More Games and Such

I decided to add 2 new links to my homework website for games since these are ones I love love love. The first is ABC pureisu. Basically you place the letters A, B, & C (and sometimes D) so that every row and every column has exactly 1 of each. You can click around the buttons to get different sizes and difficulties of puzzles. By clicking in the box, you can place your letter.

The second is a "squiggly" sudoku site. I love the different variations of sudoku, and this one also has different difficulty levels. A different puzzle appears every day. This one you have to print out.

I had put a "notes" section on my website, but ultimately knew I wouldn't keep up the copying of the notes, and I didn't know how helpful it would be. So I decided just to sum up the topics of the day/week and mention what would be important to know how to do, and then I will provide web links to various sites that show/quiz/video/tutor/etc the same topic. That way the students have a different way of learning the same thing, and maybe a different explanation will make things click for them or just let them review more. It also gets them in the habit of searching the Internet using the topic name, and they can find other help.

Testing Scribd

I gave the following quiz today in Algebra 1, and I've had "Scribd" on my radar for some time, and then I saw it used on the "f(t)" blog, so I thought I'd test it out here to see what's what.

http://www.scribd.com/doc/5267432/graphing-points-quiz

Hmmm, not exactly perfect, but I'll work on it.

My Book Love Affair

I have passionate feelings for this resource and turn to it whenever I need great ways to ask questions or great real-life examples. I got my copy at an NCTM workshop, and am doing the happy dance ever since. For example, in precalculus today we were talking about function notation, and after we did some "math" graph and table and equation examples, I pulled 2 context examples from the book. One was a table having to do with NFL revenue for a number of recent years, and one was a velocity vs. time graph for a man going to the store.

They both generated discussion about the amount of money NFL made (billions!) and interpretations of the velocity graph and why it may be so "wiggly" going up and down and such and how you knew when he reached the store. The questions were worded such as: find v(24) and interpret the meaning. So they had to think about what "24" meant in this problem and what the "y" value meant and put it all in a coherent sentence.

We also started a discussion on graphs such as y = abs(f(x)). We first refreshed our memory on abs(x) (much needed for some folks). Then I had them make a table for f(x) = x*x - 2 and graph it. Then I had them hold up their hands in the shape they thought y=abs(f(x)) would be .... some, of course, held up "V" hands. So we made the table values and graphed JUST the points, and then I showed them the visual of "flipping" all the negatives "up". Ooh, ahh. That was a good segue into doing the same table/graph thing with f(x) = x ..... then doing y = abs(f(x)).

On a whiny note, my 6 class sizes so far are: 31, 22, 17, 26, 39, 34.

I'm just saying. .... but maybe that's the norm in other schools. BUT, I rember my math teacher friend in another state complaining that she had LARGE classes one year .... "26".

Wikki Stix & Me

A while back I was first introduced to Wikki Stix at a calculus workshop where the presenter showed how she taught slope fields by having large pieces of graph paper around the room, and each group had a differential equation and each person in the group had a point or 2 or 3, and they were to calculate the slope and stick the piece of wikki stix on that point in the appropriate slope. Super cool.

I was at a teacher supply store the other day, and found 48 for $5.95, and bought them thinking I could find some use for them. Well, now I have 2 things so far. On the first day of school, I will review functions and lead to function notation and how to read f(x) and find f(3) and find x such that f(x) = 6, etc, by first handing out premade graphs/grids/coordinate planes to each student and one wikki stix (stick?) to each kid. I'll first instruct them to plop down a "graph", and maybe have them decide if they're functions or not and maybe have themselves walk with their graphs and separate into 2 camps of functions and non functions. They can then self correct by glancing at others and discussing it amongst themselves. Then I'll say find your f(3), and separate yourselves into like groups (how to deal with non integers .....???). Anyway, you get the idea. I could do more.

My second idea is what I think is an improvement on an old activity I've done with precal in the past regarding learning the sine and cosine graphs. But my teacher friend (who I first learned to teach with/from) in another state basically does the same activity but with Wikki Stix. She has them do the measuring of the angles and the heights, not with a string, but with the Stix. Also, once they measure the "height", they snip the Stix into that length and "stick" it down on their graph. So ultimately, later on you have a Wikki Stix sine curve graph. Way cool and something I'll try this year .... though with 3 precal classes of (current sizes) 37, 32, 30ish, how much will that cost?

New Skills

I was at a math workshop today, and from a participant I learned a great calculator skill that left me saying, "where have you been all my TI-83/4/silver edition/titanium life?".

Suppose you're graphing, and suppose you simultaneously want to see the graph and the table screens. Well: mode > G-T, and poof, when you hit graph, voila, split screen. Then you can toggle between the 2 parts by hitting the "table" or "graph" button, and then you can do whatever you want on that part of the screen.

Also, you can split the screen horizontally (mode > horiz ...) and then you can show the graph and either the main window or the lists or a table, etc.

Ooh, aah.

First Day Back Haiku

Inservice Monday
Meeting, meeting, lunch, meeting
Where did summer go?

Addiction

Ackh! In the process of updating my homework website further, I thought I'd add a "games" link that showed some fun thinking/math/logic games. Well, of course I had to try them out to see what I was linking. .... Too many hours later, I'm addicted to 2 I found at http://www.coolmath-games.com/ : "walls logic" and "bloxorz". The first has you building diagonal walls on each of the tiles in a grid, and you can't form loops, and you have to follow "# of walls rules" for certain intersections. The second has 33 levels, and you basically move a brick around to get it in a hole. ... Okay, must stop playing and go do other things.

On a side note, as I was trying the new games, I found myself getting blurry eyed just reading all the instructions, and I just wanted to jump in and test the waters instead of reading about it. Hmmmm, sounds familiar. So now I'll try to think of each school lesson in a new way: how can the students get started right away doing something and then learning what they need to know about it at various stages of the class.

First Day Algebra Activity

It looks like on 8/25 we're starting right away with 1.5 hour block classes when school starts (as opposed to meeting all classes and having an "alpha" period with about 40 minute classes). I need about 40 minutes to call roll and ask for pronunciation corrections, have them fill out a seating chart (I like them to sit where they want the first time, so I see who can/can't sit together when I soon make a seating chart), take pictures of groups (so I can memorize names), and talk about the syllabus. While all this is going on, I like them to be doing something. Here's my something:

They'll work on it quietly while I'm calling roll, and then I'll prompt them to check and work with their group and meet everyone in the group while I'm snapping pictures. Section "A" prompts them about "PEMDAS". Section "B" has orders-of-operation problems with 2 answers to circle, one for the common mistake and one correct answer. Section "C" has a fraction/decimal/percent table with one column filled out where they fill in the other 2 with equivalent expressions. Section "D" has four "4"s and an answer, and they're to fill in operations to get the right answer.

Here's part of their first assignment (and parent homework):

This is a math autobiography and asks questions about past classes and school experiences and such. It also asks their parents to indicate "I am proud of my child because" ....

This will tell me many things about the student: if they do work on time, if they are neat/verbose/last-minute/thoughtful. They also get to see their parent's bragging comments (and sometimes if there are no comments, I'm sad for the kid). I also have a good opportunity to get their parents' e-mail address for future grade sending.

