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.

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

Attitude

I think I've learned to perfect the, "what do you MEAN you're not going to do the thing I've asked you to do?" look/attitude.
The, "of course you'll do it" look.
The, "there's no other option" look.
The, "I'm amazed you'd even think to ask such a question" look.
The, "don't be silly" look.

I got to use it Monday when I prepped my AP Calculus kids on the fact that they had homework that was due Tuesday even though I wouldn't see them due to the state test, and they'd better walk their butts over to school from whatever vacation they think they're getting and hand in the no-lates-accepted AP-exam--multiple-choice corrections to me.

Of course I'm semi-bluffing and know I'm asking a lot of them, but I think the "look" gets them to get off their duffs, and maybe I'll have a higher turning-in rate because of "the look". I also reminded them of the fact that the AP exam is coming up next week, and don't give up now, and you can do it, and it would be a shame to work so hard all year and flake out now and miss the opportunity to pass, and rah-rah-rah ...

Plus I get to practice being a bad-a** when I think I'm a softy inside ... but maybe I'm fooling myself, and I've become mean and cranky with high expectations. Oh well, they usually rise to the challenge - and I guess it's our job to push them to do their best, even though it's their job to resist and try to get away with what they can. Our little teaching tug-o-war.

Idea for post AP exam calculus

The last 2 years I've done different things after the AP exams in my calculus classes. One year we did a rubber foam volumes of cross sections project. One year we discussed "multiple" integrals and (non calculus) counting and adding and multiplying in different-than-10 bases.

I just had a thought I haven't fleshed out for what to do this year. I'm thinking of getting a list of topics that span the calculus year, and having the students make short videos that teach or showcase the topic. That way I can post the useful ones on my website for the next year's students to have a different perspective on things they may struggle with. Also, the students are creative, and I think they may come up with good stuff.

Grading? I'm thinking there has to be a time limit (less than 4 or so minutes), effective (to be judged by other students), creative (again judged by students), done on time, ....

One issue may be various student access to video equipment. Another issue is size of groups working on one video. We'll see ...

Shhhhh

I was at an AP Calculus prep session for the students most of the day today. There were 3 sessions running in parallel, and 4 different time slots throughout the day. I sat in on the sessions and worked along with the students. One teacher had great problems, and he'd keep talking and talking and say, "okay now you work the problems", and then he'd only give us 1 second (or so it seemed) before he started talking again - either about something else, or to start working the problem.

It made me reflect and wonder if I do this more than I should. I know I try to shush up with enough time for the kids to work, but at the same time I'm clock watching and stressing about finishing in time and getting everything in and then maybe rushing the kids.

I also tried something different in BC calculus on Friday. I handed them my notes from "math camp" on parametrics, and then also handed them a separate packet of problems with answers provided in the back. On each of my "camp" notes, after each problem that had been worked out, I had written on their copies, "now work problem so-and-so". I barely talked to them at all, and only monitored to see if there was any clarification needed. They worked like champs all period, and were doing all the problems. Hopefully, they'll continue over the weekend, as I told them there'd be a "free response" quiz the next time they came to class.

Testing Testing

Okay. It finally got to me. All year when I've announced tests and given tests, there's ALWAYS some students absent. Then it becomes a game of, "when are you going to make up the test". Then days and literally weeks would go by before some students made up the test. They all eventually do, but really! It usually didn't annoy me TOO much, but now during this last test about 1/5 of my class was gone from each period during the test.

In the past I was diligent about mentioning and then checking up on whether the students were cutting or not, and then they had zero chance of making up the test. This year, I had other things on my plate.

I'm giving a test this week on Wednesday and Thursday (block scheduling). I mentioned ahead of time, "if you are absent the day of the test, the next time you are in class, I will put you out in the hall, and you will make up the test during class time and miss the current lesson." Hopefully, this will make it less appealing to the students to all of a sudden feel really ill on the day of the test and use that as an excuse to drag it out.

I heard another teacher at the beginning of the year announces: every time everyone is here for a test, everyone gets a bonus point(s). She found that then the students were policing each other to make sure they were there.

I guess my method will work (I hope), because either way, the students will finish the test within a week (unless they're super skipping class).

Getting In Trouble

We recently had an incident in our school regarding relations between a teacher and a student. Phew! The repercussions of that. Part of me thinks: WHAT was the teacher thinking. There goes the career, the chance to earn a living, the student's psyche, ...

We had to all go to "harrassment" training for 1.5 hours. All the way up to the meeting I was grumbling to myself: I didn't do anything wrong. I have classes to prep for during my prep periods. I know right from wrong. Grumble. Grumble. Then as these things sometimes go, I learned some things.

1. Even if the student is 18 or over, it's still cause for dismissal.
2. If you hear any rumors about other teacher/student goings-on, and you don't say anything to the authorities, and it's later found out that you knew/suspected, you are in the wrong and could face .... whatever.
3. Even if your relationship is innocent (and later proven so) with a student, if others perceive it as fishy and the rumors start to fly, you could lose your job because the public has "lost faith" in your ability to be effective in the classroom (hmmmmm)
4. If students get too friendly with you and develop a crush, and you don't nip it in the bud or make sure you're never alone with one student, etc. one of them could become jealous and start spreading rumors about you (creepy) that may cause you to lose your job.

There's probably more, but that's depressing enough as it is.

Parents

Two weeks ago I was scrambling and rushed for time, so I did not complete the official "progress report" sending via the school (every student who is failing or within 3% of failing receives a progress report). So. Within the next couple of days, I printed up IGPro grades, 4 to a page, chopped them up, attached them to a 1/2 sheet stating that parents should discuss this with their child and write me a note and sign it that they've done so. I made it a SMALL quiz grade to guarantee I'd get them back, docking off 10% per day late.

