Rough but hopeful

The past few weeks have been very rough on me. I’m on a few hundred medications or so, and by Friday, if nothing seems to be working, I need to consider surgery and get parts of my intestines cut out. Ulcerative colitis is terrible–make sure you take your probiotics if you’re on several amounts of antibiotics. I never knew, and so I’m in this mess.

Several students are suspended, mostly in thanks to me and one of the new history teachers. Some kids were saying unusual comments, we brought them to New Headmaster, an investigation was conducted, and thus the punishment was meted out.

I’ve been given the rest of the week off. Or rather, I’ve been forced to take it. My health is so deteriorated I might as well not really even be alive, much less drive out to school and teach. Surprisingly, my teaching ability hasn’t diminished. I think it largely has to do with my focus towards all the new changes this year and my motivations for the year.

The environment here is upsetting as usual. Too many parents have absolutely no faith in their kids’ abilities, nor do they have any real motivation to push them. I don’t understand why they’d pay money for private school other than to make sure their kids go to an all-white school. I’m already looking for employment elsewhere; I deal with kids who don’t wanna learn all the time. I can’t deal with a community that actively destroys learning. What do I mean by that?

Religious as we are, most people take very heavily into consideration what their preachers tell them. Upwards of eight (EIGHT!!!) preachers are running around telling kids they don’t really need to worry about school, that God will sort it all out, and they should just focus on having fun. Any adult can look into those words and find some semblance of responsibility; however, that is not something you tell a hormonally charged teenager who has little desire to do anything except have fun and goof off. It’s a mess. I don’t even believe this is typical of religious communities. This is just a giant disaster, and it disgusts me. Anyway, you can imagine the results of that. We’re a bit up in arms since we found out. They’re not interested in apologizing (something about pride and vanity…).

The kids are taking well to these new books (and so am I, which is probably influencing my teaching). The topics are nicely paced with nonsense thrown out, unlike in the other book where nonsense was rampant. As a result, all these kids are doing significantly better. They’re fitting into a better mold, and as a result they’re pushing themselves a bit more. It’s a situation of “If I think I can, then I can, and so I want to,” which is a great attitude. Only one class is resistant, but its little rebels are diminishing fast as they discover that Geometry actually isn’t terribly awful.

A student who I thought didn’t really care for me at all came to tell me she got accepted into my own alma mater. I was thrilled for her. She is a fantastic student, and I gave her the congratulations she deserved. Now if only we could get her ACT score up a few more points to get her the award she rightly deserves. I think I was surprised more than anything else when she told me. ….Hopefully she doesn’t just go there because her boyfriend will be going there. That would be silly, and he has more reason to go there than she because it is an engineering and agricultural school, and he’s doing engineering. She wants to get into psychology, and there are two other universities I know of whose psychology programs are better than mine. I talked to her about graduate school, and she can fix things from there. She’s not naive, at least, and that’s good.

Finally, I was forced into a meeting. Or rather, push came to shove, and all the ripples I’d caused last year in the “math education” community of the entire region was put on as I was asked to give a lecture on the state of math education in our community. Where are we lacking, how we can improve, etc. I was given all the numbers I needed to form a hard, coherent argument.

I had two options. I could either detail the technological limitations and math education spending as well as ACT changes and textbook NON changes and how outdated we all were, or I could be a blunt jerk.

I opted for a combination of both. It is certainly a big deal that our area is using outdated textbooks for ACT purposes, and, ultimately, within the context of the state of math education period. But I wanted to stress this idea of “pat idiots on the back” and how wrong that was. I get it; schools everywhere bend over backwards for particular students they shouldn’t. But I’ve done my research; our area does it significantly more so in that we’re a lot worse about it. I didn’t just prattle on about abstract What Ifs, though; I called several teachers out and shared their stories with me and challenged them to accuse me of lying if I was.

They didn’t. For the most part, everyone was agreeable. I was talking to math teachers and administrators from about 9 different schools. However, I’m not a fool; I wasn’t there to be on a soap box and preach to them.

A boss once told me that there were three kinds of people:
1) Idiots
2) Intelligents
3) Wise men

An idiot will tell you there’s a problem. Any idiot can point out problems, after all. An intelligent person will point out a problem and then offer a solution. A wise man deals with the problem on his own such that before anyone finds out about it, it’s no longer a problem. I’m no wise man, but I think of myself intelligent, so I offered solutions. The first of which was a textbook upheaval.

The second solution was a very carefully mapped out set of changes to middle and high school math curriculum. Every school should see some standardization within itself; there is no reason the Pre-Algebra of 2008 should cover 3 more chapters than the Pre-Algebra of 2009. That’s too significant. One chapter? Sure. Several sections? Definitely. But 3 whole chapters? Not at all.

The third solution had more to do with my own school, but noticing nods and looks from other administrators, it seems they have a similar issue. We had to stop bunching groups together. I used my own firsthand experience: 10th grade Geometry has been with each other for so long, and they’re so unmotivated, that they grew up “not caring” together for a long time and now there’s probably no real of fixing them. A few of them are finding more motivation, but that’s an uphill battle that will ultimately be lost. That spark just isn’t there. Groups must be mixed and mingled, and that translates to what has been called to me as a “logistics headache.”

They must mix grades. We’re finally doing it here, and it’s a logistics headache, apparently. But it must be done.

I then met with teachers one on one for about 3 hours total trying to detail things that correspond to their own schools. I’m well researched in all the schools around here because people for some reason want to meet me. I don’t know why; I’ve never been interesting to them.

In summary of the meeting: I hated it.

I hated being put forth as this paragon of knowledge. When I’M the person they all turn to, with as little experience as I have and naive, hopeful gestures I can offer, we must be in a really sorry state. I hate that I have no experienced math education leaders to actually talk to; they’ve all retired or fled (or both!). Every single teacher that sat before me as I spoke, I can comfortably say that only a small few of them are “above average.” It’s mean of me to say, but for Christ’s sake, one of them was a HISTORY TEACHER before he was just forced into teaching math because the other guy quit, and then since he’d taught it for three years they just kept him at it.

I also hated the fact that I know, I know that my concrete ideas are ultimately going to be dismissed because it’s not a light switch that will fix everything in one year. And it irritates me. I feel like everything would have best been done over a small private meeting done multiple times to genuinely interested parties, but even then I still hate this idea of putting me on a pedestal.

What the hell do I know about education management? I don’t have a clue. I don’t have a group of people to converse with about new math programs or tested math programs. I’m basically doing all the research on my own, I have no way of seeing how things stack up for our community (some of these programs just won’t work with our limitations), and while it’s interesting to me to see how I can modify some programs, ultimately it’s all a lot of stress I feel was unfairly placed on me. I need to have a group of colleagues to discuss with, not shoulder the burden of math education for all these schools.

It’s stressful. But it is what it is. Here’s hoping something works out the way it should.

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Geometry, Racism, and Proving Stuff

I want to start this entry with a big ole bit of racism against the Chinese. I won’t say “Asian” because I know Asian culture well enough that what I’m about to explain absolutely does not apply to the Japanese, Thai, or Koreans, and definitely definitely definitely NOT the Vietnamese. It only ever seems to apply to the Chinese, and, sadly, it applies to every single Chinese person I’ve ever met.

I took Numerical Analysis I and II when I was an undergraduate and made an A in both. I moved on to graduate school, and unfortunately there was not a lot offered I hadn’t already taken (at this school, I was required to complete four “I and II course” sequences. My choices were Linear/Nonlinear Programming, Real I and II, and Complex I and II. I needed one more. I had the option of Mathematical Statistics I and II or Numerical Analysis I and II again. I wanted the latter because easy A I’d already taken it (and they were using the exact same book!!), and after making sure this was in fact allowed (they said I just had to do a minor project to give me graduate credit that could override my undergraduate credit), I did.

My “minor project” was actually a big one–I had to prove a variety of theorems in the book that weren’t proven. So I did.

Most of mine were correct (actually, all of them were, and that’s the point of this story). However, two of my proofs were not pleasing to the professors. They told me these weren’t the correct proofs. I had two choices: accept a lower grade for these two marked as incorrect/incomplete or rewrite them to get the correct one and accept a late grade.

I called a meeting with several professors instead; I was going to prove to them that my results were correct (which they were. I actually legit made a minor error on one proof that they accepted as correct, and I acknowledged that).

And I did. Four of them still didn’t like it, but the rest of them, which was over half, did. There were 10 total. The six who agreed? German, Indian, American, and Vietnamese, in some combination. The four who didn’t? Chinese. One of them was curious how any other proof could be done for one of the problems, and so one of the Chinese professors (all of them were experts in numerical analysis, by the way; computational mathematics, because of its precision and application in engineering, is a hot topic among Americans and Chinese) got up and proved it.

