Counterexamples

We're moseying along in geometry and are now doing truth tables and "Laws of Inference". Soon we'll be taking it to one step proofs and then real proofs. Before we get there, though, I want the kids to start thinking about what proves and what disproves things. Is it enough to consider EVERY EXAMPLE IN THE WORLD and if they're all true, then the statement is true? If you just find one counterexample to a statement does THAT make it a false statement (what if you find an example that makes it true?)?

Anyway, along those lines, I made up the following sheet:





I love the document camera because we worked on the 1st few one at a time, and then I could put various students' papers up there and we discussed if their drawings were suitable or not and how to fix them if they weren't.

Comment Board Outcome

I mentioned earlier that I was going to implement a comment board in my classroom, ala Whole Foods. This is what it looks like:



The response has been good so far. The kids mention that if they have any concerns, they can just post a comment. Among the various comments I got, I'm happy about 2 things that came up that I probably wouldn't have been aware of otherwise. Here's one:



I'm never angry or frustrated when kids ask questions. At least I'm never outrightly frustrated. I know I scrunch up my face or have a set look on it sometimes, but that's just me thinking of another way to phrase some explanation or it's me concentrating on what the kid is asking. Now after this comment, I've been making sure to reiterate that I totally need them to ask questions and to know that my expression is not a reflection on my frustration.

Here's another comment:



In the mornings I'm rushing around and scrambling to get ready, so I was JUST having tutorings in the afternoons. Well, I got enough comments about kids being in band every day and not being able to make it, that I started tutoring one morning a week.

So all in all, I'm glad I implemented this this year. Here are 2 other posters I like in my room (made them from old calendars and cut out or hand written extras):

My Day Has Been Made

Today was grueling. I promised myself I wouldn't mention the "T" word (tired), since that seems to be the 1st thing EVERY DAY that comes out of my mouth when people ask how I am. I must sound like a broken record. Anyway, I did pretty well not mentioning it, until last period when I slipped twice. They're my chattiest class, and I keep shushing them, and feeling/sounding crabby.....

Anyway, I came home to this message on FaceBook:

Ms.Cookie,

I am not sure if you remember me or not but I am an ex-student of yours. I was in your Pre-Cal class at ***** in the 06-07 school year. I'm the guy that never did homework. I failed your class by one point actually.

Anyway, I'm just writing you to let you know that despite sucking at math in high school (and just doing bad in general), I'm majoring in math now at *******. Well, physics and math. I guess it just took me a little longer for me to realize that doing homework helps one understand things. So thanks for not passing me, it helped me change a few things about myself and I'm doing better now!

Now off to bed smiling and uplifted.

Logic

We've reached one of my favorite units in geometry: logic. Today we just learned about conditionals, hypotheses, conclusions, and the 4 types of statements. I tried to be all interdisciplinary, and when we got to the part where the students had to i.d. the hypothesis and the conclusion, I said, "you know, it's just like science." Then everyone got the guess wrong. Well, duh, in science, the hypothesis reads something like, "if ____, then ____". So I revamped for my NEXT class, "you know how words have different meanings in different contexts? That's how it is with hypothesis here....". Here's the in-class sheet I used.

Tomorrow truth tables, mwa ha ha ha.

In fun news, here are my Lindy Hop aspirations.

Homework Location

Before school started I was talking with a middle school English teacher, and she mentioned that one of her 1st assignments is to have the kids keep a log for a little while on where and when they read and what effect it has on their reading. They read in 4 different types of situations and answer some questions about how it went.

I'm thinking that's a great homework assignment for my math students. Something to the effect of:

For the next 4 weeks, attempt doing your homework in a variety of locations and situations and discuss the effect this had on the success of your work.

Examples of place: at the kitchen table, on my bed, in the cafeteria, in the library, on the couch, ...

Examples of time: the night before it's due, the night it's assigned, the same day it's due, 5pm, 8pm, 11pm, first hwk I do, last hwk I do (from various classes),...

Examples of situation: while watching TV, while listening to the radio, while texting friends, in silence, while my family is noisy about me.

Make sure you write about at least 3-4 different combinations of the above, and make sure you analyze how it went in terms of being able to successfully think about and concentrate on your homework.

