You're Welcome

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

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

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

Finals Shminals

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

Last Week of the Fall

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

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

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

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

Bullying

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

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

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

Voiceless

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

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

Holiday School Holiday Sandwich

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

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

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

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

Nonmath Moment

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

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

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

Continuity...(it never ends)

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

Identifying Coasters

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

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

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

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

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

Helicopter Parents

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

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

Cheating

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

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

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

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

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

Opinion Changes

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

So far I can think of these students:

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

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

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

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

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

Take 4

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

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

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

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


oh! and a joke I read on You Tube:

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

Linear Speed Reteach

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

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

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

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

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

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

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

3. # feet/sec convert to miles/hour

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

4. #rotations/sec convert to feet/hour

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

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

Never Assume

Two cases:

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

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

Notations in my planbook reflections for next year.

Memory Wheel

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

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

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

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

Yay (Yeah?) Learning Logs

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

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

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

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

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

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

Learning Logs

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

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

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

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

Learning Trig with Special Triangles

Angular Speed

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

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

Learning Greek

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

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

Em(pi)nadas

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

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

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

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

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

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

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

Quick Assessment

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

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

Sleep Deprivation and the Modern Teacher

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

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

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

I'm Scary

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

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

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

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

Piecewise Functions

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

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

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

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

One Week Down

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

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

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

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

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

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

Surface Area Activity

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

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

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

We're BAAAaaaaackkkk

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

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

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

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

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

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

Teaching Analogy

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

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

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

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

Judgmental Cookie discusses Lock-Step Teaching

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

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

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

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

Ew.

Vicious Cycle

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

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

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

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.