Then I have about 50 minutes left. I'm thinking of a "box plot" activity and a "meet and greet" activity. ... still in the planning stages, though.

Whew! Two tasks done.

My Summer Vacation

Just last week I went to an aerobatics contest my husband was in. It's small, so EVERYONE is wrangled into volunteering somehow.
I got to be a boundary judge and learn the skills of how to read a sequence card and how to call the ins and outs and how to survive blistering heat and curious cows and carcas sightings. First my partner and I (another wrangled wife) had to drive 10 minutes to the location.


Here is an actual corner boundary that the pilots would see from the air.

This is the other wife sitting in position ready to call outs/ins. The contraption is uber cool and thought up by an engineer/pilot who used a compass and his brains. AND there's math involved (what else).
There are 2 sets of 2 strings lined up perpendicular to the other set, and you line up the strings of one set with your eye and .... since 2 lines form a plane, you can determine when the aerobatic planes cross the boundary or not. We were at the "southeast" boundary, so our job was to call "out south", "in south", "out east", "in east".

Boy were we stressed about doing it right. We're not pilots, and we had to figure out what squiggly lines on the cards matched what things the pilots were doing in the air. Eventually, we mastered it as a team. Here are some things that kept us company each time we went out.

Website Goals

Well, I am glad I started my homework website last year, and I'll continue it this year. I found many benefits:

* I made one of the 1st homework assignments be for parents to look at the site and send me an e-mail. This gave me their address for sending home grades, and it also made them aware.
* It gave me a place to post extra worksheets and solutions where they could download them (I didn't do this too much, but maybe will increase it this year)
* Students had an easy way to find homework assignments for whatever reasons.
* Parents now had a place to see/check whether their children had homework or tests coming up.

This year ... (with my 4 PREPS!) I'll continue it, and I want to enhance it:

* I want to somehow incorporate quick easy-to-make-&-upload videos showing various math techniques (I'll film them).
* I potentially want to link to videos from TeacherTube (since YouTube is blocked at our campus).
* I want to post notes for students that are absent (this one I'm iffy about for a variety of reasons: difficulty, space issues, student accountability, ...)

All in all, I'm happy with weebly.com. Hopefully, it will continue to be free or even cheap, and hopefully they'll resist putting ads on their/my page since that was a big draw for me.

Passive Learning

I picked up the AP Calculus exam scores for my students, and while I had a good number pass, there weren't as many passing as I expected or knew that COULD pass. This made me reflect over the school year and day-to-day activities and behaviors of the students. For the ones that didn't pass (but that could have), I see a pattern. They were seemingly attentive in class. They did their homework. They did reasonably well on tests. However, they did not pass. I think a big key is the "seemingly" attentive in class. They learned to play the game and knew to make the "paying attention" actions, meanwhile, maybe for a large portion of class, their minds were elsewhere. (this also goes for my other, nonAP classes).

I've never consistently had daily assessments at the end of class (of some form or another) to see who's getting it, and who's not. Yes, I've walked around class and they practice the skills. Yes, I know who's struggling. Yes, I suggest they come in for help. BUT. There was no consequence to them whether they followed up or not. My tests were structured in such a way that they could do corrections and earn back some points, and that was enough of a safety net for students.

On the plus side. Many (all?) of my students care about their grades, so I've started thinking. There are 6 weeks in a marking period. On block schedule, that means I see them roughly 15 times. Each day I could have a quick assessment (5 minutes?) at the end of class. Everyone getting a different problem (or at least everyone in one group of 4 getting a different problem) ... or 2 problems ... based on the day's topic. This could be worth 1 test point and so by the end of the 6 weeks, totally, this would add up to approximately 1/2 a "normal" test. They'd get 100% if it's correct. If anything is wrong, they have the option of coming after school to make it up. Each time it takes them to make it up (to 100%), their grade goes down to a B then a C, etc. Their tests are weighted about 75% of their total grade, so this would be significant enough to make a difference.

This way, they'd have more of an incentive to ACTUALLY focus and learn during class time because they'll be held immediately accountable for the information.

Possible "cons":
1. more paperwork (though it's only 1-2 problems per student and maybe I can have a limited # of total problems and put the problems on the overhead so they just have to have paper).

2. Would it have the desired affect? (well, I think so, and won't know until I try it) ... maybe I have to incorporate other things, too.

Differentiating Instruction in High School

I know it's a good idea. I know it's what we're supposed to do. Maybe I'm even doing it sometimes (most times?) and don't even know it. BUT. There's always a part of my brain saying, "too many kids, too little time, not enough resources specifically for math or for high school ...". Everything I have read in the past seems to be, "give projects!" and that seems to be the bulk of what I got from their suggestions.

This book (http://www.amazon.com/Differentiating-High-School-Classroom-Strategies/dp/1412917166/ref=sr_1_1/105-4459711-7881269?ie=UTF8&s=books&qid=1216748751&sr=1-1) seems to be different (from my glance and quick read through at the bookstore and through reading the 1st 5 pages and looking at the bulk of what each topic is about). I like the fact that the woman is (was?) a high school teacher. She has taught not just the "cream of the crop". She's not a PhD researcher who only knows theory. She talks about many obstacles and how to overcome them. She talks about the fact that, yes, we do have lots of things that get in the way. AND. The best part. It's geared to high school. Hopefully, I'll absorb the material and be able to use it as a springboard to make some progress this year on my differentiation.

Cumulative Knowledge

I've been batting an idea around in my head for a while to deal with the following problem. Students in AP Calculus need to remember information from (say) August on when they take their exam in May, and students/people have a very hard time recalling information they haven't seen in months even though it may have been "easy" for them in the past.

I don't want to give cumulative exams because I believe:
1. either the students will just shrug their shoulders and give up those "past" problems for lost points,
2. it seems more punative even though it's for their own good
3. I won't be able to cover ALL old topics every time
4. it would only be a (possible) review for students (say) every 2 weeks or so

So my thought is that I want to assign cumulative homework basically every class, and as we are on a block schedule, I'll give them "2" homework assignments each class, one for new material, and one for old. I don't want to have to scramble for old material every time, and I want it to be accessible to the students, so that the review process is not so painful. Here's my germ of an idea:

Have a designated folder on the computer for cumulative work. Have a pre-mapped idea of what we're learning for the whole year (and its timeline) and how many assignments I roughly need. Each time I teach a new topic, I'll have some notion of how many times I want it to appear for all the documents and I want to spread it out, so that day/week, I'll just take the basic problems (?) and cut and paste them into all the appropriate files with an "answer bank" (in some form) on the bottom of the page. It's fresh in my mind since I just taught it, so I don't have to waste time coming up with new problems for them to review. Also as time goes on, the assignments will either be completely filled with problems, so I'll just touch it up and print it out, or it'll need just a wee bit of extra work. I believe I'll also put the date(s) we learned the topic near the problem, and since they'll date their notes ("hey baby, want to go to the math movie tonight?"), then they'll be able to easily flip back and brush up. Also, since the answers will be there, they'll have immediate feedback if they remember the process correctly or not.

I'm also thinking that at the beginning of the year, it'll be slim pickings on "review" material, so I may assign things like (along with a brief tutorial on the page) finding equations of lines given various information, fraction work, factoring work, ... the basics that seem to need extra gentle and not so gentle revisits every year.