I'm curious if they've already figured out what's best for them, but I'm guessing that since their lives are so jam packed and they're teens and they want to talk with friends and leave things until the last minute, that maybe they haven't played around with changing things up to see if they can do better.

Homework Questions Update

Oy what a day, but I think by working through the struggle, I had a new and improved idea I want to try.

Before school started this year, I pondered how to get my "average" students to start going beyond the homework problems that they could INSTANTLY understand and do because they remembered from class, or we did something EXACTLY like it or it was EASY. So my initial thought was this idea.

Then as things do, I made sure to pass it through to my department chair, and it sort of morphed to a "homework completion grade rubric" that the whole department was strongly encouraged to follow (which included my original questions, but my main idea was embedded in other things).

Flash forward to 4 weeks into school. I've had hit or miss success with it. Some kids (literally a handful) buy into it and use it to their advantage and make progress on problems they can't originally do. Most kids either ignore it or just pay lip service to it.

One conversation I had a week ago:

Average Girl In Class (AGIS) while we're going over the previous day's hwk: I didn't get that. We didn't do anything like that in class.
Me: Okay, so what did you do about it to make progress?
AGIS: I wrote the answers to the "extra" questions.
Me: what did you write?
AGIS: "I didn't know how to start. We didn't cover this in class."
Me: okay, so then what did you do.
AGIS: blank stare.
Me: pause.
AGIS: still staring.
Me: It doesn't help you just to answer the question, you actually have to put forth an effort to make progress beyond your original stumbling block.
AGIS: wide-eyed and silent.
Me: (I got nothing!)

So, flash forward to today. I taught 3 classes of "average" geometry students. During the 1st class when they started in on the "those last problems were hard", and "we didn't do anything like that in class", I gave them an analogy. I said, suppose you wanted to run the mile and had never run it before. Do you think you'd be successful your 1st time out? No. You'd fail and fail again, but you'd keep trying and eventually your progress would eek you towards your goal. With the hard problems in math, if you just look at a hard homework problem and then give up immediately, then it's like you're taking off your running shoes and not even practicing on the track. You can never do hard problems unless you attempt hard problems.

Okay, so then I was all strutting my stuff and proud of myself for my little motivational speech. Then my 2nd class comes. I trot out the same story (except for some reason it morphed to a 10K race, but ....). Then my subconscious must have been working because I added while we were going over a hwk problem that they did NOT get: okay, say you are at home and attempted this problem. I'm guessing you just sit there and stare at it with big question marks. Here's the question I want you to ask yourself: okay, I may not know how to solve the problem, but what DO I KNOW about ANYTHING in this problem? Then I had them discuss in their groups and brainstorm about anything they knew. Then I just called on people, and we got a ton of ideas down. Then with a wee bit of guidance, and me continually prodding them about what they knew, they started to be all, "OHHHHHH, then I can do this, or this....", and we eventually solved the problem.

Then my 3rd class came. This spiel morphed into not just the 10K, but potentially throwing free throws or playing the guitar or whatever. Did the same questioning and such with 3 problems. But now I added the story of: even I'm continually learning. I wanted you to be able to do hard problems on your own, and I attempted something, and now I see it's not working well, so I have to go back to the drawing board and ask myself, what do I know? what can I change? etc.

Bla bla bla. Who knows if it'll get through, but maybe I'll soon have a homework for them that includes 5 HARD problems. And I'll stipulate that I don't even want them to solve them if they can't, but to get ANY CREDIT beyond a ZERO, they have to brainstorm and answer the questions:

well, what do I know about this?
what do the words mean?
what formulas might apply and why?
here are some calculations, I don't know if it'll work, but I'll do them anyway .....

FYI here were the stumping 3 problems for them:

1. AB is parallel to CD. A, B, C points are given. D is on the x-axis. Find D.
2. EF is perpendicular to GH. E, F, and G are given, and H is (5, y). Find y.
3. J,K,L are given points. Is triangle JKL a right triangle?

To be continued...

My Dream Teaching Gig...

