So I'm sitting in court yesterday waiting for my 15 seconds of infamy... "Guilty, Your Honor"... (and the opportunity to pay $300 in court costs) because I had been driving with a suspended license. I had been driving with a suspended license (unknowingly) for nearly a year, because I had been driving without insurance (unknowingly) for over a year, because (I'm guessing) as I was moving from one state to another, back to the first state and then two more moves before finally settling in where I am now, I missed several notices from my insurance company. I apparently also missed a notice from the state, telling me they'd suspended my license, but all of this is not why I write. (Aside: the cop who ticketed me for driving with a suspended license was incredulous that I could have gone a year without paying my car insurance, and not noticed that fact. Clearly, he doesn't know me very well.)
Before he started hearing cases, the judge took about 15 minutes to explain the rules of the court and the process that would occur depending on the outcome of the hearing. After the first 4 people came before him and answered "No" to the question of whether they'd obtained a valid driver's license, he sighed and began a 5 minute lecture on the importance of taking care of the problem now, before it becomes a bigger one (with a 5 year prison sentence possibility), just for driving without a license.
While edifying, the thing that really struck me was how much he sounded exactly like me in the classroom, admonishing my students that they needed to do the class work and homework... not for my benefit, but their own. The more he spoke -- with that exasperated tone that said clearly he knew his words were falling on deaf ears, but he felt the need to say them anyway -- the more he seemed to be in exactly the same role as I am in every day. He's talking to a lot of people who don't want to be there. He has information they need. Information they are fighting to avoid learning, and that he's fighting to make them learn, despite the fact that he receives no benefit from their learning it, and they receive enormous benefit. It's like force-feeding wounded birds to keep them alive. It pisses them off, it does you no good while saving their lives, and they're not only not grateful, they're actively hostile.
As Buckaroo Bonzai said many years ago, no matter where you go, there you are.
Tuesday, January 11, 2011
Tuesday, December 7, 2010
It Takes a Village Idiot
My tenure as a Pre-IB teacher ended today, not with a bang but a whimper. The story I've been told (and I believe, for the most part) is that my "demotion" from pre-IB has to do with student and parent complaints about my teaching rather than my outburst in the faculty meeting a few weeks ago. I can live with that.
My teaching philosophy tends to be "If you're willing to work at it, I can not only teach you a considerable amount of valuable mathematics, I can also show you some of the beauty of the subject along the way." It isn't "I consider it my responsibility to find a way to teach you the bare minimum of mathematics you must know to pass the state-mandated tests, whether or not you're willing to cooperate in that attempt." That second philosophy is a great one to have -- possibly even the only appropriate one to have -- when teaching a standard course at a school such as the one at which I find myself. The low-level kids who need to pass the state-mandated test to get their high school diploma are not now, nor ever will be, interested in the beauty of mathematics. The ship upon which travels their capacity to absorb any but the most rudimentary mathematical concept has long since sailed. They need a teacher who cares about them, individually, and wants to help by making the math they must learn as digestible as possible. It is a noble calling, and I admire the teachers who heed that call. But it is a cold and barren field in which to toil for someone who loves mathematics as I do.
I was enormously excited when I learned I'd be teaching all honors courses, including an AP class and two Pre-IB classes. Here, I believed -- particularly in the Pre-IB courses -- I could loose these students on the subject while acting as tour guide, pointing out surprising depths lurking just beneath the simplest concepts, taking short excursions onto strange and esoteric landscapes (Mandelbrot sets! Riemann manifolds! Mobius bands and Klein bottles!), mapping out tougher but more beautiful trails for the strongest of the group to explore on their own, and generally stoking the fire of their natural curiosity in the hope that mathematics would captivate them as it has me.
In the real world, my expectation that they would take responsibility for their learning -- seeking tutoring when they were confused about something, getting together with other Pre-IB students to help each other struggle through difficult concepts, and going back to the textbook to teach themselves the material they hadn't understood in class -- was met with the reality that their standard reaction to adversity is to find someone to blame, then complain about that person to everyone they can, in the hope (justified, as it turns out) that their complaints will eliminate their adversity by removing the person responsible for it from their path.
It shouldn't be surprising that students complain about the difficulty of their path. It is, I believe, our job as educators to look for the greater good -- funnel the students who can't or won't make the required effort into other, less challenging courses; inform, as often as necessary, the students who remain (and their parents) that success in the program will require dedicated effort; insist that the resources the kids need (supplies, tutoring help, places for small student groups to meet) be made available; and most importantly, hold teachers, students, parents and administrators to a higher standard of education for these kids, which will necessitate a more difficult path. In this way, we could be providing our best students (most of whom do not have the option to attend a magnet or private school) the opportunity to truly excel both in high school and beyond. Why shouldn't our students go on to study engineering at MIT, or music at Indiana, or marine biology at UC San Diego, or economics at Carnegie Mellon?
