My precalculus students have recently taken a test on sequences, series, & the binomial theorem. The students run the gamut from they-could-teach-themselves-out-of-a-book to please-take-my-hand-and-do-the-problems-with/for-me-over-and-over-again. It dawned on me while I was helping this latter type of student to study that she had no concept of what might have been some good things to study and review before taking the test: formulas for explicit terms, partial sums, pascal's triangle ...
I thought over the notes they took, and I'm wondering if it ALL was so foreign and important sounding to her that she saw it as:
sdlkfoe sdoowieur sdeoe 5 = sdlfoein sdifuoeen
oeiwonewio sdf e3dof soieen sdeid nli lskejoi i9 dflk
so maybe she couldn't parse through it all and figure out what was important to know. I know when I was presenting the stuff, I had them do examples, and I had them write down the formulas and I discussed why they work and how to think about them .... but apparently, for some students, I have to stress what's important before, during, and after. And then maybe I should make them get out their red pens and BOX all the key things.
But this doesn't sit well with me. It seems that I'm doing the thinking for the students that way, and they'll never learn to sit back and reflect on what may be important to know without someone spelling it out for them all the time.
Thursday, May 29, 2008
Saturday, May 24, 2008
Stress City
Good riddance to a bad week. I had 3 bad run-ins with kids that left me so angry.
Run 1: I've had issues in the past with students conveniently not showing up on exam day. Then they'd take weeks to make up the test. Two tests ago I started the new policy of, "you miss the test, you make it up during class the next day". This helped. Then this past test, I had 2 students mysteriously absent on test day, last period of the day. I checked ClassXP, and, gee, mine was the only class they were absent for. I decided to use technology to my advantage and pop a quick e-mail home to mom: "is there a reason your child is absent from my class today?". This got results, and it alerted the parents without sounding accusatory (they could have had a dentist appointment). Well, it turns out one kid lied to his mom about where he was, and I found out, and thus he got a zero for that test. So, here we are Friday, and he's in my class just sitting there fuming all period. One and a half hours. Yay. So, not really a "run-in", more like a long, drawn out sit-in with teenage angst of getting caught and having to sit and take it.
Run 2: One child is in NHS, and has been slacking off on the homework department and just general character department all year (okay, all 4 years). After a bunch of stuff had happened, the NHS sponsor would only let him wear the "stole" at graduation if he got letters from his 4 core teachers that he deserved it. So he comes in to my class and tries to good-naturedly try to bully me and guilt me into writing his letter. He still didn't get that it's his actions that brought this on. He still thought/thinks that "we" are doing this to him. That left a bad taste in my mouth.
Run 3: Oh my. We're doing projects during calculus class, so it's a wee bit more unstructured as a class period than I like or am used to. Some kids are doing videos, and one kid in particular doesn't have any of his equipment at school, so just basically sits in class and says he'll work on it during the weekend. That's all a side issue for this run-in. He comes into class on Friday and does not look physically well, so I basically don't bother him much. Towards the end of the period, one student had turned to him and asked what he was doing. Apparently, he had unbuttoned his pants and unzipped them a ways because he was uncomfortable and didn't want to put pressure on his stomach. Well, okay. So I catch this interaction, and say to him, "well just put your shirt over your pants, so we don't have to see your unbottoned pants." Then he starts arguing with me. I keep asking him to just pull his shirt over and that it's just not socially acceptable to sit there like that. This goes on for about 3 rounds as he's refusing. Then he suddenly turns all creepy and lowers his voice menacingly and leans forward to me and says, "I'll decide what is socially acceptable and I'm NOT going to button my pants so you can be on your power trip and .....". Oh my god. I was livid. I told him to stop talking to me and that he was being completely inappropriate and he just needed to either leave the room or button up his pants. Holy Cow. Jerk. Excuse me while I jump off my teacherly manner and just fume about the brat. Okay, deep breath and the knowledge that I only have to see him for 2 more days.
Anyhow. WooHoo for weekends, especially 3 day ones. And only 7 more school days.