I would love to have the freedom (or feel I have the freedom) to drastically adjust the speed and amount of content of my classes. For example, this year, I just graded a geometry test, and let's just say that there was a ton of creative algebra flowing around. Did you know that if 2x + 13 = 8x - 7 needs to be simplified, why you can simply divide the 2x and the 8x by 2! That pesky 13 and 7 don't mind. Oh! and did you know that if a ridiculous x squared is embedded in a problem, why, poof, you can separately take the square root of each individual term on each side (or even just the terms that are squared). AND, that's not all folks, sqrt(2x*x) = .... you guessed it 2x.

What I would like is to at this point, stop what we're doing for a day or so and concentrate on attempting another pass at teaching these concepts. Or let's say that the kids get intrigued by fractals by the slight mention of it, then I can plan a mini unit on the spot. But if this happened throughout the year, then there's a ton of geometry I wouldn't cover. I semi see the problem, but I also see that I could make some adjustments that wouldn't be too troublesome (transformations, eh, they've done them before, so if they happened not to see it again this year in a deeper form, not too much of a hindrance).

Anyhow, maybe in lieu of this, I'll plan a self-teaching homework assignment to touch on these algebra concepts, or I'll piecemeal work them into my problems, or something.

Okay, when I'm queen, things are going to be a wee bit different around here. Via la nap time!

My 1st foldable of the year

My geometry students had a test at the end of this week, and I didn't want to waste the remaining 30 minutes of my block schedule, so I had them take notes on congruent and bisector and the symbols involved. But wait! We can make this "fun" by creating a foldable to glue/tape into their composition notebook and they'll just CLAMOR to study these new words. I even told them that if they got bored over the weekend, and their parents asked them what they wanted to do, they could suggest that as a family, they study and test each other with the foldable. Hours of enjoyment.

Funny side note. As you'll see on my pictures, I had and issue with spelling "length" and I had no "yellow out" and had to refer back to my personal friend "white out". It bothers me, but I've moved on with my life. The story is that I have this student in class that wants to do EVERYTHING perfectly, and when we first started cutting the flaps, she was being very precise with her cuts, and shockingly she wasn't ready when the rest of us started writing and she wanted us to stop and wait for her and oh no I'll be behind and oh this rushing is going to make me mess up and ..... Phew! That's going to be a hindrance to her, the such strong need to be perfect that she doesn't efficiently get her work done. We'll work on it (or she'll develop a nervous tic from my class) one or the other or both.

Nibbling at the Elephant

Phew! Who stole summer and plopped a ton of to-do-list items on my life? After 3 weeks there are still "beginning of the year" tasks I haven't done, and in addition, I have to keep all the altered schedules and field trips and extra responsibilities in order without going bonkers.

I don't know why, but there's one phrase that has been keeping me sane (and I find it funny that I like it since I'm a vegetarian):

"How do you eat an elephant? One bite at a time."

I'm putting my blinders on and just focusing on the next "emergency", and keep repeating to myself, "one bite at a time" while envisioning a large elephant, and shockingly, things get done. ... okay, p.s. (that's not really a post script but anyway), someone told me a story (and I'm choosing to believe it without checking), that there's a gentleman that wanted to get into some "book of records" for eating an airplane, so he would systematically grind/break down (whatever) the metal into "manageable bites" and in some long period of time, ate the whole airplane. ... Makes me feel better about my life choices. And even if it's not true, I STILL have my superiority thing going by comparing myself to the person who made up the story. And no comments about people who choose to believe such stories (cough cough).

Almost time for 1st Geometry Test

My geometry class practiced current concepts in class last time, and boy did they need it. I'm trying to get them to be more reflective this year as students and making them answer such questions in their notebook about how they're doing so far and what they need to do to learn. No matter what year I teach, I always feel like I'm in a rush to cover stuff. Rush, rush, rush. This makes me not want to "take a day" to have them practice in class. Ridiculous because most times I have them practice in class and just walk around, I hear great conversations and errors in thinking resolved and such. I must be a slow learner because I'm sure later on this year I'll be all, "oh! can't take a day to just practice. MUST. MOVE. ON." Oh well, maybe I can get an IEP for this and have a helper remind me periodically that it's REALLY not a race.

Here's what they practiced with in class: