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.