Lead, Follow,or Get Out of the Classroom

I don't have much to say lately. Even when I have the time to blog, I don't have anything interesting to report. Today happens to be an exception. First, let me quickly get the auto-biographical particulars out of the way. I am nearing the end of my first semester, still maintaining a 4.0 GPA, and registering for next Spring. There, now we can get on with the show.

Last Saturday I was invited to attend a conference on Teacher-Leadership held at Colby College in Waterville, ME. When I say that I was invited, what I mean is that the opportunity presented itself and I volunteered. (As with the last conference I attended, I was disappointed, but more on that later.) In addition to my desire to master the content I intend to teach, I am very much curious about systemic design of the current education system. From my lay perspective, it looks to me like many schools are still stuck in what is essentially a one-room schoolhouse paradigm. Although, there are more of those rooms under a single roof, the individual classrooms are run autonomously from one another, with little to no coordination between teachers. This self-isolation makes it very difficult for teachers to learn from one another.

Some schools are seeking to change that. They are transitioning into a new kind of structure, where teachers are encouraged to cooperate and "compete" in a less-superficial way. By "compete," I don't mean literally fighting for their very job, as the high-stakes testing/accountability advocates intend. I mean the kind of friendly challenge that helps both parties reach new and unexpected heights together.

That is what the conference was supposed to be about, and it started out well. The opening address was passionate and to the point. The speaker outlined what constitutes teacher-leadership. He pointed out the self-similarity between layers of a school. Just as students learn from one another and drive each other to greater standards of success, so should teachers. Currently, unlike students who are keenly aware of each others methods and their relative successes, teachers are in the dark when it comes to what is happening next door. Instead of the once a year visit from the administration spies, we ought to be volunteering to sit in on each other's classes and welcome peers into our own. Only in this way can we strengthen our own abilities and the cohesion of our departments and schools.

After that, it all went downhill fast. Immediately following the opening address was a panel discussion, only the panel was made up mostly of students with no real understanding of teacher leadership, so the audience questions went largely unanswered. Then we divided up into several break-out sessions which had been decided upon before hand. I had selected one entitled "What a New Teacher Needs," reasoning that I would soon be a new teacher and would like to know what I will need. Unfortunately, that question was never answered. The presenter based the session on her ongoing doctoral thesis, in which she interviewed first year teachers at several points during the year, and made note of their personal success and intent to continue. Now i know that sounds like a great opportunity to learn something, and I would agree, if the sample size had been greater than four.

That's right, four. Out of all the first-year teachers in the state of Maine, she interviewed exactly four. Two of them had never really intended to go into education in the first place and one of those experienced an unfortunate lawsuit during the first month of school. All told, only one of them continued into a second year. Now what can we possibly glean from all this? I was hoping to start with a large sample of eager, well-educated young teachers, find out what obstacles they might face, and some possible ways in which teacher-mentors can recognize and solve those issues. Instead, I got a lot of poetry and rhetorical questions. It was an utter waste of time, and I seriously doubt that her thesis will pass review.

After the session, and on the way to lunch, I fell in with a group of students and their teacher who were likewise disgruntled. It turned out that they were from the ETEP graduate program at my very own USM. I introduced myself and complained along with them. It was the highlight of my day.

Lunch was adequate and featured round table discussions of teacher-leadership from those in the field. It turns out that many teacher-leaders are unsure as to exactly what their job entails. They are also reluctant to take the responsibility, fearing that the nail sticking out is the one to get hammered down.

To summarize, it was a well-intended conference which from my perspective fell short. I am still very much in support of the concept of teacher-leadership. At some point, an organization grows too large and bulky for top-down leadership to work. There must be a combination of bottom-up and top-down for the system to reach optimization.

Even Better "Graphing Stories"

Nothing against dy/dan, but this is how two dimensional graphing should be taught.

Must-See Mobius Vid

Truly brilliant animation. Well worth two minutes. Hat tip to MarkCC for finding it.

Sometimes Close Enough is Good Enough

Join the exciting adventures of Math Girl. Thanks to ConcernedCTParent at Mindless Math Mutterings for pointing this one out. Check out the second episode here.

Respect Your Roots

Have a look at this square root algorithm. It's interesting that it is posted by a reform math advocate. Many reform math programs are accused of overemphasizing estimation and rounding to the exclusion of precision and accuracy, yet in this case the typical traditional solution method involves estimation while his method involves precision. Curious.