Instead, parents, school administrators and, I am given to believe, the district honchos in charge of IB, don't want a tough program for elite students. They want an elite (i.e., high prestige) program that affords its enrollees wonderful benefits without requiring any payment of dues. Unfortunately, I believe all of those constituencies will discover relatively quickly that this is one more arena in which the aphorism "No pain, no gain" is apropos.
It is the students who could have scaled mountains but were directed only to molehills who will suffer.
My teaching philosophy tends to be "If you're willing to work at it, I can not only teach you a considerable amount of valuable mathematics, I can also show you some of the beauty of the subject along the way." It isn't "I consider it my responsibility to find a way to teach you the bare minimum of mathematics you must know to pass the state-mandated tests, whether or not you're willing to cooperate in that attempt." That second philosophy is a great one to have -- possibly even the only appropriate one to have -- when teaching a standard course at a school such as the one at which I find myself. The low-level kids who need to pass the state-mandated test to get their high school diploma are not now, nor ever will be, interested in the beauty of mathematics. The ship upon which travels their capacity to absorb any but the most rudimentary mathematical concept has long since sailed. They need a teacher who cares about them, individually, and wants to help by making the math they must learn as digestible as possible. It is a noble calling, and I admire the teachers who heed that call. But it is a cold and barren field in which to toil for someone who loves mathematics as I do.
I was enormously excited when I learned I'd be teaching all honors courses, including an AP class and two Pre-IB classes. Here, I believed -- particularly in the Pre-IB courses -- I could loose these students on the subject while acting as tour guide, pointing out surprising depths lurking just beneath the simplest concepts, taking short excursions onto strange and esoteric landscapes (Mandelbrot sets! Riemann manifolds! Mobius bands and Klein bottles!), mapping out tougher but more beautiful trails for the strongest of the group to explore on their own, and generally stoking the fire of their natural curiosity in the hope that mathematics would captivate them as it has me.
In the real world, my expectation that they would take responsibility for their learning -- seeking tutoring when they were confused about something, getting together with other Pre-IB students to help each other struggle through difficult concepts, and going back to the textbook to teach themselves the material they hadn't understood in class -- was met with the reality that their standard reaction to adversity is to find someone to blame, then complain about that person to everyone they can, in the hope (justified, as it turns out) that their complaints will eliminate their adversity by removing the person responsible for it from their path.
It shouldn't be surprising that students complain about the difficulty of their path. It is, I believe, our job as educators to look for the greater good -- funnel the students who can't or won't make the required effort into other, less challenging courses; inform, as often as necessary, the students who remain (and their parents) that success in the program will require dedicated effort; insist that the resources the kids need (supplies, tutoring help, places for small student groups to meet) be made available; and most importantly, hold teachers, students, parents and administrators to a higher standard of education for these kids, which will necessitate a more difficult path. In this way, we could be providing our best students (most of whom do not have the option to attend a magnet or private school) the opportunity to truly excel both in high school and beyond. Why shouldn't our students go on to study engineering at MIT, or music at Indiana, or marine biology at UC San Diego, or economics at Carnegie Mellon?
Instead, parents, school administrators and, I am given to believe, the district honchos in charge of IB, don't want a tough program for elite students. They want an elite (i.e., high prestige) program that affords its enrollees wonderful benefits without requiring any payment of dues. Unfortunately, I believe all of those constituencies will discover relatively quickly that this is one more arena in which the aphorism "No pain, no gain" is apropos.
It is the students who could have scaled mountains but were directed only to molehills who will suffer.
Thursday, November 25, 2010
Weather Man
Many years ago, I had a fascinating conversation with Walt, a friend who worked in marketing for a cigarette company. (This was back when working for a company providing legal, but politically incorrect, products was a matter of personal conscience, rather than an invitation to be the target of hate mail, death threats, physical harassment and occasionally even violence.) He told me a story about the company's research department presenting an advertising research study and concluding Ad A was better than Ad B because of its higher recall scores, higher favorable ratings, etc. Walt stopped them, and said he wanted to see the scores of the "Marlboro Man" ads using the same methodology. (Marlboro wasn't a brand owned by Walt's company, but it went from an also-ran in the category to a dominant number 1 when Philip Morris introduced the now iconic rugged cowboy image.) Turns out, Marlboro's ad scored lower than either A or B, which was what Walt expected. He told the research people that, until they began basing their conclusions on the results of studies in which Marlboro was the clear winner, those conclusions could not possibly be considered reliable.
