Student Teacher Interactions

My 2-week training is over, and now all that's left to do is practice, practice, practice and map out what I'll teach when. It was put on by these folks, and everything was so professional and well-thought-out. I also know from other teachers who teach the curriculum that you are well-supported throughout the year.

For 2 weeks I was in a class with 16 other varied-ability people - lots of time for reflection on how teachers respond to students and how different students handle their learning. Two people had their hands in the air basically the whole time - asking for tons of help and being a little gun-shy of exploring on their own. I'm wondering if there was something non-demeaning the teachers could have done to make them more self-sufficient. Maybe something along the lines of, "I'm confident that you can figure out the answer. Try 3 things first to see what happens and then I'll help you." or "Here's a hint, explore it for 3 minutes and then ask me." Instead, every time they went over to help them on the program, the teachers would take the mouse in their hands and solve the problem. To me that just kept the people helpless.

Another 2 students had already had a lot of exposure to the program, so something that would take me all night of homework to figure out, they finished during class. They weren't rude or bragging about it, but it was clear that was what was happening. But. By the 3rd day of our 2-week workshop, the teachers would frequently make comments such as, "I bet R. has it finished and has improved on it.", or "I bet C. has already figured out how to do that.", etc. As a student, that got annoying to hear. I'm thinking it wasn't helpful to either R. or C. because maybe they felt singled out, and the other students (me included) would feel that much slower. Then I started wondering if I did that in my class. I'd better stop it if I did/do.

Okay, one workshop down, 4 to go. Mwa ha ha ha.

My New Love Affair

Dear Webcam,

I love you. Today we started a "reverse engineering" project (don't ask), and you came through for me by easily allowing instant digital photos needed for our engineering notebook. Contrary to what your lens tells you, this is NOT a gun. It's a tape dispenser that we are to improve in some way. Thus, the inspecting and analyzing and taking apart and sketching and improving and drawing. Because of you, my technical toolbag has grown.

I also like your friend, Skype. We are concurrently working on a virtual project with other students in Ohio, Colorado, and South Carolina. Fancy Schmancy new skills.

I had to tell my husband about us. He now suggested I should reverse engineer the vacuum cleaner that keeps breaking because of SOMEONE'S long hair that keeps tripping up the inner workings. Good luck on that account.

Love,

Me (click click strike a pose)

Core Set of Knowledge

I'm currently at an engineering teaching workshop (ooh, math teacher teaching engineering) with many other teachers from all sorts of disciplines - math, english, science, computer languages, ... and during lunch or breaks or in the course of our training I have had various conversations with many people.

During one conversation, I was talking to a middle-school math teacher who was mentioning that she was helping out her science-teaching friend with one piece of their homework that involved plotting points on the coordinate plane. The other teacher was having trouble with the negative y-axis. During another conversation, I was helping my table partner figure out how to put one dimension from the paper (a radius length) into the computer which demanded a diameter length. I thought she was having trouble reading where the paper number was located on the busy drawing, so I pointed out the radius number, and waited for her to convert it to the diameter length. She blankly stared at me. We finally got her to the point of doubling the length, but I was astounded that she didn't know this basic D=2R fact.

This got me to thinking of what I assumed was basic adult math knowledge regardless of your job. I got on my high horse and was scared of what I was seeing. Then I flipped it around and wondered what science teachers would assume I should know, or what english teachers assumed I should know, etc. Maybe I'm one of those people who cause others to inwardly raise their eyebrows and say, "you don't know THAT?!?!"

I went to dinner with another participant who's a biology teacher and asked her what she thought was an example of what I should know as core science facts. She thought a while and said: what are the functions of different body parts (liver, kidney, pancreas) ... as one of her questions. Eek, eyebrow raising.

Sooooo, hmmm, I assume some math adults should know/retain-from-schooling:
basic circle, square, rectangle facts
plotting points

... so I started that list and then thought: why should they know that (for what purpose)? why did I think they should know that (because I thought those were "easy" to remember and basic)? Maybe it's more of a case of "I'm surprised they don't remember those facts .... like I'd be surprised if they didn't remember how to add, subtract, etc.".

