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.

My Summer Vacation

I read about the cool "Red Scarf" project over at Now Norma Knits and watched the video here and am now in the process of making this:

What a great idea that provides care packages for college students with no traditional family support. I remember diligently checking my mail for letters and cookies and such from my friends and family. I guess I still do, so I'd better get busy writing cards and letters of my own, so that maybe some day my box will be filled with stuff other than bills and junk and the ever-popular BedBath&Beyond 20% off coupon that you'd better USE NOW because you won't be getting another one for at LEAST a week.

I'm also furiously working on this which I need to finish before Wednesday, so I can wash it and have ready to go for my brother-in-law's wedding. I didn't want to make a full "bed" quilt that they'd have to politely use even if they didn't like the color choices, so I made a size that's suitable to cozy up with on the couch when you're watching the telly. Well, "made" is used loosely as I'm not done and am blogging instead of working on it.

Okay, off to the sweat shop ... or is it snack time?

It's Who You Know

I just returned from visiting friends in Louisiana and East Texas. Both women are active activists in their own way. One is volunteering in various ways with the Katrina aftermath, and one is highly involved in animal rescue and fostering and placing of animals.

My "Katrina" friend is surrounded by people doing good and being a community and her outlook is that people are inherently good. My "animal" friend sees the worst that people can do to animals and sees people as inherently evil. This has become a second-nature thought for both of them.

Growing up I was surrounded by a dysfunctional, alcoholic, ethically-challenged, "the world is out to get you" family, and I was sure I didn't like people and ultimately wanted a job where I worked in isolation. After I went away to college and met different sorts of people and grew up and saw "good", my outlook changed.

So now when I see my students in class and they behave in a variety of good and bad ways, I rest assured in the fact that the "bad" behaving people can only benefit from being repeatedly exposed to "good". Even though this may be how they act now, that doesn't mean that will always be their behavior.

Survey

Thanks, Tony, for the idea. Just out of curiosity, which ones do you think of as bottles when you look at the pictures? (ooh, pretty small picture and letters for an old lady's eyes)

Jar or Bottle

Last night at dinner I was opening a small spherical glass container of mustard, and my husband and I got into a discussion on whether it was a jar or a bottle. Then we started thinking of other glass containers and tried to sort them into the jar and bottle camps. Yes, I know, scintillating. Tonight maybe we'll discuss pennies: pros and cons.

Of course then I started thinking of geometry when we hit the unit of being precise with definitions of triangles and squares and such. I looked up the jar/bottle definitions via google, and I'm not completely impressed with the output. The word "wide" is used, and I think that's subjective. And the jury is still out on the mustard bar/jottle.

Enthralling Book

While I was on vacation up north, I read Rafe Esquith's, "Teach Like Your Hair's on Fire" and loved it. Even though he teaches 5th grade, I still jotted down notes on things I want to explore and think about later on for my high schoolers. Some things that resonated with me (that my tired brain can remember while my lazy body does not want to go upstairs to retrieve my 4 pages of notes):

* don't settle for mediocre
* incorporate art somehow into your curriculum
* teach manners and behavior (he lists 6 levels and has his kids strive for the highest) ***
* assign short term (1 week) and long term (1 month) projects consistently to teach time management (hmmm, this one I'd have to think how to manage and teach)

*** (the levels came from another book and were of the effect:
1. I behave because I don't want to get in trouble
2. I behave because I want a reward
3. I behave because I want to please someone
4. I behave because I follow rules
5. I behave because I have empathy for others
6. I behave because I have my own moral compass and want to do the right thing because it IS the right thing

There's much more, and it was an inspiring read.

Living in the Neighborhood

I live in a different part of town from the HS at which I teach, about 40 minutes away. Though I could do with a shorter commute, I do like the fact that when I go out in public, I don't have to have my teacher persona on all the time. I can go out without makeup and in shorts and a t-shirt and not look over my shoulder when I buy feminine supplies at the grocery store and such.

Today my husband and I were out doing a chore way down by my school. I was grungy looking, and we were hungry, and I remembered a great food place to stop at. My stomach won out over good sense, and we stopped in. I got lucky and didn't see any students while we quickly downed our food and made our escape. Whew.

Summer Slugfest

If I could get a guarantee that I wouldn't blow up enormously and be unhealthy and start to smell, I think I could pass all my days lolling on my huge couch reading, knitting, puzzling, quilting, napping, movie-ing, etc. As it is, I already sit around more than I do during the school year, so I'm having my 3rd annual let's-gain-summer-weight festival. I am lifting weights and doing step, so maybe it's all muscle. Yessssss, muscles that are so big, that my pants are getting snug. As a weight lifter (cough cough), it's hard to find clothes to encompass my muscular thighs.

Okay, off to do step and get one "step" closer to a beach body. But, as my friend reminds me, there are all sorts of beach bodies.

Blogging Question

I would like to create a website for the next school year that contains my homework assignments and news for each of my classes. I looked at schoolnotes.com and classhomework.com, but there were various things I didn't like about them: ads, layout, accessibility, so I'm thinking of simply creating a blog that I can update daily after school gets out.

I would like to have the blog divided into different math class sections, so that a student or parent can simply click on, say, precalculus, and that information is all in one place. I have not found this capability information on the web, but I believe I've seen it on other blogs (that I of course can't find now). Is there a simple way to do this with an available template, so that I don't have to write (much?) html code?

Does anyone have insight into this? Thanks in advance.

Large Classes

I was talking with my "math specialist" friend the other day, and she mentioned that she went to the NCSM meeting in Atlanta and heard something interesting. One gentleman was doing preliminary work on class size and found that some higher performing schools had up to 40 students per math class. Can you imagine? And, they seemed to do better by whatever scale they measured these things by.

His theory was that with 40 students in a class, the teacher does not have the time/resources to help each kid individually, so the kids are forced to fend for themselves and help each other out, and the process of this involves them talking math to each other and forming their own knowledge and this in turn makes them retain things better.

Either that, or maybe it's a sink or swim situation. Maybe the kids that are discipline problems or such somehow are weeded out. I don't know. But the talking it out theory gives me something to think about even though I don't have THAT many students in class.

New Principal

Next year we're going to have a new principal. We don't know who it is yet, and I don't know if they've even hired him/her (himer? herm? himher? them?). I guess I'm feeling like the kids feel at the start of each school year:

Ooh, new teacher. Will she/he be nice? Will she/he like me? Will I like her/him? Will he/she do a good job? How long will it be before he/she knows all our names? What can I/I expect?

Block Schedule

Next year our school is going to block scheduling. I'm not too happy about it (how will I successfully get the students to practice good skills every day? how can I adjust the topics so that they learn all I want them to learn? how in the world did they get 20% more work out of us without paying us 20% more?) , but since it's happening, I will use the summer to get ready. My strategy is to read a book our school provided for us (Teaching to the Block) and to scour the internet for ideas. We're going to an ABC block, I believe, Mondays (C) all 8 classes, T/Th (A) 1,3,5,7, W/F (B) 2,4,6,8.

Things I need to do:

* Plan a toolbox-full of ways to structure each class in general so they don't sit in one place for too long.
* Rearrange the topic list (especially AP calculus) so that we learn enough.
* Other stuff/issues/challenges I'm probably not aware of yet.

On top of that we're starting school 2 weeks later than usual, and I'm stressing about finishing up my AP Calculus topics in time to review for the AP exam. Deep breaths. I can do it.

Learning

This past Saturday we had our last full-day National Board Cohort meeting before the summer. Again I learned things about learning and teaching since I was in the student mode. For one activity we were to learn about 3 of the 4 portfolio entries we were to submit. There are 3 HS math teachers going through the program, so we each learned one and then "jigsaw" taught each other. There was a sheet of paper we were to fill out with prompts for information we needed to focus on. I liked this scaffolding and want to adapt it next year to help the students get used to reading math textbooks. I did a bit of it last year, but I think with our new textbook adoption, the new books will be more readable.

I learned that I hesitate to ask questions when the others seemed to be working so efficiently. There was one prompt I couldn't find an answer to, and instead of "looking dumb" and asking the others, I floundered around for a while. Sheesh, it gives me empathy for students not wanting to ask questions and such.