On a related note, I just got my hands on some teacher manuals for TERC Investigations. It's an outdated elementary level book, but it still should provide for an intriguing read. I will be posting my personal assessment shortly.

(Teaching) Math is Hard.

When I tell people that I want to be a math teacher, the first thing I hear is usually some intellectualized version of Yuck! Then as the person composes themself, they try to comfort me and my terrible decision by assuring me that since math only has one right answer, it will at least be easy to teach. If I'm in a good mood, I thank them for taking an interest in my future and move one. If not, I begin by laughing, then quickly move verbal abuse.

For some people, as for Barbie, math is hard. They don't understand it and they marvel at those who do. That I can understand and forgive. For others, math comes easily, and so they feel that the teaching of it must be easy as well. That is just plain insulting. While it is true that in math, there may only be one "right" answer, in math class the answer often takes second stage. Instead it is the process that is important. How did you arrive at your conclusion? Have you mastered the current skill and in which cases to apply it, or are you masking confusion by employing an earlier method instead? Math teachers must not only be able to produce the correct answer to every problem they assign, but to predict and explain the umpteen most common wrong answers.

There is nothing easy about it.

Unfortunately, it isn't just laypeople that underestimate the role of math teachers, it is the school systems and state education boards. They are the ones responsible for the low standards set for teacher experience in their designated subjects. Before you can teach math, you have to understand math. That doesn't mean simply manipulating algorithms to get the right answer and it doesn't mean being a step or two ahead of your students. You have to be light-years ahead. You have to have delved far enough into the wonder that is mathematics that you are adequately awed by its mystery, yet be approachable enough to share some of that mystery to share with your students. It's a fine line that only the best can walk.

It is often said by people who should know better that those who can do, and those who can't teach. I would hazard a guess that ours is the only culture where such an asinine statement could ever become a cliche. In other countries, the teachers are hand picked from the best of the best. They are the privileged few, the Top Gun fighter aces. We will never be able to compete on the same level we once did if we don't first learn to appreciate the inherent difficulty and skill of a good math teacher and second, have institutionalized standards and incentives to entice more of them into the field.

Girl Power

It's pretty good to be a woman in America. I'm sure my female readers would beg to differ, and it's true that there is still rampant inequality and prejudice toward women. Women are overlooked for jobs, paid less than their male counterparts, and frequently deal with sexual harassment. They are criticized by one side for having a career and by the other for stooping to the stereotypical role of wife and mother. They are expected to do everything a man can do, only to do it backwards and wearing heels. But let's be realistic. Compared to most women around the world, American women are living the high life. I mean, there are still cultures where women are treated more as currency than as human beings.

Yes, it's true. Young girls in the USA can grow up to be electrical engineers, computer scientists, and applied mathematicians. The problem is, well, most of them don't. For whatever reason, little girls want to be Britney Spears or Paris Hilton. If that sad fact doesn't wake people up, I don't know what will. When we worry about how our nation can compete with the growing economies of China and India, most of us happily ignore the elephant in the room- that the most obvious and effective solution is to inspire more than 51% of our nation's children to pick up a calculus textbook and put down the Barbie doll.

Thankfully for the future of the world, there are organizations devoted to doing just that. Since 1950, the Society for Women Engineers has made it their mission to show young girls that careers in science and mathematics are not just for the guys. The host programs from kindergarten through college, and from coast to coast. Krystal Grube, an SWE representative says of an upcoming event in Minnesota,

On June 3rd, hundreds of girls in St. Paul, Minnesota will attend an event hosted by SWE called, “Wow! That’s Engineering!” Through hands-on activities, girls will learn how solar power works, the wonders of deep sea diving, and even develop their own lip-gloss. Most importantly, they’ll realize that engineering is not just about working behind a computer; it’s about making a difference in the world.

There has never been a better time for the next Marie Curie or Emmy Noether to show the world that women can not only compete with men in these subjects, but with the right touch of genius and self-confidence, can leave them in the dust.

Support our Troops

MarkCC over at Good Math, Bad Math pretty much sums up how I'm feeling today.

To Infinity and Beyond

I just finished watching Infinity, a 1996 film directed by and starring Matthew Broderick about young Richard Feynman. The movie is mostly a love story, and depicts Richard's relationship with his wife Arline, her losing battle with tuberculosis, and his work at Los Alamos. It is a touching film and captures the greatness of the man. There is a particular scene early on that I think speaks toward the ongoing calculator controversy in our schools. Feynman challenges a Chinese shopkeeper to a duel of arithmetic, pitting his mental algorithms against the abacus. Feynman loses the addition round, ties on multiplication, and wins hands down on cube roots. Afterward, he explains to Arline that his win was inevitable, saying of the old man "he doesn't know numbers, he only knows beads." It is a wonderful scene, and a wonderful movie.

