Last year from a workshop I learned of a fun activity with which to introduce volumes of revolution to my class. It involved candy, the kids seemed to get it. They loved it. We all walked away with smiles on our faces. But then they got home and couldn't do homework involving revolving regions about various axes. Granted in class, we only went through 3 examples, I talked them through it all the while giving them a chance to process it. But still, no.
This year, I was looking through my files and came across another way to introduce volumes of revolution. It's (free) from www.mastermathmentor.com . And there are TONS of calculus AB and BC (did I mention free) worksheets there. I'd hesitated using it before because it looked TOO LONG to get through in class. Then the homework was TOO LONG. Hey genius :), just because all the problems are there, it doesn't mean you have to use them all.
I used this sheet this time. I slowly walked them through the 6 parts of example 1. I kept stressing the questions to ask yourself, and I weaned them off my help so that by the 6th problem they could do it by themselves. Then for homework I assigned them examples 2 and examples 3 (12 problems) from the class work worksheet. Wouldn't you know it. They all got it right. AND they could then go on and do more challenging problems. Success.
I keep having to teach myself that not every student can get by on just one to two examples to teach a concept. Some students need 5 or more examples. But then there's always the time factor and the other kids in class that can get it with just one example. Anyhow. I'm now excited because I've found a new effective way of teaching this topic.
Monday, March 31, 2008
Thursday, March 27, 2008
Seeing Pink
Well honestly, seeing Red, but since I'm not doing anything about it other than losing sleep last night, it's been downgraded.
Apparently, our algebra, geometry, and algebra 2 teachers have been told to stop teaching the curriculum and start teaching to THE TEST. The state-mandated, must-pass in junior year to graduate, must-pass in sophomore year to make our school "acceptable", must pass in freshman year or else the uppy-ups start to panic and worry you won't pass in 10th or 11th grade ... TEST. And for how long are they to teach to this test? FOR 3 MONTHS. That's 3 months of math knowledge they won't have the next year, and the next and the next. Oh my god that is so short-sighted.
Honestly, if I was teaching one of those classes, I don't know what I'd do. Would I refuse? Would I teach part of my class to the canned activities that they all must follow and then teach the curriculum? Would I raise a big stink and even go so far as to quit in protest? And why am I not doing something now? Just because it doesn't directly affect me (it will when they're in precal and calculus)? If you know something is wrong, and you keep letting it continue, aren't you just as guilty for it perpetuating? Argh.
Apparently, our algebra, geometry, and algebra 2 teachers have been told to stop teaching the curriculum and start teaching to THE TEST. The state-mandated, must-pass in junior year to graduate, must-pass in sophomore year to make our school "acceptable", must pass in freshman year or else the uppy-ups start to panic and worry you won't pass in 10th or 11th grade ... TEST. And for how long are they to teach to this test? FOR 3 MONTHS. That's 3 months of math knowledge they won't have the next year, and the next and the next. Oh my god that is so short-sighted.
Honestly, if I was teaching one of those classes, I don't know what I'd do. Would I refuse? Would I teach part of my class to the canned activities that they all must follow and then teach the curriculum? Would I raise a big stink and even go so far as to quit in protest? And why am I not doing something now? Just because it doesn't directly affect me (it will when they're in precal and calculus)? If you know something is wrong, and you keep letting it continue, aren't you just as guilty for it perpetuating? Argh.
Saturday, March 22, 2008
People Watching
I was out with my friend this weekend, and we went to a tea house in an upscale, outdoor mall. It was fun to people watch, and there were all types - pregnant moms with little kids in tow, glamour teens with their high-price accessories, vogue 20-somethings, everyday people in shorts, lots of girls in sundresses. I started thinking about the things that go through your head when you watch people.
I'm wondering if a lot of the mind chatter is like - oh I wish I had abs/legs/arms/etc like that, or I wish my hair swung like that, or I wish I looked like that .... and I'm wondering about how much that affects how you live out your life or the choices you make.
What if the mind chatter went more like - oh I wish I was as generous as that, or I wish I could forgive like that, or I wish I could contribute to my community in that way like that, or I wish I was as good a person as that ... more inside stuff than outside appearances.
I'm wondering if a lot of the mind chatter is like - oh I wish I had abs/legs/arms/etc like that, or I wish my hair swung like that, or I wish I looked like that .... and I'm wondering about how much that affects how you live out your life or the choices you make.
What if the mind chatter went more like - oh I wish I was as generous as that, or I wish I could forgive like that, or I wish I could contribute to my community in that way like that, or I wish I was as good a person as that ... more inside stuff than outside appearances.
Thursday, March 20, 2008
Counting To Ten
I know we hear that once you ask a question of a class, you should "count to 10" to wait for the students to think about it quietly before you proceed to ask for an answer. And I guess when we're tutoring students, and trying to walk them through a process, you "count to 10" after you prompt them for a piece, so again they can process the information.
I literally "count to 10" in my head, and sometimes twice. Now not 1,2,3, ...., 19, 20, but 1, 2, 3, ..., 10 then 1, 2, 3 ...., 10. I'm wondering if other people do the literal counting in their heads while they wait.
Then again, I count the stairs in my house when I'm going down or up them (5, 8, and 6). I count the "bumps" in one piece of the highway on my way to work (10).
I think the counting is good. I sometimes count to 10 after I am "giving them notes", after short bursts of speech, so that they have time to process what I just said before I burst some more (I'm sure they're on pins and needles waiting for the pearls to fall from my mouth instead of thinking about boys or girls or prom or music).
I'm thinking of this one reporter on NPR. He always sounds different from the others. He's the one in Florida, and he talks really fast (compared to the other reporters) and it just sounds different and noticeable and you just want him to slow down. I don't want to be that "reporter" teacher, but I know I talk fast, so hopefully I'll keep counting to remind myself to slow down.
I literally "count to 10" in my head, and sometimes twice. Now not 1,2,3, ...., 19, 20, but 1, 2, 3, ..., 10 then 1, 2, 3 ...., 10. I'm wondering if other people do the literal counting in their heads while they wait.
Then again, I count the stairs in my house when I'm going down or up them (5, 8, and 6). I count the "bumps" in one piece of the highway on my way to work (10).
I think the counting is good. I sometimes count to 10 after I am "giving them notes", after short bursts of speech, so that they have time to process what I just said before I burst some more (I'm sure they're on pins and needles waiting for the pearls to fall from my mouth instead of thinking about boys or girls or prom or music).
I'm thinking of this one reporter on NPR. He always sounds different from the others. He's the one in Florida, and he talks really fast (compared to the other reporters) and it just sounds different and noticeable and you just want him to slow down. I don't want to be that "reporter" teacher, but I know I talk fast, so hopefully I'll keep counting to remind myself to slow down.
Monday, March 17, 2008
Snacks
A while ago I got into the habit of keeping snacks in my classroom in a big plastic (dark, non see-through mouse resistant) tub. I like to keep, graham crackers, pretzels, cheddar bunnies, Newman cookies, CheezIts, cereal, etc. It seems to be an incentive for kids to come in for tutoring at the end of the day, or at least to have them stave off their hunger (or ruin their appetite for dinner) as they're getting extra math help. I found that baby wipes and extra napkins and maybe small paper cups for pouring treats into are helpful.
There have been some incidents. Once during first period, a student mentioned she hadn't had breakfast and wondered if she could have a snack. I said sure, and envisioned her quickly taking something, closing the tub, and getting back to work. After I continue with my lesson, I glance over at her, and there she is in all her glory, open tub next to her, and an array of snacks on her desk. We quickly fixed that, and I made a mental note: no "tub" during class time.
Another time a student asked (during class) to have a snack. I said, no, that it was only for after school. Then she tries on her pleading voice, "but I really like them, pleaaaaaaasssssse". Ew. No means no. I'm reminded of a TV talk show I once saw where the message was, just because someone asks for something nicely, it doesn't mean you should give it to them, their example was: "oh I LOVE your diamond necklace. It's so beautiful and elegant. Can I please have it?"
Then there are the "vacuum" kids after school - not many of them, but, sheesh. All snacks inhaled, and thank you very much.
But mostly it has been something I think I'll continue.
There have been some incidents. Once during first period, a student mentioned she hadn't had breakfast and wondered if she could have a snack. I said sure, and envisioned her quickly taking something, closing the tub, and getting back to work. After I continue with my lesson, I glance over at her, and there she is in all her glory, open tub next to her, and an array of snacks on her desk. We quickly fixed that, and I made a mental note: no "tub" during class time.