I also learned that I didn't like the jigsawing too much. Maybe I'm too much of a control freak, but in the back of my mind, I kept thinking, "well, I can go over this more carefully myself later". Or maybe I'm missing the point. Maybe each person concentrates really well on one topic and learns it to teach it to the others and then when the others are teaching their topic, you're to go along and skim the pages while they're teaching and ask good questions and learn that way.

We also did this brainstorming activity where we were to write down all our teaching duties and accomplishments and how we contribute to the profession. The leader gave us sticky note pads, put us in a group of 2 or 3, and we were to write one accomplishment per note. Then we were to share with each other and combine the notes and organize them into categories. At the beginning of the activity (come to find out afterwards) we were all thinking that we didn't do much and how could we think of anything. Then through the discussion with our group mates, things one person noted prompted us to remember more than we could if we were by ourselves. And then the organizing of it all made it all stick in my mind more effectively. So, I don't know how I can use this as a teacher, but I know there has to be some learning task which lends itself to this in math. Not just remembering of facts or processes, but something.

It's REALLY the last day

We just have to go in today to check out and pack up and celebrate our successes. Also, our school is named after a still-living phenomenal educator, so this person will come to our last luncheon. Good times.

Ultimately, I can say that I had good kids this year. Translation: no mean-spirited, nasty-in-class, drag-down-the-atmosphere students. Whew. I even ended up liking my pain-in-the-butt will-you-stop-TALKING students.

I had a student leave an interesting comment in my "year book". Now this kid basically stopped working in AP Calculus. He did not turn in one shred of homework the last 6 weeks. I was constantly on him, but not effectively. Anyway, in my book he wrote, "thanks for caring enough to bug me about my homework". Hmmm, that gives me incentive to keep it up.

I also worked graduation. This year, I was not in charge of a row of students, but got to stand in the back. At first I felt like an extra, but then I saw the great advantage here. As the kids filed back to their seats from walking the stage, I was in a prime hugging spot. And boy were there lots of hugs and tears. I've known a ton of these students for 3 to 4 years. I lost it a couple of times just thinking about not seeing them again.

I also snuck out "early" one day this week after finals for my 4th annual end-of-the-year matinee (Waitress). I'm usually either the only one in the theater or there's at most 2 other people. This year, there were about 10-14 people. What I want to know is, why aren't you at work people? Did you all just get done giving finals? Maybe today I'll start my 1st annual 2nd matinee during finals week tradition (Namesake).

End of the Year

Yippee! One more week of school, and it basically is all finals. Love. It. On Friday I gave my AP calculus students an in-class "final" of writing either a "Dear John" or a love letter to calculus. I handed out colored paper because for some reason, things are just more fun to do on nonwhite paper. Shockingly :), most of the letters were of the "we're breaking up" variety. I gave them specs that they had to have at least 2 compliments with explanations and at least 2 faults with justification and that they had to add something extra to "wow me" and that it had to be a page long.

Boy are they creative. Some highlights:

"I like you sister, precalculus, better"
"Things were fine until I met your crazy relatives - related rates"
"You're too complicated for me. I need a simple relationship"
"How dare you cheat on me with Physics"
"p.s. you're following me to college, not the other way around"
"thank you for making me feel special. You made me feel like I could do any problem that was thrown at me"
"I love how you make me think all the time, even though sometimes you hurt me"
"It's not you. It's me. You're cutting into my personal time"
"We had our problems and had to get counseling from Ms. Cookie. Then things got better"
"You pushed me to the limit"
"I know I won't miss your related rates, which relate to my painful headaches"

Doing Your Best

There's a girl in my precalculus class, a junior, who has spotty attendance, and by that I mean that there have been weeks at a time when she would show up maybe 3 total times. I had her 2 years ago in geometry, so I know her. I also asked her algebra 2 teacher from last year if she had any problems with her, and she mentioned her multiple absences.

When she came back from her last absences, I asked her what the deal was in a nice teacherly way, and she just shrugged. I asked her if everything was okay, and she said it was, not too convincingly. I asked her if she had someone to talk to, and she nodded. She said she was trying. So I basically left it at that, and said that if she needed help to please come in, and to make sure she got caught up.

Well, she keeps saying lately that she has a ton of work to turn in to me, and that she keeps forgetting it. She also came in after school today and got tutoring. And I don't mean the fake tutoring where the student makes a show of getting help, but just wants to quickly complete the assignment just to get the grade. She was asking good questions and actually getting it. I have a good feeling that she will turn in all her work that she's missing.

... I've started this new exercise program with these videos of weight lifting and cardio, and the trainer has all these goofy sayings, but one keeps running through my mind: do your best, and forget the rest. What a great thing to live by. As long as you're putting out your best effort, it doesn't matter what others are doing, it doesn't matter if it's not "good enough". If you can honestly say you've done your best, then that's what it's about. Now I don't know if it's this girl's best effort, but maybe it's what she can do right now. At least she's coming back and not just shrugging her shoulders and giving up because it's too much to make up. Go her.

Recent Reminders

* Sometimes students are happy when you change their seats away from their friends. Now they can concentrate on the lesson.

* Students don't always make the right choice about how they choose to study for the AP exam. No, it's not a good idea to just let them work problems without turning them in. It's too easy to let it slide.

* Just because 7th period made you grumpy, it's no reason to start 8th period in a bad mood.

* Snacks are always appreciated and may even make some students work more effectively.

* Learning is hard work. Humor helps.

Memory Tools

Yesterday I had passed out a colored sheet of paper and asked my calculus class what topics they want to review as a class and also any suggestions on how we spend our class review time. They were to list a topic, and if their topic was already listed, they were to put a check mark by it, so I could gauge popularity. One of the topics they stressed was derivatives of trig and inverse trig functions.

Today, I listed the 12 trig and inverse trig functions on the overhead and discussed memory tools I had for the derivatives of the 6 trig functions (all the "c" ones are negative; there's always 2 secants and a tangent; cotangent is like the pesky little brother of tangent and wants to be just like him; cosecant ditto to secant). Then I gave them 3 minutes, and they were to come up with memory tools for the inverse trig functions. I didn't know how it was going to work, but there were several good discussions going.

As we met back as a class, the ideas were slow at first, and then I don't know what happened, but as a class they came up with several good ones to remember the derivatives of the inverse trig functions (sin^(-1), cos^(-1), ...):

* if the name has a "t" in it, then there's a "+" (1+xx) which looks like "t"
* if there's an "s" anywhere in the name of the function, it involves a "s"quare root
* anything starting with a "c" has a negative (think grade c-)
* we learn sine and cosine 1st, so those are "1-xx" (as opposed to "xx-1")

Whew! I think those may even help me remember the inverse trig derivatives :).

Review

Yesterday I gave a mock AP calculus exam for my students while the rest of the school population was taking the state-mandated exit exam (yay TAKS). Three hours and 45 minutes or so of testing. Oh my goodness. For the most part (aside from doing some chores here and there), I took the BC exam with my students. Whew! I got exhausted from the extended mental challenge, so I can empathize with them when they come back from the test looking drained.

I can also empathize with them on another aspect. This is the first year I'm teaching BC, so it's the first year in a long time (and maybe ever for some topics) that I've seen various things: calculus on polar functions, on series, parametrics, logistic growth, etc. And in my treadmill type of year, I haven't revisited those topics since I taught them weeks and weeks ago. So. As I'm taking the exam and the topics come up, I felt like the students. I remember seeing the topics. I know I understood them when we were doing them. I'm not a stupid person. I just don't remember the details on some of them. I guess I must be human.

Here's to me not thinking of review in class as a "wasted day when we could be learning something new and why don't they review on their own what kind of students are they and I'm enabling them by hand holding them through a review oh my gosh the next thing you know I'm going to have to wipe their noses for them". Here's to me thinking of a review as a necessary part of the learning process that's worth "taking a day for". I could also think of it as money in the bank for the later part of the year when we take many days to review for the actual exam. Maybe it'll be an opportunity to think of memorizing tricks.

Aside: as a class we came up with a good one for memorizing the Taylor series expansion of sin x, cos x, and e^x. The sine function contains the odd numbers of the pattern, the cosine contains the even numbers, and the e function contains all the numbers in the pattern. So. The "i" in sine looks like 1, and that's odd. The "o" in cosine looks like zero, and that's even. And. "e" for everything. Woot woot. It worked as I was taking the test.