Engineering Education Workshop

On Saturday I went to a free workshop about teaching engineering. It was pretty cool. We got to experiment on how to create "penguin houses" out of various materials for ice-cube-penguins to keep them from melting in 20 minutes of a heat-lamp-induced stay (conduction, convection, radiation) while keeping under a $200 budget. We got to build boats out of aluminum foil to see how many would fit before the boat sank (bouyancy). We got to create lunar landers out of cardboard and straws and index cards and such to land from shoulder height without jarring the astronauts (marshmallows) out of their shuttle (cup). ... and other activities.

It was a fun day and showed me what I DON'T know about engineering, and what I want to explore more about. By the way, our group's penguin house cost $2000 and only preserved 6g out of 10g of ice (whereas others cost less than $200 and preserved anywhere from 8g to 9.1g). Go us. But the presenter did NOT have to make a face when she read our results out loud.

I liked the concepts. Most seemed to assume you were teaching science or had the freedom to use up lots of time to do these things. So now, as a math teacher, I have to see how I can break these lessons up into smaller chunks to wedge into a packed curriculum. I do think the activities were worthwhile, now I have to see how to incorporate them into algebra 1 and geometry.

I did see one geometry connection. When we were making our lunar lander, our accordian shaped index-card "legs" kept flaying out. Then I recalled that triangle shapes are sturdy, so we fashioned some extra supports that used this geometry fact ... of course it didn't prevent our marshmallow astronauts from bouncing boisterously out of the cups to their sure death on the moon.

I did like their continued stressing of the fact that your 1st attempt was not it. As an engineer, you learn from your mistakes and go back to the drawing board to rethink and recreate.

I also liked the talk related to NASA and "Design Squad". There are videos of the DS show you can stream and discuss. It's broken down into chapters (she said), so you can show snippets. NASA has a ton of free resources for teachers. Also, there are video profiles (Pro Files) of engineers (on DS site) that show cool things they do and non-stereotyped people who work as engineers.

Whew! Stuff to think about.

Center of Mass Fun

This is an activity I did with my calculus students post AP exam. We had talked about center of mass, and we calculated it with integrals in a previous class. Then I saw this problem in my new favorite book, so I decided to run with it. I first had the students try to balance one ruler on the desk top with the condition that it should go out as "far as it can".

Then I gave them 2 rulers and said they should line up and for the future tasks, if a ruler is on top of another ruler, it should be farther out than the one below it. So they were to play around and get the whole system to be out as far as it could be.

You can get the total out 9". There's a pattern and a reason, and I'll be mean and not give it away yet because half the fun is figuring it out. Then they got 3 rulers with the same rules.

Do you see the coolness ... almost off the table (you can get 11" with 3 rulers). Then 4 rulers.

Woot! 12.5". And just for fun, 5 rulers:

13.7" off the table edge.

Stating the (not so) Obvious

You know how you go around all the time interacting with a set of people, and you have nice opinions of them in some sense but you never voice these things because in your mind you're thinking, "oh. THEY know that about themselves." Well, it turns out that either they don't, or they're unsure, or they just like to hear other people confirm what they *may* suspect or hope is true.

For example, I have a lovely friend in tap dancing. She's in her late 50's and funny and pretty and vibrant and wise. She's also a teacher (at a different school in a different subject), and she always has some common sense take on school occurrences. I'm forever thinking these things about her. Well, today she was telling me about meeting a gentleman for the first time and how unsure she is about her "package". Holy cow! I had to tell her that she was gorgeous, and he would be thanking his lucky stars when he laid eyes on her. She seemed totally taken aback and did not seem to think this about herself.

Now I'm wondering what other friends I need to pounce on and tell them all the good things I constantly think about them.

Alternate Finals

All year in calculus I told the kids that if they signed up for and took the AP Exam, and if the proctor mentioned that they worked hard and didn't put their heads down or doodle or such, then those students would have an "easier" final exam in my class. Everyone this year took the exam, and I debated what final to give them.

I had a discussion with an AP English teacher whom I respect, and she mentioned that she gives the kids (in the same situation) a college-style text (poem?) to read, and they have to analyze it in some such way. That got me to thinking that even though I want to teach textbook reading skills to my kids, I never seem to get it together to manage such a thing effectively. Then, VOILA, idea. I scanned some books and found a section on probability using calculus. It "looked" like heavy reading from the perspective of a high school kid, but once I plowed through it, I saw that it was very friendly and gave examples and such for the problems I had them do for their final.

I prefaced the final with, "you will be reading such things and learning on your own in college, so this is your chance to practice it. Read through the section, and look carefully at the examples, and do the 6 problems I've circled". They (for the most part) worked hard, and I got a wide range of scores back, and it was enlightening for me.

At the same time, I'm thinking of various precalculus students I have. They scored in the high 90's all semester, and I know that the final would just be an exercise of spewing back stuff to me. So for those kids, I copied some sections of a precalculus book on a topic or 2 that we didn't cover, and did the same thing with them. I did not get to cover induction proofs or binomial theorem this year, and those were my topics of choice. In my mind, I'm thinking of just averaging their semester grades and giving them that for their final exam grade, but I also wanted to challenge them a bit. It was extremely fascinating to see how various students handled it. Some just dove right in and tripped a bit, but with a wee bit of help did fine. Some quietly plugged away without asking any questions, but when I went over to see what they were doing, they were lost. Some were completely flustered at not having a good handle on things. They were so out of their comfort level and had to keep being reassured.

This makes me think that I want to give such a test to the whole class some time periodically, to give them an incentive to truly read a text for understanding. Of course the problem is time, time, time. We'll see.

Wrapping Up the Year and School

Technically I have 4 school days left with children. I teach 5 of 6 classes that have seniors in them, and since seniors are having some finals early, I have NO FINALS ON THE LAST DAY. Woo Hoo. That will give me a huge chunk of time to pack up all my stuff and do "leaving chores".

I have to say that in my 12 years of teaching, this fall counted as my worst ever. This was not kid-related but adult-related, so in January I decided to look for a new school to teach at for next year. I found one, and based on several e-mails and encounters with my soon-to-be coworkers, I think it'll be a great place to work.

That doesn't mean it's not sad leaving a place I've worked at for 6 years, leaving students I've grown to love and would have been teaching calculus to next year, leaving many other teachers that I respect and enjoy being around, leaving a comfort zone of routines that I know, leaving a place where students know me.

And then there's the constant battle of thoughts in my head:
- you're jumping ship when you should have stayed and fought for what's right
- you can't work for people you don't respect
- you're moving to a functional place
- you're deserting the kids
- you'll have better mental health next year and more to share with the kids
- you'll never see these teachers again
- change is good
- change is scary
- will it be weird
- will it be better

Crabby Pants Cookie

Raowr! It's really quite shocking that students would rather text with their friends or chit chat or stare of into space lately than learn super cool math (redundant, obviously). I'm shocked, I tell you. I do have some kids showing snippets of interest and other kids showing tons of interest, and I'm most likely at the end of my patience with this particular class because of year-long behavior of a handful of students.

Cases in point:

One student flitters in and out on attendance, and has missed some classes lately and all of a sudden (1 week before the end of his school year ... seniors take finals early) wants to make up a grade from 6 months ago, and can you please show me what I missed and can you please make copies of it for me and thank you so much.

One student after constantly coming in all year and starting every other class with, "oh miss, I was going to skip today, but I decided to come," has been absent the last 3 classes (one was valid, the other 2 shady). I gave her a zero for the quiz she missed on her shady day. Her current average is now a 25%. She suddenly shows up and has an interest in class and wants to please know what she can do to make up the grade. I question her about the validity of her absence. Oh, I went home sick. Cough cough. Oh, I'll get my mom to write a note. Oh please reteach me EVERYTHING I missed oh and thank you very much.

Two other girls start "maam-ing" me when they know they're getting on my nerves from disruptive behavior. "Yes, maam. No maam."

Deep breaths. They're just kids. They're still pushing buttons and learning how to act. It's spring. Repeat.

On positive notes: various students come up to talk to me after class about what we did and wanted to talk through further thoughts on the matter. Many students mentioned they'll be sad I'm not teaching at this school next year. Handfuls of students stop by periodically and chat about life and such. A student who got pregnant with twins her senior year 3-4 years ago and still managed to graduate now has cute little girls and comes to visit periodically and is going to school to become a nurse. A student I had last year who was so edgy and ADHD and rudely violent in the hallways last year has turned out to be one of my favorite students this year. She's pleasant (still edgy) and interesting and humorous.

A cool fact a student shared with me in calculus today while we talked about breaking the sound barrier: The 1st man-made object to break the sound barrier was ........ the whip. Cool.

Post AP Exam

After the AP Calculus exam every year (of the 4 I've taught it), I've done different things. The first year I did a volumes of cross section project with foam and hot glue and a ton of grief. That was the year I had a screaming match with a student outside of class. The 2nd year I took a break from that and did various other snippets of math topics with mini quizzes. No screaming matches. The 3rd year I revamped the volumes project and tossed in a volumes of revolution project with foam and hot glue and stricter guidelines. That year I had a child sit in class with his pants unzipped and then tell me later that HE WILL DECIDE what is socially acceptable.

This year I'm teaching snippets of advanced calculus to my 2 classes with "easy" quizzes at the end of each class that should be ace-able if they simply pay attention. So far I have one class being good about it, and I've even had one student finally perk up and get out of his morose I-suck-at-math state and pay attention to be able to pass the quiz. The other class was great for one day (when the loud students were gone for other AP exams).

There are students in that 2nd class though that are enjoying things. They come up to me after class to discuss the topics some more.

So far we've "covered" (just given them a taste of) double integrals used for calculating volumes of weirder shapes, surface area calculations, and Gabriel's Horn Paradox. I think I also want to do Fourier Series with my BC class and centers of mass and .... who knows what else. I have a great resource ... the Smith calculus book. It's the THICK blue one, and it has amazing problems and historical snippets and ideas. Anyhow, busy busy busy trying to learn things right before I teach them.

I was also intrigued by the Hubble Telescope news of late, so I assigned my precalculus class an assignment of bringing back 3 facts in their own words about anything to do with "Hubble". I told them that I wanted to learn about it, too, since I didn't know much about it, and I would also do the homework. I told them that we couldn't just exist in our own little bubble of everyday existence. We had to be informed about the world. Then a student said, "we'll bring Hubble into our bubble."

I told them to explore the "what,when,where,who,why, & math" of the situation. Anyway, I went on a particular website, and WOW, the pictures it sent back from space are breath-taking. Can't wait to see what they find out.

Surprising Gap of Knowledge

My teacher friend was having her advisory class address envelopes to their parents the other week to send out invitations to an acadamy picnic. She quickly realized that more than 75% of the class did not know how to do this and was shocked. After she relayed the story to me, I asked my freshman class and my mixed class of juniors and seniors if they knew how to address envelopes. I basically had the same result. We went through a quick lesson. In my freshman algebra class I wondered out loud when I had learned it and why it was useful (because they think they can just text and e-mail their way through life). I told them that it was fun to get letters in the mail, and when I was a kid, I had pen pals in different states. They then wanted to get pen pals with "littler kids" in other math classes. Hmmmmm, I think it's too late in the year, but maybe it's an idea for next year.

NCTM goodies

I went to NCTM in Washington D.C. last week and learned and bought some useful things.

One talk I went to was about how to incorporate web tools into your class. They mentioned a great website, "Everything 2.0", that lists techy websites the blog author finds. There's a phenomenally easy-to-use graphing site that you can use and then save as a document or such to put on your worksheets. You can find this by scanning the list on the left of the page and clicking on calculator 2.0.