Volume of Revolution Project

This past year I tried something new with my calculus students for the "volumes project" in the oh-my-goodness-what-to-do-after-the-exam phase of the year (closely linked to the eek-I-hate-giving-class-time-to-do-projects-and-can-they-waste-any-more-time phase of teaching calculus).

I did the project with the kids to see what was involved, and I told them it was the first time I'd done this, so we'd learn the pitfalls and tips and such together. I also was vague on how they should display the projects at the end. I said, "wow me" and "whatever you do, have a good reason for it" and "think of the best way to display it to use as a learning tool".

The general idea was that we'd all have the same starting 2-dimensional region (y = 4 - xx), and we'd each revolve it around a different axis of revolution, and thus each have different solids at the end.

She wowed me with her final presentation:
This is mine (I now realize I took the picture upside down). Hmmm, spaghetti/math-tool ... probably not too long lasting:


Before she started, she kept saying, "I want to make it into Saturn", so I guess she continued with her space theme:

He was so funny, "tell me what to do. tell me what to do." Me, "no. no. NO.". He finally came up with it himself:

Hand Holding vs Solid Examples

I feel like a flippy-floppy fish on this whole topic, but I guess I could "spin it" as I'm readjusting my attitude as I gather more data. For the last few days, I've been studying statistics for the N.B. exams I had to take today. I went right to the source and bought a prep book for AP Statistics. Since it's a prep book, they don't TEACH every topic in depth, they just review it and do SOME examples and then give practice tests. ... Maybe not the best way for me to review something I haven't seen in ... oh my ... 16+ years.

I found that as I was learning one of the topics, they kept describing each piece/terminology of it in many ways and then building on and then redescribing each piece/terminology, and I found myself saying: JUST SHOW ME A SOLID EXAMPLE FOR THE LOVE OF GOD. And then I had to laugh and say, "oh what, you want them to HAND HOLD YOU through the stuff? can't you piece it together yourself for the joy of learning?"

"Gripe 2": there were SO many new vocabulary words that I'd understand in the context while I was learning it, and then when the book refered back to such a word, oh say 50 pages later, I was thinking, "yesssssss, that SOUNDS familiar, but holy cow, don't ask me to use it in a sentence other than: _____ is a word related to statistics.

All this to keep circling back to the topic of how my (any) students learn and retain math. I guess mostly I write this, so I can get over my uppity self and keep in mind that learning anything new and hard for students is, well, hard, and students should be provided with scaffolding and good-humored reminders that they're doing something hard and should pat themselves on the back between note-taking and problem doing and such. AND teachers should keep this in mind and keep spiraling back to old topics and bla bla bla.

WooHoo! The School Year is Over

The students' last finals were on Wednesday 6/4/08. We had to come in on Thursday to check out, and our graduation was held in the early afternoon. I went in on Friday to finally clean up the rest of the clutter in my classroom. And now ... I'm at home completely done. Whew. As usual, it sneaks up on you and is over before you know it. (unless you're still in school, and then it NEVER seems to be over)

I had a bit of drama (still ongoing) with a parent EXTREMELY upset because of my grading policy for the last 6 weeks. Ultimately her child got an 87% for the semester, but that's not acceptable to her, and I've ruined her child's life, and she'll be speaking to my administrator to make sure I don't have this opportunity EVER again to do this to another student. Deep breaths. I've talked with various other teachers and friends and have calmed down a bit, but obviously I'm still bitter.

In brighter news: I've started "playing" the guitar (and by playing, I mean random strumming and posing and trying to look cool while screechy sounds eminate from the instrument as my tongue sticks out of my mouth to aid in better concentration) and am self-teaching myself (that sounds redundant) via books and cds and dvds. It is so fun.

I'm also planning on making a simple big-square quilt for our guest room this week, so that when my friend visits, I won't have to subject her to the 80's style black-neon-pink-&-green-&-purple syntheticy cover.

Calculus project news. I liked how my volumes of revolution foam projects turned out. BUT. I have an idea I want to play around with for a teaching tool for next year. I'm thinking of getting card stock or laminated color paper and cutting the same shape out many times. Then I'll either cut a hole in each one or a slit in order to string all these shapes onto a circular thin wire or stiff cardstock that is curved into a circle. Then I can "fan out" the shapes or clump them together, and the students can get a better visualization of a "volume of revolution". I'll have to experiment this summer.

Note Taking

My precalculus students have recently taken a test on sequences, series, & the binomial theorem. The students run the gamut from they-could-teach-themselves-out-of-a-book to please-take-my-hand-and-do-the-problems-with/for-me-over-and-over-again. It dawned on me while I was helping this latter type of student to study that she had no concept of what might have been some good things to study and review before taking the test: formulas for explicit terms, partial sums, pascal's triangle ...

I thought over the notes they took, and I'm wondering if it ALL was so foreign and important sounding to her that she saw it as:

sdlkfoe sdoowieur sdeoe 5 = sdlfoein sdifuoeen
oeiwonewio sdf e3dof soieen sdeid nli lskejoi i9 dflk

so maybe she couldn't parse through it all and figure out what was important to know. I know when I was presenting the stuff, I had them do examples, and I had them write down the formulas and I discussed why they work and how to think about them .... but apparently, for some students, I have to stress what's important before, during, and after. And then maybe I should make them get out their red pens and BOX all the key things.

But this doesn't sit well with me. It seems that I'm doing the thinking for the students that way, and they'll never learn to sit back and reflect on what may be important to know without someone spelling it out for them all the time.

Stress City

Good riddance to a bad week. I had 3 bad run-ins with kids that left me so angry.

Run 1: I've had issues in the past with students conveniently not showing up on exam day. Then they'd take weeks to make up the test. Two tests ago I started the new policy of, "you miss the test, you make it up during class the next day". This helped. Then this past test, I had 2 students mysteriously absent on test day, last period of the day. I checked ClassXP, and, gee, mine was the only class they were absent for. I decided to use technology to my advantage and pop a quick e-mail home to mom: "is there a reason your child is absent from my class today?". This got results, and it alerted the parents without sounding accusatory (they could have had a dentist appointment). Well, it turns out one kid lied to his mom about where he was, and I found out, and thus he got a zero for that test. So, here we are Friday, and he's in my class just sitting there fuming all period. One and a half hours. Yay. So, not really a "run-in", more like a long, drawn out sit-in with teenage angst of getting caught and having to sit and take it.

Run 2: One child is in NHS, and has been slacking off on the homework department and just general character department all year (okay, all 4 years). After a bunch of stuff had happened, the NHS sponsor would only let him wear the "stole" at graduation if he got letters from his 4 core teachers that he deserved it. So he comes in to my class and tries to good-naturedly try to bully me and guilt me into writing his letter. He still didn't get that it's his actions that brought this on. He still thought/thinks that "we" are doing this to him. That left a bad taste in my mouth.