Class Atmosphere

Last night in tap dance class, as sometimes happens, the teacher started teaching us a combination I swear at a revved up speed. She kept showing us the steps (say 8 sounds) quickly, and before I knew it it was over and I'd maybe got one sound. Then she'd do it again and I got the 1st and the 2nd sound. Then again, and I got the 1st, 2nd, and 3rd sound, etc. I was getting frustrated. She was getting frustrated. "Come on people. These are all steps you know. This class is about putting these steps to a different rhythm. If you're not getting it, then you're not practicing your basics at home. You've all seen this before."

I had a teaching epiphany. I eventually got the steps. But she was going too fast for my comprehension. She was chastising us for not practicing. It wasn't that I didn't want to learn and master the steps, it was just that I needed it taught in a different way. I started getting mad at her, and I didn't even want to hear the sound of her voice. It wasn't MY fault, it was HERS, I muttered to myself.

Then I thought about my teaching. I could see myself in class getting frustrated (hopefully internally) with the students as some of the them struggle with basic concepts that we've gone over in the past that I thought should be second nature to them, and they still didn't get it.

I hope to remember from last night's experience that everyone is human, people have a lot on their minds. It's not that they don't want to be successful in class, they just need a diplomatic reminder of past concepts and a helpful hand to guide them to understanding and mastery.

Moment of Clarity

I'm going along, happily teaching logs and 10^x and e^x and ln(x) and making sure to put in cool examples and practice and descriptions. I especially was proud of my continual stressing to them to ask the question of themselves, "what is it asking for?" when faced with the equation y = "log base something of something".

I made sure to stress that log of a particular base can be rewritten in an exponential form and visa versa, and I said that they basically represent the same information. I also made sure to stress that logs of a base and that base to a power are inverse operations of each other. Can you see where I'm going with this one?

Well. Today when a student was reviewing for a test she casually mentioned that in the equation y = log a c you can just replace the right hand side with a^c because it means the same thing. Argh. Big miscommunication. I hopefully cured her of her nonunderstanding, but how many other kiddies are lurking out there thinking the same thing?

Random Things

I like when I individually tutor my kids after school, and in that 1-on-1 time, it's easier for me to probe their misunderstandings and ask the right guiding questions to get them on the correct track to solving a problem. Then I can use that information later in class because I'm sure that there are others having similar problems.

I like how being part of the public education system and interacting with kids every day forces me to take a deep breath and start anew every day even when I had a rough day yesterday and REALLY disliked a particular kid's behavior. I have learned (mostly :) ) to dislike the behavior and not (mainly) the kid (on a good day). (apparently with all my "(" and ")", I still have some learning to do).

I like how I constantly learn things from my kids. The other day 2 students were talking, and I didn't hear what the boy said, but I heard the girl's response, "wow, that was really gross. I don't know how to respond to that", and how she put it back on the boy instead of being embarassed.

Playing Catch Up

Hey, maybe someday soon I can come up for air from beneath all the piles of grading that are taking over my classroom desk and spreading to other pieces of furniture. I sure miss having my student aid (who got pregnant and left and is now only coming to school part time). It doesn't help that I went on my 3 trips (2 over spring break and one to NCTM) and didn't take papers to grade. ... Get over it and grade.

I remember when I first came to Texas 4 years ago and went to a local math workshop and somebody casually mentioned that she collects and grades homework EVERY day. Me, coming from another school district in another state, who only glanced at homework in class at most 3 times a week, I was stunned. Who has the time? Ew. Now I've joined the land of daily graders (only on completion and effort, though). Apparently, I'm not a full-fledged active citizen yet, though.

NCTM

I just got back from NCTM, and as usual, absorbed some great math and bought some potentially useful books. I loved Steve Leinwand's talk. He made several good points. For example, he does (did?) 5 minutes of cumulative review EVERY day. That adds up to 15 hours of instruction a school year, and his argument was that no one learns a topic after 2 lectures and 2 homework assignment. They need refreshers. He also uses the review to pause and point out meanings of various vocabulary terms, indicating that the really low-performing students are stunted by their lack of knowledge of what you're talking about (meanings of math terms).

I also learned a great calcululator trick. To graph a piecewise function, you can do it all in Y1 as:
Y1 = (x+1)( x<2)
+ (3x-7)(x>2)
all on one line to graph x+1 for values less than 2 and 3x-7 for values greater than 2.

A North Dakota teacher discussed how she teaches polar graphing of limacons and lemniscates and flowers so that it sticks in the students' heads.

I bought books on differentiating instruction for high school math (woot woot, you never find it for this level and this topic) and a "share & compare" strategy book for math. There's also a math joke book from Nasco for calculus I had to have.

Someone shared with me that the fun math ladies (?) instead of always putting name_____ on the top of tests vary it like:

math star ______
_______ loves fractions
future mathematician _______

etc.

So all in all, useful conference.

Saving Weekend Time

I used to be so excited that I found a way to wash my overhead slides on the weekend. I'd put them in the sink with water, and then swoosh them around one by one and rinse of the excess ink and then put them in between pages of a large phone book.

I used to be so excited ... until it started taking about 45 minutes or so every weekend ... that's when I started slacking off on the job and cursing the slides.

It finally clicked in my head, and what I'd seen many others do and I hadn't been "ready to learn yet" ... well, I finally got it. So last weekend I bought a small spray bottle (5" high or so), and confiscated some of my husband's tired old holey socks, and this week so far, right after each class, that's me. Spritz, spritz, spritz. Wipe, wipe, wipe. No weekend slides. If my calculations are correct: about 5 slides per class x 5 classes x 5 days each week = a bazillion slides I now don't have to dread cleaning each weekend. Bring it on.

I Don't Trust Past History Enough

Every year when I get a new crop of students, we go through an adjustment phase. With some students and classes, it's immediate. With others it takes a while, and with the few rare others, summer comes, and we still haven't adjusted to each other. But like clockwork, every year about this time in mid to late February, we seem to hit our stride, and even though I may have liked or not liked so much various classes, then BY NOW, I really like them all the majority of the time. Yet every year I say, "no this year it's different. I'm not going to click with this class." And most every year I've been proven wrong (slow learner). I've started clicking this year.

A funny moment today: my last period class was trying to sway me to have some free time or something or another today, and they all start chiming in. I interrupted with, "this is not a democracy. It's a monarchy." And then someone piped up with, "yea, but aren't monarchs basically powerless?". We got back to our lesson.

Promoting Smart

Today I was out doing chores, wearing my PCMI t-shirt that says "Computational Complexity Theory" with an intricate Turing Machine picture. The teenage girl cashier at Target kept glancing at my shirt off and on while she was scanning my items. ... I choose to believe she was thinking, "gee it's okay to be smart" (instead of, "who's this geek I'm helping, and why is she advertising her geekiness").

In the current culture of idolizing celebrities and materialistic behavior with gucci this and prada that and who got botox here and who's divorcing what actor there, I want to start promoting smartness - not in the obnoxious "I'm smarter than you" way, but in the "hey, being smart and working hard is something good to strive for" way.

My list of t-shirt logos I want to make/buy:

Fractions Are Your Friends
Math Rules
Nerdy Girl
I *heart* Math

.... maybe I'll be crafty and make some with my school name on the back so that I can wear them on "spirit" days.

What Do Mathematicians Do?

I've had this inkling of an idea for a while now, but I never seem to have the time or umph to put it into action, and here comes a student after school today who reminds me. She wanted to know what you could do with a math degree and what sorts of jobs there were and what did the people actually do all day and did they interact with others or did they just sit and do math at a desk for hours and hours.

My idea was to interview different people who had jobs heavy with math duties and make posters to hang up either in my room or around the hallways. The posters would have a picture of the person, their job title, their degree, and various specifics about their job and how they got it and such. That's just the bare bones of the idea.

This student really wanted to know because she was testing out different versions of her future to see what would fit. After we talked for a bit, she said that maybe the students should do this for credit (or extra credit). Hmmmmm, I'd have to come up with the specifics and such, but it just may work .... or at least be worth trying.

Teaching in a Vacuum

Most times I get so caught up and busy in preparing and teaching and such, that I forget to talk to other teachers about teaching things or things that happen during teaching. Last Friday I had the chance to chat for about 10 minutes with another teacher, and now I have to remind myself to do it more often.

