Difficulty vs Rigor

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

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

One More Week (yippee!)

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

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

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

Three Student Interactions

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

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

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

"What are finals?"

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

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

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

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

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

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

Parent Contact

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

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

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

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

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

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

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

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

Random Thoughts

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

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

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

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

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

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

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

Seating Charts

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

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

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

My Classroom Clock

Classroom Clock
Originally uploaded by math_mambo.

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

Practice

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

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

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

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

Testing Testing 123...

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

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

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

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

Old Age Benefits

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

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

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

Last Day of Grading Period

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

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

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

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

differentiating instruction

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

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

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

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

Words

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

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

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

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

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

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

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

Perceptions

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

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

Sayings & Young Students

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

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

Differentiation: part 2 (3? 4?)

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

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

Monday Blues...

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

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

Expectations

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

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

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

"Favorite Class"

It's hard to bypass the following question gracefully:

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

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

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

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

A Funny

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

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

Different Perspectives

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

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

Feeling Bad, but not THAT Bad

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

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

Progress but not Perfection

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

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

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

Spaghetti Sine Curves

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

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

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

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

Skills

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

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

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

Insomniac Math Teacher Thoughts

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

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

Mastering Skills

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

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

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

A Giggle & a Quandary

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

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

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

Reviewing Angst

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

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

Homework Checking System

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

Hi Dan,

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

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

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

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

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

Changing Impressions

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

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

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

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

Radian Technique

Last year my kids struggled with visualizing the placement of radian angles in standard position. They either had to convert (say 7 pi / 6) into degrees and then draw the angle accurately, or they just shook their heads at the crazy things their teacher asked them to do.

Over the summer my retired teacher friend mentioned that he used to teach the pi/6 and pi/3 parts by having them look at the clock and noticing that (say) from 3 to 9 (moving counter clockwise as a positive angle does) there are 30 minutes. Break that into 6 parts. They notice that's on "the hours" 2, 1, 12, 11, 10. Then the kids go back to their unit circle and place dots all around signifying the "hours" and those are the pi/6 separations. Then they go from there. Similarly, from 3 to 9 counterclockwise (a full pi), if we want to break it into 3 parts (pi / 3), that's every 10 minutes.

I had great success on Wednesday with them accurately placing the angles without converting. Woot. Woot. Hopefully, it'll stick in their heads better this year.

I also didn't do a great job last year with having them memorize thoroughly (and "get") sine and cosine of any multiple of 45 degrees or 30 / 60 degrees. They still had to work at it without immediately being able to answer. This year, I'm going to laminate page size unit circles. Then everyone gets laminated 30-60-90 and 45-45-90 triangles that have the side lengths and angles in degrees and radians on both sides and that fit nicely on the circle. Then we'll do an activity where they will place the reference triangles on the circle for various angles I give them. Hopefully, this will allow them to later on picture in their heads the height/placement of the reference triangle and quickly be able to recreate sin 135 or cos 5pi/6. We'll see.

Start of the Year

Right now after 10 days of school, I finally can place student names with faces (if they're in their seats in their period). Soon, hopefully, I'll even recognize and name all of them in the halls (out of context).

My homework policy of having them correct their work in a different color in class (I grade on completeness), was taking too long (15 minutes or so sometimes), and I was rushed and couldn't get through the current lesson. I figured out that they were dawdling and taking forever to get out their homework after the bell rang, and then they were talking too much and joking with their friends (some of them), but then we had to wait for everyone to be done. So. I have now brought in a timer, and when the bell rings I told them I won't remind them to get out their homework, I'll just start the timer and have the answers on the overhead. After 5 minutes I'll turn it off and take questions for at most 5 minutes. Any unanswered questions, they can write on their homework, and I'll answer it there. They are partly graded on their complete "grading", so hopefully this will be successful.

I'm still getting to know the kids and their abilities. I know I have some very bright ones, so I'll have to find more time in the day (hmph) to find extra challenging problems for them.
Anyone have any extra time they'd like to pass my way? I know we all just sit around and daydream most of the day.

Growing Pains

My class sizes in order are: 31, 19, 30, 24, 28. In my first class I already have chatters that just WON'T BE QUIET. I've done seat changes, I've done the stern teacher look, I've waited patiently. Today, I think there will be some field trips outside the door (either for a discussion, or maybe I'll just leave them there). In my 3rd class (gee, it happens to be the 2 largest classes) one of the problems is that they all know each other and have had math class with each other forever, AND it's right after lunch and they're hyped up on FDNVs (an acronym I just saw sprinkled all over a memo indicating that Texas will no longer allow the selling of FDNVs for fundraising during school hours .... "foods of diminished nutritional value").

I love my last period class - sweet hard-working slightly-goofy kids. What a nice way to end the day. I also am quietly thankful that 2 of my duty stations are completely hassle-free, and I can get work done while I'm monitoring hallway doors.

In other news, it's starting again/already where someone who has had me before is now in another teacher's math class, and it's just too ________, and it's not _______, and they wish _________ (fill in the blanks). Invariably as the year goes on, they get used to the new teacher and actually like it and all complaining is forgotten, so now I just have to reassure them and mention that they have to get along with and learn how to be successful in a variety of teacher's classes.

Math Autobiographies

At the start of every year, I have my students write a math autobiography: tell me about yourself, tell me about good/bad experiences with math, tell me about good/bad ... effective/ineffective experiences in any previous class (no teacher names), etc. I like this because I learn something about the kids, and I learn about what their take is on how they learn best.

This year I learned some interesting things. I have an 11th grader who has moved around various countries and has been homeschooled up to this year and is a wee bit apprehensive about public schools. I have a girl originally from Jamaica who is tired of being stereotyped and has some strong words to say about how people treat each other. I have a creative child who put her autobiography in the form of a fairy tale. I have a student who wants to enter the air force and got his first ride in an aerobatic (or jet??) plane this summer. I have a few students who are brand new to our school. I have (already!) a pregnant student. And as usual, I have funny, fun, studious, laid back, intense, happy, apprehensive, unique students.

