Saturday, June 30, 2007
Lately I feel like I'm seeing double. It seems like everywhere I look, I see another pair of twins. They are absolutely ubiquitous. Twins in the movies. Twins on TV. Twins in the White House. Minty fresh twins that double both my flavor and my fun. Freaky "Come play with us" twins that give me nightmares. Julia Roberts has twins. Geena Davis, twins. It seems that every uterus in America is offering double occupancy.
At first I thought maybe it was my imagination. I figured it was the fallacy of memory, where the event stands out in your mind precisely because it is what you are trying to remember. But then I started doing some research, and it turns out that we are in an absolute epidemic of multiple births. Since 1982, the twinning rate has risen 300%. The numbers are even more staggering for triplets. Up until recently, and with good evolutionary purpose, the rate of twins occurring naturally in the human species was 1 out of every 80 births. Triplets occurred once in 8000, quads 1 out of 800,000, and quints 1 in 40 million. As of right now, for a variety of reasons, the twinning rate is roughly 1:33!
As I mentioned, there are several factors that have led to this. Women are becoming mothers at later ages, when there ovulation is more erratic, making them more likely to drop two egg cells, or oocytes, in a single cycle. Also age related is the number of women using fertility drugs to conceive, again adding to the incidence of multiples. Then there is assisted reproduction, where multiple oocytes are fertilized and implanted in the hopes that at least one will take. More often than not, several of then will.
This increase is bound to affect our world in countless ways. Beyond the obvious increases in infant mortality and premature births, there are all the additional expenses in time and money that parenting these broods to adulthood. I started to wonder how this would affect the school system. There doesn't seem to be any consensus as to how multiples should be handles at school. Some districts mandate that the children be separated from the beginning. Others try to keep the kids together. Either way, there are sure to be unhappy parents with different ideas.
I am interested in hearing from my readership how this subject has affected their schools. To me, it seems like a non-issue. There is no need to treat these children differently than the others. Just plug their names into whatever class distribution algorithm currently in use and see what pops out. If the kids are in different classes, fine. They have to get use to being apart sooner or later. If they are together, great. They can't possibly be more disruptive than all the other giggling best-friends out there.
(Incidentally, if you ever happen to be writing a blog post about twins, and decide upon its completion that an image of a multiple birth ultrasound might make for a nice addition, do not simply Google "twins" with the Safesearch off. )
Friday, June 29, 2007
Thursday, June 28, 2007
Humans, as powerful as we have become, are still subject to certain constraints on time and space. We simply don't have enough resources or energy available to reach all of society's goals simultaneously. Many times we will be required to choose between doing one thing really well or two things mediocre. The continuing struggle for school desegregation is one of those times.
School desegregation has been a great thing. The days of governors standing at schoolhouse doors are over. Anyone of any race can attend their neighborhood schools and receive the same education as everyone else (in that particular school, of course.) But in the days of accountability, NCLB, and with myriad talk of catastrophe and crisis from both sides, maybe it's time we focus on teaching instead of stirring our melting pot.
If it were up to me, there wouldn't be diversity. I wish there was one single human culture. I don't understand people who want to preserve all of the special little idiosyncrasies that separate us and lament each time a tradition falls to globalization. As far as I can tell, it's the celebration of those historic distinctions based on arbitrary geographic and social boundaries that make it so easy for us to keep killing one another. And I've had just about enough of that, thank you very much.
But that perfectly homogenized, randomly distributed population isn't going to exist any time soon. In the meantime, based purely on scarcity of time and money, I think our nation needs to decide on a tighter focus. Let's work on educating the kids first. Of course, some schools will have an easier time of it than others. Yes, those schools will most likely be affluent suburban schools with limited people of color. Yes, that is a sad reminder of just how much farther we have to go. I believe in many Liberal ideals, but I would just as soon get all the kids to pass their basic skills tests. Then, and only then, can we try to tackle the diversity issue.
Tuesday, June 26, 2007
Monday, June 25, 2007
- I have the most tender feet known to man. I was not allowed to walk barefoot as a child and if I accidentally step on a tennis shoe in the night, I will fall down.
- I once memorized 140 digits of pi in order to get out of class. It was 3/14 and I didn't want to miss out on the fun.
- I am an Eagle Scout.
- My right forearm is missing a muscle. If I tense it up, there appears a strange divot where the muscle should be.
- I did not cry when either of my grandfathers died, but I get teary every time I hear Over the Rainbow by Israel Kamakawiwo'ole because it was playing in the background when Mark Green died on ER.
- My biggest guilty pleasure song is Holding On for a Hero. It will be featured heavily in my wedding ceremony, which will have a superhero theme.
- I am constantly assessing every room I'm in for escapes or weapons to use in a possible zombie or terrorist attack. (I have seen way too many movies.)
- I would happily give up at least twenty IQ points if it would give me enough ups to dunk a basketball.
The setback doesn't seem to have hindered Frederick too much; he's now living and teaching in China. But how much has it affected the civil liberties of the rest of America's public school children? Frederick himself admits that it was not an exercise in free expression so much as a publicity stunt, saying that
the words on his 14ft (4.26m) banner did not relate to drug use and were meant to be funny in an attempt to get on television.
I suppose he could have just as easily mooned the cameras and achieved roughly the same effect, although I have to give him props for creativity. If he had chosen this more trite route, he would have received the same suspension and moved on. Unfortunately, at least for our legal system, he is a better humorist than that. So instead the battle raged all the way to the Supreme Court. He lost his case, but it was close. 5-4. Not a solid victory either way.
Though I am a staunch civil libertarian, I have to disagree with my beloved ACLU on this one. I don't believe Frederick's right of free speech was violated. If his banner had read Impeach Bush or Make Love, Not War or even Legalize Marijuana, then it might be a different story. If the kid were actually trying to make an important statement, I would support him, whether I agreed with it or not. Instead I have to agree with my conservative pal Darren over at Right on the Left Coast. Frederick admitted that he wasn't trying to promote drug use, Christianity, or any combination of the two. He was trying to be funny. I believe he succeeded, and like every good class clown knows, sometimes you have to take the punishment for your craft.
He broke school rules at a school sponsored activity, and they were well within their rights to discipline him.
I fear the fall-out from this case will be severe. Students do have to constantly fight for their rights. They are in a unique spot. Unlike other minority groups, they can't take their fight to the election booth. They can't vote about anything. So they have to convince adults to do it for them, and that can be tough to do, especially when well publicized cases of stupidity like this get conservatives up in arms. I would never wish for anybody's rights to be violated, but it certainly wouldn't hurt the cause if a more easily defensible case came to light, and the sooner the better.
Little girls always seem to have their fathers wrapped around their little fingers. They smile their sweet little smiles and throw their tiny arms around you, and you feel like the biggest strongest man in the world. What wouldn't you do for her? You will protect her from all the world's evils. You will teach her how to drive, how to dance, and how effective a good old-fashioned knee to the groin can be. You will be there for her, celebrating every milestone- each birthday, her high school graduation, the day she goes to college, and her wedding day (although there is no man who will truly deserve her.) She will always be your little girl.
Just as girls have a tremendous power over their dads, so do men have a great responsibility for shaping the woman that little girl will become. By your words and actions, you will pass along your particular meme for gender identity. She will learn how to make herself attractive to the opposite sex by batting her eyelashes at you. Humans are highly adapted social creatures. We aren't exactly mind-readers, but we are capable of transmitting an unbelievable amount of information through non-verbal cuing. You may think you are telling her one thing, but she may be hearing something else.
"We've known for a while now that females do as well as males on tests that measure ability in math and science," said Pamela Davis-Kean, a psychologist at the U-M Institute for Social Research (ISR). "But women are still underrepresented in science, technology, engineering and math graduate programs and in careers based on those disciplines."
It's as if women are saying, "I can, but I don't want to," according to Davis-Kean.