The day before had been horrendous. A kid had MAJORLY back-talked me in class, and wasn't even sorry about it. I found out my calculus answer manual had been stolen earlier in the week. I had the audit hanging over my shoulders feeling guilty because I hadn't finished it yet. And finally, I needed to finish the National Board Certification application.

So here I was having a pity party in my head and not feeling very chipper. I started telling her about the one thing (poopy kid), and she related a similar incident with "entitled" girls in her last period. I mentioned the theft over the weekend, and she said her room was in disarray (drinks spilled and not cleaned up), too, from some unannounced use of our rooms. I started feeling better, so then I mentioned the other 2 things, and she was also struggling to finish the tasks.

Whew! It didn't make my grief go away, but it sure lessened it to hear sympathetic noises from someone else. I must share more often and maybe find I'm not alone in these minor and major annoyances of the school day.

A Tough School

A senior was telling me today of her recent college interviews with alumni.

A little background here. Our school apparently has a reputation as a "tough" school (translation: people think that because most students aren't white that maybe there are more fights and drugs and gang activity here as opposed to the wealthier whiter schools around). I don't know what people imagine, but I'm guessing they think they wouldn't feel safe at our school. Who knows. I am a perfectly safe whitey, and I teach great kids. The only "poopy" ones are the few bad teenage attitudes in the halls when I (heaven-forbid) ask them to comply with various rules (hats, music, cell phones, wandering...), and I get that from a nice variety of races.

So anyway, this one alumni to interview her lives here, and one of her first questions was: "So is ____ a tough school?". My student replied, "yes, all the classes I'm taking are pretty challenging." (not knowing her implication). The lady asked again, apparently, in another way, and my student defended our school. Woot woot.

We then proceeded to be verbally angry with this woman. But I guess we're guilty of the same thing as she was at times. When we hear of ______ down the street, our wealthier/whiter counterpart, we conjure up all sorts of stereotypes about their monied existence. Whose misjudgment is worse?

National Board Certification

I've been thinking about applying for a while, and this week I went to an informational session for national board certification. It sounds like a TON of work and time, but it seems like it will be something that will force me to actively think about teaching and have the incentive to reflect more effectively. (and it's a ton of work and time). Our district is all gung ho about it, and will basically pay the ~$3000 it costs (youch) if a teacher sticks with the process. There's also the $2000 extra a year in the paycheck that doesn't hurt. ... Well, I have until mid February to decide.

Eye Contact

Last Wednesday I was at an all-day textbook adoption meeting listening to the publishers promote their wares. Interesting, tiring and enlightening all at once. There was one lady who talked very fast. I wouldn't have noticed it (maybe) if she hadn't been in a group of other speakers to compare to. But, sheesh, I found myself shutting down soon because I didn't have enough time to process her words before she moved on without a break. Then that got me to thinking about my teaching. I think I'm guilty of talking at that speed at times, and now I can see the effect it has on listeners. SLOW DOWN for processing purposes.

Another gentleman turned me off almost immediately. He was a professor and very engaging but seemed to be full of himself and at one point rudely shushed his co-speaker so that he could continue. Ick. Then I couldn't look at him for the rest of the time he was speaking. I listened to him, but I felt uncomfortable looking at him because of my distaste for his actions.

Other times at other talks I was so tired from sitting all day that I seemed to need to stare down at one inanimate object while listening to the speakers. That way I didn't have more stimuli than I could handle in the afternoon.

Of course, then this made me start thinking about my students and their eye contact with me in class. Sometimes I think they're not listening to me because they're staring off as I'm speaking, but then if I ask them about what I was just saying, they can repeat the information accurately.

The book(s) I loved were the ones with fascinating math history vignettes. There was love and duels and theft and all sorts of "non dry" tidbits for the kids (and me). I'll have to bring more of those into my lessons.

Sleepy (take 2,146)

Sheesh ... deprive me of more than 2 hours of my 8 hour sleep, and my patience goes out the window the next school day. I guess I'm used to it now, so about 60% of the time when I'm just about to snap at a kid, I realize that I'm a sleep-deprived zombie with no impulse control on the sarcastic comments, and I can stop them (the comments 60% of the time / the kids the other 40%) . I think I was okay about 62% today.

One funny thing. My kids sit in groups of 4, and when I pass out homework, I put them all on one person's desk in the group for them to pass out. And when I collect homework, I ask them to put them on one person's desk to be more efficiently collected. So I'm walking around while they're working on a calculator activity, after I've passed out returned homework and after we've gone over the current night's homework (but before I've collected it). I see a pile on one student's desk, and I assume he forgot to turn his homework back to his group. He's a funny kid that I like, and I jokingly reprimand him as I point to the pile, "hey! you've got DUTIES, mister." We look at the pile and then I realize that it's the homework I had yet to collect, and he turns to me and says, "no. YOU'VE got duties." Oops.

Student Insights

One of my students came in before school last Thursday just to use my room as a study place for her vocabulary quiz that day. She was mildly grimacing about a variety of things such as:

"I don't get the students who say their AP classes aren't preparing them for college. I'm studying to learn and honing my skills in the process. Whereas they're just doing enough to pass the tests."

(commenting on the fact that I'm there at 7:30am even though I don't teach my first class until 11:00am) "Some teachers wouldn't be here until 10:30 even though they should, and they talk to us about responsibility and work ethic. It makes me sad for the world."

Another student in my precalculus class refering to the upcoming test:

"I don't think a lot of us know how to study for math (tests) because up to now we haven't had to, so we don't have the skills."

Another student at the end of the period after I had moved him for constantly chatting with this other boy:

"I think you should permanently move me so that I can learn better and not have to be rude to this person that talks to me ALL the time."

Snow in Central Texas

For the 2nd time since we moved here 3.5 years ago, it snowed in our city. Okay, snow, sleet, rain, pellets, snow. I guess the whole city shut down over 1/4 inch accumulation. On the one hand that makes me smile coming from NJ where we still would have had school today, on the other hand, I know they don't have the infastructure down here to deal with 1/4" of snow to have business as usual (and why should they).

On my 3rd hand (or 1st foot), school was cancelled today AND tomorrow. Woot woot for a 5 day weekend. Boo Hoo for at least 2 extra days tacked onto the school year now. On my 2nd foot, I'm going stir crazy since I can't go driving anywhere. There is quilting and knitting and web surfing and reading and puzzles .... oh yea, and schoolwork that's sitting lonely in the corner (LiC), and AP calculus audit work (LiC), and textbook committee work (LiC). Hey, they should get together and complete themselves, so that I don't feel too guilty for choosing crafts over work. Tomorrow I'll work more .... yesssssssss, that's it.

Blocks & Pieces

BLOCKS

Well, it looks like we're going to block schedule next year. Blach for 3 reasons.

1. "Higher Ups" kept up the pretense of asking for our opinions, but those never seemed to be addressed, and then suddenly the decision seemed to be made.

2. I'd love it if someone would prove me wrong, but now I teach 5 classes of students, and so have approximately 25 students per class (and more often more than that). With block, I'll have 6 classes of students, and so will have 20% more students/papers-to-grade in the same amount of time for the same amount of money. Texas is going towards (to) 4 years of math per student, and now POOF they will have more teacher hours in essence for free. I do NOT mind hard work. I WORK hard to make sure I'm doing a good/great/acceptable-to-high-standards job. I DO mind being taken advantage of.

3. I think students need daily math practice. I think they need time to absorb material, so I can't necessarily cover 2 topics in one day and expect it to be successful.

PIECES

I just introduced piecewise functions to my precalculus classes on Friday. The first year I taught it, I was surprised it wasn't a "gimme" topic. Students were confused by the notation and couldn't always successfully graph/analyze/use such functions. The second year, I tried a different way of teaching it, and still I had more confusion than I was comfortable with. This year, I think I nailed it. (famous last words??)

I started with an electric company example where they charge 10 cents per ___ for the first 500 ___ of electricity per month and 15 cents per ___ for anything more. We talk about why it may be structured that way. I stress the company charges per partial ____ too (continuous). They get to the point where they see the shape of the graph. Then I keep alluding back to this example later to make the connection.