I have one awesome kid that is always in for tutoring, asks questions in class, does all his homework, scores very well on tests, takes "retests" (bane of my existence) every time if he does not get a perfect score, has a 99.63% average at the time of the reports. His mom writes back: I know he can do better. I will make sure he comes in for tutoring so he can improve.

Compare this with another student who has a 93% with the parent comment of: my son is so great!

Compare this with another student who has a 3% and who scratched out his mom's comment to call her.

Fun vs. Effective

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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".

Human Ellipse

Earlier in this winter January week in Texas with 60 - 70 temperatures, I was staring out my classroom window and remembering one event in my high school years. I don't remember the class/teacher/activity-purpose. All I remember is that one day we got to go OUTSIDE during class. This memory has lasted 26 years or so. So I related this to my 6th period class, and after their clamoring I promised we'd do something mathy outside some day.

Well, we started conic sections this week, and Friday was going to be a wee bit disrupted from other things, so I thought we'd go outside for part of the class and build a human ellipse to start off the unit. I had a long stretch of nylon yellow rope that I tied into a loop. Two students were the foci, one student was the pencil. Those 3 were inside the loop. The foci stayed fixed, and the "pencil" moved around while keeping the rope taut. The rest of the students were the "pencil traces" and moved to the "pencil's" spot after she left it.

We made 3 or so ellipses and I prompted them first each time about what they thought would happen if the foci moved in or out. We discussed circles. We got some sun. I think they have a sense of the ellipse properties now for when we get to them.

Extra Practice Calculus Worksheets

I keep forgetting to mention this great resource I found at NCTM one year. If you know of the Pizzazz worksheets, it's sort of like that, but for calculus (ooh, aah). It's published by Nasco, and called "Calculaughs Joke Worksheets", by June Oliver - who apparently was/is a calculus teacher and made up a variety of joke practice sheets for derivatives, mean value theorem, integrals, etc.

I've already used them when I want to come back to a topic after we've moved on. It's a nice way for the students to refresh their memories. I LOVED the types of questions on the MVThm sheet. I could never find enough satisfactory problems elsewhere for my kids to practice with. It also gave me some ideas on other types of activities I can have for that topic.

Here's a link I found: http://www.enasco.com/action/search?catalog=math&q=calculaughs&x=0&y=0

I'd also love to hear of other such resources for precalculus or for calculus ... even for algebra 2, because it's nice for the kids to refresh their memories on OLD topics.

Nature Break

Over winter break we went to Red Rock Canyon: Death Valley:

Death Valley:
And Zion National Park:
Every place was more stunning than the one before, and we had many hikes and long nights of sleep and surprisingly tasty dinners in small towns.

You're Welcome

The e-mail one father should have sent me:
Thank you:
-for coming in practically every day at 7:30am and leaving at 5:00pm and tutoring and teaching my child,
-for giving her retest opportunities throughout the fall to improve her grade,
-for curving the finals grade so that even though she missed 21 out of 40 questions, she had an opportunity to pass for the semester,
-for allowing a notecard on the final to relieve added stress of a big stakes test,
-for only putting 40 multiple choice questions on the final with an ample 2 hours to complete it.

The one he sent instead:
"K. indicated that she was not allowed to finish her final, was there some reason why? Usually they have been allowed to finish in the past, please advise..."

(translation: you ripped the test out of her hands while she lay sobbing and laughed maniacally while you informed her she could not finish)

Finals Shminals

My favorite note ever was handed to me today by a student before her finals: please allow W_____ to check on her chickens after her math final.

Last Week of the Fall

As usual it just seems to zip by. Last period of the last day of last week - antsy chomping-at-the-bit squirmy students. I jokingly told them they'd drive me to drink, and then in my mind I was thinking about the glass of wine I'd have later.

I also had a student leave class and not come back 30 minutes into our 1.5 hour block. Oh my was I furious. I debated referrals, calls home, e-mail to the kid. I ended up calling his mom and describing the incident and venting. She said she'd talk to him. I see now that I have an e-mail from him on my school account titled "apologies", but I'm not ready to read it yet.

He's a funny, good-natured kid who's struggling with the math, and his way of dealing with it is to not come in for help, and to turn in work late and to apologize after the fact and swear up and down that he'll change his ways, and then continue on in his fashion. Let's see if a miracle occurs, and he figures things out next semester.

On a positive note, we started our optimization unit in calculus, and I created an activity that I think will aid them in their understanding. I cut up colored paper/cards with 6 problem statements. Then in a different color I cut up pictures related to the problems. In a 3rd color I cut up main equations and "helper" equations. They were to match up all scenarios, then write them down on a prepared sheet. The last part was to use the "helper" equation to reduce the main equation down to 1 variable, and then to finally graph the main equation with their calculator and draw a good sketch of it on the sheet. No solving yet. They worked in groups and eventually (we didn't finish), I think we'll have a good discussion about the domain of the variable and then the "solving" will be work they've done before. We'll see after break.

Bullying

This past Saturday we had an AP Calculus and Statistics prep session at our school for 7 area high schools. There were 4 simultaneous sessions going on, with 3 different time slots for a total of 12 sessions. As students were deciding which sessions to go to, one boy from another school was by me and mentioned that everyone seemed to be sticking with kids from their own school, and then he mentioned that everyone at his school hated him, so he wanted to be in another session. I don't remember what I said. I didn't know the student, so I probably made some light remark and got him on his way.