Already Behind

Sheesh, 2 days into school, and my to-do list never seems to be completely accomplished. Oh yea, and then there's the actual prep for "teaching". I guess it's all the initial set up of the year: organizing the online grade book, starting your lesson plans, setting up the room, teaching the students your procedures, learning all their names, striving to remember your 4 extra duties and when you're supposed to be when, waking up at 4:30am every day from bad dreams and then not falling back asleep, getting all the proper furniture in your classroom, so that you're not tripping over computer wires or overhead wires, etc.

Then I never cease to be amazed at how frequently my first impressions of a student are way off. For example, a girl that I thought yesterday was a "toughie" and "sullen" turns out on the 2nd day to be the sweetest quietest mild-mannered girl with a "tough" exterior. I guess that's a good example of waiting and seeing and being able to be nicely surprised by all the nice kids I'll meet.

Inservice Week Over

Our first week back at work is over, and I think I have a pretty good start on things this year. We have 5 new (out of 20) math teachers, and I'm wondering if we'll ever level off. I've already seen some of my kids who are working away on a project at school, and I've seen a ton of other friendly faces. That's one of the nicer aspects of going back, seeing work friends that you don't see over the summer.

Here's a picture of the wedding cake my husband and I made for my sister-in-law. Pretty snazzy if I do toot my own horn (or really my husband's horn since he did the constructing while I made the royal icing and rolled out the marzipan and put on the flowers and such ... and of course helped make the EXTREMELY delicious fruitcake base that even the Americans liked).

It's modeled after a Mayan Temple since she's an anthropologist and studies bones found in/near them. We found cool chocolate rocks to sprinkle around the base. We (he!) used a toothpick to put creases in the shape of stones in the icing. And voila! A wedding cake.

whew. But not WHEW! yet

It's practically the last day of "teacher" summer as Tuesday (tomorrow) is our first day of inservice (lasting a week) before we start back with the kiddies. For about the last week or so we've been inundated with my husband's family that have come for his sister's wedding (which was yesterday, so most of the chores are over). ... I don't care how nice people are, it's still challenging to have houseguests for a bazillion days. Currently there are a total of 7 people sleeping at our house. Okay, I say "sleeping" but that doesn't include a certain someone who seems to be getting up at 3am and not falling back to sleep and is looking forward to having bags under her eyes for the start of school.

And this wedding thing. It was nice and all, but I still feel it's uncomfortable to be a voyeur at a pretty private-seeming (at least to me) moment. All these emotions are out on the table and the future bride and groom are getting choked up and professing all sorts of love for each other and it feels invasive to me.

On a funny note, my husband's brother's girlfriend is a hoot, and she also wanted to see if she could fry an egg on the sidewalk (this being steamy hot Texas to a Canadian). We cracked an egg on the pavement in front of our house. I didn't feel it was a terribly hot day (98F or so), and it was cloudy at the time, so it felt cooler. The egg white ran and basically disappeared. The yoke did "cook" after about an hour or so, and there were then all these attractive (fire?) ants feasting on the buffet. Our laziness (or something) has the egg still out there 2 days later, and most of the yolk is gone. Yum.

Summer Reading

Every summer I reread all or parts of each of these books to refresh my aging memory on the kind of teacher I want to be.

"How to Talk So Kids Can Learn" Faber & Mazlish (ISBN 0-684-82472-8)
This is a great book on how to interact more successfully with students (well really anyone) and to make them (and you) better people.

"Tools for Teaching" Fred Jones (ISBN 0-9650263-0-2)
I love his methods on discipline. Here's just one thing that sticks in my head: no means no. So if you say no the first time and then the student/child keeps pestering you or whining and you finally give in, then you're teaching them to whine again in the future. But if you're consistent with your "no", that works out better in the long run. He also has a section on body language of the students and their compliance and such. I don't use all his methods, but several things have helped me.

Three David R. Johnson books: "Every Minute Counts", "Making Minutes Count Even More", and "Motivation Counts".
They're all math related, and he has great ideas on how to ask questions, collect homework, structure a class, etc.

This year at an airport bookstore of all places I found "Fish for Schools". I was excited because I'd heard of it before. It's basically a structure for living that's based on 4 concepts the authors developed by watching the Pike's Place Fish Market workers. I like their ideas, and I was eager to see how this book could help, but alas, it seemed to be just an advertising to get their school video package. I wouldn't have minded, but it was really pricey. Still, the book had some great ideas and teacher stories.

I also skim through "The First Days of School" by the Wongs to remind myself of (for example) what 7 things (7? ... better start skimming) students want to know on the first day of class, etc.

Any other teaching book recommendations out there?

Note Taking / Using Your Notes

I'm batting an idea around my head about actually teaching "note using" skills this year in all my classes. It seems to me that a majority (or at least too many to be comfortable) of my students don't know how to use their notes once they get home. They seem to be just humoring me by "taking notes" and then don't really see the point of them later (or their book for that matter).

I've not fleshed everything out completely yet (all ideas are welcome), but here's what I've come up with so far. Every so often during a class (10 minutes? 5 minutes?), I'll pause the class and ask them to quickly scan over what they've written and then put a noticeable star or mark near things that they need clarification on or more time to think on. Time seems to be in short demand in class, and there are those students who don't need the extra time, so I don't know if I'll spend too much time in class going over every concern. I also want them to become self sufficient and confident in their skills of figuring things out on their own, so maybe I won't address concerns.

Then I'll discuss or teach them how to use their notes when they're at home doing homework. ... Maybe a poster up in class (and give them a copy) as a constant reminder:

"How to do homework"
1. scan over class notes to refresh your memory
2. spend time figuring out the starred/confusing sections (ponder / look in book / call a friend / go on line)
3. start your homework (with header: page #, problem #s, date, topic(?)). attempt every problem.
4. for those you do not know how to do, make a start / look for examples in book/notes, write down specific reasons you got stuck
5. in class as we are going over answers, IN A DIFFERENT COLOR, put a check by correct answers, indicate wrong problems and write down the answer. Make sure to ask someone (me / groupmate / friend) for help on the ones you didn't understand.
6. later on make sure you go over incorrect ones and find out how to do it (friend / notes / book)

Hopefully, this will grab some extra students and make them more successful. I think when I check homework, their points will be based on: attempt, in class corrections, header.

Nightmares

TMI alert.

It hasn't happened lately, but who's to say it won't again. Invariably when I have to get up at night to pee, you know, that mind-ping-pong: "but I'm tired. but I'm uncomfortable. but I don't wanna get up. but you'd better" feeling, right when I wake up, I realize I've had another "pee nightmare". Maybe I'm not the only one.

The dreams often occur in public restrooms and one or more of several things occur. Either there are no doors on any stalls, or there are doors, but the bowls are filled to the brim, so that you would not want to sit down, or there's no paper, or there are a lot of people in the bathroom and one or more of the previous things occur. Or there's the dreaded "dippage": somehow a piece of your clothing gets dipped in an unflushed toilet.

I guess that's my mind's way of waking me up and prodding me to take measures.

Calculus Workshop Ideas

I just returned from my weeklong workshop, and now I feel more secure in teaching BC this year. Except it won't be strictly BC, I think, because of numbers, I may have a "stacked" class of mixed AB / BC students together. Maybe I'm being totally unrealistic, but it was either that or no BC, and I wanted the challenge for the kids (and me) that signed up for it.

The workshop teacher was mostly a lecture type of teacher, and she commented that since BC goes at such a fast pace, she doesn't feel she has time for explorations or "fun" activities or such. So in that sense I didn't get any "fun" ideas directly from the workshop. I did get some teaching-mechanics ideas from her.

She seemed to like Staedtler MEDIUM nonpermanent pens for her overhead. She found them at art supply stores, and I liked the fact that you could buy individual ones. Purple, here I come.

She also had a teeny water bottle (3" high?) with paper towels nearby, to clean parts of her slides instead of using her fingers all the time.

When a kid asks something she didn't know, she said, "I don't know. I haven't thought about it. What do you think?" And that seems to get good discussions going.

On the overhead, do scratch work on the side in a different color to keep everyone on the same level and the "not so quick" students will have a point of reference instead of not asking and feeling stupid.

Her homework policy is to walk around the room for a quick check and chat with the students (with grades given and such). The main thing about that (instead of collecting it) she feels is that they have to look her in the eye and tell her they didn't do the homework, and she felt this got more of them to do it. Also, it builds a sense of community and the kids felt acknowledged.

I thought of having an activity or several activities where the kids analyze a multiple choice question. I found that last year, the kids all thought the MC questions were easy because they found their answer and moved on. It didn't occur to me to ever teach this skill that the test makers know what types of mistakes they make and will have such answers. So my activity is for them to do one problem and circle an answer. Then give the right answer. Then they have to go analyze the other choices and literally figure out what types of mistakes would have gotten that answer. With this hopefully they'll build an awareness of checking work and being careful on MC tests.

I'm thinking of having a suggestion box up front for various comments students want to make but don't have time for in class. There'll be a template of what's acceptable/needed ... mainly date, period, and maybe name, and comment. Maybe I can also have a Whole Foods kind of wall where comments are displayed and responses shown.

Some (rough) poster ideas of ones I want to make and display in my room:
"What do you do when no one is watching? Do the right thing."
"Get more sleep"

Summer Activities

How lucky am I? Today we're going to Canada for a week to visit my husband's family, and from there I'm coming back to go to a week-long calculus workshop. And THEN the traveling is done for the summer. Whew. Then we get to continue on our quest of "making a wedding cake that doesn't embarrass us".

My husband's sister is getting married (another mixed marriage - Canadian to American), and apparently, the tradition is for someone in her family to make a wedding cake (fruitcake base). Yeah, yeah, I know, but we actually have a great recipe from their grandmother. It's dark, and you smother it in brandy (you keep "feeding" it for a long time after it's done). And it keeps forever - apparently, all that pickling does it good. And maybe we say it's tasty because after eating it, we are slightly tipsy, and think it's tasty.

What we're practicing is the shape and the icing (type and technique) and the decorations around it. So we're eating a lot of practice cakes, and inviting people over to share in the calories of our trials. We've had 4 run throughs (hmmm, maybe that's why my clothes are getting snug), and I think this last one is really close.

Inevitable Europe Pictures

(Later Note: Ackh! Apparently, I am not savvy on all the ins & outs of picture linking. Thanks to Heidi, I can mention that you can click on the beautiful rectangles to see the pictures ... out of order, of course.)

We had a boatload of fun in Europe and have almost completely returned to normal life. Now it's time to bore our friends and family with pictures. Here are five that sum things up.

If I do it right, the first one is of the Tower of London. We spent about 4 hours in there exploring all the parts and reading all the information. I was fascinated by the torture information and the fact that the Tower of London was mainly a residence. The second picture is a main :) reason for going to London: scones & clotted cream for me and fish & chips for my husband.

The 3rd picture is at the Grand Place in Brussels. This is a large square and there happened to be a free concert that night of Pagliacci. We had walked ALL day and could only take standing for an hour at the opera. It was in Italian with electronic subtitle boards in Dutch and French. Bon.