The point here is this: so far this year, I've given my kids 11 state-, district- or school-mandated tests (2 more scheduled next week) so that we have pre- and interim-assessments on our kids, in order to better guide our instruction so that they will perform better on the one that actually counts (sort of), at the end of the year. But no one is able to determine whether the assessments actually measure anything of value, and even if they do, whether the results can be effectively used to improve the kids' test grades on the end of year assessment, and even if it does, whether that translates to improved quality of education. Of course, on a macro level, only one thing is absolutely crystal clear: whatever we've been doing hasn't been working.
Everyone, it seems, understands public education is in deep trouble. From teachers in classrooms to principals in schools to Superintendents of county school systems to the President of the United States, each individual in that chain cares about, and is actively working on, improving education. This has probably been true since 1647 (the year Massachusetts began requiring towns of at least 50 families to hire school teachers to educate their children), but has certainly been true for the past 30 years. For the most part, these people are well-intentioned and reasonably bright. Sure, there are snakes in the woodpile, but no more, and no more venomous, than the snakes in woodpiles elsewhere in America. So why has American public education been declining rapidly, by all accounts, and reached a point where America's students are near the bottom of virtually every list of industrialized countries in terms of math and science skills, reading comprehension, and probably several other measures I haven't stumbled across in my quest to find data on the subject?
The issue cannot be money. According to TIMSS (Trends in Mathematics and Science Study), the US is educating its students in mathematics on a par with the Russian Federation, Slovenia, Lithuania and the Czech Republic. And while our spending on public education as a percent of GDP is a "middle of the pack" 5.85%, it is roughly equal to Slovenia's 6.02% and well ahead of Lithuania's 5.18%, the Czech Republic's 4.55% and Russia's 3.67%. Japan, which kills the US (and everyone else) on all these lists of best educated students, spends less than Russia on a GDP basis.
Here's one possibility. I work in District A. District A is one of (if not the) worst districts in the state, as measured by drop-out rates and state-mandated standardized test scores. An adjoining district, cleverly named District B, is the best district in the state on these measures. Now, admittedly, District B is much richer than District A, and that's always the rationale one hears when people discuss the stark difference between the districts. But I'm not buying it. Yes, I think parental involvement is hugely important, and without question, parents in poorer districts are less involved (mostly because they're running as fast as they can just to keep food on the table, or the kid is living with his older sister and her boyfriend, or a dozen other reasons that are money-driven, not concern-driven). But I teach honors classes this year, and the parents are very involved, for the most part, but their kids are still not doing as well as anyone would like.
However, there's another phenomenon that is very different between the districts that I believe has been completely overlooked, but may be enormously important. District A has 17 high schools, of which 3 are academic magnet programs. Those 3 academic magnets are very successful - on a grading scale, they're all A's - whereas of the remaining 14 high schools, 9 are D's and F's, and the other 5 are C's. District B has 6 high schools, none of which are academic magnets, but one of which is a "technical" high school, where kids who are not academically inclined go to learn the standard subjects, but also to be trained in culinary arts, automobile repair, HVAC maintenance, etc. Essentially, it's a trade school. Of the 6 high schools in District B, 5 are A's and 1 is an F. Even the F school - the trade school, of course - is comfortable with its place in the hierarchy. They understand that their students will not perform well on the standardized tests, but they make an effort to prepare the kids to do well enough, and to give them skills they can use when they finish high school. So about 85% of the kids in District B get a very solid high school education in a traditional academic setting, and the other 15% get a decent education and some skills. Whereas in District A, about 15% of kids get a top quality high school education and 85% get at best a mediocre education and no particular skills.
The 5 "A" schools in District B have very high academic expectations - higher than I can even dream about in District A. I think it's worth looking at the "technical" vs. "academic magnet" high school model to see if one of them is better for the overall educational level in the district. My money's on "technical."
The point here is this: so far this year, I've given my kids 11 state-, district- or school-mandated tests (2 more scheduled next week) so that we have pre- and interim-assessments on our kids, in order to better guide our instruction so that they will perform better on the one that actually counts (sort of), at the end of the year. But no one is able to determine whether the assessments actually measure anything of value, and even if they do, whether the results can be effectively used to improve the kids' test grades on the end of year assessment, and even if it does, whether that translates to improved quality of education. Of course, on a macro level, only one thing is absolutely crystal clear: whatever we've been doing hasn't been working.
Everyone, it seems, understands public education is in deep trouble. From teachers in classrooms to principals in schools to Superintendents of county school systems to the President of the United States, each individual in that chain cares about, and is actively working on, improving education. This has probably been true since 1647 (the year Massachusetts began requiring towns of at least 50 families to hire school teachers to educate their children), but has certainly been true for the past 30 years. For the most part, these people are well-intentioned and reasonably bright. Sure, there are snakes in the woodpile, but no more, and no more venomous, than the snakes in woodpiles elsewhere in America. So why has American public education been declining rapidly, by all accounts, and reached a point where America's students are near the bottom of virtually every list of industrialized countries in terms of math and science skills, reading comprehension, and probably several other measures I haven't stumbled across in my quest to find data on the subject?
The issue cannot be money. According to TIMSS (Trends in Mathematics and Science Study), the US is educating its students in mathematics on a par with the Russian Federation, Slovenia, Lithuania and the Czech Republic. And while our spending on public education as a percent of GDP is a "middle of the pack" 5.85%, it is roughly equal to Slovenia's 6.02% and well ahead of Lithuania's 5.18%, the Czech Republic's 4.55% and Russia's 3.67%. Japan, which kills the US (and everyone else) on all these lists of best educated students, spends less than Russia on a GDP basis.
Here's one possibility. I work in District A. District A is one of (if not the) worst districts in the state, as measured by drop-out rates and state-mandated standardized test scores. An adjoining district, cleverly named District B, is the best district in the state on these measures. Now, admittedly, District B is much richer than District A, and that's always the rationale one hears when people discuss the stark difference between the districts. But I'm not buying it. Yes, I think parental involvement is hugely important, and without question, parents in poorer districts are less involved (mostly because they're running as fast as they can just to keep food on the table, or the kid is living with his older sister and her boyfriend, or a dozen other reasons that are money-driven, not concern-driven). But I teach honors classes this year, and the parents are very involved, for the most part, but their kids are still not doing as well as anyone would like.
However, there's another phenomenon that is very different between the districts that I believe has been completely overlooked, but may be enormously important. District A has 17 high schools, of which 3 are academic magnet programs. Those 3 academic magnets are very successful - on a grading scale, they're all A's - whereas of the remaining 14 high schools, 9 are D's and F's, and the other 5 are C's. District B has 6 high schools, none of which are academic magnets, but one of which is a "technical" high school, where kids who are not academically inclined go to learn the standard subjects, but also to be trained in culinary arts, automobile repair, HVAC maintenance, etc. Essentially, it's a trade school. Of the 6 high schools in District B, 5 are A's and 1 is an F. Even the F school - the trade school, of course - is comfortable with its place in the hierarchy. They understand that their students will not perform well on the standardized tests, but they make an effort to prepare the kids to do well enough, and to give them skills they can use when they finish high school. So about 85% of the kids in District B get a very solid high school education in a traditional academic setting, and the other 15% get a decent education and some skills. Whereas in District A, about 15% of kids get a top quality high school education and 85% get at best a mediocre education and no particular skills.
The 5 "A" schools in District B have very high academic expectations - higher than I can even dream about in District A. I think it's worth looking at the "technical" vs. "academic magnet" high school model to see if one of them is better for the overall educational level in the district. My money's on "technical."
Saturday, November 6, 2010
Turns out, sleep IS important.
I lost my cool on Wednesday, and yelled at the principal. In a faculty meeting. And used the f-bomb. Truth is, it had virtually nothing to do with the subject we were, um, discussing, as I suppose these things usually don't... I was frustrated with my classes, hadn't slept more than about 3 hours a night since Sunday, and troubled by a number of other things that aren't going the way I want them to. Nothing big, just a bunch of minor annoyances.
One of my minor annoyances is that I don't feel we (the teachers) get very much support from our administration. For example, this happened a couple of weeks ago:
I had a student transfer into my class about 2 or 3 weeks into the quarter, a few days before the first test. He had (he claims) a 93 in the class he left, but I knew he hadn't taken any tests, so his 93 was in homework and classwork, which counts for only 20% of the grade. Skipping to the end of the story, he failed my class miserably, by virtue of not doing any work and not passing any of several tests and retests. When I told him he was going to fail, he said his 93 should be averaged in, to give him a good grade. I explained that it didn't count for much, because the tests were weighted at 80%. So he went first to the counselor to complain. He then told his father I wasn't counting his transfer grade, and his father called the counselor. After I explained to the counselor what was going on, she (I assume) told him he was out of luck. So he went to the principal. Now, at this point, if I'm the principal, my response to the kid is to say "I'll look into it," then actually have somebody look into it and get back to the kid with the answer. But my principal walks out of his office with the kid in tow, tracks me down (on my planning period), and confronts me about it. I was taken aback, but explained that when he transfered into my class, he hadn't taken any assessments, so his grade was just classwork and homework. The principal then starts probing... "What about pre-assessments? What did he get on the pre-assessments?" I responded that I had no idea, but that he hadn't passed any of my actual assessments. He left me with, "Well, you need to count pre-assessments if they help."