Then I make sure they have colored pencils and a fresh sheet of paper. On the top (as I do on the overhead), I make them draw a number line across the page from -5 to 4, say, (spanning the whole page). I break it into 3 regions and 3 colors and talk about neighborhoods and if x is in one neighborhood, f(x) is ___. Then in the appropriate colors RIGHT under the number line in the correct neighborhoods, we define f, and make a table (all in the right color). Then on the bottom 3rd of the page, we make a coordinate plane, where the x-axis lines up directly with the one at the top of the page and graph the pieces in the right colors.

Then I say, that's too much work to explain this way every time, and we're "lazy/efficient", so here's the shorthand way of writing a piecewise function, and with the same pieces, write it as normal and make the connection with what each piece means. Hopefully, this year, it will be a "gimme" topic.

Vacation's Over

It was a nice long one. One great thing about Texas is we consistently get 2 weeks off for the holidays. I had a chance to sleep in about 8.5 - 9 hours. Luxury.

Things I want to concentrate on this semester (or make further progress on):
1. I'm trying to assemble a workable plan for getting the kids to keep track of their grades. I know as a human it's always easier to sit back and let things be done for you: how many homework assignments are you missing? what's your current average? My rough plan is to make a blank skeleton sheet with room to write each assignment as it's given and turned in and returned. This sheet will be turned in weekly for a grade ... how feasible is it that I will check its accuracy? Maybe that's a quick scan on the grading program. Maybe it will also have room for a parent's signature and comments.

2. I keep thinking about but never actually doing this: teaching kids some simple ways on how to effectively use their notes. Sticking points for me: how do I get them to buy into it, how do I assess their attempts?

3. Okay, my baby step is to read my brain-based learning and teaching for memory books at least 30 minutes once a week, and by the end of this next 6 weeks incorporate one new strategy until it's a habit for me.

Difficulty vs Rigor

We had an interesting math department meeting yesterday to discuss ways to bring rigor into our classrooms. One activity was to look at a series of math tasks and deem them "high rigor" or "low rigor". For example: "Find a smallest integer that has exactly 13 factors". (note: we weren't supposed to solve the problems, just determine their rigorousness ... though being the math geeks that we are, we had to discuss solutions and attempt some problems).

Different people had different perspectives (shocking :) !). We had discussions on, "well, if you just taught the concept for some of these problems, they are low rigor" ... "if a child sees this problem a couple of years after it was taught, it will be hard for them .... does that make it rigorous or just difficult?" ... "is there a set definition of rigor?" ... "can you have a rigorous problem that is accessible to all levels of students in one class?" ...

One More Week (yippee!)

It's all over except for the "tired lady making and grading the finals" for next week. Most of my kiddies have been really good about using class time and homework time to study. Most of my homework has been of the "go through old tests, reviews, book work and redo 10 problems that are challenging for you from a mixture of topics" variety.

I'm also about to get the last batch of cards from my 2 calculus classes to bundle up into books. I had everyone in class write on an index card something nice about every other person in class and decorate the card. They also had to write a card for themselves in which they list memories of this year and things they're proud of themselves for. Then on finals day, everyone will get their own book of memories from the class. There are some great cards that have been turned in (lots of thought and effort), and there are some "eh!" cards .... I guess it represents the different types of people in class.

I've also had my precalculus kiddies make a "cheat book" out of colored paper that they can write formulas in for their final: fold an 8.5" x 11" paper hot dog, hamburger, and twice more in the hamburger direction to get 8 squares when unfolded (4 down and 2 across). Then you strategically cut the middle 2 folds (fold in a hamburger fold and cut from the folded part up to the middle so that when opened and held in a "regular paper" direction you have a vertical cut in the middle through the middle 2 "squares"). Then fold paper into hot dog, holding out at the ends, and "squish" in, so that a + sign appears when looking at the paper. Then while looking at the + sign, fold all the segments of the + sign up, and voila you have a booklet ... "sharp creases are your friends".

Three Student Interactions

Act 1: I have a stacked AB / BC Calculus class with about 13 BC students (and those with a mix of kids that took AB last year and some that haven't) and 6 AB students. We've all done the best we can (well, most of us), and I'm differentiating up the wazoo, and today was a topic I'd covered for some of the kids last year. So. I had a worksheet with 16 problems and let the "oldies" get started on it independently. I taught the "newbies" what's what, and we worked through 3-4 examples from the sheet. The rest of the worksheet was for homework. One of the "oldies" comes up to me after class and says, "I just wanted you to know that we only got through 6 problems, so if WE can't do it, don't expect the new people to finish their homework tonight", in a patronizing sort of way. Oh my. Get over yourself, is what I say.

Act 2: In that same class, at the end, I made the announcement that next semester, if they still want the AB designation, they may think of switching to the other period which is ALL AB and goes at a much slower pace (as it's designed to do). Something for them to think about. Also, if they wanted to stay in this period, they'd go on independent study and just review while I moved on with the BC students. So. Later on, a friend of some of the students in that class who does not have me for math this year, but comes by to visit as I've had her before, comes and says to me (in what I think of her ever so helpful voice), "I wish your BC class wasn't so hard that people had to switch down to AB". OH MY. What was today? Give advice to teacher day?

Act 3: I guess my speech the other day about passive learning actually sunk in to some students. A kid that is bright but has been coasting (and not to well) on his former success in math by just breathing, is not doing so well in calculus with his old ways. We had a discussion about his notes and about how he could use them more effectively and such, and he seemed genuinely surprised at the suggestions, like it had never occurred to him to read over his notes every night to refresh his memory ... or to go back and look at examples in his notes for suggestions on how to do problems. He mentioned something about, "well, hmmmm, maybe I'm being a passive learner like you had said." Hopefully, this will spur him to action.

"What are finals?"

I have a German exchange student in one of precalculus classes, and this was her question. Soon to be followed by, "are they hard?" after I'd answered the first one.

I'm trying to promote less passive learning since I see the trend at this school is: what's on the test? are you going to give us a review packet? oh! SATs on Saturday? Did I study with a workbook or online? No, why would I do that?

My first review assignment last week was: create a list of at least 20 topics that we've studied so far (I prompted them for suggestions on where they could find such crazy information: book, notes, test, homework...). Number the list, and by each topic write 2 things: approximate date "learned" (tee hee), and E/M/H for the difficulty level you experienced then and/or now on topic.

My next review assignment: choose 10 of the most challenging topics for you, and on an index card on the front write topic and a representative problem. On the back write a correct, worked out solution and maybe some hints to yourself. "make it worthwhile for yourself. don't just do it to complete this assignment."

I talked with them about passive learning and gave them a pep talk about, "you could probably write the final because think about what I'm going to do: make a list, pick some representative problems ....". I guess I just want them to reflect on the topics, and even just the act of writing the 10 index card problems will jog something in their memory. I'm also hoping that this will give them an idea of how they can study independently in other classes/schools/college/SAT...

This weekend I want them to practice their cards ... and yes, I'll have some review material next week and spend some class time ... I don't know what else I'll have them do with their cards and such, but I should do something.

Parent Contact

I got chewed out through a string of e-mail messages with a parent yesterday. ... But first a little background. I teach juniors and seniors, and if there are problems, I mostly deal with the kids. I figure that it's time to snip the apron strings and have them take more ownership for their learning. It's worked for me so far, and I mostly have students step up to the plate. I still have parent contact, and I keep them informed of the grades regularly by e-mail. But... -

head on desk? make them sit up/find out they're working 40 hours a week or not sleeping/feel bad for them/keep prompting them to sit up.

cussing in class? stongly discourage it with humor/stern looks/constant reminder until it stops.

Not turning in homework? highlighting the fact to them/sending their grades via our grading program and e-mail to all available addresses/prompting them to come in for help/accepting late work/tutoring.

And if a parent initiates contact with me, I'll make sure they're on the e-mail contact list, and keep them updated.

So. This child is failing my class. She turns in her homework late, in a rush, during the last weeks of the grading periods. She has come in for help maybe 3 times during the year. She never turns in her test corrections. She "yeses" me about coming for help, but doesn't follow through. I still send home grades and progress reports every week and a half or so. I have never heard from the parent. Well, unknown to me, somehow her mother's e-mail address got "unchecked" in the grading program, and she hasn't been receiving this child's grade updates. The only way I guess she found out her current grade was to check her daughter's e-mail. (after thinking about it, I remember that the girl had come in one day and told me that her e-mail address had changed and gave me the new one. I didn't think anything about it, since we have many parents that don't have e-mail, and I had no reason to doubt her, and so I changed it. Bad move.)