There was also a session about "Visual Thinking Activities" that had some great ideas. Two ideas were:

"talking graph". He gives them a graph (say of a line). They have to verbalize some (any) information regarding the graph; they have to make a table; they have to symbolize (equation) the graph.

He gives a picture of the xy plane and plots the point (1,1) without any scale on the axes. Then he randomly puts another point somewhere and asks the students to estimate the point. He spends time with each answer and does not stomp on any estimate. Just through discussion, the student may either stand by their answer if it's reasonable, or self correct if necessary. The point (1,1) may or not result from identical scales on the x and y axis, so that was cool. He does the same idea with the (1,1) but has it on a line and asks them to estimate the equation of the line.

I also went to a useful talk about "jump starting" your class - basically activities related to your topic of the day that take about 5-8 minutes or so. They gave a link that lists all their ideas in a word document. I liked the culling through foreign math textbooks and presenting a page covering your same topic. They suggested going online to search or finding YouTube links to show to class.

There was also a funny guy presenting various math related humor and activities. One example: "Algebra - an intense study of the last 3 letters of the alphabet."

Finally, I bought some books:
"Managing Your Classroom with Heart" good ideas from a high school teacher about relating to students
"The Inspired Teacher" discussing ways "unaware" and "aware" teachers handle various situations that inevitably come up in the teaching day/year.
"Geometry Teacher's Activities Kit" because I have their Algebra book, and it has some good resources to copy immediately and use, and because in my NEW SCHOOL next year, I'll be teaching geometry.
"Math Games: ..." more of thinking activities for the students.

Inappropriate Religious Jokes

Whew! TAKS is over, and today we resumed our regularly scheduled program of classes. I taught the basics of sequences and series in my precalculus preAP class 1st period. I had lunch. On my way back to my classroom after lunch, I ran into a student who walked and talked with me down the hall to my classroom. She was gabbing at me once we got into my class, and then all of a sudden she half shouts, "Jesus!". I quickly turned around to see where she was looking, half expecting to see a mouse or rat or bat or some such thing.

But, no, she literally meant, "Jesus". There was a 1.5 inch doll / flashlight in the form of Jesus on the floor. She proceeded to put sticky notes on him and hang him on my overhead. The notes said, "Math Jesus" and (being a calculus student) "integral of f(x) dx".

Oh my. In the remainder of the day, I had to make reference to the Jesus on my overhead:

Jesus wants you to stop chatting and do your work.
Jesus says to study this weekend for your AP Calculus exam.

Boo Hiss.

School Schedule Craziness

Whew! It's TAKS week in TEXAS high schools. Four days of altered schedules and proctoring not-your-kids and not being able to teach "real" classes for most sections because otherwise the other classes would be off whack. AND to top it all off, thank goodness, we got the go ahead to hold some AP prep sessions during TAKS, so our seniors wouldn't miss a whole week of learning right before the AP exams. AND the schedule was such that I still have my 2 calculus classes all week. AND I'm holding an AP Blitz after school every day from 4:30 to 6pm to "rah rah rah" and tutor my calculus kiddies. Whew! (a "whew" sandwich).

I also see one of my 3 precalculus preAP classes this week, so I can't teach new stuff, but I don't want to have them just sit there, so I did a fun topic. I also gave them a quiz they were sure to get 100% on at the end of class, so that the "good kids" who actually showed up to class would be rewarded for doing the right thing and not skipping class.

I taught a topic I love that can be done in any amount of time. I had about an hour, so I covered: counting numbers in different bases. Then converting between base 10 and other bases (back and forth). Then adding in different bases. Then subtracting in different bases. THEN multiplying in different bases. I liked their wide-eye understanding of what it means to "carry" the 1 now in base 10 and how to "carry" in other bases. I also love what happened with one student. She has been struggling ALL year. She is never completely comfortable with a concept. She feels stupid. She's failing, and yet she shows up to class every day and pays attention and does not quit.

Anyway. This topic started out much the same for her. She sat there all frustrated, but she kept asking questions. Then. BLING. She got it, and she was whizzing through all the things we did. Then she was helping others. Then she truly got 100% on the end-of-period quiz. She walked out a happy camper.

