What is the most important math to teach?

This morning's Register-Guard contained a letter to the editor about the cost of the war in Iraq. In the final paragraph, it computed as follows. The American population of 298 million spends $69.6 billion on the war annually. That's $2335 per person.

By coincidence, on Sunday I was in a discussion with some friends, including a former high school math teacher, about the relative importance of different aspects of mathematics. I deprecated algebra, they defended it, but in the end we agreed that statistics and probability were given short shrift in public schools.

If I'd seen this letter at the time, I would have moved another subject to top of the "most neglected" heap, namely mental order-of-magnitude calculations. In these days of ubiquitous calculators, getting the mantissa to a dozen decimal places is easy. The big mistakes tend to be orders of magnitude. You can usually catch them by some simple reality checks.

If 298 million people spend 298 million dollars, that's a dollar each. If they spend 298 billion, it's going to be a thousand bucks each. Anything less than that means less than $1000, so the Iraq War can't cost $2335 per person. In fact, it's $234 to the closest dollar. A substantial amount but, nevertheless, a tenth.

There are lots of complicated math problems presented to Oregon high school students during the CIM exams. None that I've seen are of the form, "Without using a calculator, which of the following answers makes sense?" There should be some.

Why is teaching the only profession where we can't tell good from bad?

The notion of a "profession" usually includes some sort of barrier to entry, designed to separate those who have competence from those who don't. In Oregon, you need to pass a test in order to become a hairdresser. You don't in order to become a public school teacher.

All you need to do is attend college classes and not flunk. For any person of average intelligence, not flunking is not difficult. Show up, turn in the work and take the test. You're bound to pass.

So if getting into teaching is so easy, shouldn't there be some effort to sort the wheat from the chaff afterwards? Even in professions like law and accounting, where passing the bar or CPA exam is a huge challenge, those who pass the initial barrier are sorted out by competition. Smart lawyers and accountants get ahead of those who are mediocre. In universities, there are processes the sort out instructors, assistant professors, associate professors, and full professors.

The official line from the teachers union is that competency tests are not a good indication of teaching ability and that administrators can't be trusted to make objective evaluations. Both of these may be true.

However, a minimum competency test seems reasonable. If you don't know how arithmetic works, you can't teach it. You may know it and not be able to teach it, but not the reverse. Competency tests might at least weed out the worst of the lot.

As far as administrators being incapable of evaluation, that's perhaps true but if so, it's a challenge to creative thinking, not an answer. The present evaluation-free environment is bad for students. We are treating the whole problem from the standpoint of teachers and trying to guarantee that under no circumstances will they be unfairly judged. The world is never going to be 100% fair, but our biggest concern should be the students. If we can't clean out the worst 10%, that means that 10% of our students are being taught by bad teachers. That's a situation we should be willing to take some risks to correct.

Oregon Teacher Compensation -- You can't separate what you reward from what you get.

If you've been doing the same job for eight years, are you going to be better at it in your ninth year? It's possible. It's just as possible that you've fallen into a rut and your performance is going downhill. But in Oregon schools, it's simply assumed that you're better so you'll be paid more.

Suppose you're a young journalism teacher and one day, a newspaper offers you a one-year contract to write about city government for them. Do you take it? If you do, your teaching after you return to the classroom will be infused with real experiences that you can share with your students. And your paycheck will be lower than it would have been if you'd just hunkered down in your teaching job. It will remain lower year after year until you eventually get to the top of the scale.

Will you get paid better if you get good grades in college? No. Will you get paid better if your graduate courses are in your field, rather than near-useless classes in pedagogy? No. Can you get better paid for outstanding performance in class? No.

The practices followed by almost all (perhaps all) Oregon school districts reward plodding conformity, risk avoidance, minimal classroom performance and irrelevant education at least equally with, and sometimes higher than, all the qualities we want to find in our public school teachers. The Oregon Education Association insists that this is the best possible approach. I suppose it's possible, but it seems awfully unlikely. I'd like to see at least a speck of evidence that it is.

What is the Experience that Teachers Need Most?

Ben Bernanke, the incoming head of the Federal Reserve, has a great academic background but some worry that he doesn't have the "street smarts" of his predecessor, Alan Greenspan, who spent years in the real world of Wall Street before leading the Fed.

Everyone knows that there's a difference between learning something in a classroom and experiencing it in real life. Experience gained in the trenches is something that we all recognize, value, and reward.

Except in public schools. In public schools, the principle is that only one kind of experience for teachers is valuable, and that's standing in front of a class. The compensation system in place throughout Oregon rewards those who, on the first day after college graduation, get a job teaching and never spend another day in outside employment. The discrimination against those who get real world experience first is so great that after ten years, it's almost impossible for one of them to turn to teaching.

Consider the following scenarios. Six students graduate from an Oregon university the same year. Three of them go into public teaching: in business, English, and woodshop, respectively. The other three get outside jobs. One becomes a retail store manager. Another spends five years as a newspaper reporter before switching to copy writing at a PR firm. The last works as a carpenter, first working by the hour and then starting his small contracting business.

Let's suppose again that these three suddenly decide that they want to work with young people and share with them what they've learned. All three apply for jobs at the Middleville Oregon School District. Are they welcomed? Hardly! Despite having college degrees and ten years of experience in their fields, they will be considered unqualified unless they take some extra classes to get an Oregon teaching certificate.

Fair enough, it takes a little training to switch careers, so our three outsiders get the classes and come back. They are now "qualified." But how are they going to be compensated? As though their experience is worthless.

Meanwhile, their three fellow alumni are doing fine. Experience in the classroom moves them up the union scale automatically and a few courses each summer at some university will get them a masters degree. In teaching, mind you, not in the field they teach. A masters degree like that won't even qualify you teach Advanced Placement courses in high school. AP teachers need a real masters degree, in the field they are teaching. But the MA in teaching is good enough to put our first three teachers far up the pay scale.

How far up? Probably $15,000 a year. Enough that they are getting fairly comfortable, while our three outsiders face starting over at an entry level salary. If you've built any kind of life for yourself, you're not likely to accept that option.

In truth, there may not be a lot of people who want to bring their real world experience to a public school classroom, but we should welcome any who do. Instead, we make it nearly impossible for them to make the switch. It doesn't make sense.

Are English teachers as hard to find as physics teachers?

There are many problems with having unions representing what ought to be professional services, but if the arrangement is going to work, it needs to be at least sensitive to the realities of the market. This means having job descriptions that differentiate difficult-to-fill positions from the easy-to-fill.

Unfortunately for the taxpaying and student-parenting public, this is not the case with the near universal arrangement between Oregon public school districts and their teacher unions. It may be universal. since I've never heard of an exception.

Under standard union agreements, there is one class of teacher. Compensation is based on years of education and years of experience, but not on the area of specialization. The theory is that all teachers are equally valuable, that all teach subjects that are important for young people to learn, and that all should be equally rewarded.

It's a wonderful theory and no one would object to it being the economic principle in some voluntary commune, but it doesn't work in public schools. We live in a high tech world and for people with skills in math and physics, there are many alternatives to public teaching.

For many disciplines, teaching is just about the best possible career choice. If you love literature and want to be involved in it daily as you earn a living, there hardly are any better opportunities than public teaching. A few jobs are available in higher education and a tiny number in fiction writing and publishing, but generally speaking, a high school teaching job is about as good as it's going to get economically.

Absolutely not true for those with math and science talents. Research, engineering, software development, all these career paths beckon and they offer a lot more money than public teaching. Our kids need teachers with talent in all areas, but especially math and science. This isn't going to happen as long as we view every teacher the same.