The 4th picture is of the Rijksmuseum in Amsterdam. It is/was Rembrandt's 400th birthday this year and they were having a special exhibit. We tried 3 times to get in and never quite managed it. The first time they were closed because some crazy person threw acid on a picture and damaged it, and the museum had to deal with that. The second time the line was long, so we thought we'd go back later. Later, the line was longer, but we stood for about 30 minutes and were 1/2 way through the line. We flaked out, and a funny thing happened. A woman was riding by on her bike with her kid in the cart on the bike and was talking to her kid and said, "we should tell them (the queuers) 'it's not worth it'". Hmmm. We did finally see a nice Rembrandt exhibit at the airport on the way out. The last picture is of a representative canal in Amsterdam. Apparently, there are more canals there than in Venice. Okay, travel show over.

Two+ NYC Experiences

I visited my friend in NYC when I was up north (with the Yankees ar ar), and we saw, "Mama Mia". I was so looking forward to it, but it just didn't do it for me. It didn't help that I had a bonus singer in the form of a little girl behind me who knew ALL the lyrics and could belt them out loudly. It also didn't help that I started feeling my 40+ years, and all the young kiddies in the cast (20+) looked like babies. BABIES.

We also went to to Josie's (I think it was), this eclectic healthy food frou-frou restaurant up on 74th and Amsterdam. Delicious food. Pricey, but I guess that's NYC. When we went in, the hostess scanned us up and down and proceeded to sit us in the back near a noisy table and the kitchen area. My mild-mannered friend asked if we could have a less noisy table, and we were shown to a nice window seat. Now maybe it's just my interpretation of "good" and "bad" tables, but why don't they fill up all the "good" tables on a first-come-first-serve basis? Too weird.

My next weird experience was on the train going back to NJ. Oh my goodness did we have some loud gangster rival groups in our car yelling and threatening to fight and being all kinds of noisy. You just wanted to muffle them. Then the other people in the car got into it and started yelling, "Jerry. Jerry. Jerry." Blach. It basically settled down one stop before I got off. Whew, blessed silence.

Parent Visit

I'm off to the northeast tomorrow to visit friends, and when I get back, my dad is coming to visit for 4 days with his girlfriend (a word that definitely sounds funny when applied to a 72 year old). Holy cow, I just realized he's older than I'd thought about lately. He usually seems so young.

Anyhow, this will be an awkward visit (like all of them). I love my dad, and I know he loves me, but we never have more than a handful of words to say to each other. Oh goody, now there'll be another witness to the awkwardness. Hopefully, she's a talker, and I can have my husband as a buffer, and with those extra 2 people, maybe there'll be enough conversation to make us seem like normal people.

Yeesh, and that Sunday is Father's Day. Okay, now I have to plan something, ... horrible daughter that I am.

Teacher Pay

I was just watching TV while making dinner, and there was a "Union" ad on. It had 4-6 different smiling people saying things like, "I like my union because ...", and then they all proceeded to say bad things in the vein of fatcat union bosses lining their pockets, money going to politicians the workers don't support, huge union dues that cut into paychecks etc. Oh my goodness! Is that why there is effectively no teachers' union in Texas - the anti-union people have worked their magic?

All I know is that in NJ we had a strong union, and as a teacher I felt more respect than I feel in Texas (I took about a $14,000/yr pay cut as a teacher moving from NJ to TX). In NJ, any extra duties were compensated. In TX "what do you mean you won't perform this yet-another duty for free? it's not about you, it's about the kids!". Somehow they make you feel like a money grubber for even thinking about pay.

Ew, see it's already seeped into my pores because I now DO feel like a money grubber. A poorly paid money grubber.

Exercising

I guess I forgot that "teaching" requires a ton of standing and rushing around the halls making copies and standing and walking at your duty stations and such. Shockingly, in the summer when you're on your duff, if you eat the same amount of food, you gain weight. Who knew?

Okay, new plan, walk in the mornings and walk at night (less skin cancer potential, and less Texas summer heat issues). I'm still going to yoga 6 times a week, so that's good, but that apparently does not make up for sitting around all day. All this energy stressing about weight and health. You think THAT'D burn calories.

I'm not a total slug, though, I'm finishing a quilt (finally) that I started too long ago to mention. I made a skirt. I'm still practicing cake decorating (yea, more food to eat/not eat).

Fun Facts

Here are some things I came across while surfing the internet (which I'm doing way too much of). Now I haven't verified them, yet, but EVERYONE knows that anything you read must be true, right ahem?

The longest living cells in the body are brain cells which can live an entire lifetime.
Porcupines float in water.
The human body has enough fat to produce 7 bars of soap.
The elephant is the only animal with 4 knees.
Frogs sometimes eat enough fireflies that they themselves glow.
Because heat expands the metal, the Eiffel Tower always leans away from the sun.

Today I must do some gardening to get me outside instead of inside reading and doing puzzles and napping all day (though I have been going to yoga every day). I loved yesterday's teacher. You know those people that just glow from within? That was her. She just exuded honesty and beauty and knowledge.

Hello Summer

A most excellent start to the summer: 6 rented movies (5 were great), 1 matinee, sleeping at least 8 hours a night, a math party, a dinner party, starting in on my stack of novels, time, time, and more free time. I also get to go visit friends in the northeast, AND go to London, Brussels, Amsterdam, AND go to a BC Calculus workshop, AND make a wedding cake with my husband for his sister's August wedding in Texas. Yea. Let the fun begin (continue)

Things I've learned so far:
1. Royal icing tastes terrible
2. Your secret design based on your sister-in-law's profession, is not that secret
3. Butter flavored crisco in a buttercream frosting is not as bad as I thought it'd be (I HATE margarine)
4. People make fun of a fruitcake for a wedding ... even though it's a Canadian tradition and even though we really do have a great recipe handed down from a grandmother (I'm a picky American eater, and I think it's delicious) .... but whatever.