Anyway. I present it by talking about how we can think of numbers in base ten as filling up bins from right to left. Each "chip" or "1" in a bin means I have "1" of that type of number. Once the bin reaches 9, and I try to add one more chip, then I am overflowing in that bin, and I have to scoop all 10 chips in my hand and put a "1" or chip in the next bin over to the left. The bins are:

... 10^4, 10^3,10^2,10^1,10^0 (and so on to the left)

So in (say) base 4, the capacity of each bin is 3 (one less than the base number),

... 4^4, 4^3, 4^2, 4^1, 4^0.

For example, 231 in base 4 means you have 2 16's, 3 4's, and 1 1's, so your base 10 number that means the same thing is 2x16 + 3x4 + 1x1, or 45.

I also peaked their curiosity about what decimals would mean in different bases.

Two Funny Incidents

Some of my precalculus students were staying after school to (gasp) study for a test coming up in a couple of days (new behavior). Anyway, they were working through logarithm and natural log problems, and one of the students muttered, "what are these used for (good for) anyway?". Then another students quickly pipes up with, "shhhhh, she'll assign us a project!".

This made me laugh. Throughout the year, I've given them various small "projects" to research things like:
* how do the conic sections show up in real life (what is it about their properties that lends them to the use).
* who uses imaginary numbers
* how is trigonometry used and find one fact you find interesting about it.
* what are fractals and what's one use of them.
etc.

These are usually small posters (8.5 x 11) or just handed in on paper. They have to cite their sources and have a good presentation. This way, I make them do the work, and sometimes, I have nice posters to hang around my room.

The other funny incident happened while they were reacquainting themselves with log and ln and "e" and their calculators. After a bit, I asked them to look on their calculators and notice the positioning as a pair of ln & e ... and log & 10^x ... and linked it to the positioning of x^2 & sqrt(x), and cos x & arccos x. I made the connection that they are all inverse operations of each other, and that's why they're placed that way. Then a student comes up with another example of inverse operations: "oh like the positioning of the ON & OFF keys".

Reteaching

Since it's the end of the 6 weeks, shockingly a hoard of students are now just realizing they better get their act in gear and turn in late work or do "retests" to bump up their smelly grades. Because of that, I ping-pong back and forth after school from one kid to another reteaching or helping and such.

Yesterday, two kids wanted their memory refreshed on old topics so they could understand their homework or take a test. I was just about to sit down and talk with each of them, when I thought to show them the textbook in one case and some copied notes in another case. I made one kid look in the index for his topic (solving systems of inequalities), and I showed him how to look through the examples and try to understand it. I told him to ask me when and if he had questions. With the other child, I gave him the same instructions with the notes (on graphing polynomials and finding their zeros). I told him to look at his old test and find similar problems on the notes and to ask me questions when he had them.

Whew. That worked out great. They both diligently poured over the texts and worked things out for themselves. I guess this is one skill they need to practice/learn: how to learn for themselves without thinking someone else is the ONLY source of knowledge.

High School Kids

Two funny incidents happened within the last week. In one class I was giving a polynomial test, and allotted an hour. Some kids were done early and put their heads down to nap. This is the ONLY time I allow this. At the same time I'm back at my computer taking roll.

We hear a key in the lock and see the door open, and the principal comes in. He frequently does this visiting of classroom thing. I instantly feel guilty being back at the computer. Then my brain kicks into gear, and I quickly glance over at the 2 kids I knew were sleeping. Their heads were up, and they were studiously pouring over their tests. I laughed on the inside. Boy do they know how to play the game. As a class after he left, and the test was over, they mentioned it and laughed about it, and I had to thank them for not getting us in trouble.


In my second class, I have a periodic visit from another man who basically oversees a math program at various schools. I like to talk with him, and we have many conversations about the state of affairs in education. I consider him a friend. Anyway, he left after a brief visit to discuss something during one of my precalculus classes, and a few girls started giggling. "Ooooh, he likes you. Is he your boyfriend? He's cute." etc. Oh my.