It was quickly acknowledged that this was the standard proof for this particular theorem, the proof that’s in every single textbook ever published because of its accessibility to students in the course (even though most students in Numerical Analysis don’t fully understand proofs, but that’s a different topic altogether). My proof was just different. The expert in computational fluid mechanics actually asked “I don’t get what the difference between the two proofs is. Yours just uses error tolerances and his (mine) uses functional and real analysis.”

The professor couldn’t explain because the professor was not an expert in real or functional analysis (neither was I, that’s for sure. I made a C in Real Analysis I that semester with not having a clue what was going on).

A bit of arguing went on among the professors while I stood there meekly, and it was finally convened that my proofs were perfectly fine. One of them was better, but one of them wasn’t as good as the standard proofs, but that didn’t mean it was incorrect.

That was my first exposure to what I would discover as the Chinese having a very, very strong habit of memorizing anything and everything. Not understanding; just memorizing. I watched Chinese students pick apart proofs like an English teacher picking apart syntax errors, NOT like a Math teacher picking apart logic. Like computers assigning data to an array and correcting this data when a correction had to be made. There was no flow from one cell to another; just the array itself.

But the point was, to them, if the proof didn’t look precisely like this, it was incorrect.

My first exposure to a proof was everyone else’s, really–a two column proof in high school Geometry. I didn’t really like my teacher (though I grew fond of her near the end), but she graded the logic in my proofs as she had to because all of us had more or less the same proof, but someone might have used a slightly different approach to it.

And now I have here my students’ first Geometry proofs, and after just responding to a fellow blogger in which I actually talked about proving an idea in Geometry (because she’d taught Geometry), well.

I’m glad the comments were made between us. I knew, and I’ve always known, that I had MY way of doing something in math, and another student might have HIS/HER way of doing it. I knew it, but that doesn’t mean it applies to me; as long as my way is right, that’s all that matters.

Now I’m being forced to examine others’ ways of doing things (and many of them do it differently than I did, but then that’s because my way is either the absolute shortest way or one of the longest possible ways, depending on how technical I am). Before, I only cared about someone else’s ideas in proofs if my own were not sufficient, and then we students would compare our work and bounce ideas off each other.

It’s eye-opening, that’s for sure. And I’m seeing very quickly that I absolutely must not ever teach Geometry again if I can avoid it.

I was a mathematician; I’m used to big boy proofs that require a very powerful sense of precision with details and ingenuity or intuition with direction.

For example, we’re on the idea of using angles to prove lines are parallel. My own head is saying “these lines must first be coplanar or on parallel planes!!!” so I want to give people a -1 here and there, and I’m also convinced that there needs to be an extra step or two of justification (which is NOT me being pedantic; it’s me using the book’s own earlier sections of “Properties of Proofs” in which we use the Reflexive, Transitive, Symmetric, Substitution, etc. properties).

And yet the book makes it clear that we’re good to go.

And I UNDERSTAND why this is okay; it’s a blasted introductory Geometry textbook trying to get students to be good at manipulating geometry, not trouble itself with pedantry.

Which is why I don’t need to be doing this. In Algebra, I can demand precision all I want and it works with the students. Here, although students can go everywhere with their proofs, and I’m fine with that, I feel like occasionally better justification should be given.

I already get annoyed with every Geometry book ever in its “theorem” of “if two lines intersect, they do so at exactly one point,” which is incorrect. The correction is just one word: the lines must be unique.

The point of Geometry is actually to get students to understand that precision in mathematics is important. Algebra I and under are just “hey let’s do neat tricks.” Algebra II and higher, however, are “hey let’s do neat tricks but make sure we only do it for this reason on this set-up and not that one” that students can only be good at if they understand the precision of the language. It’s also to show how two different subjects can be treated the same way (we even have Algebraic Geometry and Geometric Algebra, two very very different courses. The former is too hard for me to be good at, and the latter we just call Analytical Geometry, aka “calculus”).

Oh, well. The students are mostly doing these well enough, at least. Or well enough for these being their very first proofs they have to do themselves.

How do you motivate someone who has never understood the idea of motivation?

Motivation is a tricky devil. You cannot actually motivate anyone at all regardless of what you may think; it is a trait that comes entirely from within. However, just as we often have words on the tips of our tongues (words we know but have currently forgot) or we’re aware of processes or tasks that need to be done but forget to actually do them, we need a trigger that typically gets mistaken for the actual motivation.