Why don't they want to? Could it be because women who go against traditional gender roles, the brave few who thumb their noses at the patriarchy, becoming mathematicians or engineers, aren't exactly filling up their dance cards? Don't misunderstand. Any man who doesn't want to be with a strong, intellectual, independent woman isn't worth a damn, in my book. Any man who can't handle being with a woman who is smarter than him, or makes more money, is a small, sad, little golem. And you probably feel that way, too. I'm sure you tell her she can be anything she wants to be. You would be proud of her whether she was the prom queen or president of the math club. But actions, oh how they speak louder than words.
In a study presented recently at a campus meeting, Davis-Kean and colleagues analyzed how parents' values and attitudes affect children's math performance and later interest, and how these attitudes vary by the child's gender. They used data from a longitudinal study of more than 800 children and a large group of their parents that began in 1987 and continued through 2000.It isn't enough to simply tell her all the things she can be; you have to make her want to be them. There are organizations galore devoted to promoting women in the sciences. The Society for Women Engineers is one I have mentioned in the past, but there are myriad others. None of them have the power to shape a young girl's image of what a woman can be more than daddy.
They found that parents provided more math-supportive environments for their sons than for their daughters, including buying more math and science toys for the boys. They also spent more time on math and science activities with their sons than with their daughters.
You're a modern man. You've left that Victorian chauvinism behind. You believe women are your equals. At least, that's what you always say. But do you really mean it? Ask your daughter what she wants to be when she grows up. You might be unpleasantly surprised.
Sunday, June 24, 2007
As I study calculus, I am reminded of this past mistake and am taking pains not to repeat it. I speak the words aloud as I work through a problem, rather than simply processing symbols and manipulating formulas. I get the same answers, but I gain more understanding.
Friday, June 22, 2007
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.
Wednesday, June 20, 2007
- Finish reviewing Calculus and decide at which level to re-enter (Calc A,B, or C)
- Add more cardio to my work-out routine. I'd like to trim down a bit more.
- Design and implement a comprehensive basic skills tutorial program for my one existing client. His parents feel he has responded well to me and would like to see if we can milk that further.
- Climb Mt. Katahdin, preferably on the one year anniversary of the completion of my AT thru-hike.
- See Live Free or Die Hard, Transformers, and Resident Evil 3.
- Continue honing my blogging skills. I am getting a few regular hits, but I would like to get more feedback in the way of comments.
- Read as much as I can, since I won't have any time for that in the Fall.
- Find a new apartment.
- Practice low-level parkour.
- Visit Boston. Last time I went it was too cold to enjoy.
These are just a few of the things that I have in mind. I should have more than enough to keep me busy.
Tuesday, June 19, 2007
There is no question that our country is preoccupied with sex. Not just prettied up white-wedding sex. Christina Aguilera dirty sex, too. Sex, as they say, sells and in
Western civilization has always had a love/hate relationship with knowledge. It may have gotten us kicked out of
A reasonable predictor of a group’s success lies in how it handles the welfare of its youngest generation. By necessity, we invest a tremendous amount in our young people, and it is in the best interest of everyone to see them safely through danger. Topping the list of landmines they may encounter are those stemming from a lack of accurate sexual education. Teen pregnancy and STDs are the tip of the iceberg, creating nearly insurmountable obstacles to success and contributing to the cycles of poverty and general hopelessness that form the ugly dark side of the Land of the Free.
For opponents, this is a moral issue. They feel premarital abstinence has been clearly prescribed to us by our Creator, and that it is the only guaranteed preventative for the aforementioned social ills. This desire to transform personal morality into state mandate would be forgivable if it were effective. Fortunately for public policy makers, reliable information gathered through peer-reviewed studies shows that “abstinence only” proves a miserable failure on multiple levels. When these guilt-based programs fail and the graduates do engage in sexual relations, they do so without the knowledge required to be safe and responsible. Even if premarital virginity is miraculously preserved, the potential risks of sex do not end at the wedding alter. Biology, it seems, is largely unimpressed with human cultural tradition, as unwanted pregnancies and disease occur inside of wedlock as well.
As our nation’s ongoing obsession with sex continues, we have a simple choice to make. That decision is not whether or not to teach our children about sex, but rather who will be the instructors. We either equip our schools with open, honest, and medically accurate sex-ed curricula, or we continue to allow our children to learn the facts of life from Paris Hilton and Britney Spears.
Monday, June 18, 2007
I finding this especially true as I follow the epic saga of the Math Wars. As always, I find it only fair to mention that I am not yet a certified teacher and have no experience other that tutoring, so my opinions remain untested. But I do not think one needs to be a tenured educator to fully appreciate the state of math education in America. The situation is readily apparent. Americans, on average fear and despise math. It does not seem to be a recent phenomenon, as far as I can tell. I do not think it is something we can blame on TERC or Everday Math.
I will admit that people who learned math twenty or more years ago tend to be faster at arithmetic, both in their heads and on paper, though I suspect that cheap calculator technology is more at fault than any new age math reform. Nor can we say for sure whether this is a bad thing. The technology is too young for those kinds of evaluations. Farming, perhaps the greatest invention of mankind, did not immediately prove itself superior to the traditional hunter-gathering ways. Sure it was convenient and it's practitioners no longer had to follow their food supply, but there was a huge sacrifice in terms of overall nutrition. It wasn't until relatively recently that we have achieved the average nutrition of Stone Age diners. So I am reluctant to pass judgment too swiftly on the poor TI-89s and their ilk.
I remember Dan making a list once of all the skills that a great teacher needed to have (though I can't find the post I am thinking of right now.) I also remember him admitting that the list could probably added to ad infinitum and be no more comprehensive. It seems to me that teachers need as many weapons in their arsenal as possible, since there are exactly as many learning styles as there are students. It is because of this simple fact that I believe tradition and reform should not only coexist, but even cooperate. There is no "best" way to teach mathematics. What worked for one student may not work for the next. The very idea of a superlative runs counter to the reality of a multi-dimensional world. Let me describe it in terms of a fitness landscape. Competitors in a system ,whether life forms or educational theories are subject to a natural selection process that can be usefully modeled with a topographic relief map. Individual genes or memes attempt to climb in elevation, seeking relative maximums and thereby increasing their success or "fitness." This model, while helpful, can be deceptive. It masks two key facts about the real world. One, the real system is not static. The hills and valleys rise and fall with time. What reigned supreme in one era will be eaten alive in the next unless it continues to move and evolve. Two, the real system is not low-dimensional. If we consider each teaching style to be a point on the landscape, we must assign to that point all of the component elements of that style, which as Dan pointed out are quite numerous. This creates a multi-dimensional space that may not even have relative maxima in the way we are used to thinking.
So I say, when it comes to math education, the more the merrier. As a pragmatist, I go with what works here and now. I am not overly addicted to traditions, yet I am respectful of their proven track record. I am not mesmerized by the reforms for their newness alone, but I am excited by their search for something better. It is clear to me that the combatants in the Math Wars are passionate about what they do and that their first concerns are for their students. I just think everyone needs to take a deep breath. As with most arguments, the opposing sides probably have more in common than they think.
Thursday, June 14, 2007
The very first thing I want to see is some empirical data. So far, all I am finding is anecdotal evidence, which you know I hate. Anytime you ask a person to subjectively rate an experience, especially those based on memory, you can easily cherry pick opinions for or against anything. These opinions are therefore completely useless when it comes to decision making. Even when the opinion comes from someone I hold in high esteem, like my blog-friend Rebecca, I still need to see some evidence.
This recent article provided little in the way of hard data. Actually, there were some red flags that caught my attention, like the following exchange.
Are there disadvantages or challenges to same-sex schooling?
For the book, I looked at single-sex schools that were recommended by friends and colleagues. I investigated seven new girls’ schools, (including Archer), three of them public institutions; I visited six established single-sex schools.
I can find no disadvantages for any students who attend any of these thirteen schools.