This Little Piggie Did Calculus, This Little Piggie Stayed Home

Scientists in Great Britain have just completed a study that shows a correlation between finger length and math ability. When I first came across this article, I was all set to be annoyed. I thought for sure that it was going to be another adventure in data mining, but I was wrong. The finger length is not the proximal cause, but rather a result of prenatal hormone surges. Testosterone, which is known to affect growth the right half of the brain where spatial reasoning is located, also causes the ring finger to be slightly longer than the index finger. A digit ratio of less than one correlates with left brain development, or language skill.

Now from the little bit I've read about this, I can find no obvious fault in the methodology. There was a predetermined hypothesis, evidence was gathered, and a conclusion was made. I do find major fault in the reporting. Here is how the article begins:

Parents may be able to predict how well kids will do in math and reading by measuring their fingers, British scientists claim.

Now I understand that journalists have to front load the hook. Their goal is to get people to read the story. Fine. But shouldn't they feel some obligation to present the material in a responsible manner as well? Most researchers don't get the opportunity to speak directly with the public and are forced to use the media as a go-between. For most people, the only science the read about is in their local newspaper. So placing a statement like this right up under the byline can be very dangerous. Sure the author used passive tense and employed words like may and claim to slightly erode confidence in the conclusion. But they should know that when it comes to predicting test scores, parents will latch on to anything remotely scientific, especially if it comes from the British, because we all know how smart they are. I mean, just listen to them talk.

Here is how those same British researchers present their conclusion in the final paragraphs;

Finger length is by no means a measure of intelligence or ability, Brosnan stressed.

"You may well look at a finger and say, all other things being equal, they may well have a leaning towards mathematics," Brosnan says.

"Or if they have a child who has a digit ratio that suggests very good verbal skills and a struggle with mathematics, this might suggest that, to explain mathematics to that child, you use a lot of verbal strategies and you cut down on the graphical, visual information."

By their own admission, the results of the study are less meaningful than this article would imply. The scientists appreciate the power that their work might have on desperate parents and rightfully suggest that not too much be read into it. These results are interesting at best. There is by no means a single definitive predictor of skill or intelligence.

I'm also very sensitive to boy vs. girl related math myths lately. After reading Rebecca's post earlier in the month, I have been thinking a lot about all things sexist in mathematics. Now to be fair, this was not a gender study, per se. It was a study of androgen surges, and because both males and females have both testosterone and estrogen, a continuum is possible which matches the evidence. Generally speaking, if the measured difference between groups is less than that within groups, then the phenomenon is fairly impotent. So if there is more variance between girls scores than there is between the average of girls and boys, than we can't really link the difference to gender. But that's not what this study is doing, so I can still only argue with the reporting.

Numerous studies have been done lately that conclusively demonstrate the harmful affects societal stereotypes have on test scores. Girls are known to do worse on a math test if you tell them before hand that boys do better. It's a horrible reality, and as a future male teacher (currently male, not yet a teacher,) I desperately want to avoid contributing to this problem. I wish that the authors of these articles felt the same way.

Mathematician Moms

An excellent Q & A session on instilling a love of math in your children from someone who ought to know.

More resources for moms (and dads.)

A 100% Sincere Letter to the MPAA

Dear Motion Picture Association of America,

I am writing to thank you for your recent decision to add cigarette smoking to your list of criteria leading to an "R" rating. I have been hoping that you would come to the rescue of America's lung health and only wish you could have done it sooner. Since the implementation of your benevolent ratings system, all but a handful of social ills have been completely eradicated from our culture. Premarital sex is a thing of the past. No longer are sickos and perverts allowed to freely engage in coital permutations outside of God's cherished missionary position. Violence and drug use have dropped so dramatically that some are advocating turning our nation's prisons into factories for Bibles and cotton candy.

None of these great achievements would be possible without your invisible hand. Proving that life imitates art, you have molded this world in your image and this movie goer thanks you from the bottom of the heart. I don't know where I would be without you.