Well. ...oh my god you're a horrible teacher...why didn't you contact me if her grades were so bad ... I see you've given up on her ... I'll be speaking to her counselor ... I'm not your average parent, I care about my child's grades ... and back and forth.

Note to self: Make SURE you have some working e-mail address for any potentially failing student.

Random Thoughts

* Sometimes it's just nice to have a full period of just practice on current topics without feeling you have to physically "teach".

* Kids that are chatty and goofy to you and seem to disrupt the class are welcome diversions for some other students ("thanks for making class fun").

* Sometimes students just feel like zoning out by 7th period because they've had to sit in their seats ALL day, and they're tired after lunch, and they need a brain break.

* Having kids volunteer to go caroling to another math class with your "fraction song" is fun.

* Some kids are so shy they never talk to their group mates, and so their groupmates never talk to them, and so the kid feels like no one likes them. Note to self: take another groupmate aside and ask her to make a special effort to talk with this shy one.

* Losing your school keys and STILL not finding them after 2 weeks even though you KNOW you opened your classroom door with them and then POOF they were gone is creeping you out.

* What stays in the corner but goes around the world?

Seating Charts

The natives are getting restless, and chatty, and so it's time for new seating charts. I used to feel semi-bad about moving them around and deciding where they sit, but now I don't. As I tell them
1. it's not fair to always have to sit in the back/front/etc for the whole year
2. it's nice to meet new people

I poll them on quarter sheets of colored paper before I switch seats, to see if they have issues (eyesight/air conditioner/strong dislikes...), and to see how everything else is going in class and in life. I've gotten various positive comments back about seating charts, and I've noticed students actually making new friends after seats have been changed, so I guess it's a good thing ... AND quiet for a while.

And if I remember, the first day after seats are changed, I make sure to put 2 questions on the overhead for them to discuss with their new group (they sit in groups of 4 seats) for about 5 minutes, and then we class share, so that they get a chance to be forced to interact and learn each others' names.

My Classroom Clock

Classroom Clock
Originally uploaded by math_mambo.

A couple of years ago my student aid showed me this great idea for my classroom clock, and I've used it ever since. Now my frazzled mind does not have to remember the quirky ending times of each period. I can just glance up and see how much time I have left for my fascinating mathematical lectures.

Practice

I bought an intriguing book a few weeks ago, and I've been reading snippets of it. It's about "how the brain learns", and I just read a section that gave me pause:

Practice doesn't make perfect. Perfect practice makes perfect. If a student is just learning something new and is starting their practice of the concept, but does the method incorrectly over and over at the start, that's going to stick in their brain and will be harder to unlearn later.

Well that's kind of scary, and I can see how I now want to rush around the room and make sure they're all doing it right the first time.

I also read on another thread someone's thoughts on how we teach math: if we taught English the way we are prompted to teach math, then we'd never teach Poetry or Shakespeare. You'll never use them in real life. However, your education would be remiss without being exposed to them.

Testing Testing 123...

I tested in all my classes today. I re-remembered (?) a strategy I've used before for particularly chatty/social classes - the ones that take about 5 minutes to settle down to start a test. I stand at the door and hand them the tests as they enter the room. That way, they immediately put their stuff away and get to work, and I don't have to "shhhh, shhhh" them at all. Note to self - don't forget this strategy. Note-note to self - who are you kidding.

I also noticed yesterday that my precalculus classes were all stressed out because I was going to make them remember trig sum/difference/double/half formulas. So I pulled out another trick today. I "sold" them a formula sheet for one point off their exam (out of 30 points). If they chose not to use it, I added a bonus point to their exam. Sheesh. I hope it worked for some of the kiddies.

I again differentiated my calculus exams. They're onto me now, though. As I'm handing them out, they all (the upper level ones) pipe up with, "are there different versions?", and they watch how and to whom I pass out what, and I don't even say anything, and then they answer themselves with, "yea, different versions."

Okay, now I get to grade the things. Yay, grading.

Old Age Benefits

In precalculus the other day, I was demonstrating with my body (ooh, tactile learning) how angles can be coterminal. I propped out one arm to signify my original angle, and then did a windmill type motion with my other arm to signify going around 2*pi times to end up at the same place. I was exuberant in my delivery and went around a couple of times.

A few kids in the front rows started giggling. "Can you do that again?". Giggle, giggle. I realized they were staring at my arms ... specifically at my "tricep" region that didn't stop moving when my arm did.

Hmph. I fake grimaced them and asked if they were laughing at my fat, and warned that they'd be there some day. Little pipsqueaks.

Last Day of Grading Period

I was uncharacteristically on top of my grading and entering this week (thanks to my student aide in a big way), and I was trying to have no work to do this weekend because it's our 12th anniversary. Well, wouldn't you know it I had about 5 or so students stay after scrambling to turn in late work for partial credit and do retests and a "hail mary pass" to try to pass for the 6 weeks. Some of them made it, and some didn't.

Hey! here's an idea. Turn in your work on time and come in for tutoring BEFORE the last day of the 6 weeks. Well. I guess some of them are still learning how to learn, and I believe they need to fail before they see the need to actually change their ways.

Funny joke from a Laffy Taffy wrapper from my students: Why was the policeman in bed?

He was an undercover cop. (ar ar ar ar)

differentiating instruction

For my last calculus test, in both classes, I gave 3 versions of the test to the students, and I decided silently which to give to whom. I had a bulk of studetnts take the "middle of the road tests" that was challenging but doable. For my struggling kids I gave a basic straightforward "regurgatate what I taught you" test with teeny "twists". Then, for the elite "yawn, I can do this in my sleep" kiddies, I gave a 3 question super hard exam with the unspoken thought that I'd give them full credit (which they would have earned on any of the other versions) if they just put out an effort.

No one knew what I did, and as the test began I watched the "elite" faces. They looked at the test, looked at me, looked at the clock, looked back at the test, looked at me. I just smiled and made the "come on what are you waiting for" motion with my hands. They rallied forth. They didn't finish, but I quietly went around and stuck sticky notes on their tests to tell them to finish at home and turn it in the next time or whenever they finish.

Several have turned it in. A few have questions, and I gave them hints. A couple of kids have come in for tutoring and I set them to work with each other, and they fed off each other's brains. I keep reassuring them, "I wouldn't have given it to you if I didn't think you could do it". Most are doing fine. Only one kid keeps saying, "it makes me feel stupid". He's the one that was a wee bit cocky about his abilities, such as they are. Hopefully, he'll step up to the plate.

No other news. Except a ton of kids come after school for tutoring. I provide snacks (graham crackers and "cheddar bunnies" and such), but I make sure to kick them out in time to go to yoga or tap :). Sheesh, they're demolishing my supplies. Must. Go. Shopping.

Words

A student was recounting to me her "horrible, awful, very bad day" of a few days ago and just generally venting about things. One incident that happened was that a counselor had given her a key to the teacher copy room to go retrieve something. Now at our school we have a variety of hall wanderers and kids skipping class and not being where they are supposed to be, so it's easy to get into the habit of treating every students you see outside of class during the day as someone who's "doing something wrong" since they're not in class. This student is not that type at all, but she got flustered when a teacher started giving her the 3rd degree about why she had a key and who's was it and what was she doing there. And I guess he said some off the cuff remarks to her.

As she was recounting this to me, she said, "you know, teachers should know the power of their words to students - whether they're good words or bad, they greatly affect us. Maybe you guys don't know how much".

It also helped remind me not to treat every student I see in the halls as "criminals". I've put on more of a concerned air (where are you supposed to be, sweetie?) as opposed to a police air (where's your pass!?!). This has led to some interesting short conversations with kids:

- my teacher kicked me out of class because I smiled and she thought I was being disrespectful.

- I was kicked out of TMC because I had my head down, and the teacher said, "Robert, put your head up", and I didn't respond because my name is not Robert, and the other kids laughed, and the teacher thought I was being fresh.

- I have to go to the school store to buy "female supplies" but I don't have money, and I can't find my sister, and the next period teacher won't let me be late because she's mean.