Another time a student asked (during class) to have a snack. I said, no, that it was only for after school. Then she tries on her pleading voice, "but I really like them, pleaaaaaaasssssse". Ew. No means no. I'm reminded of a TV talk show I once saw where the message was, just because someone asks for something nicely, it doesn't mean you should give it to them, their example was: "oh I LOVE your diamond necklace. It's so beautiful and elegant. Can I please have it?"
Then there are the "vacuum" kids after school - not many of them, but, sheesh. All snacks inhaled, and thank you very much.
But mostly it has been something I think I'll continue.
Tuesday, March 11, 2008
Spring Break
WooHoo! Nine days off to relax and catch up and stuff. I went to Portland, OR for a few days just to wander around, and the rain gods must have been busy elsewhere because it only rained on the night I came in and on the night I left. Note to self: red-eye flights bad, but made better due to the fact that I had a whole glorious row all to myself to "stretch" out in for 4 hours of interrupted sleep.
As I was wandering around and needing a caffeine fix, I started looking for either the *green* popular coffee shop circle/emblem or the *red* one. Then I got to thinking how that's so ingrained in our brains, and we now have instant recognition of logos and various signs even if they're too far away to read, we've memorized them. Then that got me to thinking about various things I want/need my calculus students to know: derivatives/integrals related to e^x, ln(x), trig functions, etc.
My thought before spring break was to have various posters around the room with "need to know" things on them. Maybe in different colors or styles, and just the fact that the kids have to stare at them every day may help them when the AP exam comes around, and they can close their eyes (maybe) and "see" what they need to know. Then I thought I'd force the issue and periodically (daily?) have us recite the posters. Then after my trip, I thought maybe we can design some sort of logos for these things. Anything to make facts stick in their heads when they have SO much to memorize.
Must think about this some more.
As I was wandering around and needing a caffeine fix, I started looking for either the *green* popular coffee shop circle/emblem or the *red* one. Then I got to thinking how that's so ingrained in our brains, and we now have instant recognition of logos and various signs even if they're too far away to read, we've memorized them. Then that got me to thinking about various things I want/need my calculus students to know: derivatives/integrals related to e^x, ln(x), trig functions, etc.
My thought before spring break was to have various posters around the room with "need to know" things on them. Maybe in different colors or styles, and just the fact that the kids have to stare at them every day may help them when the AP exam comes around, and they can close their eyes (maybe) and "see" what they need to know. Then I thought I'd force the issue and periodically (daily?) have us recite the posters. Then after my trip, I thought maybe we can design some sort of logos for these things. Anything to make facts stick in their heads when they have SO much to memorize.
Must think about this some more.
Tuesday, March 04, 2008
The Old Days
Today in precalculus we went over / reviewed / saw again / learned Long Division of Polynomials and Synthetic Division of Polynomials. I told the kids that I had mixed feelings about teaching the L.D. because I thought it was on its way out due to graphing calculators but I still thought it was worthwhile because it was cool and it allowed them to practice their algebra skills and solidify their knowledge of factoring.
Anyway, I mentioned that I had a friend that was about 10 years older than me (so she probably graduated high school in early 1970s), and she mentioned that she had to learn how to calculate square roots by hand, and these days we don't teach that anymore.
Another student asked, "didn't you all have to look up the sine and cosine and stuff in tables?" And that got me thinking. Yes we looked them up in tables every time we did trig, and so that visual memory was there, and we had constant reminders that you took sines of angles and the result was a number and all those numbers seemed to be between -1 and 1. (now I don't remember if it was between 0 and 1, and we had to think or not).
I seem to have too many instances now where in a situation, students don't intuitively know in sin x = y which is the angle and which is the number/ratio of sides. It seems like maybe we've/they've lost something from not having that table to help.
Anyway, I mentioned that I had a friend that was about 10 years older than me (so she probably graduated high school in early 1970s), and she mentioned that she had to learn how to calculate square roots by hand, and these days we don't teach that anymore.
Another student asked, "didn't you all have to look up the sine and cosine and stuff in tables?" And that got me thinking. Yes we looked them up in tables every time we did trig, and so that visual memory was there, and we had constant reminders that you took sines of angles and the result was a number and all those numbers seemed to be between -1 and 1. (now I don't remember if it was between 0 and 1, and we had to think or not).
I seem to have too many instances now where in a situation, students don't intuitively know in sin x = y which is the angle and which is the number/ratio of sides. It seems like maybe we've/they've lost something from not having that table to help.