Well, yesterday he stopped by again to give me some information. It happened to be during that same class while they were practicing some problems. Though happy to see him, on the inside I was groaning because I knew the kids were on full alert. A third of me is listening to him, a third is keeping my ears open for my kids to see what they're doing, and a third is hoping he'd leave quickly, so we wouldn't have an "incident". RIGHT after he left, the kids stopped pretending they were working and started teasing me again about him being my boyfriend and gently mimicking things we were saying but in a sappy sweet tone of voice. Oh my goodness. I had to laughingly admonish them and say thanks because every time I see him now, I simultaneously see my class saying, "ooooooh".

I'm going to miss these kids next year.

Students With Issues

My algebra 1 preAP class started out horribly 2 days ago. It's the first period of the day, and as I'm herding kids in, I notice one girl with big sunglasses on. I asked her to please take them off. She ignored me. I waited to see what she would do before asking again about 30 seconds later. Again with the nonanswer. The bell has rung now. I don't want to make a big issue of it, but I can't ignore it and have any credibility with my students. She's a touchy, edgy kid I've gently butted heads with before. I stand right in front of her and ask her again. She refuses. I ask her to step outside and that I will talk with her in a bit. I start my kids on checking their homework, and go outside.

No she does not want to take them off. No she won't tell me why.
"I don't want to."
"Not the issue," I reply.
"I don't want people to look at me"
I can sort of see through the glasses and nothing seems to be wrong. This goes on for a few seconds. I indicate that now she has taken it to the next level. She's directly disobeying me, and if she continues to keep them on, I'll have to send her to the AP. I tell her I'll give her 3 minutes to decide and go back inside.

All the time while I'm teaching my other 20-some kids my mind is racing:
-ackh. I hate calling the office
-what's the office number?
-what's the procedure?
-how long will it take to fill out the paperwork and what a waste of instructional time.
-take OFF your glasses for the love of pete and just come inside
-heyyyyy, her bag and her beloved cell phone are still in the room.
-maybe I'll just let her sit out there all period.
-ackh I hate this.

She never decided to come in, and I never sent her to the AP. I like to deal with my own discipline problems whenever possible unless they're skipping or doing harmful things. The 1.5 hour class ended. I felt bad. I called her mom and left a message. Her mom called me later because the girl had texted her. Apparently, they'd had a HUGE fight that morning about my class and her mom wanted her to get tutoring and the girl is all frustrated because she's not used to not getting concepts immediately, and she's struggling this year. So I'm guessing the girl had red eyes from crying and didn't want to attract notice. Can you have just TOLD me that somehow! I'm so glad I didn't send her to the office.

Then later I sent home an e-mail about a calculus student who I haven't seen in a bit. His attendance has been spotty, and I'm worried about his grades and AP exam outcome. My class is the only class he has on campus one day, and it's at the end of the day. My cynical mind is thinking he's just finding it hard to make it back from the community college.

Hmph to me and my cynicism. Apparently, he's had this soap opera existence for the last little while, his mom wrote me. People and animals have died lately, and she's been gone a lot, and he's been sick tons, and and and. Today I saw him, and on the positive side, he's very smart, so he can quickly catch up.

A 3rd student has had horrible attendance in another 1st period class of the day. Starting around Thanksgiving she's been gone more than she's been here. Another teacher gave me the heads up that she was going through some personal issues. On one of the days I saw the girl (who I like), I asked if she was okay and did she have someone to talk to. She did. But then again with the hit and miss attendance. Today I saw the other teacher again and said I was worried about the girl and did she know if she was okay. Okay, TMI time. The teacher told me what was going on. Ahhhhhhh. But still. Come to class, don't fail. You're too smart. And now I have this other knowledge running around in my head.

Then there's the kids I know of who have moved out or have been kicked out of home. There's the super poor ones that have to ride the bus 2 hours each way to come to school. There are the ones that go on crying jags during advisory.