I later looked up the actual grade he had in his previous class (I'd assumed he was telling the truth and gave him a 100 homework grade rather than deal with further complaints, and because it didn't matter - he still flunked). Turns out, his grade in the previous class was (wait for it...) "0." He'd done nothing.
So a few days later I ran into the principal and told him I was a little upset with him confronting me with the kid at his side, and he said "Hey, I'm here for the kids. It's all about the kids." He then went on to claim that once he heard my side of the story, he immediately turned to the kid and sided with me, which isn't the way I recall it happening.
This was, as lack of support goes, pretty minor, but indicative of the larger issue -- it feels to me that if there is a choice between the student's word and the teacher's, they go with the student's. Moreover, all issues seem to me have the same solution:
Kids aren't paying attention? The teacher isn't engaging the students well enough. The teacher needs to work harder.
Kids are talking or texting in class? The teacher hasn't made the policies and procedures clear enough. The teacher needs to work harder.
Kids aren't doing the work? The teacher hasn't made the content relevant enough. The teacher needs to work harder.
Kids don't understand the material? The teacher hasn't unpacked the content and chunked the learning effectively enough. The teacher needs to work harder.
I believe it was once the case that if a kid flunked a class, it was an indication the kid wasn't working hard enough. Now, it's the teacher who isn't working hard enough. The principal visited my room during my planning period about a week ago, and questioned me about the 14 kids in the pre-IB program I'd flunked.
Which is why I had been getting about 3 hours of sleep a night, and was cranky when my students didn't even make an effort to do the classwork I'd given them. Which is why I should have stayed in my room, as I seriously considered doing, when the faculty meeting started.
Within 10 minutes, the principal was talking about teachers giving out too many hall passes, so I piped up with a "But Mr. Teacher, it's an emergency." He responded "You'll just have to wait." I piped up again with "But it's an emergency." This continued for several iterations (with both of us getting more upset) until finally we're yelling at each other, and he yells (something to the effect of) "I can't do your job for you. You have to have control of your classroom," while stabbing his finger my direction. To which I responded (loudly) "So I'm begging you for help, and you're saying 'Fuck you, you're on your own.'"
At that point, he kicked me out of the room. It remains to be seen what the fallout from this will be. He can't fire me, but he can make life miserable.
One of my minor annoyances is that I don't feel we (the teachers) get very much support from our administration. For example, this happened a couple of weeks ago:
I had a student transfer into my class about 2 or 3 weeks into the quarter, a few days before the first test. He had (he claims) a 93 in the class he left, but I knew he hadn't taken any tests, so his 93 was in homework and classwork, which counts for only 20% of the grade. Skipping to the end of the story, he failed my class miserably, by virtue of not doing any work and not passing any of several tests and retests. When I told him he was going to fail, he said his 93 should be averaged in, to give him a good grade. I explained that it didn't count for much, because the tests were weighted at 80%. So he went first to the counselor to complain. He then told his father I wasn't counting his transfer grade, and his father called the counselor. After I explained to the counselor what was going on, she (I assume) told him he was out of luck. So he went to the principal. Now, at this point, if I'm the principal, my response to the kid is to say "I'll look into it," then actually have somebody look into it and get back to the kid with the answer. But my principal walks out of his office with the kid in tow, tracks me down (on my planning period), and confronts me about it. I was taken aback, but explained that when he transfered into my class, he hadn't taken any assessments, so his grade was just classwork and homework. The principal then starts probing... "What about pre-assessments? What did he get on the pre-assessments?" I responded that I had no idea, but that he hadn't passed any of my actual assessments. He left me with, "Well, you need to count pre-assessments if they help."
I later looked up the actual grade he had in his previous class (I'd assumed he was telling the truth and gave him a 100 homework grade rather than deal with further complaints, and because it didn't matter - he still flunked). Turns out, his grade in the previous class was (wait for it...) "0." He'd done nothing.
So a few days later I ran into the principal and told him I was a little upset with him confronting me with the kid at his side, and he said "Hey, I'm here for the kids. It's all about the kids." He then went on to claim that once he heard my side of the story, he immediately turned to the kid and sided with me, which isn't the way I recall it happening.
This was, as lack of support goes, pretty minor, but indicative of the larger issue -- it feels to me that if there is a choice between the student's word and the teacher's, they go with the student's. Moreover, all issues seem to me have the same solution:
Kids aren't paying attention? The teacher isn't engaging the students well enough. The teacher needs to work harder.
Kids are talking or texting in class? The teacher hasn't made the policies and procedures clear enough. The teacher needs to work harder.
Kids aren't doing the work? The teacher hasn't made the content relevant enough. The teacher needs to work harder.
Kids don't understand the material? The teacher hasn't unpacked the content and chunked the learning effectively enough. The teacher needs to work harder.