Later on, in one of the sessions I sat in on, this boy was in there, along with, apparently, at least 4 other students from his school. This boy would listen to the teacher, and frequently make remarks or contribute to the discussion or ask questions to clarify. It was clear he was not up to speed with the topics, and was just trying really hard. Every time he made a comment, the 2 students near him would look at each other and semi-silently laugh. Every time. And 2 other thuggy looking boys that sat farther away would make louder comments, but not loud enough to warrent a comment from the presenter. I finally couldn't stand it any more, and when I didn't think the other students would hear me, I turned to the 2 laughers from my back seat post and warned harshly, "stop it". I gave the one of the other boys a dirty look, but that was about it.

This poor kid. Yes, he was annoying. But imagine going through the whole day, and maybe the whole school year with a wrought up gut knowing others are laughing at you all day. ... I sat in on another session, and the laughers didn't seem to be laughing at him any more, but maybe I'm just seeing what I want to see. Sheesh, I hope I'm not blind to this in my classroom as I'm up front with a million other things on my mind. I try to make an all inclusive class, and I do have a similarly challenged kid in my class. I need to be more diligent with how others are potentially making under-breath comments.

Voiceless

I felt a cold coming on last week at the start of the week, and then, wham, on Thursday and Friday, I guess my tonsils were so swollen, they constricted my throat, and I basically had no voice. I don't like to take days off, so I plowed through and sounded throaty and squeaky and husky and not as loud as I wanted to be. My kids were great, though, and they shushed each other, and we got through it. But oh my goodness, it's Sunday right now, and I still speak funny.

I tried something different in all my classes. After we went over homework, I handed out a 1/4 sheet of scratch paper, and put a 1 question "homework quiz" on the overhead (cough cough ... document camera, that is ... I'm so lucky). They couldn't use their notes or talk with people. I walked around and checked their progress, and made suggestions as needed. After a wee bit, I asked them to write down their status "yes I got it", "I needed to look at my notes", "I got help from ____ and then got it", etc. We discussed answers, and I collected them. This will give me a better sense of who needs help, and it will also allow me to make comments on the "quizzes" that they can read when I hand them back tomorrow.

Holiday School Holiday Sandwich

We went to Idaho Falls, Idaho and Jackson Hole, Wyoming over Thanksgiving break. Here is a picture taken after the "lighting of the elk arches" in the town square of Jackson Hole. Apparently, there are vast numbers of elk that migrate around the area, and their antlers just drop off like matchsticks, and people collect them, and, hey, let's build 4 arches made of elk antlers to welcome people into the square.

We also hiked around the Grand Tetons for 3.5 hours, the first 2 hours of which were great, but then (no names mentioned) someone started getting hungry and cranky and did NOT want to hike to the 2nd lake because it impeded their eating schedule.

Now it's back to school, and I was cranky about that - just the rush rush rush feelings of "am I going to get everything done" and "will they successfully learn what I want them to learn", but then I get to school, and the kids are funny and it's good to see them and talk with them.

They are learning my annual fraction song, and today I quizzed them on it, and maybe we'll put it on YouTube because I think it would be a riot. I don't know if that's kosher to tape them and put it on there, but it's not kiddie porn or anything, and the students think it'll be a hoot, so we'll see.

Nonmath Moment

Last Monday in one of my classes a student asked, "if my dad dies in debt, am I responsible for paying everything off?". She was worried because apparently he has never sent child support and apparently has debt, and she didn't want to have to pay. Then my other students started piping up with, "yes you have to pay" in so many ways and how they were so sure that was the case and they'd discussed it with so-and-so and basically you were responsible.

Ew. I didn't know the answer, and we went on with our math. After class I looked it up, and no, you are not responsible, so I sent out a quick e-mail note to my students with the links just so they wouldn't stay under the false impression.

Well, I sent this via our gradebook program that allows you to just send notes, and one of the parents sends back: What are you doing looking into our debt? You shouldn't be teaching this! ...... So I sent back a note explaining the situation, and he calmed down, with no apology of snapping at me and assuming we were all going online and doing credit checks on parents and making big charts to show to the class. Oh my.

Continuity...(it never ends)

Blach! I'm having the hardest time getting the bulk of my calculus students to follow a (seemingly simple) recipe for proving continuity. Come on people, it's 3 steps. I've given you worked out examples. We've drawn pictures. We've modeled it with our hands. We've talked ad naseum about it. I made you write about it. Three steps! It's all I ask. Don't make me hurt you.

Identifying Coasters

I know I have kids in class that are polite and quiet and pay attention (or look like they do) in class, and attempt the homework, and yet are just not getting it. They don't come in for help. They don't ask questions in class. It's easy for them to just not be actively involved in the learning in class and coast and "pass" (though maybe not on tests).

I have various strategies when students answer questions in class to get everyone to participate: talk to someone next to you quietly about ..., help someone or have someone help you with ..., give me a thumb vote on the answer to ..., write down your answer to ____ and I'll walk around and check.

But as I'm walking around or waiting for them to talk to each other or ask questions, there are still kids "fake" doing it. So I debate whether to call them on it or not. I don't think I can do this every time and reach every student because the lesson has to go on and that seems like it would take too much time and maybe have a negative effect. Students can just look busy or look like they're working, and maybe they are, but they're not done by the time most others are done with the current task.

Today I was starting the calculus class, and we were going over homework on the "1st derivative test" to identify maxes and mins. I asked the class as a whole, what were the steps of doing the "test". The usual suspects started to answer, and I stopped them and did something I hardly ever do. I picked on a random student by name. "I don't know". I picked on another (making sure not to pick the kids that got it). "I don't know". So I stopped class and said, "look over your notes from last class, and I'll pick on random people to answer various questions about this topic". Well. That got the motivation up. Everyone was looking through their notes and discussing things with their neighbors and one student was so excited, "I GET it, it's this and this and this". Then I picked by name random students to answer the remaining questions.

I don't do that enough. I've gotten set in my ways and rely on the strategies I mentioned way above, thinking that everyone would get a chance to discuss and learn things before someone called out the answer, and I failed to notice that there are kids not participating too many times, and that it was easy to just sit and vegetate.

Helicopter Parents

I just read this term the other day, and then had an experience with it myself soon after. Apparently, these are parents that hover over their children and are super involved in their school and other activities and help run the kids' lives without letting the kids figure things out for themselves and make mistakes and learn and fend for themselves.

I just gave a 2 question, short quiz in calculus. I thought it was doable. The related rates problem involved a right triangle, so I expected the students to look at it and think, "hmmmm, right triangle, what sorts of equations do I know about right triangles" and then go from there. Well, oh my god, you'd have thought I asked them to prove Fermat's last theorem. One girl immediately started hounding me about it. Then after class she hovered and said that I shouldn't count that question as a grade. Then 20 minutes later I notice my message light is on for my phone, and it's her mother saying that E. was upset about the test and didn't feel prepared and could I please call her. Ewww. It creeped me out.

Cheating

I want my precalculus students to know (at least) sine, cosine, and tangent of all the special angles (at least) in the 1st and 2nd quadrants by heart and quickly. Therefore, I told them early last week that they will have a daily timed quiz with 14 questions that they know in advance, and they have to answer ALL correctly in a set amount of time. I took the 1st one with them and told them I'd double my time and that would be their time. It turns out they have 2 minutes for 14 questions. Doable. I keep giving them a pep talk. You can do it. It's not brain surgery. I'm not smarter than you, I've just been doing it longer. Study. You only need to be able to do each question in just under 10 seconds each. And so on.

They get a 0% until they get all right in 2 minutes, then they get 100%, and they can take it as many times as they need to in the remaining weeks of the 6 weeks. I've already had 3 kids pass in the first few days, and many are close.

Then there are those that seem to make no progress. They don't study for it, and they don't memorize (yet?).

Then there are the 2 boys I caught cheating with the weird "oh, let me look at my palm while I'm taking the test. What a fascinating life line I have." ... or "oh, let me look down at my lap, what a great leg I have.". I stared hard at the boys. I stood by the boys. I didn't say anything directly to the boys. They did not pass, and were nervous while I was standing near or looking at them. Why didn't I say something? But now I can no longer trust them. I also mentioned to my OTHER 2 classes about the cheating without naming names, and discussed how that was trust lost and very hard to earn back.

Blach. I should have a palm check before the quiz, or a stand up and let me look at your lap check. But how silly and weird.

Opinion Changes

It's always nice and surprising how my first impressions of students and students attitudes in class improve (generally) as the year starts rolling. I guess they get used to a new teacher and how tests are given and what's expected of them. They get out of their summer mode of thinking and start actually doing work and coming in for tutoring.

So far I can think of these students:

"M" was twice absent on calculus test days. When he made them up, he complained about the difficulty and how I didn't give a formal review sheet (I told them what was on the test and they had old homework and answer keys to study). I told him that I didn't want to hand hold him, and if he needed to review, then he had to put out an effort. This last test he VASTLY improved his scores, and in class he's actually been participating.

"R" was goofy in class and talked talked talked. He was not doing well on precalculus tests. Lately, he's been coming in for tutoring and zeroing in on specific things he was having trouble with, and he's grasping things much better.

"E" has a surly haughty expression in calculus class and always seemed annoyed with everything I did. And yet, she advocates for herself: can you repeat that? can you wait a bit? can you explain that another way ("in English" another student pipes up). She really wants to grasp things, and now she has started cracking the occasional joke.

"M2" is STILL absent frequently in precalculus class and he's still constantly sleepy in class, but he makes up all his work and when he comes in for tutoring, he asks intuitive questions and has unique, clever ways of solving problems.

There are more, but I love as the year goes on how my kids grow on me.

Take 4

1st period/time through the spaghetti sine graphing activity:
me: read the instructions, they're clear, and you can follow them, and you'll be amazed at the results of graphing y = sin x without a calculator or ruler.
them: help. help. help. I don't get it. help. help.
me: running around helping everyone with the same questions over and over.

2nd period/time through the activity:
me: let me give you an overview of what you're doing here. overview. read the instructions, they're clear, you'll be great.
them: help. help.
me: running around helping.

3rd period/time through the activity:
me: here is a detailed overview with hand puppets and motions on the overhead of what you'll be doing. let me do it slowly and clearly. the instructions are VERY CLEAR. Read the instructions before you ask me any questions.
them: help.
me: I help. Class, ... so-and-so is now an expert on instruction 4. If you have questions on #4, ask so-and-so. ... So-&-so is an expert on instruction 5. Ask him/her.
them: so-and-so, help.
me: (nothing to do).

4th period/time through the activity:
me: (see 3rd time through) with the addition of: the instructions are VERRRRRRYYYYY clear. You'll be great. I expect great things from you. Did I mention that the instructions are clear? Here, look at my hand puppets.
them: help
me: (post-help) so-n-so is an expert on #4, etc. Ask so-and-so.
them: (scurrying over to student to get help)
me: (do dee do dee do ... nothing to do but walk around and watch them work)


oh! and a joke I read on You Tube:

What did "0" say to "8"? ..... "Nice belt".

Linear Speed Reteach

It turns out too many of my students STILL could not successfully work linear and angular speed problems. You'd see this look of abject fear in their eyes if you even showed them such a thing. While I was stressing about it one morning when I couldn't sleep, I remembered an old conversation with a science teacher that mentioned using little cards that the kids could manipulate and turn around and change one unit into the other.

I made up 6 little cards (I fit 4 x 6 on one sheet of colored regular paper) of approximately the colors above (color coded), and handed them out to the students. In about 30 minutes or so, we worked through 4 or so problems of graduating difficulty. At the end it looked like all of them could successfully switch from one set of units to the other. We'll see on Monday. Next time, with more prep, I may even have homework for them on this day!

My problems in order:
1. 200 in/min to convert to miles/min.

I made up some picture of me on a bike and what I was doing yesterday and had them write this down in their notes with a big space between the first and last statements. Then their pencils went down, and they were to pick the appropriate cards in the appropriate orientation to do the conversion, and "place them so I know you know what you're doing".

At first only 40% or so had the right cards in the right orientation. It was easy to walk around the room and spot check and ask if the inches canceled or if you got inches squared. Then they had to transfer that to their notes, and we discussed how how to put the numbers in the right places. Some kids still resisted writing the units, and they invariably put the "12" or the "5280" in the wrong places. We fixed that.

2. 10 mi/min convert to in/min.

Same process. This one was a kid's name riding a unicycle with the appropriate goofy picture. It also helped that the final answers came out really unrealistic - cause for more laughs and stories.

3. # feet/sec convert to miles/hour

Now there was some whining, but we talked about doing distance first, then time. They got it. (power walking? tricycle?)

4. #rotations/sec convert to feet/hour

(Human wheel like in cirque du soleil? Again a kid's name, and radius needed)

Anyhow, I think there was much joy in linear-speed-ville at the end. Hopefully, this will translate to understanding and accuracy on problems.

Never Assume

Two cases:

1. A student was asking me about a linear speed problem in precalculus, and in the problem statement I had that the radius = 14". When I was probing him for the units of circumference, he hesitated a long time, and I pointed to 14", and he said, "oh, that looked like 14 to the 11th power." I KNOW I didn't even mention the notation for feet (') and inches ("). I didn't think it would be an issue.

2. In calculus, a student came in to practice for our next test. We have just covered the quotient rule and the product rule among other things. He was asking me when we know to used the quotient rule, and I was taken aback. I asked him what quotient means, and he didn't know. And this has been about a week or so since we started it. I KNOW I didn't expressly mention that a quotient was a division problem. I thought it was obvious from the statement of the rule.

Notations in my planbook reflections for next year.

Memory Wheel

In calculus, we just finished learning the derivatives of the trig and inverse trig functions, and in the learning log, one student asked if we could make something to help memorize all the formulas. We had gone over some tricks in class, but now they're faced with the daunting fact of memorizing (gasp) 12 things.

I came up with making a wheel like the one above, and after a trip to a craft store for some card stock and some small (are they called?) rivets, I made the one pictured. I quite like it, and it wasn't too difficult.

Steps:
1. Use a compass to draw 2 different size circles on card stock and make sure to mark the center.
2. Cut a "window" out of the small "top" circle (I used cuticle scissors, but I guess an exacto knife would work).
3. Join the circles with a rivet (it was doable with a hammer).
4. I used a sharpie to write the functions on the outside circle. I could fit 14 things with my handwriting. It seems more are possible.
5. Write the derivatives (or whatever the answers are) inside the window as you rotate it around.
6. Voila.

Now let's see how much class time I want to devote to this, or how much I can make them do at home. Everyone has hammers, right?

Yay (Yeah?) Learning Logs

These are my "overhead projector" hands that cause lots of interesting conversations along the vein of "Ew. Take a shower, piggy."

I've tried the Learning Log for all my classes just once now, and I love it. I left 5 minutes at the end of class to quickly say why I was doing this (I get a chance to answer questions that may not otherwise be answered and I get a chance to "converse" with students that never say a word in class). Then I after I explained the procedure, they had at it, and I collected it before they left. It didn't take me too long to look through them and respond to everyone - either a "check" or smily face if there were no questions, or a "good job in class" message to the quiet kids who always do the right thing and are not squeaky wheels and who sometimes get ignored, or an explanation to answer their questions (either on the paper or on an attached large sticky note).

That day in trig we were learning how to "draw pictures in your head" to quickly without writing anything down be able to calculate sine and cosine of special angles all around the unit circle. And in calculus AB they were learning derivatives of trig functions. And in calculus BC they were learning implicit differentiation.

Here are some of the trig questions/issues:
How do you place 3pi/4 on the circle?
How do you tell when the answers are positive or negative?
Is your hair naturally blonde?
I'm still not getting the "quick" special angle calculations...
I liked learning the fast way to do this ...

Here are some of the calculus questions/issues:
Could we have more practice?
Slow down!
Do you always sprinkle dy/dx anywhere you have a "y" in an implicit function?
Is there a way to figure out "y" in an implicit function if you find dy/dx?

I'm hoping as this becomes more of a routine, more of the kids will use it effectively.

Learning Logs

Some of my students are still falling through the cracks of learning in my class, and they're not coming in for tutoring, and they're getting further and further behind, and I'm not catching it in time. I catch it after a test or after I send out official reports every 3 weeks. So I'm going to try something new starting this week.

In the last 5 minutes of class, they're to quietly read over their notes and process what we did that day. Then they're to fill out this form (enlarged and "weird" to get it in here):

I will collect them and respond and return them the next class to start the process all over again. Hopefully, this way I can nip some problems in the bud, and it won't be too cumbersome to grade since it's short and many of the students won't have concerns. Also, I can connect with kids I that never talk in class. I'm printing this sheet front to back and stapling 3 sheets together for a 6 weeks grading period.

We'll see how it goes and adjust as needed.

Learning Trig with Special Triangles

Angular Speed

We started working on linear and angular speed, and I presented a few examples of what you would calculate and how to calculate, but some students still struggled. Today in one class this seemed to work. I was looking around for something familiar to link their knowledge to, and lo and behold, THE CLOCK. So I asked them to quietly ("let other people figure it out for themselves") find the angular speed of the second hand of the clock (I had to call it the "red stick" for the students that didn't know the term). "Ahhhhhh". Then we worked on the angular speed of the "long black" stick (minute hand) and the "short black" stick.

I also handed out colored paper that had a large unit circle on it (I bought it special for you at the store) and thin spaghetti (everyone gets one especially chosen for them). We worked on initial and terminal sides of angles in standard position. Then to start discussing reference triangles, I said that they were joining a math cult today, and every time we passed each other in the hall we had to repeat our special phrase: always drop the perpendicular to the x-axis. We practiced our cult voices for a bit. Then I assessed their reference triangle knowledge with the spaghetti. Hopefully, this will prevent students from drawing their reference triangles incorrectly as some have before.

Learning Greek

Last year in precalculus I had each student pick a Greek alphabet letter out of a hat, and they were to make a small (8.5" x 5") colorful poster with the capital letter, the lower case letter and the pronunciation of the letter. Then I hung those around the room, so we had a reference when we were using the letters as variables in trigonometry. I liked the activity, but then the students only got familiar, for the most part, with one letter. This year I made an "elementary school" type sheet where they have to trace over the capital and lower case letters 4 times each while simultaneously saying the pronunciation. They'll get bonus points if they can recite them all in order by memory. I'm liking this activity, so now I have to possibly make the letters myself because I still like them displayed. If anyone wants a copy of the activity, I'll send you one via e-mail (math_mambo@yahoo.com).

I'm also excited about my teacher website. Whoever suggested weebly.com and google calendars, Thank You. They were both easy to use and link together, and in just one weekend I created a usable site. I made it as a homework assignment for the students to have their parents visit the site and either send me e-mail or call that they did so. Yay technology.

Em(pi)nadas

We started trigonometry at the end of last week, and I know from past experience that my fraction-phobic students have trouble with placing pi/3, pi/4, pi/6, etc. angles in standard positon, so I tried something new this year.

I drew a semicircle (flat-side down) and made up some story that involved having and "em(pi)nada" for lunch and said it was so delicious that other teachers wanted to share it with me. I had them draw 4 em(pi)nadas and draw how they'd slice them in pie cutting fashion into 2, 3, 4, 6 equal parts to share and eventually they shaded the 1st piece (thinking of angles in standard position). They had no trouble slicing them equally, and I think it helped later on when I linked pi radians to 180 degrees, and they then drew pi/3, etc angles around the circle.

Then I introduced radians by first saying that for so-and-so's birthday I gave her a circle, and her mom gave her a string, and so-and-so was SO bored that she decided to do math by cutting the string the length of the radius, and she wanted to see how many times it would go around the circle. They were then to discuss how many times they thought it would fit. I got various responses, 3, 4, 6, 10... We finally got to the fact that you're just measuring the circumference. They then proceeded to equally tell me the formula for circumference was pi*r*r and also 2*pi*r. So then I had to sing them a song a student taught me, and then we all sang it together a few times:

Twinkle, twinkle little star
Circumference equals 2, pi, r.

Lovely (it brings a tear to the eye). We then defined radians.

Anyway, after I used my math tools (thin spaghetti to sweep out angles on the overhead), and we practiced placing various radian angles in standard position, we called it a day.

An interesting side note: another teacher friend mentioned a while ago how he linked the clock with the unit circle and that seemed to help his kids place 30, 60, 45 degrees more successfully around the circle. Well, I also brought that up, and in a side note, one student mentioned, "you know, I have a hard time reading analog clocks. I never learned, and now it takes me a while to process it."

Quick Assessment

Last week with about 8 minutes left of class, I handed out scratch paper that was cut into 4ths, 1/4th to each kid, and put 3-4 quick "pop quiz" questions on the overhead (3 math, and 1 "spell my last name" since they always mess it up and it eased the tension of a "pop"). They could use their notes but not talk with anyone. We happened to be studying function composition. I told them to write down the problems, show their work, and box their answers.

They took it seriously because it was for a grade. I liked it because I could walk around and scan their answers and see who was getting it and who wasn't. After a couple of minutes anytime I saw a wrong answer, I quietly mentioned to the kid that they should check that problem. That way, later I had an easy time to grade them, the kids felt better about the "pop"ness, and I then could concentrate on the 3-4 kids that I saw just weren't getting it and help them through quickly or suggest they come in for tutoring later.

Sleep Deprivation and the Modern Teacher

1. We were supposed to calculate (for a grant) how much extra time we spent after school last year tutoring students. So I figured on average I spent 3 extra hours per week at about 30 weeks that year. Wow, I calculated, I spent 900 hours tutoring! I rock (though apparently not at multiplying 3x30).

2. As the week goes on I get more and more sleep deprived (that's my excuse preamble for the following). I also daily wear my wedding ring that I never take off, and many other silver rings that I take off at night and put back on daily. So on Friday I get to work, and to my classroom, and I instantly feel and see that I have all my rings on except my wedding ring (of almost 13 years). Gasp! Oh no! Did I get too skinny (cough) and it slipped off on my way from the car to my classroom? I obsessed about it all day. That night, I went home and saw that it was in my ring tray. I don't even remember taking it off. I don't remember realizing it wasn't on all morning. I don't remember seeing it and sifting around it in the morning while I'm putting on my other rings.