Guilt Tactics

Today was the last day of school for teachers, to finish up administrative chores and check out. Usually it ends with a faculty meeting where the principal gets up and gives a "go us" speech and says goodbye to any faculty that's leaving. Today there was an extra 1.5 hours devoted to something else.

We had 217 juniors (out of about 400 or so .... dang, that's a LARGE %) who did not pass at least one of the 4 subject areas of our exit exam. Oh my. Our principal thought she'd try something new this summer (I started getting a bad feeling) where she'd dole out the names to the 150 or so faculty to be mentors - mentors that called the kids at least a couple of times to remind them of tutoring available over the summer and of tests dates. She "knew" not every faculty would step up to the plate, so maybe those who knew the kids and had already formed a relationship with them would take 3 or so kids.

Well, she started calling out names of students and teachers raised their hands to mentor them. And on and on and on. Intermittently, she would interject with comments like "our school is made up of people / individuals", "this test is what we're about", "our kids have to pass this test". I kept waiting for names of kids I knew. None came. Then I started obsessing that I wasn't choosing anyone. Then I started to feel resentful that I should be manipulated into picking someone. Then I started not actively choosing students.

After the last name was called, here was her zinger, "and for the people who didn't choose a student, I want to thank you, because we don't want anyone to volunteer and not have their heart in it and to drop the ball and not call the student". Is it just me or was that saying one thing and meaning another? I HATE that kind of manipulation. It's so offensive. We bust our butts all year coming in early in the morning, leaving late at night, tutoring practically every day after school. Tons of people were volunteering. Why not honor that and end it on a good note instead of calling to fact that there were people who did not volunteer for this ONE task. It's like I see her panning the room and committing to memory the nonvolunteers .... okay HERE are the people on my poop-list for next year. Great. Have a terrific summer.

Yearly Ritual

I just want to document what I did today (2nd annual), so that if and when I come back to read this a year from now (minus a week), I won't go wa wa wa and not go to the matinees on the last week of school for a fill-in-the-blank reason.

I got off my fanny and made sure I finished all my last-day chores at school today and high tailed it out of there at 1:15 pm to make lunch and a 2:30 showing of "Kinky Boots". This year I wasn't the only one in the theater (good. more people enjoying life), but I still had a great time. Even though I have/had 6 rental movies waiting for me at home, there's still something about going out to the movies. Every time I go by myself, I wonder why I don't do it more often. How ridiculous that we get so bogged down in the chores of life that we don't stop and do plain simple fun things more often.

Great movie, by the way. I love shows where the underdog "wins" and wise things are said and you laugh and lose yourself in the film. ... Of course, now I just finished one of my rentals, and oh my, guess I have to go watch a third before it gets too late. A triple feature. How decadent.

Graduation

Even though we have one more "student" day of school on Thursday (ice day make up), tonight (Wednesday) was graduation which I worked. The kids were so cute - hugs galore and all dressed up and mostly serious. Our principal makes it a big deal about decorum and such, and our funny head AP models the hug-em-and-ooh-and-aah-while-you-pat-them-down-for-contraband moves that we're to perform to make sure no beach balls and silly string and tortillas (?) make it through. Oh, and they're supposed to arrive withOUT their robes on, so that there is no repeat flashing incidents during their walk across the stage. Ahem. All in all you just wanted to pinch their cheeks.

Learning Attitude

What if all students approached school and class challenges like yoga. Your teacher shows you something difficult, and then you try it and don't get it the first time, but you take a deep breath and every subsequent time you try it you get closer and closer and MAYBE eventually you get it, but you are persistent and don't get (too) frustrated and know the struggle is in itself a learning experience because it teaches you a wee bit something new about the situation, and eventually you can meld all the pieces together to figure the whole thing out.

Okay, I'm looking skyward for those flying piggies.

Next year's (lofty) goals:
1. more differentiated MATH instruction for the weakest to the super strong
2. stay more on top of students who are struggling in calculus and don't let the year slip away with them being totally clueless
3. a stricter late work policy and homework policy (now I just check for "mostly" done. I want to check for "all" attempted and no fakers)
4. create a parent e-mail group and send out a mass mailing about upcoming tests/projects/...
5. have students keep track of their own grades (and that will be for a grade) ... maybe have their parents sign off on it periodically (ownership of their learning)
6. incorporate "some" games into the learning (saw some cool precal ones at an AP Central / college board workshop that I want to try)
7. more: chocolate / movies / laughing / crocs / visits with friends / sleep

End of Year Happy Dance

Can't stop the big smile on my face as I think that within a week I'll be able to sleep more than 6 hours a night, go to matinees, go to yoga every day if I choose, be a book reading glutton, ... Ahhhhh summer.

I was also "mean teacher" on Friday to my calculus classes (last Friday of their last full week). I was tired of handing out bonus points if they did the daily activities we did (with their hideous attitudes), and I certainly did not want them sitting around doing nothing for 50 minutes, so I taught them about the binomial theorem (which for this particular class is something they did not learn last year) and how it can be used to multiply out binomials to any integer power. Then I gave them a 1 question quiz at the end of the period. Sheesh, you should have heard the whining (only from a select rude few). But there I was with the grin on my face. As my fellow lunch duty teacher said later, "it's pay back time". Oh well, it's good for them, and it's useful information. And I had baked them cookies the night before.

In other news, if anyone wants a copy of the cross section project I did with my students, send me e-mail at math_mambo@yahoo.com (that's math_mambo ... in case it doesn't show up), and I'll send you a copy. It's basically what I handed out with some extra things I learned this first pass through. I certainly did not create the project, but I had fun doing it.

Funny Ha Ha

We had a staff development during one of our prep periods on Thursday, and we broke into little groups to discuss collaboration of teachers and how to hold teachers accountable for various tasks/duties (we have a LOT of teachers that just don't show up for their duties). Well, in our little group of 5, as we're talking about these 2 things, one guy is reading the school newspaper, and the other is working a math worksheet. I don't think they got it.

Parting Gifts

Usually I don't like receiving gifts from students. I feel awkward (they shouldn't have), and I'd rather they wrote me a nice card or note (those I save). But. Yesterday a senior I've had for 3 years gave me a plant and a great note. Apparently, the plant is an offspring from one of his plants he's had for 11 years, so he writes that he's leaving a legacy of himself with me. He also decorated the pot with funny things he remembered from class. I'm tearing up just thinking about it. What a sweet and memorable thing to do.

It's going to be hard to say goodbye to the ones I've known for that long (most of them :) ). AND. After next year, there'll be kids I've had for 4 years. That will be harder. I don't know that that will ever happen again because I don't seem to be teaching geometry and algebra 2 next year. I love teaching calculus and precalculus, but I'll miss the goofiness of some of the younger kids from geometry. Maybe that's a blurred memory talking there.

Sticky Notes

What have I been thinking all these years? Usually when I go around helping kids, I ask first, then I write on their papers any hints or math steps they need, or I find a piece of scrap paper and do the same. Well, yesterday after school I just happened to be carrying around one of my many pads of sticky notes (girly colors, about 3" x 3"), and I proceeded to write on it and then stick it to their papers. I got so excited, I rushed around and gave more help and more sticky notes, "oh here, let me show you the steps on my hot pink paper and then let me stick it to your review sheet."

Who forgot to tell me of this idea?

On a side note, after I told my husband of my "new" discovery, the CostCo "maniac" said that then we'd better buy them in bulk there, so that we don't deplete our retirement money. .... only if they have cool colors is my thought.

Finals Review

On Monday my precalculus students turned in their packets for finals review. I asked them to make a study schedule, a list of topics we'd covered, a list of book sections covered, and to gather together tests and homeworks. I graded it on the spot while they reviewed and handed it back that period.

Most kids did a great job. The funny thing is that the 2 students that were complaining the loudest did not turn in anything. It was also interesting to look at their study schedules. They ranged from "I will study every night", to a breakdown of "M 20 minutes, T 1 hour, W none ...", to "M 20 minutes: limits, T 30 minutes: polynomial zeroes, quadratic formula".

Oh my. One student budgeted herself about 5 minutes each night for a week of studying. I had a talk with her in disbelief and asked if that was all she was going to have to study. She said yes.

Anyway, I'm proud of them for rising to the task. Hopefully, they'll now use the stuff. I'll have to keep it fresh in their minds and/or keep hounding them and/or have another assignment that guages whether or not they're studying.

In other news, I've had requests for the cross section project write up. I've started it. I'm guessing I could e-mail it to people unless someone has a better idea on how to make it available. ... My kids turned in more projects on Monday. Oh my are they creative. Another kid had a tornado, and then drew lots of cute animals on foam, and then stuck them all over the cross section.

Calculus Project

triangles on a parabola base
Originally uploaded by math_mambo.

Here are a few of the finished (and almost finished) projects from my math class. The kids surprised me and themselves with their creativity. The "rocket" boy still claims he is not creative. I have to admit that I didn't know what to expect when I assigned the "turn them into something" aspect of the project (that I got from a summer workshop), and I'm pleasantly surprised with the outcome. Note the tornado picture and the guy flying through the air. What you don't see is the cow flying through the air on the other side. Mine is the green and purple one. Someone suggested that it looks like the wicked witch's hat, so that's what I'll turn it into (especially appropriate since I'm listening to the "Wicked" book on CD to and from work).

artsy test picture

artsy test picture
Originally uploaded by math_mambo.

I'm expanding my blog knowledge and posting my first picture - taken while on vacation. Hopefully, soon I can post the calculus project pictures.

My New Friends

This is my LAST week this year of TMC duty during one of my prep periods (for kids late to class .... who get to sit in the cafeteria instead of wandering the halls or disrupting class to show up late). It's been the usual week of being cussed out, being disobeyed, and being snarled at on my duty. BUT, it made my job easier because zip zip I write a referral, and POOF! they disappear to ISS and out of my hair, "bye bye surly children. thanks for visiting."

Anyway, today it was a light load (only 8 children / 6 per row) and they were all polite. I started talking with one girl, and she proceeded to tell me all about the piercings she wants to get: 10 on her tongue, 2 rows down her back (so she can lace ribbon through them), several around her mouth, and then one in her ear so she can hang a chain from ear to mouth, .... I forget the others. Then (and I hope she was joking) she said she wanted to split her tongue so that she'd have more edges with which to line rings. Ew.

Then the boy next to her started to show me his tongue stud, and we had a lively discussion about foods that get stuck there and how it was a proven fact (he said) that every tongue piercing you get knocks off 5 years from your life (so being a math teacher, I then calculate that the girl would be dead ..... yesterday ... or really soon anyway).

Super goofiness.

Passive Learners

Finals are starting soon. During the last week before finals, here's the usual scenario:

I debate how much class time to spend reviewing (too little and I can't be sure they review at home, too much and they get antsy in class)
I make a list of topics we've covered
I make review sheets
I monitor class to make sure they are all reviewing.

Hmmmmm. I guess I must be part of the problem of creating passive learners. On Tuesday I had many interesting conversations with various students: "when are you going to give us review sheets, so we can study?" ... "I can't study yet, my teacher hasn't given me review topics/sheets." ... "how will I know what's on the final by myself?" ... "it's the teacher's job to give us review materials." ... Ew.

I had a little discussion with my advisory about how THEY might take ownership of their learning and study on their own. I think I'll take my own advice and give the following assignment on Friday, due Monday:

1. go over your notes from January to present and make a list of topics we've covered
2. for each unit find a relevant quiz/test and at least 3 homework assignments covering that unit.
3. make a list of the textbook sections that cover the topics.
4. make a list of the days available until finals and map out a realistic amount of time you can devote to studying for your math final every day.
5. gather everything together in a paperclip and hand in. NO LATE WORK WILL BE ACCEPTED ... (worth 2 homework assignments).

Shoes

I love Crocs. They're so comfortable, and I can wash them, and they're ventilated. Goodbye tired smelly shoes, hello Crocs. I started out with 1 pair (pale yellow), then fell in love and instead of wearing the same pair of shoes every day (to be alternated with birkenstocks), I bought another pair (light blue). Then (and I do NOT have a shoe problem) I felt I needed a "formal" pair to go with my darker clothes, thus I bought a brown pair (for when I cough cough dress up while teaching) .

So then I started getting the bug. I HAD to HAD to HAD to have a purple pair. And this was no impulse purchase. I thought about it long and hard and searched and searched, but alas, it was not meant to be. Then, while in St. Louis at the math conference we went to the mall one evening (to be true, ahem, Americans you have to go shopping at a mall while in new cities) my eyes grew wide and my breath caught, and I saw a kiosk full of Crocs. And, yes, you guessed it, they had purple in my size. So now I have 4 pair. So far.

Now it's a given that students may not remember math formulas or recall facts they learned from yesterday, but they will notice when you are wearing new attire. When yet another student mentioned my new purple Crocs and asked where I got them, I mentioned that I bought them in St. Louis. Then I said, "you know like a souvenir". Ar ar, I thought I was being funny. Well, another student topped that by saying, "don't you mean a shoe-venir?"

Horrendous Days

After a horrible day like Friday, I want to go back in time to my morning self, innocently getting ready for work, and either hug me or warn me somehow (Run! Run while you can!). .... Or sometimes, when I'm getting ready for work in the morning, I'll look me in the eyes and wonder, "is this going to be one of those days ... how will I know ... when will it happen ... oh no ... dun DUN dunnnnnn (cue in the creepy/eerie music)?".

And then there's the obsessing about "the incident" for the rest of the day. What kind of human goofiness makes you take just one small chunk of your day and replay it over and over and over and let it consume you for much more of your time than it's worth?

Creepy/whiny/calculus girl was in a prime state today choosing to use her time not to actually work, but to loudly proclaim how selfish and inconsiderate I am to assign a project that's due next week when she has 2 more AP exams to take (they work on the project in class. there's no outside work. it should look really cool when done). I had to send her outside and have a discussion with her. Oh, I'm sorry, not a discussion, but a whining session on one side and a disbelief and frustration on the other. Ew.

It helps (mostly) to remember that I've had other "painful" students in the past I've obsessed about in the moment, and now I give them barely a thought. This too shall pass. Deeeeeeeeeeep breaths.

Good Looking

What is it about good looking people that makes others gravitate towards them? Or makes people give them special favors or thinks their opinions are "all that" - like they occupy a higher plane of being? Is it just human nature that people want to be around or look at pleasant things? I mean, I think most people know deep down that just because you're good looking, it doesn't mean you are smarter or more apt than others. I've also seen situations where people try to impress good looking people, as in, if this "looker" thinks I'm special, then I really must be worthy. ... I just find it a curious phenomenon.

Play Pool

It worked! During 1st period, we had time to test out the elliptical pool table, so we set up the "shelf" cut out on a table and used their calculated values of a, b, & c to locate the foci. We had a rubber "jax" ball (super bouncy ball), and poof "most" of the time the ball traveled from 1 foci to the other after it bounced off the wall .... no matter where we bounced it from. We did a little yelp of excitement and kept testing it out.

I had to share the thrill with my calculus class the next period. After I finished describing it, Miss Snotty Girl sneered, "oh. I thought you were going to say something cool like it went back to its original spot." ..... (you're whiny and your shirts are cut too low) ... BUT, theoretically, that should be what happens since it went through the 2nd foci. I'll have to test it out.

In other nail-biting news, the AP Calculus exam is Wednesday at 8am (today!). Oh man, they'd better pass. I'll be crossing my fingers all day.

Reminder

A college counselor at our school reminded me today to concentrate on / recognize / praise the "good students". She said that at the beginning of the year she made a conscious decision to celebrate the kids that are doing what they need to be doing and furthering their applications and such. She felt that so often we drain our energies correcting and noticing and obsessing about the students that are goofing off, not turning in their work, skipping class, ...

I'm guilty of this. I'm guessing the kids that are always quiet and doing the right thing are easy to ignore because they make no noise/trouble. Something is seriously wrong with that scenario.

NCTM Fun

I had a great time with my coworkers in St. Louis at the NCTM conference. I went to talks on assessment, questioning, struggling learners, fun math, challenging brain stretchers .... I'm revitalized to end our school year.

Here's one puzzle I got from a presenter. She puts up a new line every day, and her students have to guess the pattern (and/or guess the next row of numbers). I'll put up a few, but of course it goes up in stages and can go on forever (and lead to interesting follow up questions).

1
11
21
1211
111221
312211
....

Pool Tables are Ready

My sweet husband cut out the 3 elliptical pool tables from our left over shelving material. I wasn't home when he did them.

The first one went fine. He just cut along the outline my 1st period made. He also did the 2nd one, but felt the outline was too close to the edge (within an inch), but cut it anyway. On the 3rd one, he decided to cut uniformly about 1/2" in from the outline of the ellipse because again, he felt it was too close to the edge.

Well, unexpected, but a great question for the students: is this new shape still an ellipse by definition? I posed it to them on Tuesday without resolving the issue. I'll let them stew over it (or in most likelyhood forget about it) while I'm gone for 3 days .......... to the NCTM conference in St. Louis.

When I get back, we'll try out the tables and see how accurately we can shoot from one focal point anywhere along the edge to see if it bounces back to the other focal point. Tres exciting.

I guess I'd better go pack since I'm leaving for the airport in 45 minutes!

Expectations of Students

I gave my practice AP Calculus AB exam this past weekend. The students had to show up at 8:30 in the morning and sit for about 3.5 hours and take the "mock" exam. Of course they whined about coming in, but I just put on my stern teacher face and just went on like, "of course you'll come in. Why would you NOT come and sit for an exam? (on the weekend, early in the morning, using your brain before it has woken up?)" ... on the inside I was wondering how many would show up. Well, 23 of the 28 showed up (woot woot).

They did not do as well as I would have liked, but on the bright side, they made silly mistakes that if they could fix, they would have boosted their scores to passing and getting college credit. They'll be working on that this week. I felt like I had to walk a fine line on Monday cheering them on to step up to the plate, and admonishing them for not studying harder before. It seems to be the culture of this particular school for most (but definitely not all) students to just do the bare minimum and not put out any extra effort to excel.

I had a discussion in the work room with a teacher who said, "no student is a competitor any more". He basically seemed to think that it's pointless to try to get them to work hard. I can't believe that. You can't just discount a whole generation of people, and say that they'll never improve. There has to be a magic combination of things that you do as a teacher such that various actions on your part will affect various students to do better. I've seen it. I haven't seen it consistently, but that's my battle to overcome, to "do better and to improve".

Cool Facts

We found a great way of getting a sense of relative sizes of BIG things today. One of my students told me that she was reading her math text the other night. First I thought she was joking, like, "I was sooooo bored, I actually read my math book". But she was serious (woot woot). She mentioned a cool thing she learned.

In our text they compare a million (10^6), a billion (10^9), and a trillion (10^12) with the following questions. Now, I couldn't figure out a fast way of putting a drop down menu with the answers here, so I'll put the answers in the comment section.

1. How much time is encompassed in a million seconds? (in hours or days or years) ..... don't use a calculator, just go by gut feeling.

2. How much time is encompassed in a billion seconds? (again, no calculator ....)

3. How much time is encompassed in a trillion seconds? (drop that calculator!)

How cool is THAT .... and how mind bending.

Two Nice Surprises

In the last 2 days I have "had to" be present at things I was not too sure were going to be worth the time (and or money). .... But having reached the ripe old age of 41 and having been in these situations before, I always hold a glimmer of hope that I'll either learn something or be pleasantly surprised or something good will come of it (since this always seems to happen). Well. It happened twice in the last 2 days.

On Tuesday, our 11th graders were not testing for TAKS, so we had a motivational speaker come to the gym to try to hold their attention for a good part of 90 minutes. If you've ever been around high schoolers, you know that's quite a challenge. We've had "motivational" speakers in the past, and I've been disappointed in the kids' behavior and had to search hard myself for the motivation in the speech. Not so this time. Joseph Jennings came and had their undivided attention for as long as he chose to speak. He's a former gang member, and now he travels the country talking to kids. He was articulate, real, honest, and carried a lot of good messages for the kids. He discussed what it meant to be a "man" or a "woman". He talked about respect. He talked about choices. LOVED. HIM.

And tonight we had a substitute for tap dancing. Part of me wanted to sneak out, but then the more mature part of me kicked that part in the butt and stayed for class. What fun. We laughed; we learned; we swiveled our hips to do double pull backs. A nice way to end a great day.

On a side note. A student said to me today, "you should write a blog". Hmmmm. I said something noncommittal. Actually, I've told nobody that I blog. Not even my husband (though I've hinted at it). I guess when I started, I figured it wasn't worth mentioning because I felt like a poser. Now, after a year and change, part of me feels like if I DID tell someone, and they knew me, and I knew they were reading, I'd start self-editing and not be "true". Who knows.

Questioning & Learning

I love when you are teaching and the students are not getting it (okay, THAT'S not the part I love) and then through some encounter with a student you realize what their misconception is. ... Then you totally revamp how you are presenting the concept, and they then all say, "Ohhhhhhh!".

For example, we (they) are learning sequences and have to deal with subscripted variables: an, an+1, an-1 ... I kept mentioning that the "n's" just indicate where you are in the sequence, but once they tried to apply it, they'd mess up. So .... "n" is the place you are (1st, 2nd, 3rd, ...) and "an" is the number in that place.

Well, I finally saw today that a student was mixing up things like an+1 and an +1 **, and then worked around to clear up THAT with the class. Ohhhhhhhh.

** let's say your sequence is:
n: 1,2,3,4,.....
an: 5,10,15,20,.....

Then a1 = 5, a2 = 10, if n = 4 then an = 20 and an-1 = 15 and an-1 = 19.

From the TMI Department

Friday we were off from school, so I scheduled 2 doctor's appointments - a mammogram and a skin check. I was actually surprised they were open on Good Friday, this being a fairly religious region of the country.

I've never had a mammogram before, so I was a wee bit hesitant based on what I've heard. Some woman had mentioned a funny article on how to prepare for the experience: slam your breast between the refridgerator door a few times / roll over it with your car in the garage ...

It wasn't so bad, except for in the beginning when I was trying to make conversation with the person while she was visually checking out my breasts and then switching out plates on the machine. There were 2 different black plates, and she made a decision to switch them out. I asked what the difference was, and she said, "that one (the one she took out) is for larger breasted women. This one (the one she'd use on me) is for .... medium sized breasts (hmmmm, maybe small was the adjective she wanted?)".

Then on to the skin doctor. I've had this little scab on my nose and under my eye for about a year or more and they never go away, so I'm thinking "skin cancer" in a it-can't-really-be scenario. Turns out it's kitosis (?) and IF skin cancer develops, that's where it would manifest, so he recommended me freezing them off. He had a canister of liquid nitrogen (?) and did some spurts on my face, and that was that. WELL. I guess it takes a while for them to slough off. After a couple of days, now I look like I have small boils on my face. .... Oh yes, that's my wife/teacher/friend .... the one with the boils.