Absolutely, completely, sincerely yours,

American film lover

Here We Go Again

When I read stories like this, I actually want to call up the author and verbally berate them. Evidently, someone decided to look at a large group of school children and see if there was a correlation between math test scores and birth dates. Not a particular correlation, mind you. There was no hypothesis. They weren't looking for a particular pattern, just any relationship would do. Shockingly, they were able to find one. In this case, it's that summer birthdays lead to poor performance, and they actually attempt to pin the blame on pesticides used during this season.

I don't know how many times studies like this have to be shot down before people get it. If you look at a random group of people, some people will do better and some will do worse. That's what randomness requires. We would not expect those good and bad scores to be evenly distributed. They're going to clump up in some months. But they could easily clump up in different months with different samples. Unless you are looking for something in particular to back up a hypothesis, you aren't doing science.

I don't have to know when this journalist was born to know that they don't no a thing about math. They've proved my hypothesis for me.

What Not to Do

I asked my blog-friend Rebecca to do the next in her semi-regular series Ask an Applied Mathematician about sexism in the classroom. Her reply, while I'm sure completely off-the-cuff gave some good examples of what not to do if your intention is to promote a safe, nurturing, and fair learning environment.

Capital Letters

I just finished reading Ian Stewart's Letters to a Young Mathematician. The book is a compilation of letters written to a fictional math student named Meg, but it is really aimed at the math student within us all. Though you never see an of Meg's letters, you can imagine her frustration and her failed efforts to understand exactly what mathematics is. It is a question that even the most mathematically inclined among us ask and one with no straightforward answer. Stewart weaves a thoroughly enjoyable yarn and leaves the reader feeling at least awed by mathematics even if they are still a bit confused. It should be required reading in any math class.

So Easy a Caveman Could Do It

On the way home, I heard an ad on the radio for All State, warning me that I may live in one of the most dangerous neighborhoods in the country. Of course, I feel quite safe in my neighborhood or I would move. But according to statistics, which never lie, I am more likely to have an accident the closer I am to home. I guess I'd better start looking for a safer address.

I can forgive this little piece of propaganda. I understand that it's all about marketing, and that when it comes to insurance ads, making you afraid is the number one goal. It did get me thinking about all of the other insurance related issues that bug me. The first of which is that lately people don't seem to understand the very nature of what insurance is and is not. It is a mathematical gamble, no different from a trip to the casino. It is not a guarantee of anything. The next time you hear a politician talk about universal health care and affordable insurance for all, ask yourself this. What possible incentive would anyone have for operating an insurance company other than to make money? Let's go back to my casino analogy and expound. The owner of a casino knows that people are greedy by nature and that if they can be cajoled into playing long enough, the house will always win. Gamblers play against the odds and hope to hit that big pay-off early and take the house for all they can. Insurance agencies operate under similar principles. They have complicated actuarial tables that predict the probabilities surrounding your policy. If it is a health insurance policy, they look at your age, gender, occupation, family history, and any mitigating factors such as smoking or obesity. They make money by charging you at rates that they know are likely to have you paying in far more than you will ever take out. You are keenly aware that an accident could be waiting around the next corner and are therefore insuring yourself against the chance that it happens sooner rather than later. If not for the possibility of impending danger, you might be inclined to simply forgo insurance altogether and pay your money directly into a savings account or other interest bearing fund. For most people, this would end up being the better deal, if and only if they were disciplined enough to regularly deposit and only withdrawal for medical emergencies.

So when you start talking about insuring everyone, you are missing the point. Humans are fragile. We will get sick and we will die. The question is not if, but when. That is the question that the entire insurance industry hinges upon. If you try to force the insurance companies to enter into a gamble that they have a poor chance of winning, you have removed all incentive for them to offer their service in the first place. In the future, medical science may advance to the point when we can consider this. There are many who feel that conditional immortality is around the bend. If we no longer die of old age, then we only have to insure ourselves against accidental death and foul play. Until that time, we need insurance companies, and I can assure you they are not motivated out of the goodness of their capitalist hearts. Case in point- the act of God clause.

I just saw a great movie called the Man Who Sued God, which stars Billy Connelly as a lawyer turned fisherman. In the opening sequence, his fishing boat is destroyed by a bolt of lightening, and as you may have inferred the insurance company refuses to pay out, deeming it an act of God. Connelly decides to sue God and hauls the local heads of the major religions into court to act on the Almighty's behalf. Very amusing film; I highly recommend it. All insurance policies have this clause in their contract, and though they never specifically define what it means, essentially it is their way if insuring themselves. There are some events whose very nature depends on chaotic systems that can not be predicted using current technology. Insurance companies don't want to be held accountable for what they can't predict, so they put in this sweeping escape clause.