I believe it was once the case that if a kid flunked a class, it was an indication the kid wasn't working hard enough. Now, it's the teacher who isn't working hard enough. The principal visited my room during my planning period about a week ago, and questioned me about the 14 kids in the pre-IB program I'd flunked.
Which is why I had been getting about 3 hours of sleep a night, and was cranky when my students didn't even make an effort to do the classwork I'd given them. Which is why I should have stayed in my room, as I seriously considered doing, when the faculty meeting started.
Within 10 minutes, the principal was talking about teachers giving out too many hall passes, so I piped up with a "But Mr. Teacher, it's an emergency." He responded "You'll just have to wait." I piped up again with "But it's an emergency." This continued for several iterations (with both of us getting more upset) until finally we're yelling at each other, and he yells (something to the effect of) "I can't do your job for you. You have to have control of your classroom," while stabbing his finger my direction. To which I responded (loudly) "So I'm begging you for help, and you're saying 'Fuck you, you're on your own.'"
At that point, he kicked me out of the room. It remains to be seen what the fallout from this will be. He can't fire me, but he can make life miserable.
Sunday, October 31, 2010
Turns out, math isn't important.
An editorial, written by a professor emeritus of mathematics, statistics and computer science at the University of Illinois at Chicago is running in McClatchy-owned newspapers today, and states that math's importance to the daily lives of Americans is overrated. In fact, he claims, the attempt to make math seem essential is a marketing ploy by colleges to create and sell mathematics education programs.
He asks exactly the question my students ask, namely "How much math do you really need in everyday life?" and goes on to say you should not only ask yourself that question, but "the next 10 people you meet, say, your plumber, your lawyer, your grocer, your mechanic, your physician or even a math teacher."
I'll leave the "math teacher" issue aside, and address physicians for a moment. Consider the following scenario, a standard of every intro probability and statistics course:
You suspect you may have a brain cloud, for which there is only one cure - jumping into a live volcano. If you do in fact have a brain cloud, you will survive the jump, become perfectly healthy and live happily ever after with someone who looks remarkably like Meg Ryan. If you do not, you will die a gruesome death. However, if you have a brain cloud but do not leap into the volcano, you will die an equally gruesome death within days. So it is imperative you make the right decision, which means you need to know, as surely as possible, whether you have the brain cloud or not.
Fortunately, brain clouds are very rare - affecting only 1 in 1,000,000 people worldwide. Moreover, there is a test for tomhanksiplexy (the technical name for brain cloud) which is accurate 99.9% of the time. There are no other symptoms or indications of any kind (up until the moment of gruesome death, of course).
You go to a physician and take the test. He comes back from the lab, sadly shaking his head, and tells you that you have a 99.9% chance of having a brain cloud, and should go jump in a volcano immediately. Your response is to...
a) jump in a volcano.
b) decry the state of mathematics education in America, and wonder how anyone could imagine it's unimportant.
If you chose (a), you're not alone, but you are, in all likelihood, gruesomely dead. In fact, you're in a mathematical hell crowded not only with high school dropouts, but the vast majority of physicians as well.
Since the test is 99.9% accurate, if 999,999,000 healthy people take it, 999,999 will have false positive results. (one tenth of one percent of 999,999,000 is 999,999). If 1,000 people who have brain clouds take the test, 999 will have correct positive results. So if 1,000,000,000 random people take the test (and 1 of every 1,000,000 has a brain cloud), there will be 1,000,998 positive results, of which 999 will be correct. That's approximately a 0.000998 chance of having a brain cloud, given you have a positive result. Said another way, that means there's a 99.9002% chance you DO NOT have a brain cloud, even if you have a positive test, which is accurate 99.9% of the time.
Nobody expects "the average" person to get that problem right. But people have a right to expect that their physician, when reporting on the results of their most recent battery of tests, will understand what those tests do or do not "prove." Most physicians cannot do that, because math education in America doesn't do a good enough job equipping our future physicians and lawyers and plumbers and grocers with the math and cognition skills to think through a problem like that.
Okay, maybe doctors need math, but surely not lawyers, right? Here's the same problem in a courtroom: In a town with two taxi companies, a woman saw a man rob a liquor store and jump into a cab at 8:07 PM on Tuesday night. The witness testifies that the robber got into a Yellow Cab, which has 10% of the cabs in town; the Ocher Cab company has the rest. You've checked her ability to recognize the difference between the two cabs, and concluded she's accurate 80% of the time. Based on this information, and assuming the witness is telling the truth as she knows it, what are the odds that the perpetrator got into a Yellow Cab?