No disadvantages? From what I know of reality, seldom if ever do we find things with absolutely no negative repercussions. I decided to go in search of some more conclusive evidence, which I did find. The results of myriad studies show that girls do better in "non-traditional" classes like math and science when educated in same-sex environments. The results are not nearly as impressive for boys. Although they tend to enjoy more artistic endeavors like drama, their scores in the academic subjects do not markedly increase. I suspect this is where the systemic effects of living in a sexist society come into play. I really don't buy the whole "girls learn differently" line. I seriously doubt that the teaching methodology differs that much from co-ed to same-sex. Any positive effects are going to come from the environment. As proof of this, one study also compared class sizes and found that the positive results occurred mainly in medium size schools. Small schools weren't able to offer all of the options, regardless of gender, and in larger schools, the teacher-student ratios negated any positive effects.So I guess my take on it is this. Does same-sex public education have benefits? Maybe. But then I suspect that similar effects could be created by segregating along ethnic lines, and I think we can all agree that that is a bad idea. Should same-sex public education be made more widely available? Fine by me. But I don't want to teach there. What I would prefer is that we find a way to teach co-ed classrooms so that girls feel equally empowered as boys. If positive results can only be achieved by eliminated distractions, then to me, those results are suspect and quite likely to disappear once the disctractions return.
Wednesday, June 13, 2007
Beauty is not in the eye of the beholder. It is an abstract concept that is as mercurial as it is vague. It's nearly impossible to pin down what beauty is, but whatever it is now, isn't what it was then, nor what it will be in the future. Trends come and go. Ideals morph from year to year and culture to culture. Nothing is permanent except the impermanence of it all. No man is an island, and therefore, no one can opt out of the cycle. Unless you are completely alone, you must concern yourself with what others think, even if it is so you can specifically rebel against it.
So far, you are probably thinking this rant is aimed at the mindless sheep that are filling the void left by American Idol by droning on about Paris Hilton. I'm not, although it certainly applies to them. No, I am actually addressing the intellectual crowd- those practitioners of skepticism and reason who too often absolve themselves of the sin of pride, lust, and envy. It seems like bespectacled wags from all corners of science use a given definition of beauty to evaluate their craft, and just as in Hollywood, ugly is turned away at the door. In this world, the world of chalkboards and peer review, beauty is synonymous with simplicity. Complicated is inefficient and ugly. Occam's Razor shaves closer than most laypeople would imagine.
But everywhere, this idea of beauty is hitting walls. Particle physicists add more and more cages to their zoo, each built to house a new and unique flavor. Their cousins, the string theorists, find that what was once a Theory of Everything is turning into an infinity of theories, each with no more explanation that others. Biologists find chaos around every corner. Geneticists find that "junk DNA," while it appears to do nothing, may in fact be integral to the process of life. The list goes on. Mathematicians watch smugly from on high, contented with the delusion that they are somehow removed from it all, when in fact they are the worst offenders and it all trickles down from them. They talk of elegance and truth, when what they really want are equations that can fit on a Post-It note and proofs that can fit in the margin of Fermat's notebook. If it's complicated, then there must be something wrong with it. Oh, they'll make do with it for now. If you can't be with the one you love, love the one you're with. But there will always be that nagging feeling that today's pageant winner will one day hand over her crown to a sleeker, thinner mathematical model.
The hard truth is that the world isn't simple, on any scale or in any reference frame. It is complicated, redundant, inefficient, emergent, and mysterious. It will never conform to our ideas of beauty, so we better start conforming to reality. There's nothing ugly about complexity. It is the messiness of it all that provides the foundation for everything we humans hold dear. Regardless of how beauty is defined, the only thing that is consistent seems to be that it always represents the minority. I suggest we (and now I'm talking everyone from all walks of life,) start embracing the ugly that's left, or else we will miss out on the majority of what's worth knowing.
I know, that seems ridiculous. Teachers are well-known for their hatred of the almighty dollar. The have always appeared to thrive by living in near impoverished conditions, taking what is left of their meager salaries after taxes and food, and using it to buy supplies for their classrooms. Yes, it certainly is counter-intuitive. Who would have thought that intelligent, passionate, capable people would be enticed by MORE money? It sure is a good thing that we have experts willing to look for solutions outside the box like this. Maybe there's hope for us, yet.