Saturday, March 01, 2008
Results
Well, I tried the "blank out the correct answer on a multiple choice question" idea. None of us liked it. I asked for feedback from the kids after they worked on 5 problems, and they said, "well, it's okay if you get one of the wrong answers, but if you don't, then you don't know if you're not doing something ELSE wrong or if you're correct." I think I agree with them.
I went to "math camp" today (calculus teachers sharing materials), and I have a new appreciation for Winplot. It's a free software you can download from Exeter acadamy, and I've only used it for creating graphs for handouts in the past. BUT. One of the teachers showed how he used it for demonstrations in class and such. I'm by no means even close to being an expert, but it gave me motivation to learn more skills in the program. Apparently, they also have WinGeom, and WinStat ... or something like that. I haven't looked into it.
I went to "math camp" today (calculus teachers sharing materials), and I have a new appreciation for Winplot. It's a free software you can download from Exeter acadamy, and I've only used it for creating graphs for handouts in the past. BUT. One of the teachers showed how he used it for demonstrations in class and such. I'm by no means even close to being an expert, but it gave me motivation to learn more skills in the program. Apparently, they also have WinGeom, and WinStat ... or something like that. I haven't looked into it.
Tuesday, February 26, 2008
Multiple Choice Idea
An AP English teacher passed on this idea from a conference she attended, and I thought it sounded effective and cool and will try it soon. Give the kids a sheet of good multiple choice problems (the non answers are based on common mistakes). Say there are 4 choices. White out the correct answer choice for each question and leave the 3 non answers (the kids know what you've done ahead of time). This way, the students work through the problem, and if they see their answer there, they know they made a mistake, and work harder at figuring out what's what.
I tried something a bit different last week - something I thought would work well. Well, it worked in that it gave me insight into what the kids DON'T know.
I had a sheet with 3 AP calculus questions. Stuff we've just covered. Stuff I thought they would be great at - integral of e^(-4x), derivative of (x^2)(sin(2x)), setting up a u-substitution integral. There were 5 answer choices. I gave all answer choices. I picked 3 of the letters (one being correct). I told them for each of the 3, either indicate it's the correct answer, or describe what mistake the student made if they picked that answer.
Well, talk about a stressful time in class. First of all, things they nod at you at when you're teaching, things they do homework on, and you think they know, things you've seen them do successfully. Out the window. Don't trust it until it comes down to proving it without any aids or support or notes or hints or prestudying for a test. So, it basically worked well in that it taught me to be careful and be more thorough in checking and rechecking their understanding individually NOT in a test situation. Second of all, it was fascinating how needy some of them were: am I right? can you just tell me if I'm on the right track? can I work with so-and-so? ... I kept telling them no to all questions, that that wouldn't help me know what they know. It was very hard not to help them, but I think that's what got us into this in the first place.
Whew. I have some work to do. But better to know that now than when it's too late.
I tried something a bit different last week - something I thought would work well. Well, it worked in that it gave me insight into what the kids DON'T know.
I had a sheet with 3 AP calculus questions. Stuff we've just covered. Stuff I thought they would be great at - integral of e^(-4x), derivative of (x^2)(sin(2x)), setting up a u-substitution integral. There were 5 answer choices. I gave all answer choices. I picked 3 of the letters (one being correct). I told them for each of the 3, either indicate it's the correct answer, or describe what mistake the student made if they picked that answer.
Well, talk about a stressful time in class. First of all, things they nod at you at when you're teaching, things they do homework on, and you think they know, things you've seen them do successfully. Out the window. Don't trust it until it comes down to proving it without any aids or support or notes or hints or prestudying for a test. So, it basically worked well in that it taught me to be careful and be more thorough in checking and rechecking their understanding individually NOT in a test situation. Second of all, it was fascinating how needy some of them were: am I right? can you just tell me if I'm on the right track? can I work with so-and-so? ... I kept telling them no to all questions, that that wouldn't help me know what they know. It was very hard not to help them, but I think that's what got us into this in the first place.
Whew. I have some work to do. But better to know that now than when it's too late.
Saturday, February 23, 2008
parent homework
About a week ago I assigned my precalculus students the following homework: teach your parents something about either polar graphing or complex numbers, and have them send me e-mail explaining the experience. I've started getting e-mail back, and while some of them are simply, "yes, my son taught me," others are more elaborate and even funny "I was a willing student", "hope there's not a quiz", "thanks for this experience", "I didn't know there were such things as imaginary numbers", "I remembered how to FOIL", etc.