Run 3: Oh my. We're doing projects during calculus class, so it's a wee bit more unstructured as a class period than I like or am used to. Some kids are doing videos, and one kid in particular doesn't have any of his equipment at school, so just basically sits in class and says he'll work on it during the weekend. That's all a side issue for this run-in. He comes into class on Friday and does not look physically well, so I basically don't bother him much. Towards the end of the period, one student had turned to him and asked what he was doing. Apparently, he had unbuttoned his pants and unzipped them a ways because he was uncomfortable and didn't want to put pressure on his stomach. Well, okay. So I catch this interaction, and say to him, "well just put your shirt over your pants, so we don't have to see your unbottoned pants." Then he starts arguing with me. I keep asking him to just pull his shirt over and that it's just not socially acceptable to sit there like that. This goes on for about 3 rounds as he's refusing. Then he suddenly turns all creepy and lowers his voice menacingly and leans forward to me and says, "I'll decide what is socially acceptable and I'm NOT going to button my pants so you can be on your power trip and .....". Oh my god. I was livid. I told him to stop talking to me and that he was being completely inappropriate and he just needed to either leave the room or button up his pants. Holy Cow. Jerk. Excuse me while I jump off my teacherly manner and just fume about the brat. Okay, deep breath and the knowledge that I only have to see him for 2 more days.

Anyhow. WooHoo for weekends, especially 3 day ones. And only 7 more school days.

End-o-Year Calculus Project(s)

I ended up deciding to give the students a choice of 3 projects to do for the remainder of our time in class:
1. a volume of cross section project using colored cut foam that I've done before
2. a volume of revolution project again with foam (never done and I'm doing it with the kids)
3. a video or power point (never done before, and thanks, Sam, for your tips which I've incorporated).

I'm happy that 7 students picked the video project, and 2 picked the power point project. From talking with the kids, they mostly had great ideas and are working hard. One student is resisting everything and being really derisive and dismissive and coming up with every argument in the book as to why he shouldn't be doing this. Or talking about doing something sarcastic and such (because, you know, math just isn't that exciting). I'm working on setting him straight using my teacher voice as I'm simultaneously resisting the urge to vigorously shake some manners/sense/attitude-adjustment into him.

I'm excited about the volumes of revolution project. There are 6 (?) of us doing it. I picked the same region for all of us (y = 4 - x^2 , y = 0 , x = 0) and we're each revolving it around different lines. That way we can put them all together and see what's what.

One video pair is working on a video about someone getting ready for a "math party" and they have to cut eggplant and for some reason need to know about the volume (details will emerge). They wanted to know how to get a function that looked like an eggplant. One girl was really excited and happy to learn something new when I showed her how to plot the shape on paper, pick some points on the "graph", put them in L1 and L2 on the calculator and then do a Quartic Regression. Cool. It DID look like an eggplant when she showed me.

Limits

I was teaching algebraically finding limits today in precalculus. We got to the part where x --> infinity. I've tried various ways of explaining it in the past about how you only need to look at the highest power term on the numerator and denominator and make your decision that way.

I've likened it to "when you're plugging in REALLY LARGE NUMBERS, the largest power term is like the ocean and the smaller powered terms become like spit. They don't make much of a difference to the ocean volume." This stuck with some kids, but I don't know that all were convinced.

Well. I had one problem: (8x^3 + 2x - 7) / (-4x^3 + 5x + 100) or some such thing. On the graphing calculator, we entered 1,000,000,000 and stored it in x. Then we calculated 8x^3. Enter. Then we calculated 2x. Enter and compare. That semi-convinced them. THEN we calculated 8x^3 + 2x, and that really convinced them because it "was" the same output as 8x^3 by itself. And we all know that if the calculator says something, then it must be true.

If I was thinking (because what I did was on the fly and then I moved on), I should have also then (in the main window) plugged in the whole expression using the stored value of x .... or then putting in larger values of x and then "2nd entering" to recalculate the expression. Next time.

The Quiet Ones

For various reasons I thought it would be best for my calculus students to practice more than class would allow, so to entice them to come after school for 6 straight days before the AP exam, I called them "power sessions" and said I'd bring food every night, and we could meet from 4:30 -6:30 and just do and discuss old released exams. I had anywhere from 10 to 28 kids show up (out of my total of 40) each night. I think it helped. We were all relieved once the AP exam was over, and I think it payed off for the ones that put out more effort.

During these sessions I'd call out a couple of problems at a time, and they'd work them, and then we'd discuss them. As usual I mentioned that people should just ask questions when they had them. I always have people asking questions. This gives me a false sense of things-are-okay-for-everyone. Or maybe I'm just gauging my time and trying to get through a lot and just moving on once the questions die down. Or something else.

I know there are a couple of girls that work hard but struggle. They asked NO questions. I'd even look them in the eye and ask if they had questions. Nope. I know I should know better than that, but apparently I don't (even after 11 years of teaching). So finally I started going over to them while the class was working the problems and would say, "you're fine? or do you have questions?" and invariably they'd have some question that I could quickly answer for them to set them on their way.

It seems like each class gets a culture, and there are the talkers and jokers and more vocal participators and then after a while we all settle into a routine and maybe it's hard to rock the boat and make your voice heard if you are not used to it and the other kids are the "cool kids (?)" or the "class representatives (?)" or something. Here's to being reminded to remember the quiet ones.

Filler Classes

This past week was our TAKS week, and therefore I only saw some of my precalculus classes, and so I could not move on, and I did NOT want to have "free days". One day, I taught them about binary and counting and adding and subtracting and multiplying in different bases.

I made the connection to base 10 where you can think of each position as a bin where you drop marbles. You start filling them up from right to left. The capacity of each bin is 9, and once you try to put one more in a bin, it would overflow, and so you have to scoop the 10 you want to put in there out and place one marble in the next bin over to the left to designate a higher power of 10.

So we started counting in base 4. Each bin has capacity 3. We did the "scooping" thing. We counted to 20.

1, 2, 3,10,11,12,13,20,21,22,23,30, ..., 103, 110.

We made the connection that each bin represents (from right to left: 4^0, 4^1, 4^2, 4^3, ...). We did other bases. We then converted between base 4 (say) and base 10. And between base 10 and another base.

I also recalled a version of a game I played in 8th grade, that I still play when I need to occupy my mind and have time to kill.

Pick any 4 single-digit numbers. Then number your page from 1 - 10 (as one example), and you have to use every one of your chosen numbers once and any math operation to get all 10 numbers listed. I had them play and the first one done would get candy. Boy were they quiet and working. I'm SURE it was the math and not the candy.

For example: 5,2,8,9

1. 9 - 8/2 - 5 = 1
2. 2 + 5 * (9-8) = 2

Attitude

I think I've learned to perfect the, "what do you MEAN you're not going to do the thing I've asked you to do?" look/attitude.
The, "of course you'll do it" look.
The, "there's no other option" look.
The, "I'm amazed you'd even think to ask such a question" look.
The, "don't be silly" look.

I got to use it Monday when I prepped my AP Calculus kids on the fact that they had homework that was due Tuesday even though I wouldn't see them due to the state test, and they'd better walk their butts over to school from whatever vacation they think they're getting and hand in the no-lates-accepted AP-exam--multiple-choice corrections to me.

Of course I'm semi-bluffing and know I'm asking a lot of them, but I think the "look" gets them to get off their duffs, and maybe I'll have a higher turning-in rate because of "the look". I also reminded them of the fact that the AP exam is coming up next week, and don't give up now, and you can do it, and it would be a shame to work so hard all year and flake out now and miss the opportunity to pass, and rah-rah-rah ...

