Angular Speed

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

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

Learning Greek

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

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

Em(pi)nadas

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

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

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

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

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

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

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

Quick Assessment

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

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

Sleep Deprivation and the Modern Teacher

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

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

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

I'm Scary

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

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

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

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

Piecewise Functions

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

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

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

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

One Week Down

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

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

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

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

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

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

Surface Area Activity

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

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

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

We're BAAAaaaaackkkk

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

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

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

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

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

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

Teaching Analogy

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

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

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

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

Judgmental Cookie discusses Lock-Step Teaching

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

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

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

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

Ew.

Vicious Cycle

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

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

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

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.