Run 1: I've had issues in the past with students conveniently not showing up on exam day. Then they'd take weeks to make up the test. Two tests ago I started the new policy of, "you miss the test, you make it up during class the next day". This helped. Then this past test, I had 2 students mysteriously absent on test day, last period of the day. I checked ClassXP, and, gee, mine was the only class they were absent for. I decided to use technology to my advantage and pop a quick e-mail home to mom: "is there a reason your child is absent from my class today?". This got results, and it alerted the parents without sounding accusatory (they could have had a dentist appointment). Well, it turns out one kid lied to his mom about where he was, and I found out, and thus he got a zero for that test. So, here we are Friday, and he's in my class just sitting there fuming all period. One and a half hours. Yay. So, not really a "run-in", more like a long, drawn out sit-in with teenage angst of getting caught and having to sit and take it.
Run 2: One child is in NHS, and has been slacking off on the homework department and just general character department all year (okay, all 4 years). After a bunch of stuff had happened, the NHS sponsor would only let him wear the "stole" at graduation if he got letters from his 4 core teachers that he deserved it. So he comes in to my class and tries to good-naturedly try to bully me and guilt me into writing his letter. He still didn't get that it's his actions that brought this on. He still thought/thinks that "we" are doing this to him. That left a bad taste in my mouth.
Run 3: Oh my. We're doing projects during calculus class, so it's a wee bit more unstructured as a class period than I like or am used to. Some kids are doing videos, and one kid in particular doesn't have any of his equipment at school, so just basically sits in class and says he'll work on it during the weekend. That's all a side issue for this run-in. He comes into class on Friday and does not look physically well, so I basically don't bother him much. Towards the end of the period, one student had turned to him and asked what he was doing. Apparently, he had unbuttoned his pants and unzipped them a ways because he was uncomfortable and didn't want to put pressure on his stomach. Well, okay. So I catch this interaction, and say to him, "well just put your shirt over your pants, so we don't have to see your unbottoned pants." Then he starts arguing with me. I keep asking him to just pull his shirt over and that it's just not socially acceptable to sit there like that. This goes on for about 3 rounds as he's refusing. Then he suddenly turns all creepy and lowers his voice menacingly and leans forward to me and says, "I'll decide what is socially acceptable and I'm NOT going to button my pants so you can be on your power trip and .....". Oh my god. I was livid. I told him to stop talking to me and that he was being completely inappropriate and he just needed to either leave the room or button up his pants. Holy Cow. Jerk. Excuse me while I jump off my teacherly manner and just fume about the brat. Okay, deep breath and the knowledge that I only have to see him for 2 more days.
Anyhow. WooHoo for weekends, especially 3 day ones. And only 7 more school days.
Saturday, May 17, 2008
End-o-Year Calculus Project(s)
I ended up deciding to give the students a choice of 3 projects to do for the remainder of our time in class:
1. a volume of cross section project using colored cut foam that I've done before
2. a volume of revolution project again with foam (never done and I'm doing it with the kids)
3. a video or power point (never done before, and thanks, Sam, for your tips which I've incorporated).
I'm happy that 7 students picked the video project, and 2 picked the power point project. From talking with the kids, they mostly had great ideas and are working hard. One student is resisting everything and being really derisive and dismissive and coming up with every argument in the book as to why he shouldn't be doing this. Or talking about doing something sarcastic and such (because, you know, math just isn't that exciting). I'm working on setting him straight using my teacher voice as I'm simultaneously resisting the urge to vigorously shake some manners/sense/attitude-adjustment into him.
I'm excited about the volumes of revolution project. There are 6 (?) of us doing it. I picked the same region for all of us (y = 4 - x^2 , y = 0 , x = 0) and we're each revolving it around different lines. That way we can put them all together and see what's what.
One video pair is working on a video about someone getting ready for a "math party" and they have to cut eggplant and for some reason need to know about the volume (details will emerge). They wanted to know how to get a function that looked like an eggplant. One girl was really excited and happy to learn something new when I showed her how to plot the shape on paper, pick some points on the "graph", put them in L1 and L2 on the calculator and then do a Quartic Regression. Cool. It DID look like an eggplant when she showed me.
1. a volume of cross section project using colored cut foam that I've done before
2. a volume of revolution project again with foam (never done and I'm doing it with the kids)
3. a video or power point (never done before, and thanks, Sam, for your tips which I've incorporated).