- (in response to my question of "what's so interesting to look at out there" to a boy who was in the halls just staring out the window at the lunch time crowd) "girls", he said bashfully.

Perceptions

Beginning about last week I started to notice that I was unnecessarily stressing myself out about everything.
- Things to be graded? What? They must be done RIGHT NOW.
- Certain students not doing well (even though they're not coming in for tutoring or doing their homework)? What can I do? It's MY issue.
- More duties that eat into my prep periods? Why I'll just wake up extra early and do my work at home.
- Dust bunnies moving in with us at home? Grumpily clean house instead of napping or sleeping.

Then all my dust bunnies must have been in alignment, because I read about BRFWA, which I remember as "barf"-"waaaaaaa" (as in how I can make myself feel), which stands for
Breathe, Relax, Feel, Watch, Allow. .... That and my new mantra, "I'll do what I can do, and that's all that I can do" (not to let myself off the hook, since I still work hard, but to cut myself a break). ... riggggggghhhhht, let's see how long this inner peace will last (1 day and counting).

Sayings & Young Students

The other day a student and I were discussing teacher salaries, and he was mentioning that teachers don't get paid nearly enough, and that I probably don't earn much. I responded (thinking of how it seems to not be getting any better), "yea, it's all going to pot". He got a disbelieving look on his face, and after I understood his confusion, I explained the meaning of the saying. ... Now whenever he sees me, he teases me on how I spend my paycheck.

Another student was semi-grumpy because I wouldn't let him leave class to go to the other side of the campus to get his math notebook. After some grumbling about how life was unfair, he looked at me and said with a stern voice, "ENGLISH Rocks".

Differentiation: part 2 (3? 4?)

In my AB/BC stacked AP calculus class, I have a wiiiiiiiiidddddddeeeee range of abilities. The same holds true for my 2nd AB class. I've tried various things, but the "lower" end stays at the lower end. I just finished grading and handing back the latest test, and the "low" scores were still low. I'm talking about 4 kids out of 19 in one class and 6 out of 28 in the 2nd class. The others are fine. So I threw it back at the class and asked them to write suggestions on how to make sure EVERYONE understands every topic. I got great feedback.

Some student ideas:
* have study buddies in class. after a day or so of instruction, have a practice day where lower and higher students are paired up.
* don't teach the "tricky" stuff in class, just go over the basics so we get a good grasp.
* for homework, also include varying levels of difficulty from basic skills to AP level type questions.

Monday Blues...

You know it's time for seat changes when every 4th sentence out of your mouth is, "Shhhhhh".
You know it's time to reteach a topic when most of the students got that type of problem wrong on the test.
You know it's time for an ethics discussion when after you hand a test back, a student asks why she got one problem wrong ... and you can see the erasure marks and "revisions" on her test from her freshly updated answer.
You know the school tardy policy is not working when a pack of 15 kids are cutting and roaming the halls yelling and disrupting your class.

It was one of those days. Monday and raining and in the October slump.

Expectations

I love my tap dance teacher. She's the ultimate professional who cares about her craft, and she expects the best from us. Me? I'm usually just happy I get the steps and can remember them and string them together when the music comes on. Her? She keeps "harping" at us: "it's not a drill, folks. Dance. Listen to the rhythm. Listen to each other. Don't fake it. ....". She has high expectations for us, and I appreciate that and want to do better.

Of course, then I think about my teaching. I have kids that are happy just to pass my class. This would be perfectly acceptable for them. I have to keep remembering to "harp" at them: "you can do better. THINK. Do your homework. 70? You can get an 80 ... a 90. Put out more effort. Come for tutoring."

On another note. Usually this year, I make all my handouts either by cutting and pasting from various resources, or by hand. When I get something typed up, I'm excited to share. I have a trigonometry "shifting, period, amplitude" type sheet for sine and cosine graphs all "perty-like" that uses Winplot for my graphs. If anyone wants a copy, please send me e-mail: math_mambo@yahoo.com.

"Favorite Class"

It's hard to bypass the following question gracefully:

"Ms. Cookie, are we your favorite class?"

Some of them ARE actually my favorite class, or the favorite class of that day, or year, or such, but I'd never tell them either way, so I say,

"Yes. You are my favorite 3rd period class. This year. In this room." That seems to get us all past the topic.

I do have to say, that I LOVE my last period class of the day. Today I had to "sneak" out about 3 minutes early to make a mandatory meeting across town that started 15 minutes after my school day ended (that then happened to be canceled after I got there!). I left them with my student aide, and I was completely comfortable knowing that they wouldn't be "bad". They're good kids and goofy and sweet, and they try hard, and it's just a nice way to end the day.

A Funny

I was walking around my precalculus class while they were graphing y = arcsin x, and I was trying to inject a bit of humor into the lesson. I didn't know where I was going with the joke, but it turns out I didn't have to.

Me: Knock Knock
Class: Who's There
Me: Radians
One Girl: Go Away

Different Perspectives

Some history: In one of my first few years of teaching, I was at an upscale school where the challenging courses were actually challenging. A student in my geometry honors class was debating whether or not to switch to an easier track, and she decided to stay in class. She struggled all year, and I believe ended up with a C. At the end of that year I had the students write a letter to my next year's students telling them various things - what to expect, what to do to succeed, what to study harder than they think they should, etc. The students also put in their own comments on other things. (I would give these letters to the students at the start of the next school year). Well, this one girl in her letter mentioned that she was really happy she had stayed in the class because it proved to her that she could do something challenging. So even though she didn't get a "good" grade, she felt she was successful in this endeavor. This stuck in my mind.

This year I have a couple of students that were debating early in the year whether or not to stay in precalculus preAP. They were struggling and had/have low algebra 2 skills. I told them that I can't tell them what to do, but that as seniors, if they skip a year of math, it will be extra hard the following year in college to get back into it. They both decided to stay. One is doing fine and is coming in for tutoring. The other is still struggling with basic concepts. This morning his mother sent me e-mail basically saying, "I'm sorry he decided to stay in the class as it looks like the rest of the year will be a struggle filled with low grades". That made me sad for her and for him. I wrote back to her about how it would be extra hard the following year in college for math placement exams if he missed a year of math. I suggested tutoring for algebra 2 skills, and she asked for names, so hopefully they'll follow through.

Feeling Bad, but not THAT Bad

In Texas, football is BIG. Football, football, football. Last Thursday night, our school team had a game against a town rival. Apparently, the team members don't get home until after midnight or so. So when they came into my math class on Thursday and looked at the homework board, some of them cried, "homework?! on a game night?!". Part of me feels bad for them, but the other part of me says, no, learn to balance your priorities. There's no way I'm going to not give them an extra opportunity to practice their skills because of football.

On Friday, I had a lot of sleepy kids. Some had stayed up doing homework. Some players did not turn in their homework. So am I doing them a service or a disservice if I allow them to turn it in late without penalty? I didn't mention it to them, but if/when I get their late homework on Monday, I'll have to think on this.

Progress but not Perfection

I've been "teaching" related rates in my BC calculus class for the last 3 days, and I did change it up from last year since I saw the struggles they had with the topic. I made some improvements, but I guess there's still more to make. Finally today after watching my mixed level class stare back at me for 2 days with a wide variety of looks, from, "yea, yea, I get it already", to "great! another topic I can struggle with to add to my ever-growing pile", to "related whats? related whos?", I had an epiphany.

As they walked into class, I moved the "yea, yeas" to the back (about 1/2 the class of 19) to quietly work on old AP exam questions on related rates. My other 1/2 I moved right up front by me, and I handed out a sheet with 4 problems. I left BIG space between the problems, and under each I had 4 categories: Picture, List of variables, Equation, Solve. I walked them through each, gradually weaning them off, and then I had to cover my eyes from all the light bulbs going off by the 3rd problem with "ohhhhhh! is THAT how you do it" looks.

As one kid said, "why didn't we do this in the first place?" Why indeed. I had to be honest with him and say, "well it's a learning process for all of us. I'm also learning what works with you all".

Spaghetti Sine Curves

I heard of a great way to get the graph of y = sin x to "stick" in students' heads, so today I tried it out. You're supposed to link the graph of the function to its value on the unit circle. Most sites I searched had the students either gluing the spaghetti lengths to the paper (too messy for me), or had the students use protractors to get exact angle measurements around the unit circle to use (not necessary and too time consuming in my opinion). So, I made up my own sheet.