3. I had this lesson that was working really well on symmetry of functions (even/odd/neither) on Friday (remember, in my defense, I'm TIRED), and I divided my overhead slide into 3 rows and would graph, describe, give the rule, and give an example for each type before moving on to the next type. I was running out of room on my slide, so I slid (tee hee) it over to the left and continued writing on the overhead glass to finish up the EVEN example. I then used my spritzer bottle and rag to clean the glass before moving on to the ODD example. I got through the graph, the description, the rule, slid the slide over, and then looked above at my EVEN example, and realized that, Oh no!, I forgot to give an example for the EVEN function, and here I am on the ODD example. So I start walking them through the steps of the EVEN example, and I'm patiently waiting for them to continue, and a student asks, "didn't we just do this?". Oh my.

I'm Scary

School has been in session for almost 3 weeks now. I've given my 1st test, and there have been about 5 homework assignments, and I've passed out current grades. Therefore, various students with low grades came in after school today to get tutoring to boost their understanding and their grade. I keep mentioning in class that I'll work with the students and they're welcome any time and if they make improvements from whereEVER they are in their understanding, they'll pass (or better) my class.

It's been my experience teaching precalculus and calculus that the students are finally, "oh, NOW I have to study to actually get a good grade. ... oh, NOW I have to actually do and do properly my homework ... oh, NOW I have to come in for tutoring to make sure I get it."

There were about 8 students in my room after school, and I'm circulating around, and I'm helping this one girl with domain and range. We were working through a problem. I'm prompting her for answers. I don't think I was rushing her. I paused and waited for her responses without any physical gestures of impatience or interrupting. At one point, as I'm waiting for her response, I could see she was flustered, and she said, "oh, I'm so nervous."

Wow. I didn't think I was that intimidating. My perception of myself and how new struggling students must see me are apparently not in line. I made a joke of it, "I know. I'm scary." and we went on. But it made me remember that just because I think I'm a nice and patient teacher, a student that's just meeting me for the 1st time and is struggling sees a different person.

Piecewise Functions

The following demonstrates why I don't do "formal" lesson plans before my lesson. Well, this and the fact that I'm a last-minute (post-last-minute?) person. I eventually do get the plans down on paper, since I use them the following year to see what works and doesn't work.

I was introducing piecewise functions to my precalculus class. I started with an example of a power company in town and suggested that they may offer incentives to people who use less electricity, so if you use less than or equal to 500 kW per month, they charge you 10 cents per kW, and if you use more than 500 kW per month, they charge you 15 cents per kW. I then gave them the disclaimer that I had no idea how much a kW was and if this was at all reasonable. (future assignment for the class and me: find out how many minutes of light that is). Then to make sure they got it, I asked them to put on paper in calculator-ready form, how much my bill would be if I used 600 kW last month. I wasn't even thinking about the ambiguity, but a great question came up: is it 15 cents for everything since you went over, or is it only 15 cents for the 100 kW over? (we went with the 2nd option).

Then we started drawing the graph, and decided that there would be an initial service fee of $20 even if you didn't use any kW. I asked them to discuss in their groups the axes labels and what the left part of the graph would look like (before 500 kW). We also did the right side. Now here is where in the past I would have breezed through this and shown how it was piecewise and then went on with another "math-class" piecewise function to work with. But a student pipes up with, "ooh! I know the equation of the left part of the graph". This got us on the path of finding the 2 line equations, and seeing what and why the slopes are what they are, and discussing point-slope form (the forgotten quiet nice guy in the class of line equations) vs. the ever-popular-player-guy "slope-intercept" form of the line equation. We set them up and discussed that those equations go on forever, so how do we show someone where it's restricted to. We then got it into an f(x) piecewise format and worked with finding f(32) and f(701) and describing what they mean.

Yea! For unexpected improvements to my as-yet-unwritten lesson plans.

One Week Down

Even if I do no other exercise, that extra standing around from about 7:30am - 4:30pm HAS to burn at least 100 cal/hr. ... Okay, so that's really not my only major impression of the 1st week of school.

Ninety minutes goes by fast. I was concerned that I'd keep clock watching during our block schedule, but the only clock watching I was doing was to make sure I had enough time to do everything. In the middle of class for one set of the days I had the kids stand up, and we discussed social skills and going to parties in the future with your spouse where you didn't know anyone, and you had to meet strangers. So they had to walk around and find out the first name and the "earliest memory" that person has. I started that 1st class by calling it "cocktail hour", without thinking and then had to backtrack and say "without cocktails" after we giggled and then add "please don't tell your parents we had cocktail hour in class" (cough cough). I then had my brain kick in gear and continued calling it "meet and greet time".

For all the grumbling I was doing about block scheduling, I like the fact that on Wednesdays and Fridays, I'll mostly have taught everything the day before (save for BC calculus eventually), so that it's a less harried preparation day.

I think I've solved my homework problem. I didn't want to give double homework, since I think they'd leave it all until the last minute and not do a good job. I didn't want to give the same amount of homework as with a regular schedule, since I didn't think it'd be enough practice. So. On Mondays, our "C" day where all classes meet, I will hand out (10? 20?) cumulative-from-the-first-day math problems that will be due the following Monday. This will be in addition to their regular homework. That way, they'll get the extra practice and the extra "dipping" and review of old topics.

I also took a cue from the "Mathematics Teacher" magazine, and this past Friday assigned to my calculus classes: research who discovered calculus and find out 1 - 2 weird/interesting facts about him/her/them. (on hindsight, I should have had them cite their sources).