A kind word or gesture is typically the trigger. This suggests, however, that reference levels are established. Let’s examine an elementary example:

Joe is a high schooler who is doesn’t care about school and just wants to have fun and act silly. Teacher talks to Joe about how Joe will end up in a bad place (in jail, working at McDonalds for the rest of his life, etc.). Joe doesn’t care. Some elaborate ruse is made so Joe can see the reality of the situation he’s putting himself in, maybe by taking him to a prison and letting prisoners harass him (this is a very real thing, and, no, it doesn’t work at all in spite of what Middle Class First World WASPs, my extremely bigoted term for people so far detached from reality they think any nice sounding idea must be nice in practice). Joe decides to change his life around. Joe is now a good student.

Joe has been given a reference level. He sees bad things, compares his own carefree life to it, does not want it, and a fix is made.

Perhaps Sue is taking too many drugs. Someone intervenes by showing stories of what happens to people who go too far with them. Sue stops doing drugs. Sue now has a reference level, an ability to compare her current standing with others’ current standings and can make a judgment call.

What happens when your community is so toxic and virulent that bad people are outwardly praised by the entire community, that there are no “good” jobs available for students to even understand or be aware of, that parents and preachers and “community leaders” actively encourage students to get drunk and have sex with one another (and sometimes even participate themselves)?

You cannot motivate a student under such situations through the normal means. A more clever approach is necessary.

One thing I’ve become aware of is how “kind” and “spiritual” everyone here is. A Christian myself, I’m not entirely sure where all this “faith” comes from (actually, I know precisely where it comes from, but that’s another entry).

If people are upset, someone tells them to pray more, that they are to be pitied and we should be sympathetic to them, that they just need love and motivational speeches.

Every single person already does that for everyone else, and it clearly doesn’t work.

My role model is the English teacher here, and I do hope I become a mathematical equivalent of her. I took a page from her book: “that shit doesn’t work. Just slap ’em once or twice and they’ll get fixed.”

I pulled a student aside after the fifth student in his class complained about being distracted by him. I told him directly that I don’t care if he just refuses to do his work and just wants to act up all the time, that if he wants to “piss away” all the effort his grandmother and his aunt put into raising money to pay his tuition (which I was never supposed to know about and will be in trouble for later; they’re already having financial issues themselves, and that’s before dealing with our tuition, and we’re the cheapest school in the region). He’s free to just fail my class and be worth absolutely nothing to nobody, and then when the “shit gets too high, [he] can overdose on drugs or put a bullet in [his] head like everyone else in that situation.” But he absolutely will not bring down other students with him, and if he can’t just fall asleep like any other “moron not fit to fetch my shopping cart from the parking lot,” he can just spend every day getting his “ass whipped around by the headmaster until Headmaster does his family a favor and expels him so they can have a bit more money.”

That was a few days ago. He’s been attentive in class ever since, participating, and while he started off calling out incorrect answers, his improvements to his attention to the class have found him getting better and better to the point he was correct about every question I asked.

He came to me at the end of the day Friday and said he owed me an apology, that he would do better for the rest of the year, and he absolutely would not fail my class.

I just smiled, told him he owed me nothing, and sent him on his merry way. He had more energy during the football game, too.

And I meant that; no student owes a teacher or adult a single thing. It’s not like he asked to be brought into this world or sent to this school. And I absolutely do not take pride in anything I did or said to him that day–I look down on anyone so objectivist in this world that they abandon their humanity for the sake of “the ends justifies the means” and “the needs of the many outweigh the needs of the few.” If you can’t save one person, you can’t save many, and if you have to hurt someone to save them, you are not wise enough to be put in charge of their life in the first place.

I found redemption in another student, at least. I called a student at the end of 3rd period (coincidence, both of these students are in Geometry, but in different sections) to just ask him to hang around for a moment and that he wasn’t in trouble (he wasn’t). A few teachers mentioned how irritated they can get with him and his talking, so I wanted to use that to bring up something else with him.

Last year in Algebra I, he had a habit of throwing his hands into the air and quivering them enough to look like he wanted to explode and strangle someone. Always when he couldn’t get something or someone interrupted him. He’s better this year, and I really had no right at all to actually call him out on anything because he hasn’t actually shown anger at all. I just wanted to make him aware of his own reality and keep him aware of the path he was on and the path he is on. Again, he’s not so angry this year.

I talked to him about anger, accused him of having it when he didn’t, and told him it’s not good and he needs to find someone to talk to he trusts.

He comes in after fourth period during lunch wanting to talk to me. What he told me nearly put him in tears. Apparently he thinks I’m the only teacher who likes him (which I do; he’s a likable kid) because he’s always getting yelled at for stuff he doesn’t do (I won’t question what he does or doesn’t do, but I am willing to bet both that he gets a bit talkative and that he gets treated a bit unfairly, a lot of this stemming from his sister).

I gave him suggestions about what he can do to deal with his anger because, realistically, the problems he was facing were likely to never change.

I had my fair share of teachers we students were too afraid to confront if we felt we were being treated unfairly because we believed they’d just scream at us then play with words and get our parents involved to make everything our fault. These teachers exist a dime a dozen.

I don’t know if he felt better, but he seemed to be in better spirits at the football game last night. Still, I know he has a bit of issues, and I hope he takes my advice seriously.

…And all on the flipside, I had to “yell” at our valedictorian for the awful work she turned in, told her it was clear she was hanging around a bad crowd, and she could wind up losing her valedictorian status at her rate because we teachers were getting fed up with how she was acting. “Senioritis” already; she’s a great kid, but she has dreams of going to a very good school a state over, and she won’t make it there if she has chosen to pick up these new habits she didn’t have last year from people she didn’t sit around last year.

Of course, this all has to do with the fact that most of her friends graduated last year so there aren’t many others to sit with now. Supposedly she used to be friends with this bad lot, but then when people’s intelligences and work ethics really started coming into play during puberty, she stopped being around them and with the “good” kids who just all happened to be a year older. With them gone, she’s now rekindling flames with this bunch, only they’re morons (they’re morons. I can safely say this as a teacher, and I will tell them that to their faces).

She smiled the whole time; I know she was very upset. She was very trusting of me last year and would have never wanted me to be the one to confront her like this.

But these kids need motivation. And after 11 years, if “prayer” and “church” aren’t doing their jobs, then I’ve got a boot for their faces.

Minor abandonment

I finally got my crown, meaning, after 3 months of frequent dental visits, I am done with the dentist for a very long time (until I need some routine cleaning or a tooth bothers me). Things sure are slower around here, that’s for sure, but then on the upside they’re also cheaper, and at the very least my dentist was competent (there are three that work in the building, and I hear some awful stories about one of them).

I had to leave early 2nd period to make it to my appointment, and I wasn’t expecting to get back until 3rd. And then when I went to check out, I heard that our sub, who is the very first sub I actually appreciate because she makes the kids do what I want them to do, is having financial difficulties. She and another sub are related, and together they are combining their already struggling income to pay the tuition for one of our students (who is one of mine). It breaks my heart knowing he really does not care to even try at school at all.

So I decided to take the entire day off; a full day is double the pay of a half day for subs. I asked her, of course, not just going to drop a bomb on her if she had somewhere to be that day, but she looked eager, so I just said stuff came up and now I’ve been sitting at home.

I finally finished grading all my tests. As I expected, the 6th period Algebra II class did very well, some of the highest test scores I usually get (only three out of 17 failed, and only three more made Cs). I’m pleased. Now I just have a giant pile of homework and extra credit reports to grade (well, not so much the extra credit as not many people do it).

Teaching is fun, but being a teacher is really, really boring and agitating. I’m considering taking back up a contracting position as a researcher and just teaching part time so I can just teach upper level courses instead of the gamut of high school math. I’d make more money and have more free time, that’s for sure.

I was more or less doing that last year, only I was also teaching full time, and I enjoyed it. Right now I’m just teaching full time.

The Precalculus test is almost done. I have to finish typing it up (I’m using MS Word because I can’t download anything on the work computer and they’re not aware of LaTeX or its usefulness, and MS Word being an ugly mess with its equation editor, it’s taking a while), but the bulk of the problems are all there. Only need to finish off two, at any rate, and I’ve been doing a steady one per day since I’m trying to be very careful with wording. I don’t want to confuse students, but at the same time I don’t want to hold their hands, either. I want to be a guide, not “mommy and daddy,” and let them figure it all out for themselves.

I expect low grades on it, honestly. Bright as they are, they’ll have never seen “math” like this, even though the techniques they’ll be using are things they’ve done before. But then, I don’t care about their results (I already know the results. Why would I care about that?). I care about the time and effort they put into it and the explanations they offer, as well as their integrity. I can fix their ability, but I can’t correct any attitude issues (not that these kids have any; they’re amazing).