Now this pisses me off for several reasons. One, and these are i no particular order, they provide no evidence that God in fact exists. Two, if he does exist, aren't all events acts of God? How do they distinguish the ones they're going to pay out from those they won't? Third, isn't they entire point of a contract to strictly define the letter of the agreement so that both parties know exactly what they are getting? This practice seems more than a little archaic to me, and I really can't believe it is allowed to continue.

I feel I've reached the end of my rant about insurance. The conclusion has snuck up on me, and I find I don't have anything profound with which to close. I will just say this. Insurance is a necessary evil, just like death and taxes, and intimately related to both. Unfortunately, it is an institution which has not yet outlived its usefulness. In trying to revamp the system, we need to keep in mind the realities that it has been based upon. Some changes we have the power to make, but others will bring the whole building crumbling down around us.

My Hero

Check out Dan's graphing lesson over at Dy/Dan. So far, of all the teacher blogs I've been reading, he most strikes me as the kind of educational leader I want to be. I plan to steal extensively from him, so I might as well start kissing his ass to avoid the copyright infringement lawsuit.

Good Fences Make Good Neighbors

The state legislature here in Maine is considering legislation that would make farmers who raise genetically modified crops liable for any damages caused to neighboring farms by the spread of those products or genes. This post is likely to be a long one and it will have nothing to do with math or education, so some of you may want to tune out and others of you may want to take a quick trip to the bathroom because this is going to take a while. Ready? Here we go.

Regular readers will notice a curious amalgam of political ideologies spewing forth from my lips. I am generally a pragmatist, and I tend toward the center of the spectrum. I have friends who would happily play golf with Karl Rove and ones who will start showering again when Tibet is free. I am fiscally conservative and socially liberal, but I would just as soon get rid of states and take orders from Washington, so I can't be a libertarian. It all makes sense to me, even if it seems confusing or arbitrary to some. I mention of of this to establish some background for my opinions on genetic modification.

This past year, I thru-hiked the entire length of the Appalachian Trail. It was a wonderful experience and a life-long dream. I highly recommend it to anyone who enjoys being outdoors and wants to find out just how much they are capable of. While I was hiking, I spent some time with a guy known to me only as Cantaloupe. (We use nicknames only on the Trail.) He was trained in horticulture and it was common to see him reach down and scoop up a handful of trailside flora as a snack. He ate leeks, mushrooms, blueberries, bunchberries, snozzberries, and myriad other things. Each time he did it, part of me would cringe in fear. You see despite spending a good portion of my life in the outdoors and being an Eagle Scout, I had been taught from birth never to eat any wild berries, mushrooms, etc. After the novelty of it wore off, I started to think. I am an intelligent, capable grown-man. I have a college degree and am about to return to school for two more. But none of that makes up for this one atrociously humbling fact. I am incapable of distinguishing food for non-food. That makes me dumber than every animal on the planet.

Oh I can pick out a steak if it's wrapped in cellophane or chow down on a box of Cheez-Its, but if it isn't boxed, bagged, homogenized, pasteurized, pumped full of chemicals, and marketed to me during prime-time TV, it is not recognizable to my brain as being edible. Once I have a realization like that, I am not the kind of person to allow the situation to stand. I immediately embarked a quest to discover the origins of my food, and to decide if I really wanted to be eating it. I read several books, including Fast-Food Nation and The Omnivore's Dilemma. I watched several documentaries, including one called The Future of Food about genetic modification. After much deliberation, I decided to stop eating all the the processed crap that had constituted most of my diet. No more Coca-Cola, no more Doritos, no more corn-fed beef. I am trying to eat organic and local.

I do not consider myself a hippie. I bathe regularly and find the scent of petulie to be downright loathsome. In most other ways, I am a thriving Capitalist. I will happily save money at Wal-Mart. I am not making this change for health reasons, although I expect it to be a pleasant by-product. I am doing it because I feel that we have unnecessarily complicated to process of digestion and in doing so have developed an entrenched and thoroughly unsustainable system of agriculture that cannot be allowed to continue. Because I tend to look at things from a systemic perspective, I prefer to think of things as part of a whole. A cow is a machine for turning grass into meat. It is a highly efficient machine at that, and microbes in its gut allow it to get energy from cellulose that is useless to us. So energy originally from the sun is transfered to us through this process, and until we can teach ourselves to photosynthesize, we have to eat. Like all machines, what you get out of it depends on what you put in. Say you only a gigantic, gas-guzzling Hummer and your tank is empty. Assuming you have that kind of cash, the current oil prices probably don't concern you. Given the choice, do you put cheap low octane gas in your tank or spring for the high-test? That's what I thought. Well feeding a cow a diet of corn instead of grass is the biological equivalent of pouring some sugar into the tank along with that crappy gasoline. They weren't designed for it, and the meat suffers. They require more antibiotics to stay healthy and growth-hormone to achieve desired size. Feeding them this surplus corn allows you to raise more cows for less money, but if the food you are producing is lower quality and provides less energy, maybe there is a better solution.