I think future weekend assignments for precal and cal may include finding out about various math-related jobs. I may give 1-3 types and divvy them up per class each time (civil engineer, architecht, physicist, etc.) and have them find out specifically what they do, schooling needed, average salary, who hires them, and anything else I can think of when I solidify it a bit more. This way throughout the course of the year, they'll be exposed to more possibilities than they may have thought of before. Maybe we'll make small posters and hang them in the halls.

Surface Area Activity

In a workshop last Saturday we did a cool activity that I have to share. It wasn't new to some people, so maybe I'm the only one who's never seen it. Each group of 2-3 people was given an orange (try to get them as spherical as possible), some wrapping ribbon (or string, something to measure the circumference with), a compass, a largish blank sheet of paper, and a calculator (later she made sure there were wet wipes to clean with). We were going to estimate the surface area of a sphere.

1. find the circumference of your orange with the ribbon. Be accurate.
2. using this measurement and prior knowledge, find the radius of the sphere.
3. with the compass draw 6 or so circles with that radius.
(teacher checks the circles before kids proceed by placing orange on top of circle and eyeballing)
4. peel the orange and fill as many circles completely as you can. (only the "orange" part is the surface area)

It was great, we fit exactly 4 circles, (which are of area pi*radius*radius), so voila we had an estimate of the surface area. Ooh aah.

We're BAAAaaaaackkkk

Official teacher inservice started this week. We had a gentleman come in and teach us some strategies for engaging the students. Some ideas:

A-Z review - in a group they make a small poster for a particular topic and think of terms for each of the letters (we did "dating"). In math, I guess you could be general and do "math" or maybe "geometry", etc.

A $20,000 Pyramid type of game (I think) - you play in pairs, player A has a hidden index card and mentions the subject to player B (say calculus), and then there are (say) 6 terms on the card (derivative, integral, MVTh ...) and then player A tries to get "B" to say the terms by just giving them clues.

Make an appointment - he gave us a sheet of paper with some time slots: 9am, 10am, ...., 3pm, and we were to walk around the room and make an appointment for 9, 11, 1, & 3 o'clock with 4 different people, 9 & 11 were to be in our subject area, 1 & 3 with others. Then throughout the day when he needed us to pair up, he said, "go to your 3pm appointment and ..... ". I guess this is a way to get students to work with people outside of their small circles and comfort level (find someone who is ...) , and it gets them moving around to make the appointments.

There were other activities, too, so now I feel I have a nice treasure trove to pick from.

We also get 1.5 hours each day this week for lunch. Ooh la la. That will be a big shock when we go to 30 minutes this year!

Teaching Analogy

It's Saturday, and I was at a math inservice today. After initial grumbling (wa wa wa Saturday ... wa wa wa school hasn't even started ... wa wa wa pity party), it turned out to be a very useful day. We discussed and saw examples of what made preAP assessment questions of "preAP" caliber (options chosen from multiple representations, using variables and symbols in the question instead of all numbers as coefficients and constants, testing future topics in a scaffolded way,...). I also talked with people who had taught block schedule in HS math and got some good ideas.

I loved this analogy:
Think of a student and his/her learning as a candle being made. You have to keep dipping the wick in wax, and some of it sticks the first time and as you keep dipping, more and more of it gloms onto the wick and eventually you have a finished product. ... so basically another way of plugging for a continual refresher of all topics even though they may not be in the "current" unit, so that the more times a student sees something, the more chance the knowledge have of sticking.

And finally a student joke (old?) that still makes me giggle:

Knock, knock.
Who's there?
Interrupting cow.
Inter .... moooo.

Judgmental Cookie discusses Lock-Step Teaching

Ew. My math specialist friend is going back to teaching and being an instructional coach at a school that is apparently "2 steps away" from being closed due to low scores on the state exit exams. She mentions that every math subject teacher will now have common lesson plans and will have to teach the same things and plan together and do the same activities because the school is in trouble and this is their (last-ditch?) effort to right things.

That sticks in my craw. Suppose you have a teacher that is not successful and needs some help and suggestions on how to present a topic. Just because they're using a from-above sanctified activity, does not mean that it will automatically be successful. The same qualities of their teaching that makes them not successful will still be there with this worksheet (or such).

Sure, make sure they're covering the same topics, but then go in and make general teaching suggestions and follow through and update and check up on the teacher to measure if there's progress made. Don't stifle potentially new and better ideas and creativity by dictating what and how one should teach. I know my friend will do all of these things as she is awesome, but this "everybody does identical work" thing does not sit well with me.

This also does new teachers a disservice. If everything is handed to them/us, they/we will probably never learn to create their/our own activities and will always be at the whim of the textbook companies and such.

Ew.

Vicious Cycle

My Baton Rouge friend has a 4.5 year old and has to start thinking about school choices and is in a mental tug-of-war. From what she has heard, the public school system is not stellar, and since it's not stellar, many people choose to send their kids to private schools. And since they pay private school tuition, they LOUDLY squawk when asked to pay for public school improvements. And since no money goes into the public schools, then it stays not stellar.

She wants to believe in the public school system and support it, but then she's torn because she wants her child to get a good education. It's easy for me to have a knee-jerk reaction of "well put your child in public school and then work as a community of caring parents to change it" and then on the other hand, I don't have children, and I don't know what I'd do in this case. I know what I hope I'd do, but who ever really knows until they live it? Everyone wants the best for their kids.

The high school I teach at apparently has a nonstellar reputation, and people around the community think nothing of mentioning that to me. But then I teach at the school, and I know some of the great things that go on there (in addition to the bad things), so how much stock can you put in a reputation. There are good and "bad" teachers and admins and students everywhere and every school has problems of some sort.