They’ll be fine. Everyone will. Except for possibly one class, but I think the magnitude of their fallen grades (Geometry-02, 5th period) will shake some of them up a bit.

Oh, Geometry.

Algebra II and Geometry both took their first exams today. I need to make a serious mental note to not give four tests in one day. I graded half of them–one of each class.

The Algebra II bunch did just as I expected them to, and just glancing at the other Algebra II class’s, they did the same (better, but then they have better students). I’m actually pleased; the new books and my experience teaching Algebra II and their being used to me I think is drilling in the information a lot better to them, and they’re retaining a lot more.

Geometry, though…

They did exactly as I expected. And in this case, that’s not a good thing. Geometry is a game of rules and ideas, not of techniques and rote regurgitation like Algebra typically is. The students have refused to grasp this mentality. …And as a result they paid for it.

They actually got most of the actual math problems correct, but they didn’t get their vocabulary correct, and this is vital to a good Geometry course.

I had planned for this, however, and so they have an extra credit assignment. One of the sections in the book involved orthographic drawings and nets, a very visually oriented section with no math, only visualizations, and I skipped it because I won’t have time to cover it and still do the lessons I actually want to do. I always knew I’d give it as an extra credit assignment, though, so this lets the students engage themselves with something fairly fun and fairly creative and fairly useful.

Algebra II also got an extra credit assignment that one student was actually doing in class after everyone turned in their test. There was an activity in the probability section (very very basic probability; just “what you want divided by what you got” probability) that the book suggests is done before the lesson is implemented involving throwing an off-center folded note card and recording results and making a prediction. ….Seventy times. Yeesh. They’ll have fun with it, though.

It’s another reason I’m enjoying my new books. They’re full of activities that many books have, and I remember my high school skipping 99% of them, and I want to take advantage of them because they are very neat, so here we go.

College Algebra just did the lesson in systems of equations in two variables: substitution and elimination. “That was a lot easier than when taught us.” “Well, most things you revisit typically are easier.” I’m arrogant, but I’m not that arrogant.

Pre-Calculus, though. Man, they are troopers. We have jumped around from idea to idea, but the students are now creating equations based on limited information that most scientists have to do. Obviously this is done within a high school environment (so no differential equations or invoking something like Sturm-Liouville theorems). They’re actually really enjoying it. In fact, they want to do nothing but this and explore harder ideas.

They have a test coming up on Friday. It will be a take home test with only five questions, and I have encouraged them to get on the internet and dig through their notes. These will not be simple problems for them to do, but rather exploratory problems to basically prepare them for the world of engineering and science. One problem will actually be deriving the projectile motion equation for an object launched vertically by solving a literal differential equation:

Projectile motions are all based entirely on the basic equation that the acceleration is equal to minus g, or s”(t) = -g, and then there are initial and/or boundary conditions that ultimately give us the result of s(t) = h + v0*cos(theta)t – gt^2 /2. We won’t be using the cosine part since we’re firing straight up (and they haven’t really learned Trigonometry, nor did their Geometry teacher really cover it very well).

So they will start at s”(t) = -g and move on from there until they get the result.

They will also be modeling the equation of energy that governs explosions from missiles and bombs by using elementary indirect and direct variation ideas.

A third problem will invoke linear interpolation and teach them basic recursion theory (since they’ll have to show that the linear regression actually does not converge to the points I will give them by setting up the error formula and seeing that the error formula for a linear result is precisely the same idea as the whole “absolute value inequality” students learn in Algebra II with AND and OR problems and/or treating it as a distance).

A fourth problem will teach them basic differential calculus by actually creating the derivative formula by relating it to slope: the actual definition of the derivative as a limit of the “slope” (or more accurate: tangent) problem. They will verify that the slope of y = mx + b is in fact m by using the derivative and then testing this idea to get the “slope” of y = ax^2 to get 2ax.

The final problem will be basic inverse problem theory by exploring how y = x^2 has no inverse, but it does in fact have a pseudoinverse (as any relation does), and how, being very delicate with our range, we can actually construct a relation that is a pure inverse (most treatments of y = x^2 as an inverse problem just “restrict the domain” to the positive or negative reals and then a natural inverse can be formed. This isn’t inverse function theory. This is getting students used to the idea of splitting domains and getting inverse-finding crunching going).

By the way, these are all very advanced topics (with some debate over the tangent problem/derivative), and yet I know they can be done at a high school level and they will be done at this weak high school because all of these topics can be handled with “mere” high school education (and ours is significantly lacking, to say the least).