I'm glad I did it, and I'll add it to my notes to do next year.
I'm glad I did it, and I'll add it to my notes to do next year.
Thursday, February 21, 2008
The Wonders of Seat Changes
In both my calculus classes, I started dreading teaching, because invariably - yap yap yap yap - basically from 1 to 2 boys, but it would affect the whole class in some way. In BC, I sat 2 smart boys together thinking they would work well together. Well, they REALLY worked well together. They started discussing the problems loudly while I was teaching. They would outdo each other to call out the answers really quickly before anyone else had a chance to think - regardless of my constant, "think to yourself quietly / wait 10 seconds before you answer / etc". And when I would speak to them separately, they replied, "but we're learning". They didn't think it bothered anyone else. After numerous complaints, I separated them. Peace. Learning. They still don't think they did anything wrong, regardless of my, "you're not being homeschooled / you're not giving others a chance to learn" comments.
In my other class, the class clown got 3 - 4 other boys yapping, and they're pretty funny (in a nonclassroom situation) and I do like them. However. NOT IN CLASS. Today I moved the clown to the back away from the other boys. Now he's around some studious girls, and for today at least. Whew.
I can put aside my dartboard with their pictures on it for now.
In my other class, the class clown got 3 - 4 other boys yapping, and they're pretty funny (in a nonclassroom situation) and I do like them. However. NOT IN CLASS. Today I moved the clown to the back away from the other boys. Now he's around some studious girls, and for today at least. Whew.
I can put aside my dartboard with their pictures on it for now.
Sunday, February 17, 2008
Following a Rubric
At times in the past when I've included a rubric with my projects, I'm amazed that there are students that turn in something that explicitly do not include something that was clearly stated as part of the grade. For example, I may give requirements for "color" or "citing a source" or such.
Now I see it's either because I'm just like the kids, or because we're all human, or I don't know what. I'm writing a paper based on my teaching (national board) and following their format of answering specific questions, and it's a bunch of work, and I'm trying to do a good job, and I'm reading and rereading the questions to make sure I answer them, and I'm patting myself on the back because I'm "answering their questions". I breathe a sigh of relief when I'm "done".
Wait. Now I go back and reread ALL the instructions, and there, clearly labeled is a rubric on how we'll be graded. This is in addition to answering their questions. So this means I will go back after I think I'm done and reread my words with an eye for how it will be graded. But I can so easily see how a student might just think he/she is done because they've done the assignment and they're sick of doing the assignment and they wish for the assignment to go away and they may not want to go back and check on how that assignment might be judged.
Maybe we have to have an extra day built into the assignment, and once they bring it to class to turn in, they have to spend some time reading the rubric and honestly judging if they did what they needed to do. Maybe looking at someone else's and judging constructively. Basically teaching them how to use a rubric.
Now I see it's either because I'm just like the kids, or because we're all human, or I don't know what. I'm writing a paper based on my teaching (national board) and following their format of answering specific questions, and it's a bunch of work, and I'm trying to do a good job, and I'm reading and rereading the questions to make sure I answer them, and I'm patting myself on the back because I'm "answering their questions". I breathe a sigh of relief when I'm "done".
Wait. Now I go back and reread ALL the instructions, and there, clearly labeled is a rubric on how we'll be graded. This is in addition to answering their questions. So this means I will go back after I think I'm done and reread my words with an eye for how it will be graded. But I can so easily see how a student might just think he/she is done because they've done the assignment and they're sick of doing the assignment and they wish for the assignment to go away and they may not want to go back and check on how that assignment might be judged.
Maybe we have to have an extra day built into the assignment, and once they bring it to class to turn in, they have to spend some time reading the rubric and honestly judging if they did what they needed to do. Maybe looking at someone else's and judging constructively. Basically teaching them how to use a rubric.
Wednesday, February 13, 2008
Unclear on the Concept
Once a week we have a 30 minute advisory where we meet with one group of kids and are basically their mom/dad on campus making sure they don't slip through the cracks. We have the same kids for 10th - 12th grades. This week I printed out their progress reports in all their classes and as I was checking in with each kid, I saw that two 11th grade boys who were sitting next to each other were both failing math, and they had the same teacher. I asked what the deal was.
