a deep grasp of the mathematical and scientific foundations of the technologies that they will create. This requires what it has always required - hard intellectual labor.

The mind must be be trained to carry through lengthy and intricate deductions. This is what it is to think. This is what it is to take a seed of any idea and bring it to fruition. You don't learn this on Facebook. You don't learn it on an iPhone. You learn this today as students always have, with a text, a teacher and time.

Students often have little idea of this distinction between consumption and creation. They think they know the technology, but all they really know is its surface, its interface; and that has been designed for simplicity of use. What lies below the surface is quite extraordinary complex. How will students come to understand that? How will they learn to make something of such complexity? They must know the theory behind it. They must know the science and the mathematics. The traditional course of study isn't made irrelevant by the new technologies. The traditional course of study is responsible for the creation of those technologies. So let us continue to require that students complete rigorous courses of study in science and mathematics. This is hard, I know. Students would much rather just sit back and consume. But they don't know what they need, and we teachers must not shrink from the task appointed to us.

Could Poverty be the Root Cause?

We have problems here in the U.S., deep problems. Might this little piece get at the root of it?

What I Should Have Said

Ms. Cornelius at A Shrewdness of Apes has given us a fine read. Read this. Read it from start to finish. I beautifully captures what I've tried to say here many times.

Here are a few of the best passages:

If one listens to all of the cant coming out of the talking heads who purport to be educational experts, especially those who claim to be experts, you will notice that the dominant assumption regarding students is that they are acquiescent, empty vessels waiting to be filled. A whole passel of those alleged "reformers" like to use the "consumer" paradigm when describing how to fix American public schools. Students and their families are depicted as "consumers" of educational services. The problem with this stereotype is the absolute passivity of consumers in our consumption culture. The deluge of advertising and its claims that consumption can be transformative is probably THE seductive lie of the 20th century in terms of the lives of the common people.

I can assure you that many students in public high schools also are disinclined to value their educations since it always emphasized that this education is free. Unfortunately, they also interpret that word to mean "requires no real effort." Schools often abet this notion by lowering standards and removing consequences for failure to master concepts. However, even in the face of this trend, I do want to say there are more than a few of us in the classroom who are swimming against that tide, who seek to maintain and enforce high standards and rigor. We ARE out there, banging our heads against the wall daily for the sake of our students. We do it because we KNOW that our students CAN do the work, CAN learn the concepts and skills needed. They just have to be pushed into it.

That's just right. The primary problem in our schools today is student passivity. So very many don't really care about their education at all. At most, they grade-grub a bit and hope to get by with the minimum possible work. (Of course, many won't do even this. Such laziness there is!)

This problem is deeply ingrained, and no mere change in curriculum or teacher technique will fix it. The culture must be transformed. We must begin to value academic achievement. Indeed it must become our primary value.

Imagine the transformation that would occur in the classroom if academic achievement became as important as athletic achievement. Imagine what would happen if academic achievement became the primary goal of students and their parents.