There are many example of why I think we can raise food more efficiently and achieve better results from organic philosophies than from current commercial practices, but this post started with genetically modified crops at I'd better get back there. I don't have a problem with gene-splicing. I love technology and science, and I think that if our learned astronomers think they can build a better tomato, well then they should have at it. I do think that much more testing and evaluation needs to go into it, though. The current industry is propelled by profits and concealed by the same cultural compartmentalization that caused me to fear wild berries. Companies like Monsanto are allowed to grow their modified crops right next to other non-altered ones and then sue their neighbors when patented genes are found in adjacent fields. Those crops ought to be contained, and that's going to be tough, not to mention costly. If you have a dog who craps on your neighbor's lawn, is it your responsibility to fence your dog in or your neighbor's to fence him out? I believe the responsibility lies with the dog-owner just as it lies with the farmers raising Round-Up ready corn.

I understand that laws like this will throw up huge barriers to the agriculture industry and I am fully aware of all the commercial arguments against them. Still, I will quote a local organic farmer here in Maine.

"You grow what you want to grow, and let me grow what I want to grow."

Good fences make good neighbors.

Think of the Children

Common sense tells us that the more qualified a teacher is, and the more competent they are in their subject, the more their students will learn. Yet most elementary school teachers possess math skills that are only a few years ahead of their students. Looking back, the most qualified teachers I had as a kid, in terms of knowledge of their subject, were in classes many would consider peripheral. Music, art, phys ed, etc. The core teachers were knowledgeable about child psychology and the standards required for their particular class, but probably not more. Now of course, I am being unfair. There is no way I can actually be privy to their individual resumes, and many of them may have been extremely educated.

But I doubt it.

One need look no further than the state licensing requirements for the elementary level to see the truth. Now I have quite a few friends that are elementary school teachers, so let me clarify my point, lest I be burned at the stake. I certainly realize that what I am asking is more than a little unreasonable. No one can be an expert is as many subjects as they are expected to teach, especially while dealing with rambunctious children. I do not believe it is the teachers' fault. But I do have a problem with specific elements of the system.

Why do we treat primary and secondary schools so differently? Most secondary certificates mandate 24 credit hours of specified subject taken at the college level. Why do we expect less from primary? Why do we expect them to competently teach history, English, math, science, and anything else the school district might desire? Maybe the evidence shows that children that age learn better when they have one person they can trust. But then why do we give them to someone else for music or P.E? What if we had pairs of teachers? One to handle math and science and the other to tackle English and social studies? Or maybe they both teach everything, each yielding to the expertise of the other.

I certainly don't have the answers, but I sure as heck know there's a problem. Think of how many students claim to hate math or hate history. Isn't this patently absurd? I challenge you to find any human who doesn't use some form of mathematical reasoning on a daily basis, and history is everything that has ever happened! How on earth can that be boring? I'll tell you. Force someone to teach a subject that they are not passionate about and require them to be only a few steps ahead of their students, and you have all the ingredients for boredom. It is a feeling that will stick with those kids for life.

I am starting to see slow changes lately. In Massachusetts, the state Board of Education has passed stronger licensing requirements for elementary teachers, particularly in the area of math. I can't believe they will have anything but positive results and I hope more states follow suit. We will never stem the tide of math phobia in this country if we keep turning a blind eye to the obviously low-expectations placed on elementary school instruction. There's not much point in hiring a highly skilled roofer after you've settled for the low-bidding stone mason. Sure, the roof doesn't leak, but will that be much consolation when the foundation crumbles and your house falls down?

A New Hope

Look, I dislike W. I freely admit it. But I'm tired of hearing about how 9/11 was an inside job. It's demeaning to the memory of those who died and quite frankly my intelligence. Check out this brilliant satire of all those conspiracy theorists. It asks some tough questions about the Empire's role in the Death Star debacle.

(The video has nothing to do with it. But eetz-a funny, no?!