One boy shrugged and said, "I don't know. He puts these problems on the board, and we're supposed to copy them and then he gives us problems to do at home." The other boy piped up with, "I think it's because he's a first year teacher." I was not understanding what they were implying, so I asked for clarification. Then one boy said, "well, then the next day he just puts more examples on the board, and then he assigns us more problems."
Oh my! The nerve of this teacher assigning homework. AND. expecting it to get done and giving a grade. I'm calling Amnesty International.
One boy shrugged and said, "I don't know. He puts these problems on the board, and we're supposed to copy them and then he gives us problems to do at home." The other boy piped up with, "I think it's because he's a first year teacher." I was not understanding what they were implying, so I asked for clarification. Then one boy said, "well, then the next day he just puts more examples on the board, and then he assigns us more problems."
Oh my! The nerve of this teacher assigning homework. AND. expecting it to get done and giving a grade. I'm calling Amnesty International.
Saturday, February 09, 2008
New Kids
In the past 2 weeks I got 2 new kids from different states. They're both juniors. One's in my advisory, so I don't really "teach" him. The other is in my precalculus class. I had just handed out a survey to the kids the previous class and among other questions, I asked them to "tell me something good in your lives" and "is there anything bothering you (y/n) no details needed" and "if you answered yes above, is there someone you can talk to about it (y/n)".
Well before I read them, I saw the new student in the halls one morning this week and after hellos, I asked him if he did his homework just by way of conversation. No. Well, are you going to? I'll try. Well, try and do. Okay. I noticed that he was looking a little glum, but I didn't mention it. Later I read his survey response, and he went on about how he really missed his old friends and he has no one to talk to and he is not making new friends and such.
Of course here comes big mean teacher me: What? You're sad/depressed? I don't care! Do your math homework!
I later sent him e-mail mentioning that he could come to my class after school or during lunch as there's always some kids in there. That way I figure he doesn't have to wander around aimlessly looking/being alone while everyone else seems to be having a good time. I'm wondering how many other kids there are just dreading lunch or after school because of a big vast empty space of time with no one to talk to.
Well before I read them, I saw the new student in the halls one morning this week and after hellos, I asked him if he did his homework just by way of conversation. No. Well, are you going to? I'll try. Well, try and do. Okay. I noticed that he was looking a little glum, but I didn't mention it. Later I read his survey response, and he went on about how he really missed his old friends and he has no one to talk to and he is not making new friends and such.
Of course here comes big mean teacher me: What? You're sad/depressed? I don't care! Do your math homework!
I later sent him e-mail mentioning that he could come to my class after school or during lunch as there's always some kids in there. That way I figure he doesn't have to wander around aimlessly looking/being alone while everyone else seems to be having a good time. I'm wondering how many other kids there are just dreading lunch or after school because of a big vast empty space of time with no one to talk to.
Tuesday, February 05, 2008
Class Statistics Continued ...
I taught my 2nd 2 "box & whisker" classes today (we're on block schedule), and after some of your comments, I polled my class and mentioned that we already did hours of sleep, and we also did TV watched. Did they want to do cell phone contacts or text messages? They liked that idea, but then other ideas started popping up, and we voted. Number of songs on your ipod or mp3 player eeked out front. I don't have a cell phone or a music player, so I didn't know what type of numbers I was in for. Sheesh. Our numbers ranged from 44 to 3100.
In my next class we took a poll again, and I thought this would be not so exciting, but their choice of number of shoes they have was interesting. We decided flip flops and slippers and cleats would count. I thought boys wouldn't have as many, but some did. The numbers ranged from 5 to 80 (now, the 80 girl had a sister with the same size foot, so they shared, that was her story and she was sticking to it). One guy had 60 (I guess tons of fancy shmancy sneakers). A girl with 5 pairs widened her eyes at the larger numbers.
In my next class we took a poll again, and I thought this would be not so exciting, but their choice of number of shoes they have was interesting. We decided flip flops and slippers and cleats would count. I thought boys wouldn't have as many, but some did. The numbers ranged from 5 to 80 (now, the 80 girl had a sister with the same size foot, so they shared, that was her story and she was sticking to it). One guy had 60 (I guess tons of fancy shmancy sneakers). A girl with 5 pairs widened her eyes at the larger numbers.
Saturday, February 02, 2008
On the Fly Lesson
I planned to teach vectors on Friday, and I must have been super sleepy as I prepared earlier, because when all was said and done, it took less than an hour to cover what I needed to, and then I had 30 minutes left to fill with no plans.
Box and Whisker Plots to the rescue. We'd just discussed (as a department) how these will be on our state exit exam for the students and how they hadn't seen it since 8th grade. I cobbled together a lesson to show them what's what and how do do things on the graphing calculator. In my first class, we gathered number of hours slept last night, and worked with that data. I didn't like it so much since the numbers only ranged from 4 to 10. I polled my next class about what they wanted to count that had a wide range, and after some mis-starts, they came up with number of hours of T.V. watched in a week. Sheesh, that was illuminating. The numbers spanned from 3 to 30. I had to keep reminding them and myself to make no judgmental noises or facial expressions when someone called out their number.
As I still had time left, I asked them to figure out how to change the data without adding more data so that the box was wider. That got their minds working.
Box and Whisker Plots to the rescue. We'd just discussed (as a department) how these will be on our state exit exam for the students and how they hadn't seen it since 8th grade. I cobbled together a lesson to show them what's what and how do do things on the graphing calculator. In my first class, we gathered number of hours slept last night, and worked with that data. I didn't like it so much since the numbers only ranged from 4 to 10. I polled my next class about what they wanted to count that had a wide range, and after some mis-starts, they came up with number of hours of T.V. watched in a week. Sheesh, that was illuminating. The numbers spanned from 3 to 30. I had to keep reminding them and myself to make no judgmental noises or facial expressions when someone called out their number.
As I still had time left, I asked them to figure out how to change the data without adding more data so that the box was wider. That got their minds working.
Tuesday, January 29, 2008
Filming Yourself
As part of my national board certification, for 2 different entries, I have to tape a 15 minute segment of my class and analyze it to within an inch of its life. Even if you don't need to for any other purpose, I highly recommend taping and watching yourself (though I'm entirely sick of that 15 minutes of my life since I've watched it over and over again and can be like that annoying person at a show, "Oh, here's where she says this. Here's where they do that.")
I noticed things I would not otherwise have noticed. When I question kids of varying abilities, I reword my questions (subconsciously?) based on what I think their skill level is. Like I don't think some kids can handle a question asked some way and may need help. That's obnoxious and robs them of the opportunity to show what they know.
I also notice that when I was helping a student in a small group activity, I was bodily in the way of this other polite girl's desk, and so basically the whole time I was helping this one kid, this other poor little child couldn't do her work because BIG HOVERING teacher was in her space. Of course she was too polite to say anything, so for 5 minutes she just quietly sat there. Then when you see me moving off to help another group, boom, she starts doing stuff.
I think if you can get the right group of nonjudgmental/helpful teachers together and they each tape their own class, maybe others would have insight into questioning technique or wait time or such. People with fresh eyes will pick up on things you may not be aware of.
Of course when I invent a 26 hour day, then I'll have time to get that all organized.
I noticed things I would not otherwise have noticed. When I question kids of varying abilities, I reword my questions (subconsciously?) based on what I think their skill level is. Like I don't think some kids can handle a question asked some way and may need help. That's obnoxious and robs them of the opportunity to show what they know.
I also notice that when I was helping a student in a small group activity, I was bodily in the way of this other polite girl's desk, and so basically the whole time I was helping this one kid, this other poor little child couldn't do her work because BIG HOVERING teacher was in her space. Of course she was too polite to say anything, so for 5 minutes she just quietly sat there. Then when you see me moving off to help another group, boom, she starts doing stuff.
I think if you can get the right group of nonjudgmental/helpful teachers together and they each tape their own class, maybe others would have insight into questioning technique or wait time or such. People with fresh eyes will pick up on things you may not be aware of.
Of course when I invent a 26 hour day, then I'll have time to get that all organized.
Saturday, January 26, 2008
Speed Teaching
Right after the winter break, I finally sat down to see where I was with BC Calculus. I know I was behind from last year for a variety of reasons (new block schedule, new book, starting 2 weeks later), and I finally needed to see how far. Yeesh. I listed all the topics left, found how much time left, "did the math", and realized that if we get on the speed train of math, we can just about fit everything in with a week or 2 to review in April/May..... if I forego test days, review days, practice days, state testing days, kids-out-for-anything days. Very unrealistic. And most likely if I forego giving-them-time-to-absorb days.
I'm consoling myself with the "fact" that a lot of it is cumulative, so they'll see skills again even if we don't formally talk about it. I'm also helping the speed by every class making "skeleton" notes where students fill in blanks as I talk and the pictures or graphs are already drawn to save time, and the practice problems are already listed to save time, etc.