Plus I get to practice being a bad-a** when I think I'm a softy inside ... but maybe I'm fooling myself, and I've become mean and cranky with high expectations. Oh well, they usually rise to the challenge - and I guess it's our job to push them to do their best, even though it's their job to resist and try to get away with what they can. Our little teaching tug-o-war.

Idea for post AP exam calculus

The last 2 years I've done different things after the AP exams in my calculus classes. One year we did a rubber foam volumes of cross sections project. One year we discussed "multiple" integrals and (non calculus) counting and adding and multiplying in different-than-10 bases.

I just had a thought I haven't fleshed out for what to do this year. I'm thinking of getting a list of topics that span the calculus year, and having the students make short videos that teach or showcase the topic. That way I can post the useful ones on my website for the next year's students to have a different perspective on things they may struggle with. Also, the students are creative, and I think they may come up with good stuff.

Grading? I'm thinking there has to be a time limit (less than 4 or so minutes), effective (to be judged by other students), creative (again judged by students), done on time, ....

One issue may be various student access to video equipment. Another issue is size of groups working on one video. We'll see ...

Shhhhh

I was at an AP Calculus prep session for the students most of the day today. There were 3 sessions running in parallel, and 4 different time slots throughout the day. I sat in on the sessions and worked along with the students. One teacher had great problems, and he'd keep talking and talking and say, "okay now you work the problems", and then he'd only give us 1 second (or so it seemed) before he started talking again - either about something else, or to start working the problem.

It made me reflect and wonder if I do this more than I should. I know I try to shush up with enough time for the kids to work, but at the same time I'm clock watching and stressing about finishing in time and getting everything in and then maybe rushing the kids.

I also tried something different in BC calculus on Friday. I handed them my notes from "math camp" on parametrics, and then also handed them a separate packet of problems with answers provided in the back. On each of my "camp" notes, after each problem that had been worked out, I had written on their copies, "now work problem so-and-so". I barely talked to them at all, and only monitored to see if there was any clarification needed. They worked like champs all period, and were doing all the problems. Hopefully, they'll continue over the weekend, as I told them there'd be a "free response" quiz the next time they came to class.

Testing Testing

Okay. It finally got to me. All year when I've announced tests and given tests, there's ALWAYS some students absent. Then it becomes a game of, "when are you going to make up the test". Then days and literally weeks would go by before some students made up the test. They all eventually do, but really! It usually didn't annoy me TOO much, but now during this last test about 1/5 of my class was gone from each period during the test.

In the past I was diligent about mentioning and then checking up on whether the students were cutting or not, and then they had zero chance of making up the test. This year, I had other things on my plate.

I'm giving a test this week on Wednesday and Thursday (block scheduling). I mentioned ahead of time, "if you are absent the day of the test, the next time you are in class, I will put you out in the hall, and you will make up the test during class time and miss the current lesson." Hopefully, this will make it less appealing to the students to all of a sudden feel really ill on the day of the test and use that as an excuse to drag it out.

I heard another teacher at the beginning of the year announces: every time everyone is here for a test, everyone gets a bonus point(s). She found that then the students were policing each other to make sure they were there.

I guess my method will work (I hope), because either way, the students will finish the test within a week (unless they're super skipping class).

Getting In Trouble

We recently had an incident in our school regarding relations between a teacher and a student. Phew! The repercussions of that. Part of me thinks: WHAT was the teacher thinking. There goes the career, the chance to earn a living, the student's psyche, ...

We had to all go to "harrassment" training for 1.5 hours. All the way up to the meeting I was grumbling to myself: I didn't do anything wrong. I have classes to prep for during my prep periods. I know right from wrong. Grumble. Grumble. Then as these things sometimes go, I learned some things.

1. Even if the student is 18 or over, it's still cause for dismissal.
2. If you hear any rumors about other teacher/student goings-on, and you don't say anything to the authorities, and it's later found out that you knew/suspected, you are in the wrong and could face .... whatever.
3. Even if your relationship is innocent (and later proven so) with a student, if others perceive it as fishy and the rumors start to fly, you could lose your job because the public has "lost faith" in your ability to be effective in the classroom (hmmmmm)
4. If students get too friendly with you and develop a crush, and you don't nip it in the bud or make sure you're never alone with one student, etc. one of them could become jealous and start spreading rumors about you (creepy) that may cause you to lose your job.

There's probably more, but that's depressing enough as it is.

Parents

Two weeks ago I was scrambling and rushed for time, so I did not complete the official "progress report" sending via the school (every student who is failing or within 3% of failing receives a progress report). So. Within the next couple of days, I printed up IGPro grades, 4 to a page, chopped them up, attached them to a 1/2 sheet stating that parents should discuss this with their child and write me a note and sign it that they've done so. I made it a SMALL quiz grade to guarantee I'd get them back, docking off 10% per day late.

I have one awesome kid that is always in for tutoring, asks questions in class, does all his homework, scores very well on tests, takes "retests" (bane of my existence) every time if he does not get a perfect score, has a 99.63% average at the time of the reports. His mom writes back: I know he can do better. I will make sure he comes in for tutoring so he can improve.

Compare this with another student who has a 93% with the parent comment of: my son is so great!

Compare this with another student who has a 3% and who scratched out his mom's comment to call her.

Fun vs. Effective

Last year from a workshop I learned of a fun activity with which to introduce volumes of revolution to my class. It involved candy, the kids seemed to get it. They loved it. We all walked away with smiles on our faces. But then they got home and couldn't do homework involving revolving regions about various axes. Granted in class, we only went through 3 examples, I talked them through it all the while giving them a chance to process it. But still, no.

This year, I was looking through my files and came across another way to introduce volumes of revolution. It's (free) from www.mastermathmentor.com . And there are TONS of calculus AB and BC (did I mention free) worksheets there. I'd hesitated using it before because it looked TOO LONG to get through in class. Then the homework was TOO LONG. Hey genius :), just because all the problems are there, it doesn't mean you have to use them all.

I used this sheet this time. I slowly walked them through the 6 parts of example 1. I kept stressing the questions to ask yourself, and I weaned them off my help so that by the 6th problem they could do it by themselves. Then for homework I assigned them examples 2 and examples 3 (12 problems) from the class work worksheet. Wouldn't you know it. They all got it right. AND they could then go on and do more challenging problems. Success.

I keep having to teach myself that not every student can get by on just one to two examples to teach a concept. Some students need 5 or more examples. But then there's always the time factor and the other kids in class that can get it with just one example. Anyhow. I'm now excited because I've found a new effective way of teaching this topic.

Seeing Pink

Well honestly, seeing Red, but since I'm not doing anything about it other than losing sleep last night, it's been downgraded.

Apparently, our algebra, geometry, and algebra 2 teachers have been told to stop teaching the curriculum and start teaching to THE TEST. The state-mandated, must-pass in junior year to graduate, must-pass in sophomore year to make our school "acceptable", must pass in freshman year or else the uppy-ups start to panic and worry you won't pass in 10th or 11th grade ... TEST. And for how long are they to teach to this test? FOR 3 MONTHS. That's 3 months of math knowledge they won't have the next year, and the next and the next. Oh my god that is so short-sighted.

Honestly, if I was teaching one of those classes, I don't know what I'd do. Would I refuse? Would I teach part of my class to the canned activities that they all must follow and then teach the curriculum? Would I raise a big stink and even go so far as to quit in protest? And why am I not doing something now? Just because it doesn't directly affect me (it will when they're in precal and calculus)? If you know something is wrong, and you keep letting it continue, aren't you just as guilty for it perpetuating? Argh.

People Watching

I was out with my friend this weekend, and we went to a tea house in an upscale, outdoor mall. It was fun to people watch, and there were all types - pregnant moms with little kids in tow, glamour teens with their high-price accessories, vogue 20-somethings, everyday people in shorts, lots of girls in sundresses. I started thinking about the things that go through your head when you watch people.

I'm wondering if a lot of the mind chatter is like - oh I wish I had abs/legs/arms/etc like that, or I wish my hair swung like that, or I wish I looked like that .... and I'm wondering about how much that affects how you live out your life or the choices you make.

What if the mind chatter went more like - oh I wish I was as generous as that, or I wish I could forgive like that, or I wish I could contribute to my community in that way like that, or I wish I was as good a person as that ... more inside stuff than outside appearances.

Counting To Ten

I know we hear that once you ask a question of a class, you should "count to 10" to wait for the students to think about it quietly before you proceed to ask for an answer. And I guess when we're tutoring students, and trying to walk them through a process, you "count to 10" after you prompt them for a piece, so again they can process the information.

I literally "count to 10" in my head, and sometimes twice. Now not 1,2,3, ...., 19, 20, but 1, 2, 3, ..., 10 then 1, 2, 3 ...., 10. I'm wondering if other people do the literal counting in their heads while they wait.

Then again, I count the stairs in my house when I'm going down or up them (5, 8, and 6). I count the "bumps" in one piece of the highway on my way to work (10).

I think the counting is good. I sometimes count to 10 after I am "giving them notes", after short bursts of speech, so that they have time to process what I just said before I burst some more (I'm sure they're on pins and needles waiting for the pearls to fall from my mouth instead of thinking about boys or girls or prom or music).

I'm thinking of this one reporter on NPR. He always sounds different from the others. He's the one in Florida, and he talks really fast (compared to the other reporters) and it just sounds different and noticeable and you just want him to slow down. I don't want to be that "reporter" teacher, but I know I talk fast, so hopefully I'll keep counting to remind myself to slow down.

Snacks

A while ago I got into the habit of keeping snacks in my classroom in a big plastic (dark, non see-through mouse resistant) tub. I like to keep, graham crackers, pretzels, cheddar bunnies, Newman cookies, CheezIts, cereal, etc. It seems to be an incentive for kids to come in for tutoring at the end of the day, or at least to have them stave off their hunger (or ruin their appetite for dinner) as they're getting extra math help. I found that baby wipes and extra napkins and maybe small paper cups for pouring treats into are helpful.

There have been some incidents. Once during first period, a student mentioned she hadn't had breakfast and wondered if she could have a snack. I said sure, and envisioned her quickly taking something, closing the tub, and getting back to work. After I continue with my lesson, I glance over at her, and there she is in all her glory, open tub next to her, and an array of snacks on her desk. We quickly fixed that, and I made a mental note: no "tub" during class time.

Another time a student asked (during class) to have a snack. I said, no, that it was only for after school. Then she tries on her pleading voice, "but I really like them, pleaaaaaaasssssse". Ew. No means no. I'm reminded of a TV talk show I once saw where the message was, just because someone asks for something nicely, it doesn't mean you should give it to them, their example was: "oh I LOVE your diamond necklace. It's so beautiful and elegant. Can I please have it?"

Then there are the "vacuum" kids after school - not many of them, but, sheesh. All snacks inhaled, and thank you very much.

But mostly it has been something I think I'll continue.

Spring Break

WooHoo! Nine days off to relax and catch up and stuff. I went to Portland, OR for a few days just to wander around, and the rain gods must have been busy elsewhere because it only rained on the night I came in and on the night I left. Note to self: red-eye flights bad, but made better due to the fact that I had a whole glorious row all to myself to "stretch" out in for 4 hours of interrupted sleep.

As I was wandering around and needing a caffeine fix, I started looking for either the *green* popular coffee shop circle/emblem or the *red* one. Then I got to thinking how that's so ingrained in our brains, and we now have instant recognition of logos and various signs even if they're too far away to read, we've memorized them. Then that got me to thinking about various things I want/need my calculus students to know: derivatives/integrals related to e^x, ln(x), trig functions, etc.

My thought before spring break was to have various posters around the room with "need to know" things on them. Maybe in different colors or styles, and just the fact that the kids have to stare at them every day may help them when the AP exam comes around, and they can close their eyes (maybe) and "see" what they need to know. Then I thought I'd force the issue and periodically (daily?) have us recite the posters. Then after my trip, I thought maybe we can design some sort of logos for these things. Anything to make facts stick in their heads when they have SO much to memorize.

Must think about this some more.

The Old Days

Today in precalculus we went over / reviewed / saw again / learned Long Division of Polynomials and Synthetic Division of Polynomials. I told the kids that I had mixed feelings about teaching the L.D. because I thought it was on its way out due to graphing calculators but I still thought it was worthwhile because it was cool and it allowed them to practice their algebra skills and solidify their knowledge of factoring.

Anyway, I mentioned that I had a friend that was about 10 years older than me (so she probably graduated high school in early 1970s), and she mentioned that she had to learn how to calculate square roots by hand, and these days we don't teach that anymore.

Another student asked, "didn't you all have to look up the sine and cosine and stuff in tables?" And that got me thinking. Yes we looked them up in tables every time we did trig, and so that visual memory was there, and we had constant reminders that you took sines of angles and the result was a number and all those numbers seemed to be between -1 and 1. (now I don't remember if it was between 0 and 1, and we had to think or not).

I seem to have too many instances now where in a situation, students don't intuitively know in sin x = y which is the angle and which is the number/ratio of sides. It seems like maybe we've/they've lost something from not having that table to help.

Results

Well, I tried the "blank out the correct answer on a multiple choice question" idea. None of us liked it. I asked for feedback from the kids after they worked on 5 problems, and they said, "well, it's okay if you get one of the wrong answers, but if you don't, then you don't know if you're not doing something ELSE wrong or if you're correct." I think I agree with them.

I went to "math camp" today (calculus teachers sharing materials), and I have a new appreciation for Winplot. It's a free software you can download from Exeter acadamy, and I've only used it for creating graphs for handouts in the past. BUT. One of the teachers showed how he used it for demonstrations in class and such. I'm by no means even close to being an expert, but it gave me motivation to learn more skills in the program. Apparently, they also have WinGeom, and WinStat ... or something like that. I haven't looked into it.

Multiple Choice Idea

An AP English teacher passed on this idea from a conference she attended, and I thought it sounded effective and cool and will try it soon. Give the kids a sheet of good multiple choice problems (the non answers are based on common mistakes). Say there are 4 choices. White out the correct answer choice for each question and leave the 3 non answers (the kids know what you've done ahead of time). This way, the students work through the problem, and if they see their answer there, they know they made a mistake, and work harder at figuring out what's what.

I tried something a bit different last week - something I thought would work well. Well, it worked in that it gave me insight into what the kids DON'T know.