I taught it for 3 periods, and by the last period :) I liked how it ran. For the first 2 periods I verbally gave instructions, and then pointed to the instructions on the back and had them "make sure you follow the instructions carefully". It seemed like I mostly wasted my breath because they still had questions, and it seemed like too many kids were zoning out with the "ach, there's the teacher blabbing again. I can tune out until we have to do something" face.

I also feel I lost an opportunity for the students to learn how to read math .... and read lots of words and follow them without giving up. For the 3rd period, I just started them on their way by mentioning the instructions. I gave a little spiel about how reading math is not like reading a novel or magazine. They worked beautifully. I also used a little trick I read on someone else's blog. I kept reiterating, "the instructions are VERY clear and EASY to understand". Tee Hee.

Their graphs turned out great. If anyone wants a copy send e-mail, and I'll pass it along. Or download it here.
math_mambo@yahoo.com

Skills

I was taken aback this week. Four students have been diligently coming in for tutoring for the past few weeks, and I wanted to let their parents know how hard they've been working. Before school started I bought these pretty marble "stock" cards from the scrapbook section at Michael's. My idea was to make postcards out of them for quick notes to parents.

While 3 of the boys were in for a "retest", I got a card for each and drew a line down the middle "postcard" style and asked them one by one to address them to their parents. The first boy wrote the address first and then their names and left out the city, state and zip entirely. The second boy wrote the correct information but 90 degrees rotated. The 3rd boy did it perfectly. The next day when the 4th was in for tutoring, I asked him to address the postcard, and I prompted him with "name" first, then street address. Then he asked me if he had to put down the city and state. I asked him if he would have known what to do if I hadn't told him, and he said no.

Hmmmm, this was just a skill I thought everyone had, but I guess if you've never written a letter, then how would you know? I learned when I went away to summer camp as a kid. I do remember messing up in the following way, though, so I'll get off my letter-addressing-high-horse. At home my parents sent and received letters from relatives in other countries, so there was always "air mail" written somewhere on the front. So when I went to camp 3 hours away from home and wrote home, I also wrote "air mail".

Insomniac Math Teacher Thoughts

Whew! I finally got that last riddle, though I'm not sure if I like my husband's hint. I thought and thought and couldn't get it, and I broke down and asked for a hint after a few days and asked how he got it. (we'd already established the first letter and the last 3 letters of the "singular" word). He said, well I was thinking of you, and the word came to me. Hmmmm, is that in a good way?

Then this morning I couldn't sleep, and I thought of this variation of an oldie:
You have an unmarked 5 cup container and an unmarked 9 cup container and unlimited water and a sink. Using only these containers and being able to fill up and pour out in the sink, how could you measure out exactly: 1C, 2C, 3C, ...., 12C, 13C, and 14C?

Mastering Skills

I did something in all my classes on Friday that I think I'll do periodically. Everyone got a half sheet (to turn in at the end of the period) that said basically:
What "skill" are you struggling with currently?
What did you do in class to make progress on your knowledge?
Who (besides me) did you get help from?
What specifically are you going to do this weekend to deepen your understanding?
How will you show progress to me next week?
What would you like to tell me?

Most kids worked hard (some chose to goof off, of course). I had many verbal and written comments about how this session helped. For my calculus classes, I had "reteaching" sheets written out for 3 topics (all I could come up with on my short time schedule from when I had this idea to when I implemented it). These sheets had worked out examples and then practice problems with answers on the bottom of the page.

Riddle posed by one student this week (and I'm still working on the answer), but I thought I'd share: What word is plural, but when you add an "s" to the end becomes singular?

A Giggle & a Quandary

I'm going to have a "word wall" for calculus, and I've never had one before, so it's going up a wee bit at a time. Apparently, they're all the rage in English (ahem, language arts) classes. Well, it's going pretty slowly, and I had my student aide be artsy with the words. She got one word done: "derivative", and I thought I'd put it up instead of waiting for all the other words to be done. The next day in calculus class, I proudly pointed to what was going to be the word wall, and the students said, upon looking at the one word up there, "oh! is that the "word" on your word wall?".

I have yet to think of an effective response to students who claim: I knew all the stuff in class and when I did homework, I just choked on the test. .... or .... I understand perfectly well in class, but then when I get home, I don't know how to do things. ... or ... I just don't "test" well.

I want to say, that well, then you really DON'T understand and you're just fooling yourself. I have to think of a constructive way of saying that. I also question effective study habits. Or effective note/text reading and processing.

Reviewing Angst

Since I've started teaching older students (ones that I picture closer to college age than middle school age), I've become more reluctant to use a whole class period to review material for an upcoming assessment. My thinking is that I warn them a week in advance. I tell them what will be covered. I expect them to study at home and ask me questions if they have them. I've even started NOT handing out review sheets for them to do at home. Right. Apparently, I live in an ideal world where everything goes as it should, and all students are well-rested and don't work jobs and do their homework consistently, etc.

I still feel a time crunch and want to use class time for practice and new material. But on the other hand, I can think of a "review" day as just an extra practice day. I could even think of a "review sheet" with answers provided as extra practice. I wouldn't even have to refer to the sheet unless a student was proactive and asked questions about it. Maybe that's what I'll do in the future. Provide practice/review sheets with answers a few days before the test. ..... I still think of it as enabling, but maybe that's MY problem.

Homework Checking System

I started to leave this as a comment of my last post, but then it seemed to be getting to long (who's the babbler?).

Hi Dan,

On an ideal day I have the homework answers on the overhead (which I turn on before the class starts for the early arrivers). The minute the bell rings, I set the 5 minute timer, and they have until the beeps to correct their papers in a different color. I grade on completion because I think homework is their time to practice. I also walk around during this time to make sure no one is blatantly copying only. I also grade on work shown and header (name, date, page and problem #s listed, corrections, attempt of all problems).

During the 5 minutes, they can also ask each other or me questions. Then I turn off the overhead, and ask for more questions. I answer the popular questions (5 more minutes). If I don't cover their particular question another 5 minutes, I tell them to mark their questions very visibly on their papers, and I'll answer them when I'm checking their papers later (out of class in any pockets of time I find).

I have my student aid (or me) stamp the papers in some goofy rubber stamp. This way later on if I've accidently marked them a zero, they can prove they've turned in their paper. And visa versa, if they claim they had already turned in their papers, I can check for a stamp. I also go through each paper and check for my list of homework musts (see above) and enter the grades.

It's been the case lately that MOST of the time it doesn't take the full 10 minutes. This has been a great improvement over the BT (before timer) days when they dawdled getting out their materials and talking to their friends and then "wait! wait! I'm not finished correcting" while everyone else was politely and patiently waiting because they had done what they were supposed to do. The timer seems to focus them and curb their overchatting, and they're motivated to correct since they know they're graded on corrections.

I don't know if it's an ideal system (I still spend too much cherished time carefully going over the papers for header, attempt, questions, and maybe I'm not catching all the copying), but it seems to work best for me so far. I also figure that if someone is not using the system correctly (copying, etc), they'll pay for it on tests and such when they don't know the material.

Changing Impressions

School has been in session for 3 weeks now, and I find it interesting how my impressions change as I get to know the kids. For the first week it's all a frenzy, and I'm a bit overwhelmed with all these new faces in class that I don't know. I already start to form some impressions (chatty, lazy, depressed, good-natured...) some right and some way off base.

Then the second week comes along and I get a better sense of the kids, and I know most (or all) of their names. They're more comfortable, and hence some are more chatty in class. I keep meaning to change seats (and I have some) but I need to wait until the 4th week when I can remove some extra desks from my class. (In hind sight, I could have just left the seats but not assigned anyone to them).

Now after 3 weeks have passed, I *almost* have my classroom the way I want it. I had a day or 2 where I could walk around most of the period to help the students while they practiced on a "puzzle" sheet of trig problems (How do you make chicken napoleon? Use only the bony parts! ar ar ar ... thanks pizzazz company). I have my homework correcting system in place (with the timer it takes at most 8 minutes or so after I answer questions).

Grades are due tomorrow, so I'm now in a frenzy of checking homework I've collected and such. With all this, I'm still not fully applying some of the teaching knowledge I wanted to test out yet. Soon. Soon.