I'm happy that 7 students picked the video project, and 2 picked the power point project. From talking with the kids, they mostly had great ideas and are working hard. One student is resisting everything and being really derisive and dismissive and coming up with every argument in the book as to why he shouldn't be doing this. Or talking about doing something sarcastic and such (because, you know, math just isn't that exciting). I'm working on setting him straight using my teacher voice as I'm simultaneously resisting the urge to vigorously shake some manners/sense/attitude-adjustment into him.
I'm excited about the volumes of revolution project. There are 6 (?) of us doing it. I picked the same region for all of us (y = 4 - x^2 , y = 0 , x = 0) and we're each revolving it around different lines. That way we can put them all together and see what's what.
One video pair is working on a video about someone getting ready for a "math party" and they have to cut eggplant and for some reason need to know about the volume (details will emerge). They wanted to know how to get a function that looked like an eggplant. One girl was really excited and happy to learn something new when I showed her how to plot the shape on paper, pick some points on the "graph", put them in L1 and L2 on the calculator and then do a Quartic Regression. Cool. It DID look like an eggplant when she showed me.
Wednesday, May 14, 2008
Limits
I was teaching algebraically finding limits today in precalculus. We got to the part where x --> infinity. I've tried various ways of explaining it in the past about how you only need to look at the highest power term on the numerator and denominator and make your decision that way.
I've likened it to "when you're plugging in REALLY LARGE NUMBERS, the largest power term is like the ocean and the smaller powered terms become like spit. They don't make much of a difference to the ocean volume." This stuck with some kids, but I don't know that all were convinced.
Well. I had one problem: (8x^3 + 2x - 7) / (-4x^3 + 5x + 100) or some such thing. On the graphing calculator, we entered 1,000,000,000 and stored it in x. Then we calculated 8x^3. Enter. Then we calculated 2x. Enter and compare. That semi-convinced them. THEN we calculated 8x^3 + 2x, and that really convinced them because it "was" the same output as 8x^3 by itself. And we all know that if the calculator says something, then it must be true.
If I was thinking (because what I did was on the fly and then I moved on), I should have also then (in the main window) plugged in the whole expression using the stored value of x .... or then putting in larger values of x and then "2nd entering" to recalculate the expression. Next time.
I've likened it to "when you're plugging in REALLY LARGE NUMBERS, the largest power term is like the ocean and the smaller powered terms become like spit. They don't make much of a difference to the ocean volume." This stuck with some kids, but I don't know that all were convinced.
Well. I had one problem: (8x^3 + 2x - 7) / (-4x^3 + 5x + 100) or some such thing. On the graphing calculator, we entered 1,000,000,000 and stored it in x. Then we calculated 8x^3. Enter. Then we calculated 2x. Enter and compare. That semi-convinced them. THEN we calculated 8x^3 + 2x, and that really convinced them because it "was" the same output as 8x^3 by itself. And we all know that if the calculator says something, then it must be true.
If I was thinking (because what I did was on the fly and then I moved on), I should have also then (in the main window) plugged in the whole expression using the stored value of x .... or then putting in larger values of x and then "2nd entering" to recalculate the expression. Next time.
Friday, May 09, 2008
The Quiet Ones
For various reasons I thought it would be best for my calculus students to practice more than class would allow, so to entice them to come after school for 6 straight days before the AP exam, I called them "power sessions" and said I'd bring food every night, and we could meet from 4:30 -6:30 and just do and discuss old released exams. I had anywhere from 10 to 28 kids show up (out of my total of 40) each night. I think it helped. We were all relieved once the AP exam was over, and I think it payed off for the ones that put out more effort.
During these sessions I'd call out a couple of problems at a time, and they'd work them, and then we'd discuss them. As usual I mentioned that people should just ask questions when they had them. I always have people asking questions. This gives me a false sense of things-are-okay-for-everyone. Or maybe I'm just gauging my time and trying to get through a lot and just moving on once the questions die down. Or something else.