I had a sheet with 3 AP calculus questions. Stuff we've just covered. Stuff I thought they would be great at - integral of e^(-4x), derivative of (x^2)(sin(2x)), setting up a u-substitution integral. There were 5 answer choices. I gave all answer choices. I picked 3 of the letters (one being correct). I told them for each of the 3, either indicate it's the correct answer, or describe what mistake the student made if they picked that answer.

Well, talk about a stressful time in class. First of all, things they nod at you at when you're teaching, things they do homework on, and you think they know, things you've seen them do successfully. Out the window. Don't trust it until it comes down to proving it without any aids or support or notes or hints or prestudying for a test. So, it basically worked well in that it taught me to be careful and be more thorough in checking and rechecking their understanding individually NOT in a test situation. Second of all, it was fascinating how needy some of them were: am I right? can you just tell me if I'm on the right track? can I work with so-and-so? ... I kept telling them no to all questions, that that wouldn't help me know what they know. It was very hard not to help them, but I think that's what got us into this in the first place.

Whew. I have some work to do. But better to know that now than when it's too late.

parent homework

About a week ago I assigned my precalculus students the following homework: teach your parents something about either polar graphing or complex numbers, and have them send me e-mail explaining the experience. I've started getting e-mail back, and while some of them are simply, "yes, my son taught me," others are more elaborate and even funny "I was a willing student", "hope there's not a quiz", "thanks for this experience", "I didn't know there were such things as imaginary numbers", "I remembered how to FOIL", etc.

I'm glad I did it, and I'll add it to my notes to do next year.

The Wonders of Seat Changes

In both my calculus classes, I started dreading teaching, because invariably - yap yap yap yap - basically from 1 to 2 boys, but it would affect the whole class in some way. In BC, I sat 2 smart boys together thinking they would work well together. Well, they REALLY worked well together. They started discussing the problems loudly while I was teaching. They would outdo each other to call out the answers really quickly before anyone else had a chance to think - regardless of my constant, "think to yourself quietly / wait 10 seconds before you answer / etc". And when I would speak to them separately, they replied, "but we're learning". They didn't think it bothered anyone else. After numerous complaints, I separated them. Peace. Learning. They still don't think they did anything wrong, regardless of my, "you're not being homeschooled / you're not giving others a chance to learn" comments.

In my other class, the class clown got 3 - 4 other boys yapping, and they're pretty funny (in a nonclassroom situation) and I do like them. However. NOT IN CLASS. Today I moved the clown to the back away from the other boys. Now he's around some studious girls, and for today at least. Whew.

I can put aside my dartboard with their pictures on it for now.

Following a Rubric

At times in the past when I've included a rubric with my projects, I'm amazed that there are students that turn in something that explicitly do not include something that was clearly stated as part of the grade. For example, I may give requirements for "color" or "citing a source" or such.

Now I see it's either because I'm just like the kids, or because we're all human, or I don't know what. I'm writing a paper based on my teaching (national board) and following their format of answering specific questions, and it's a bunch of work, and I'm trying to do a good job, and I'm reading and rereading the questions to make sure I answer them, and I'm patting myself on the back because I'm "answering their questions". I breathe a sigh of relief when I'm "done".

Wait. Now I go back and reread ALL the instructions, and there, clearly labeled is a rubric on how we'll be graded. This is in addition to answering their questions. So this means I will go back after I think I'm done and reread my words with an eye for how it will be graded. But I can so easily see how a student might just think he/she is done because they've done the assignment and they're sick of doing the assignment and they wish for the assignment to go away and they may not want to go back and check on how that assignment might be judged.

Maybe we have to have an extra day built into the assignment, and once they bring it to class to turn in, they have to spend some time reading the rubric and honestly judging if they did what they needed to do. Maybe looking at someone else's and judging constructively. Basically teaching them how to use a rubric.

Unclear on the Concept

Once a week we have a 30 minute advisory where we meet with one group of kids and are basically their mom/dad on campus making sure they don't slip through the cracks. We have the same kids for 10th - 12th grades. This week I printed out their progress reports in all their classes and as I was checking in with each kid, I saw that two 11th grade boys who were sitting next to each other were both failing math, and they had the same teacher. I asked what the deal was.

One boy shrugged and said, "I don't know. He puts these problems on the board, and we're supposed to copy them and then he gives us problems to do at home." The other boy piped up with, "I think it's because he's a first year teacher." I was not understanding what they were implying, so I asked for clarification. Then one boy said, "well, then the next day he just puts more examples on the board, and then he assigns us more problems."

Oh my! The nerve of this teacher assigning homework. AND. expecting it to get done and giving a grade. I'm calling Amnesty International.

New Kids

In the past 2 weeks I got 2 new kids from different states. They're both juniors. One's in my advisory, so I don't really "teach" him. The other is in my precalculus class. I had just handed out a survey to the kids the previous class and among other questions, I asked them to "tell me something good in your lives" and "is there anything bothering you (y/n) no details needed" and "if you answered yes above, is there someone you can talk to about it (y/n)".

Well before I read them, I saw the new student in the halls one morning this week and after hellos, I asked him if he did his homework just by way of conversation. No. Well, are you going to? I'll try. Well, try and do. Okay. I noticed that he was looking a little glum, but I didn't mention it. Later I read his survey response, and he went on about how he really missed his old friends and he has no one to talk to and he is not making new friends and such.

Of course here comes big mean teacher me: What? You're sad/depressed? I don't care! Do your math homework!

I later sent him e-mail mentioning that he could come to my class after school or during lunch as there's always some kids in there. That way I figure he doesn't have to wander around aimlessly looking/being alone while everyone else seems to be having a good time. I'm wondering how many other kids there are just dreading lunch or after school because of a big vast empty space of time with no one to talk to.

Class Statistics Continued ...

I taught my 2nd 2 "box & whisker" classes today (we're on block schedule), and after some of your comments, I polled my class and mentioned that we already did hours of sleep, and we also did TV watched. Did they want to do cell phone contacts or text messages? They liked that idea, but then other ideas started popping up, and we voted. Number of songs on your ipod or mp3 player eeked out front. I don't have a cell phone or a music player, so I didn't know what type of numbers I was in for. Sheesh. Our numbers ranged from 44 to 3100.

In my next class we took a poll again, and I thought this would be not so exciting, but their choice of number of shoes they have was interesting. We decided flip flops and slippers and cleats would count. I thought boys wouldn't have as many, but some did. The numbers ranged from 5 to 80 (now, the 80 girl had a sister with the same size foot, so they shared, that was her story and she was sticking to it). One guy had 60 (I guess tons of fancy shmancy sneakers). A girl with 5 pairs widened her eyes at the larger numbers.

On the Fly Lesson

I planned to teach vectors on Friday, and I must have been super sleepy as I prepared earlier, because when all was said and done, it took less than an hour to cover what I needed to, and then I had 30 minutes left to fill with no plans.

Box and Whisker Plots to the rescue. We'd just discussed (as a department) how these will be on our state exit exam for the students and how they hadn't seen it since 8th grade. I cobbled together a lesson to show them what's what and how do do things on the graphing calculator. In my first class, we gathered number of hours slept last night, and worked with that data. I didn't like it so much since the numbers only ranged from 4 to 10. I polled my next class about what they wanted to count that had a wide range, and after some mis-starts, they came up with number of hours of T.V. watched in a week. Sheesh, that was illuminating. The numbers spanned from 3 to 30. I had to keep reminding them and myself to make no judgmental noises or facial expressions when someone called out their number.