So far in 5 (6?) block classes we've covered antiderivatives, Riemann Sums, area, definite and indefinite integrals, FTC, u-substitution, ln(x) derivatives and related integrals. I'm also spiraling homework, and their optimization "test" is a problem that they have to keep attempting for homework until it's perfect. Maybe I'll do a few of those.
I'd better assess in some informal ways to make sure things are sticking, otherwise what's the point of cramming the stuff if they don't learn it.
I'm consoling myself with the "fact" that a lot of it is cumulative, so they'll see skills again even if we don't formally talk about it. I'm also helping the speed by every class making "skeleton" notes where students fill in blanks as I talk and the pictures or graphs are already drawn to save time, and the practice problems are already listed to save time, etc.
So far in 5 (6?) block classes we've covered antiderivatives, Riemann Sums, area, definite and indefinite integrals, FTC, u-substitution, ln(x) derivatives and related integrals. I'm also spiraling homework, and their optimization "test" is a problem that they have to keep attempting for homework until it's perfect. Maybe I'll do a few of those.
I'd better assess in some informal ways to make sure things are sticking, otherwise what's the point of cramming the stuff if they don't learn it.
Tuesday, January 22, 2008
Funny Kid
Students were wacky today. Just goofy and chatty and such. In my 1st period AB Calculus class - chatty chatty chatty. While they were doing work, some of them started going off and talking in text message code: someone would say out loud, "LOL", and then they would all chuckle. Then someone else said, "ROTFL", and then chuckle, chuckle, etc. Oh my. I quieted them down.
Then. I have a unique, well-liked, has-his-own-band student who often stares off into space like he's writing his own music or thinking artsy thoughts. Well, today he was wearing 60s style pants, and after their big chucklefest died down, he had gotten up to get a tissue, and someone says, "Nice Pants," all sarcastic like, and then everyone chuckle, chuckle. And then I said something about, "oh, if the rest of you have to be such conformists and wear only what other people tell you is okay ..... ". And then this 60s pant kid pipes up jokingly, "well, if you don't like my pants, then I'll just take them off." We all laughed.
Then. I have a unique, well-liked, has-his-own-band student who often stares off into space like he's writing his own music or thinking artsy thoughts. Well, today he was wearing 60s style pants, and after their big chucklefest died down, he had gotten up to get a tissue, and someone says, "Nice Pants," all sarcastic like, and then everyone chuckle, chuckle. And then I said something about, "oh, if the rest of you have to be such conformists and wear only what other people tell you is okay ..... ". And then this 60s pant kid pipes up jokingly, "well, if you don't like my pants, then I'll just take them off." We all laughed.
Saturday, January 19, 2008
Conics Continued
I wanted to start my parabola lesson with paper folding to create a parabola. I'd done it before with other classes, and it went well since it was something different. This year I wanted to add an extra "twist" and experimented on my 3rd period (guinea pig) class .... (we don't LIKE being your guinea pigs).
Previously, they would draw a line on a piece of paper (directrix) and a point (focus) and then start folding the line over to lay on top of the focus many different times, and then the resulting pattern emerges as a parabola. Done. Move on to notes. This year I wanted to actually have them plot some of the points that were on the parabola, so after each fold, they were to use their ruler place it perpendicular to the directrix, through the focus, and make a dot where it intersected the fold.
Oh my goodness. Confusion city. Some kids got it, but lots didn't, so I just moved on and chalked one up to experience. But I think I heard the funniest line so far. One girl who has been struggling with math all year and is not getting the draw-the-dot-on-the-fold directions shrugs and funny-resignedly says, "even paper confuses me in math class".
Previously, they would draw a line on a piece of paper (directrix) and a point (focus) and then start folding the line over to lay on top of the focus many different times, and then the resulting pattern emerges as a parabola. Done. Move on to notes. This year I wanted to actually have them plot some of the points that were on the parabola, so after each fold, they were to use their ruler place it perpendicular to the directrix, through the focus, and make a dot where it intersected the fold.
Oh my goodness. Confusion city. Some kids got it, but lots didn't, so I just moved on and chalked one up to experience. But I think I heard the funniest line so far. One girl who has been struggling with math all year and is not getting the draw-the-dot-on-the-fold directions shrugs and funny-resignedly says, "even paper confuses me in math class".
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