At this point, my students tell me that if they are confronted with situations like these, they'll just hire someone who's good at math to give them the answer (which, as it turns out, is 50/50). The problem is, they're confronted with these questions every day without ever knowing it. The paper tells us that the number of dropouts in Home County has doubled every year since the consolidation in 1990. No one bats an eye. Store A provides a coupon good for an additional 25% off on pants already on sale for 30% off, whereas Store B has the same pants on sale for 50% off. People who buy at Store A think they've saved money. A group in art class makes a scale model of a building using the same materials they'll use for the one 10 times as tall, note that the model weighs 3 pounds, then are befuddled when 4 of them together can't lift the final project.
In early Mesopotamia, unscrupulous individuals would offer parcels of land for trade that had the same perimeter as the land they wanted, but much smaller area. A knowledge of geometry was vital if you wanted to avoid being swindled. Anyone who plays poker without knowing how to calculate rudimentary odds is giving away his money to those of us who believe math IS important in everyday life. Buying a house or renting an apartment, buying or leasing a car, investing in stocks or savings bonds, choosing a line at the supermarket and a thousand other daily chores are easier and more likely to lead to the outcome you want if you are comfortable with and know how to use some relatively simple mathematics.
We're not teaching kids the Pythagorean Theorem because we believe they'll be in a situation someday where they will need to know the straight line distance between Juan's house and Julie's, which is 4 blocks east and 9 blocks north of Juan's. We're teaching them those things because in their job as District Sales Rep for BigCo., Inc., they'll be much better salespeople if they have been trained to examine problems analytically, and look for solutions using the tools they have in their arsenal. High school isn't a trade school. They may never again, after high school, ponder the morality of Jean Valjean or the empathy of Atticus Finch. They'll certainly never be quizzed on them. But they WILL be better equipped to make judgments about criminal punishment and racial inequities – things they will certainly face in the real world. A similar reality exists for mathematics education, even if some math professors haven't figured it out.
Tuesday, October 19, 2010
The Law is an Ass
In researching the title phrase to ensure I remembered it correctly, I discovered things about it I didn't know. In fact, nearly everything I discovered was stuff I didn't know, so rather than write about the things that put me in mind of the phrase, I'm going to write about the phrase I was put in mind of.
For example, I thought it had been uttered by a lawyer. And I thought it was in reference to some bitter result having turned on the unintended consequences of an ill-considered law. In fact, it's much more interesting than that. It's from Oliver Twist, and is said in response to the statement "the law supposes that your wife acts under your direction." The person to whom this statement is directed is unmercifully browbeaten by his domineering wife, and rejoins "If the law supposes that... the law is an ass - an idiot. If that's the eye of the law, the law is a bachelor."
I find that verbal exchange absurdly amusing. I'm not sure why, but there it is.
For example, I thought it had been uttered by a lawyer. And I thought it was in reference to some bitter result having turned on the unintended consequences of an ill-considered law. In fact, it's much more interesting than that. It's from Oliver Twist, and is said in response to the statement "the law supposes that your wife acts under your direction." The person to whom this statement is directed is unmercifully browbeaten by his domineering wife, and rejoins "If the law supposes that... the law is an ass - an idiot. If that's the eye of the law, the law is a bachelor."
I find that verbal exchange absurdly amusing. I'm not sure why, but there it is.
Sunday, October 10, 2010
Time is the fire in which we burn
I find myself, on an almost daily basis, choosing to take the time I have available to prepare what is required in order to satisfy administrative edicts, rather than prepare a better, more interesting, more involving lesson for my students.
This pisses me off.
First, let me be clear -- it isn't that I'm attempting to determine how to spend the 7.33 hours a day for which I am paid; that time and more is spent (a) teaching - 4.5 hours, (b) in mandatory meetings - 0.6 hours, (c) standing at my door between classes and walking my students to and from the lunchroom (both mandatory) - 0.25 hours, (d) maintaining the classroom (e.g., posting the mandatory agenda board, erasing the white boards in preparation for the next class, straightening desks) - 0.5 hours, (e) recording attendance and grades - 0.25 hours, (f) typing the three mandatory lesson plans per day (note: this isn't "preparing the lesson"... it's "typing the lesson plan") - 0.5 hours, (g) grading papers - 0.75 hours (note: I spend considerably more than 45 minutes grading papers; this is just my "planning period" time).
The time I'm talking about having to allocate to administrative edicts is (all or part of) the extra 3 to 4 hours a day I spend on school work during the week, or the 6 to 10 hours I spend each Saturday and Sunday on the weekends I'm not traveling to see my children. I'm paid a little over $20 an hour for the time delineated in the previous paragraph; I'm unpaid for the time described in this one.