Don Herbert, TV's Mr. Wizard, passed away yesterday at 89. He is probably one of the great scientific influences on my life. When I watched his show as a kid, I learned that science was something that anyone could do. I didn't need to have expensive equipment or a fancy degree. All I needed was curiosity and a few carefully selected household items and the mysteries of the universe would fall at my feet. Later in life, I would be introduced to the likes of Newton and Hawking, but the real inspiration for my love of discovery came from Herbert.
He didn't have a terribly impressive academic background, just a degree from a teachers' college and some time spent in the Army. What he did have was a passion for his subject and the ability to pass it on to others. He was one of my favorite teachers growing up, even though he never knew it, and I will always remember him.
Tuesday, June 12, 2007
Sunday, June 10, 2007
To me, the entire purpose of video games and virtual reality is to be able to experience things that you otherwise could not. As a child, I enjoyed rescuing princesses from large, irritable gorillas who could express their anger only by throwing barrels. I was overjoyed by the simple pleasure of gobbling pellets in my feverish attempt to escape pastel apparitions. I gracefully navigated the jungle depths, swinging from vines, leaping logs and tar pits, and bounding from crocodile to crocodile. These activities tested my dexterity and my imagination. They don't make games like that anymore.
There is a trend in modern video games that confuses me on principle. The goal seems to be to blur the line between virtual reality and reality reality. I understand that this is taking the entire story arc of gaming to its ultimate conclusion. But the advances in technology have been made at the expense of imagination. Where are the creative minds in this business? All the games I have seen or played lately involve one of two things. I am either out to kill everything that moves with ever larger weaponry or more improved ammunition (which I suppose I could do in real life if I were so motivated,) or I am performing some task that I actually can do right outside my door. When people are getting tennis elbow from playing virtual tennis, I think my point is proven.
I know I started this post by admitting to being old, but I'm starting to reconsider. I'm starting to think that the problem isn't me. I would enjoy gaming again if the designers would put a little more effort into it. Graphics and camera angles aren't enough. Sound effects and vibrating controllers aren't enough. I want to be taken on a journey- a journey to a place I simply can't get to in any other way. That's what gaming should be about.
Thursday, June 7, 2007
These geometric sculptures are the coolest things I've seen in a while. It seems like everybody has some Escher print or another on their wall or a Klein bottle on their desk, but these things beat both of those hands down. (My birthday is September 12, if anybody was wondering.)
Wednesday, June 6, 2007
The problem comes from the application of two different conventions, one verbal, one mathematical. In English, the language with which I am most familiar , it is customary to name the positive member of an antonym pair first (And positive can be taken literally or figuratively.)
hot and cold
happy or sad
This is especially true when the second element is formed by simply adding a prefix of negation to the first.
matter and antimatter
Deal or No Deal
guilty or not guilty
Tuesday, June 5, 2007
Monday, June 4, 2007
Danica McKellar, best known for her role as Winnie Cooper on The Wonder Years, has a book coming out in August directed at aspiring mathematicians of the female persuasion. It's called Math Doesn't Suck: How to Survive Middle School Math Without Losing Your Mind or Breaking a Nail, and it's aimed at adolescent girls, who amidst hormones, emotions, and the evil that is teenage boys, often fall irreparably behind in math and science.
She hopes to change all that. I hope she succeeds.
Stuff like this is so much more exciting than Paris Hilton reporting to county jail.
This is probably one of the most popular myths of physics. It is an alleged result of the Coriolis Force, an artifact of the Earth's rotation that affects weather patterns. It causes wind patterns "above" the equator to tend toward clockwise spin and those "below," counterclockwise. But it only affects large-scale weather patterns. It's affects are totally negligible in your household drains. The direction of toilet flush has everything to do with the subtle shape of the bowl and various other minute details of fluid mechanics. Oddly, this myth is perpetuated by many science teachers, who ought to know better.
So don't believe what you hear. Credulous world travelers will assure you that every toilet they flushed in Australia flushed backwards. Like other anecdotal evidence, it's nothing more than coincidence.
Sunday, June 3, 2007
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.