I know there are a couple of girls that work hard but struggle. They asked NO questions. I'd even look them in the eye and ask if they had questions. Nope. I know I should know better than that, but apparently I don't (even after 11 years of teaching). So finally I started going over to them while the class was working the problems and would say, "you're fine? or do you have questions?" and invariably they'd have some question that I could quickly answer for them to set them on their way.
It seems like each class gets a culture, and there are the talkers and jokers and more vocal participators and then after a while we all settle into a routine and maybe it's hard to rock the boat and make your voice heard if you are not used to it and the other kids are the "cool kids (?)" or the "class representatives (?)" or something. Here's to being reminded to remember the quiet ones.
During these sessions I'd call out a couple of problems at a time, and they'd work them, and then we'd discuss them. As usual I mentioned that people should just ask questions when they had them. I always have people asking questions. This gives me a false sense of things-are-okay-for-everyone. Or maybe I'm just gauging my time and trying to get through a lot and just moving on once the questions die down. Or something else.
I know there are a couple of girls that work hard but struggle. They asked NO questions. I'd even look them in the eye and ask if they had questions. Nope. I know I should know better than that, but apparently I don't (even after 11 years of teaching). So finally I started going over to them while the class was working the problems and would say, "you're fine? or do you have questions?" and invariably they'd have some question that I could quickly answer for them to set them on their way.
It seems like each class gets a culture, and there are the talkers and jokers and more vocal participators and then after a while we all settle into a routine and maybe it's hard to rock the boat and make your voice heard if you are not used to it and the other kids are the "cool kids (?)" or the "class representatives (?)" or something. Here's to being reminded to remember the quiet ones.
Saturday, May 03, 2008
Filler Classes
This past week was our TAKS week, and therefore I only saw some of my precalculus classes, and so I could not move on, and I did NOT want to have "free days". One day, I taught them about binary and counting and adding and subtracting and multiplying in different bases.
I made the connection to base 10 where you can think of each position as a bin where you drop marbles. You start filling them up from right to left. The capacity of each bin is 9, and once you try to put one more in a bin, it would overflow, and so you have to scoop the 10 you want to put in there out and place one marble in the next bin over to the left to designate a higher power of 10.
So we started counting in base 4. Each bin has capacity 3. We did the "scooping" thing. We counted to 20.
1, 2, 3,10,11,12,13,20,21,22,23,30, ..., 103, 110.
We made the connection that each bin represents (from right to left: 4^0, 4^1, 4^2, 4^3, ...). We did other bases. We then converted between base 4 (say) and base 10. And between base 10 and another base.
I also recalled a version of a game I played in 8th grade, that I still play when I need to occupy my mind and have time to kill.
Pick any 4 single-digit numbers. Then number your page from 1 - 10 (as one example), and you have to use every one of your chosen numbers once and any math operation to get all 10 numbers listed. I had them play and the first one done would get candy. Boy were they quiet and working. I'm SURE it was the math and not the candy.
For example: 5,2,8,9
1. 9 - 8/2 - 5 = 1
2. 2 + 5 * (9-8) = 2
I made the connection to base 10 where you can think of each position as a bin where you drop marbles. You start filling them up from right to left. The capacity of each bin is 9, and once you try to put one more in a bin, it would overflow, and so you have to scoop the 10 you want to put in there out and place one marble in the next bin over to the left to designate a higher power of 10.
So we started counting in base 4. Each bin has capacity 3. We did the "scooping" thing. We counted to 20.
1, 2, 3,10,11,12,13,20,21,22,23,30, ..., 103, 110.
We made the connection that each bin represents (from right to left: 4^0, 4^1, 4^2, 4^3, ...). We did other bases. We then converted between base 4 (say) and base 10. And between base 10 and another base.
I also recalled a version of a game I played in 8th grade, that I still play when I need to occupy my mind and have time to kill.
Pick any 4 single-digit numbers. Then number your page from 1 - 10 (as one example), and you have to use every one of your chosen numbers once and any math operation to get all 10 numbers listed. I had them play and the first one done would get candy. Boy were they quiet and working. I'm SURE it was the math and not the candy.
For example: 5,2,8,9
1. 9 - 8/2 - 5 = 1
2. 2 + 5 * (9-8) = 2
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