Don't get me wrong -- this isn't a request for pity. I chose to take this job, knowing what it paid, and I choose to work the extra hours, knowing they're unpaid. But I'm sitting here on a Sunday morning with 8 items on my agenda, in order of my estimate of their value to the education of the students in my class:
(1) designing an interesting, challenging, interactive game for my students to play in small groups that involves going to different stations in the room and solving problems like the ones they did so poorly on when taking their recent test. (I have the general concept, but I need to flesh it out.)
(2) using the "Jeopardy" PowerPoint shell to create an in-class review activity for the current module.
(3) planning the next two weeks of classes for each section, so that the students have an idea of what they'll be doing between now and the end of the quarter, and they'll be able to plan how they will bring their grades up prior to the first report card.
(4) writing and printing "scholarship warnings" for all of my students who currently have a D or F in my class. This is somewhere between 50 and 70 students, because the most of them were taken by surprise by their first high school math test. I guess middle school tests were absurdly easy.
(5) grading 5 classes' tests and putting them in the grade system.
(6) printing progress reports for all students so they know what grade they have and what they need to do to improve it. Note: they could go online for this information, but we're required to print the reports anyway.
(7) creating a "standards-based bulletin board" that shows students (who never look at it) how the project displayed on the board is graded, and what a good project would look like.
(8) creating "student-generated" charts. There doesn't seem to be any other requirement for these charts, other than being student-generated. I may have three students in first block tomorrow write "This is a chart generated by a student" on chart paper and hang those up. But probably not.
Of course, it's extremely unlikely I'll get to all 8 things. If I just got to the first 3, I'd feel pretty good. Unfortunately, those 3 items are the three that my administration places no value on. The other 5 are all items that will be checked on by my administration, and for which I will receive a poor evaluation should they be missing or incomplete.
I'm already tired, and it's only 10 AM.
This pisses me off.
First, let me be clear -- it isn't that I'm attempting to determine how to spend the 7.33 hours a day for which I am paid; that time and more is spent (a) teaching - 4.5 hours, (b) in mandatory meetings - 0.6 hours, (c) standing at my door between classes and walking my students to and from the lunchroom (both mandatory) - 0.25 hours, (d) maintaining the classroom (e.g., posting the mandatory agenda board, erasing the white boards in preparation for the next class, straightening desks) - 0.5 hours, (e) recording attendance and grades - 0.25 hours, (f) typing the three mandatory lesson plans per day (note: this isn't "preparing the lesson"... it's "typing the lesson plan") - 0.5 hours, (g) grading papers - 0.75 hours (note: I spend considerably more than 45 minutes grading papers; this is just my "planning period" time).
The time I'm talking about having to allocate to administrative edicts is (all or part of) the extra 3 to 4 hours a day I spend on school work during the week, or the 6 to 10 hours I spend each Saturday and Sunday on the weekends I'm not traveling to see my children. I'm paid a little over $20 an hour for the time delineated in the previous paragraph; I'm unpaid for the time described in this one.
Don't get me wrong -- this isn't a request for pity. I chose to take this job, knowing what it paid, and I choose to work the extra hours, knowing they're unpaid. But I'm sitting here on a Sunday morning with 8 items on my agenda, in order of my estimate of their value to the education of the students in my class:
(1) designing an interesting, challenging, interactive game for my students to play in small groups that involves going to different stations in the room and solving problems like the ones they did so poorly on when taking their recent test. (I have the general concept, but I need to flesh it out.)
(2) using the "Jeopardy" PowerPoint shell to create an in-class review activity for the current module.
(3) planning the next two weeks of classes for each section, so that the students have an idea of what they'll be doing between now and the end of the quarter, and they'll be able to plan how they will bring their grades up prior to the first report card.
(4) writing and printing "scholarship warnings" for all of my students who currently have a D or F in my class. This is somewhere between 50 and 70 students, because the most of them were taken by surprise by their first high school math test. I guess middle school tests were absurdly easy.
(5) grading 5 classes' tests and putting them in the grade system.
(6) printing progress reports for all students so they know what grade they have and what they need to do to improve it. Note: they could go online for this information, but we're required to print the reports anyway.
(7) creating a "standards-based bulletin board" that shows students (who never look at it) how the project displayed on the board is graded, and what a good project would look like.
(8) creating "student-generated" charts. There doesn't seem to be any other requirement for these charts, other than being student-generated. I may have three students in first block tomorrow write "This is a chart generated by a student" on chart paper and hang those up. But probably not.
Of course, it's extremely unlikely I'll get to all 8 things. If I just got to the first 3, I'd feel pretty good. Unfortunately, those 3 items are the three that my administration places no value on. The other 5 are all items that will be checked on by my administration, and for which I will receive a poor evaluation should they be missing or incomplete.
I'm already tired, and it's only 10 AM.
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