And they just eat it up. We’ve spent a good bit of time on advanced topics similarly to these. It’s great!

AP Exams and Discipline

Yesterday was not very fun. I woke up at 7:19. Teachers are expected to be at school at 7:30. My computer wakes me up, but it doesn’t wake itself up from sleep, so I have turned off all sleep options (I’ve been trying to fix it for half a year). Unfortunately, the power cord got ripped out thanks to a certain kitten, so it ran out of power and the rest is history.

I managed to make it to school at 7:40. What a rush all that was since the drive to school is typically 13-15 minutes. I got to a room that was 74 degrees (it’s set for 68, but it was put “on hold,” an option for the thermostat typically done on Fridays so we don’t have to keep messing with it but it won’t run and waste energy/money over the weekend). What a day… Then complications arose after school, but that’s personal.

Tuesday was much better. Except for needing to talk with a student. In my 5th period Geometry-02 class, half of them are not interested in learning and half of them are, but the good half are held back by the bad half. Last year in Algebra I with this bunch (also in 5th period), I watched an A+ student drop down to a high C and barely scramble the lowest B possible as a final average because she wanted to talk and play with boys. It is week 2, and I’m already watching it repeat, so I pulled her aside (after giving her and another student break detention for talking) and explained to her that while she has potential, she will squander it if she keeps up. I reminded her of last year; she wasn’t happy.

She left with a promise that she will NOT be getting break detention again this year. I really hope that’s true. I don’t like watching good students destroy themselves because of this mentality that smart people are bad and being dumb is okay. Crab mentality, etc.

Meanwhile, during 4th period Pre-Calculus, AP Exams were brought up, specifically with regards to AP Calculus since most of that bunch will be in Calculus next year. Well, I had sent an E-mail to someone important and in the know last year, but I never got a response. I managed to find all the information I need, and I will be engaging them tomorrow about it (I don’t have much to do in class tomorrow, anyway. We can wrap up the first unit by defining boundedness, symmetry, and extrema, the last of our big people words).

I had never known any random student can take any random AP exam any year they want (provided they’re in high school, of course), regardless if an AP class was approved or taken or not. This information will put many of them in good spirits; I encourage all of next year’s calculus students to take the exam, though I will only train them for the AB exam (for reasons pertaining to what the local universities give credit for, and they only give credit for Calculus I, and they give credit for it for getting a 3 regardless if it’s AB or BC), so we will be covering only an AB Calculus next year.

With this bunch in particular, I would rather they completely master Calculus I, typically just one semester long, and be fully prepared for Calculus II, and take a year to do it, than to just get through a full year of normal calculus and they barely have any grasp of it at all. Having been through all that, I’m well aware that the vast majority of students go through Calculus I and Calculus II at the university level with no real understanding of anything at all, just an ability to crunch through problems.

Then they get to Calculus III, Linear Algebra, or Differential Equations, and suddenly you watch the grades just plummet significantly, even though Linear Algebra is significantly easier than Calculus (and in fact has nothing to do with Calculus at all except at a pedantic and theoretical level) and Differential Equations is precisely the logical “next step” in Calculus.

I’ve managed to do a whopper this year with it only being week 2–

Every single student I have wants to learn, succeed, and continue taking advanced math courses except for ten. Ten! And most of those ten are all in that 5th period Geometry. Granted, I only have about 80+ students to begin with, but that’s pretty good, I think.

A few of them say they just want to take more classes with me because I’m actually teaching them. That makes me happy. I’m already getting the same compliments from last year.

Though five are a little mad at me right now. Well, one I know is, the other four probably are just a little annoyed. Five were talking in 6th period Algebra II-02, so they all got break detention. One was extremely annoyed because she wasn’t talking as much as the others were, but she started talking the instant I decided I was going to reprimand them. It’s the entitlement of teenagers: “I want to do what I want but not deal with the consequences of my actions.” I used to be there. It’s only break detention, anyway.

College Algebra is moving along at a good pace. We’re going to be done with the entire course much earlier than is necessary and so we’ll just do nothing all the end of the year. They’re all seniors, anyway, and that’s a good break/nap for them (it’s second period). It’s a bit of a break for me, too.

Everyone’s so far about to take their first test. They’re extremely anxious and frightened; a new course, even with the same teacher, could yield anything on the test. I’m nervous, too.