I'm sending out big hugs to all of them for just continuing to plug away and *mostly* take care of business.

The "Higher" Polynomials

Here is a lesson I love because of graphing calculators. My goals for my students were to be able to look at a graph of a polynomial and know its degree and find an equation given various points on the polynomial. I also wanted them to be able to look at an equation and be able to give a quick sketch of the graph with the intercepts and shape correct.

At the start of class before I mentioned anything about shapes of non parabola polynomials, I handed out graphing calculators and we all got the same window and turned the grid on. In Y=, I had them type in y=(x-2)(x+1)(x-1) (or something similar previously checked out to make sure it fits in the window). I told them not to graph it but to think: what are the x-int, y-int, and make a conjecture about the shape. THEN they could graph and see if they were right. We then had a discussion to link the intercepts with the equation.

Then they typed in y=2(x-2)(x+1)(x-1). I asked them to think about how this might affect the graph and intercepts and shape and THEN graph and confirm their reasoning. We did one more, and then I discussed the shape and degree.

Then same process with y=(x+2)(x-1)^2. They had to think and do the same analysis as above. We then did y=(x-1)(x+2)^2 and such.

Then the fun part: I typed in an equation and just showed them the graph, and they had to match it. We did that a few times. I made sure to change the constant in front sometimes and to make it "upside down" and to have various powers. Then I asked them to find an equation for a 5th degree polynomial with 2 "bounces" off the x-axis going in the same direction (both below the axis or both above). Then for the ones that finished that early: opposite bounce direction.

Then we took notes, and I believe they had a good sense of polynomial graphs.

First Time Teaching Concepts

On my broken record mode (you know, those things that music used to come out of and were bigger than 12" diameter?): I'm loving teaching algebra 1 this year since it's so fun to show them all the cool stuff they'll see over and over again - FOILing, lines, exponents, quadratics...


But it's also daily unsettling because I don't know what they'll find difficult or what will need extra practice or how the best way to explain something will be. Today I told them we were going to do "big kid math" (they were going to start the FOIL process without me saying FOIL just yet). To build up to it I needed to teach them like terms and adding like terms of expressions such as (5x^2)(y^3) or (3xy^7), etc.


I racked my brain (okay I just googled "wracked"/"racked" ....) for a way to present this since I was tired of worksheets and notes. I decided to fold up a white paper to have 20 squares (4x5) and opened it up and put various monomials in each making sure that there were sets of 2 to 3 like terms usually. Then I did it with another piece of paper making sure to put some sort of bubbly border on each square (on one paper only). Then I copied (from 1 to 2) the papers onto various pretty colored papers. The kids then chose their color and cut out the 20 pieces (yay, less work for me) and they had the 2 sets of 20 monomials.


I chose a side (border or no border) and randomly picked a card for the overhead, say (7x^2)(y^6), and told them to find it and cull it from the herd. Then they were to find like terms in their cards (without explaining what like terms were). I wanted to see what they knew. I saw various mistakes as I walked around the room, and it was interesting. So I went up front again and said, "this is like making chocolate milk. You have 2 parts milk and 6 parts chocolate (refering to the exponents). You want to find similar "drinks", and those are like terms". That seemed to work with everyone, and we practiced some more.


Then I had them find a set of like terms, say the cards were 3xy^2, -5xy^2, and 8xy^2. I asked them to add them up to see what they'd get. Instead of 6xy^2, a lot of students got 6xy^6. I was expecting the mistake of (6x^3)(y^6), but I guess the "silent 1 power makes it stay 1!".

Anyhow then we built up the skills for that: 3x + 5x, 10x^2 + 8x^2, etc. They still had the silent 1 problem: 3x+5x = 8x, but 10x^2 + 8x^2 = 18x^4. Then what seemed to work for most (all?) kids was the EXCELLENT box again. Think of the variable parts as boxes filled with x or x^2 or such, and how many boxes do you have and when you add them what happens.

All in all, I think it went well. I also want to share an excellent resource for algebra worksheets. It's been a godsend for extra practice problems all neatly laid out.