As I still had time left, I asked them to figure out how to change the data without adding more data so that the box was wider. That got their minds working.

Filming Yourself

As part of my national board certification, for 2 different entries, I have to tape a 15 minute segment of my class and analyze it to within an inch of its life. Even if you don't need to for any other purpose, I highly recommend taping and watching yourself (though I'm entirely sick of that 15 minutes of my life since I've watched it over and over again and can be like that annoying person at a show, "Oh, here's where she says this. Here's where they do that.")

I noticed things I would not otherwise have noticed. When I question kids of varying abilities, I reword my questions (subconsciously?) based on what I think their skill level is. Like I don't think some kids can handle a question asked some way and may need help. That's obnoxious and robs them of the opportunity to show what they know.

I also notice that when I was helping a student in a small group activity, I was bodily in the way of this other polite girl's desk, and so basically the whole time I was helping this one kid, this other poor little child couldn't do her work because BIG HOVERING teacher was in her space. Of course she was too polite to say anything, so for 5 minutes she just quietly sat there. Then when you see me moving off to help another group, boom, she starts doing stuff.

I think if you can get the right group of nonjudgmental/helpful teachers together and they each tape their own class, maybe others would have insight into questioning technique or wait time or such. People with fresh eyes will pick up on things you may not be aware of.

Of course when I invent a 26 hour day, then I'll have time to get that all organized.

Speed Teaching

Right after the winter break, I finally sat down to see where I was with BC Calculus. I know I was behind from last year for a variety of reasons (new block schedule, new book, starting 2 weeks later), and I finally needed to see how far. Yeesh. I listed all the topics left, found how much time left, "did the math", and realized that if we get on the speed train of math, we can just about fit everything in with a week or 2 to review in April/May..... if I forego test days, review days, practice days, state testing days, kids-out-for-anything days. Very unrealistic. And most likely if I forego giving-them-time-to-absorb days.

I'm consoling myself with the "fact" that a lot of it is cumulative, so they'll see skills again even if we don't formally talk about it. I'm also helping the speed by every class making "skeleton" notes where students fill in blanks as I talk and the pictures or graphs are already drawn to save time, and the practice problems are already listed to save time, etc.

So far in 5 (6?) block classes we've covered antiderivatives, Riemann Sums, area, definite and indefinite integrals, FTC, u-substitution, ln(x) derivatives and related integrals. I'm also spiraling homework, and their optimization "test" is a problem that they have to keep attempting for homework until it's perfect. Maybe I'll do a few of those.

I'd better assess in some informal ways to make sure things are sticking, otherwise what's the point of cramming the stuff if they don't learn it.

Funny Kid

Students were wacky today. Just goofy and chatty and such. In my 1st period AB Calculus class - chatty chatty chatty. While they were doing work, some of them started going off and talking in text message code: someone would say out loud, "LOL", and then they would all chuckle. Then someone else said, "ROTFL", and then chuckle, chuckle, etc. Oh my. I quieted them down.

Then. I have a unique, well-liked, has-his-own-band student who often stares off into space like he's writing his own music or thinking artsy thoughts. Well, today he was wearing 60s style pants, and after their big chucklefest died down, he had gotten up to get a tissue, and someone says, "Nice Pants," all sarcastic like, and then everyone chuckle, chuckle. And then I said something about, "oh, if the rest of you have to be such conformists and wear only what other people tell you is okay ..... ". And then this 60s pant kid pipes up jokingly, "well, if you don't like my pants, then I'll just take them off." We all laughed.

Conics Continued

I wanted to start my parabola lesson with paper folding to create a parabola. I'd done it before with other classes, and it went well since it was something different. This year I wanted to add an extra "twist" and experimented on my 3rd period (guinea pig) class .... (we don't LIKE being your guinea pigs).

Previously, they would draw a line on a piece of paper (directrix) and a point (focus) and then start folding the line over to lay on top of the focus many different times, and then the resulting pattern emerges as a parabola. Done. Move on to notes. This year I wanted to actually have them plot some of the points that were on the parabola, so after each fold, they were to use their ruler place it perpendicular to the directrix, through the focus, and make a dot where it intersected the fold.

Oh my goodness. Confusion city. Some kids got it, but lots didn't, so I just moved on and chalked one up to experience. But I think I heard the funniest line so far. One girl who has been struggling with math all year and is not getting the draw-the-dot-on-the-fold directions shrugs and funny-resignedly says, "even paper confuses me in math class".

Human Ellipse

Earlier in this winter January week in Texas with 60 - 70 temperatures, I was staring out my classroom window and remembering one event in my high school years. I don't remember the class/teacher/activity-purpose. All I remember is that one day we got to go OUTSIDE during class. This memory has lasted 26 years or so. So I related this to my 6th period class, and after their clamoring I promised we'd do something mathy outside some day.

Well, we started conic sections this week, and Friday was going to be a wee bit disrupted from other things, so I thought we'd go outside for part of the class and build a human ellipse to start off the unit. I had a long stretch of nylon yellow rope that I tied into a loop. Two students were the foci, one student was the pencil. Those 3 were inside the loop. The foci stayed fixed, and the "pencil" moved around while keeping the rope taut. The rest of the students were the "pencil traces" and moved to the "pencil's" spot after she left it.

We made 3 or so ellipses and I prompted them first each time about what they thought would happen if the foci moved in or out. We discussed circles. We got some sun. I think they have a sense of the ellipse properties now for when we get to them.

Extra Practice Calculus Worksheets

I keep forgetting to mention this great resource I found at NCTM one year. If you know of the Pizzazz worksheets, it's sort of like that, but for calculus (ooh, aah). It's published by Nasco, and called "Calculaughs Joke Worksheets", by June Oliver - who apparently was/is a calculus teacher and made up a variety of joke practice sheets for derivatives, mean value theorem, integrals, etc.

I've already used them when I want to come back to a topic after we've moved on. It's a nice way for the students to refresh their memories. I LOVED the types of questions on the MVThm sheet. I could never find enough satisfactory problems elsewhere for my kids to practice with. It also gave me some ideas on other types of activities I can have for that topic.

Here's a link I found: http://www.enasco.com/action/search?catalog=math&q=calculaughs&x=0&y=0

I'd also love to hear of other such resources for precalculus or for calculus ... even for algebra 2, because it's nice for the kids to refresh their memories on OLD topics.

Nature Break

Over winter break we went to Red Rock Canyon: Death Valley:

Death Valley:
And Zion National Park:
Every place was more stunning than the one before, and we had many hikes and long nights of sleep and surprisingly tasty dinners in small towns.

You're Welcome

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

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

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

Finals Shminals

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

Last Week of the Fall

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

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

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

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

Bullying

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

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

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

Voiceless

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

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

Holiday School Holiday Sandwich

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

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

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

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

Nonmath Moment

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

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

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

Continuity...(it never ends)

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

Identifying Coasters

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

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

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

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

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

Helicopter Parents

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

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

Cheating

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

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

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

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

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