Perfect Student from last year is telling me that Algebra II is very, very difficult for her. She was the one in Honors Geometry I deliberately designed a test for that she wouldn’t make a perfect on, and she made a perfect on it. She missed only so many points over the entire year. And she said it was all very simple. She’s clearly a visually oriented person, since Algebra is not that at all except for a few topics.

I imagine she’ll do fine on the test. But she showed me a very serious issue with this entire school–

These children have no real ability to comprehend what they read. They don’t understand that if a rod can be within 0.2 inches of 58 inches, it can be between 57.8 or 58.2 inches in total. They don’t understand that decreasing by some amount means subtracting an x, and increasing by some amount means adding an x. This is not Shakespeare at all (……or Melville, as it would stand……).

Oh, well. Now that I have better books, I have more energy to devote to getting them to trying to understand these nasty “word problems.” We’ll see how it all goes.

First week

So, last year, five students failed. Two seniors, three juniors, all in the same class. They all failed because they absolutely did not want to do anything. The seniors somehow managed to graduate nonetheless, and the former juniors/now seniors are in a situation that confuses me.

Two of them just moved on to Senior Math, meaning they will get credits in Algebra I, Geometry, and Senior Math. That’s 3 out of 4 required credits. Somehow they’re able to get by with Pre-Algebra as a credit. I’m not sure how, but they are.

The other, however, has no credit in Geometry at all. He was with me for two days, but then he dropped. I don’t know how he is able to get through without it, but I’m not going to ask the counselor yet; she’s been awful busy as this is the first week and people are trying to fix and clean up their schedules.

Off that for a moment, I’ve been on probiotics for the week, and my body has had a severe reaction to them. It’s a good reaction, but painful and upsetting, and it was so bad that today I had to stay home (already taking a holiday on the first week. Tsk tsk). Weeks of antibiotics have made this necessary.

Back to school, school is going amazingly. A lot of people dreaded the difficult math classes again, but people are finding that this year is not going to be nearly as frustrating as last year. BECAUSE NEW BOOKS! Many students have already attempted to look through their books, and they’re finding that these are indeed amazing in every way.

And of course I’m most excited about how Precalculus is going. We’ve already begun an exhaustive treatment of sets and naive set theory, as well as how to build sets from other sets and talked about what something like (-4,3) U (3,7) might mean with regards to the number 3 in terms of continuity. We talked about relations and functions and how to understand them from a “domain/range bubble” standpoint (with arrows and whatnot) as well as a graphical representation.

We also introduced the idea of building functions from other functions by means of adding, subtracting, multiplying, and dividing. We have not yet talked about restrictions in the domain or how the domain/range change as we build new functions from others, nor have we really talked about domain and range, period, beyond “hey we’ll study this at some point.”

We also introduced the idea of compositions, and I showed graphs to illustrate why compositions might be useful (I considered the typical chemistry charts of how volume changes with pressure, how temperature changes with volume, and so putting them together gives us an idea of how temperature changes with pressure).

The students are absorbing every bit of it. They love it. It’s been well beyond “hey here’s a problem let’s use this technique hey another problem now we’ll use that technique.” It’s analysis.

Geometry is also equally exciting. Students are asking all sorts of useful, interesting questions, showing that they’re engaged, curious, and learning. And my second section was one I was worried about given their attitude in Algebra I last year.

Algebra II is Algebra II. The pace is going a lot more smoothly, and the students are largely responsive and paying attention.

College Algebra is amusing. The students unanimously (all six of them) agreed that I should just push on through and finish the algebra and trig as soon as possible (they’re an extremely bright bunch and I’m expecting all six of them to be exempt from the semester and final exams), allowing us to do whatever it is we want by the time March rolls around (which is good, as all of them except one are in track, and track participants miss an enormous amount of classes). It’s nice to be at a private school where we can do this. All of them know what they want to do, none of them want to do anything related to math, but all are willing to work hard to succeed beyond “merely passing,” and so I have no problems just getting their math over and done with for the rest of their lives (as far as a formal math class goes).

I’m also laying the groundwork down for my eventual leave of this school. We have the first formal, official word that states we can use last year’s lesson plans and we’re allowed to reuse lesson plans forever unless we need to make minor changes. This means I’m making very large, drawn-out lesson plans so whoever replaces me when I leave will have all the heavy lifting done for them; he or she merely needs to be a competent and exciting teacher. This could help us attract someone of such caliber when that someone knows s/he doesn’t need to do a bunch of bureaucratic nonsense.