Gush Alert...

I am a lucky teacher. There is such a gi-normous difference between my teaching experience last year at my old school and my time this year at my current school. Sure I had a rough 1st semester getting on board with all the new ways of doing things and all the higher expectations and all the students sort of eying you to see what type of person/teacher you are before they decide to like you and play along with learning. Sure I've had many times this year (in the last couple of weeks especially) when I'm asking myself, they want me to do WHAT now in addition to the other 5 bazillion things I'm doing??? Sure I've been tossed into the pool and told to swim and figure things out and then jump back out, dry off, and assess how things went and make notes for the next time we do something new we haven't done before.

But.

I'm loving it. Maybe it's analogous to life experiences in that you ultimately are more satisfied with something you've had to work hard for. Maybe you're more proud of yourself when you've agreed to try new things and not come out any worse for wear. Maybe I just work with phenomenal people that push me every day to be a better teacher/person/employee. In any case. Gush. Gush. Gush. Okay, hope you're through being queasy.

And 3 more off-this-topic observations I've been mulling around in my head.

1. A while ago I blogged about a student cheater. I don't know if I mentioned it, but this student was caught cheating on another test. This was last semester. I never mentioned anything to her, and things settled down, and I'm in general very present during tests and walk around and check up on students. Anyway. Can I just tell you I'm glad I didn't severely damage my relations with this kid by saying something that would stick in both of our minds. She has turned out to be a joy and is one of my favorites now. She makes me laugh constantly, and I'm always happy to see her. Another instance where things are not black and white, and are ever-shifting.

2. A shorter while ago I blogged about a student who had attendance issues and was frustrating me with her lack of math progress. Well, this is a poised kid who excels at other things, and I've had opportunities to see her in action and was impressed and told her so. So I guess this is an instance to remind me that I'm not just teaching math robots who only exist to come to my class and churn out math; they are well-rounded and just like the rest of us are trying to juggle many things and growing up (keep reminding myself that they're only 14-15 years old) and learning how to do things and do them successfully.

3. There are the types of people who feel they have to ask permission for everything (not talking etiquette here), and there are the types of people who just push on ahead and do things with the mindset that no one's the boss of them. Example, some of our teachers went to a meeting the other week where there were people from various schools. This one teacher was asking for help and suggestions on how to set up field trips and transportation and logistics of visiting various colleges. She seemed to be flustered by the whole idea. Our teachers just looked at each other because we had just done that with a set of our kids. Hey! we just contacted people and transportation and figured out the logistics on our own. Just get it done. Most likely your common sense or perseverance will allow you to figure things out. And if not, you'll learn from it and do better next time.

Shifting of Parabola Functions

I don't know how your school year is ending up, but at our school it's CRAZY CRAZY CRAZY. Practically every day the schedule is altered in some way, and we're all just practicing our deep breaths and our focus of just thinking of one wacky day at a time. Because of this I wanted a lesson that discussed shifting of graphs so that the kids could work independently in case I saw different classes for different amounts of time. Now I'm thinking I should do this more often. I really know I should, but other things get in the way.

Anyway, I like how this worked out. I told the kids I wouldn't help them and they had to work in their groups to figure things out while I walked around. I told them they could ONLY work on the 1st page and we'd talk before they went on. I walked around and cleared up misconceptions. We got through about 3 pages in a wacky 75 minute class after doing homework checks and such.

Here's the 1st & 4th pages: (and here is the whole packet of 4 pages)

Adding & Subtracting Radicals

I teach 3 different classes of algebra 1 preAP. My poor 1st class gets all my mistakes and things I test out. My 2nd class gets the refinement, but still not "the best" I'm going to offer this round. By my 3rd class, I've had time to mull over ideas and see what works and doesn't work and anticipate their problems. So... Here's the 1st page of what my 3rd class is going to get on Monday when we learn adding and subtracting radicals. You don't even want to SEE what I subjected my 1st period to. (here's the whole 2 pages).

Circles and Tangents and Horizons

We're on the "tangents to circles" section in geometry, and I'd assigned a standard problem of "the satellite is ____ miles from the earth ... how far is it from the horizon?" Too many kids drew goofy pictures and didn't get the concept, so I started class on Friday with the following task.

1. We had a discussion about how when you're at the (ocean) beach, and you can see the horizon, maybe you wonder how far away it is .... any guesses? And do you think tall people and short people will see the same distance away?

2. Then I had them draw the "circle" earth, and we discussed drawing them standing on the earth (as a math stick figure with a big eyeball dot on top) and made sure they were standing up straight (an extension to the radius of the earth).

3. Then I asked them to just PLACE their ruler as if it was their line of sight to the horizon and walked around to make sure they knew what they were doing and corrected some misconceptions.

4. After they drew the line of sight to the horizon, they had "AH!"s of the right triangle possibility of finding the answer.

5. I asked them what information they knew or could find out, and we looked up the radius of the earth in miles on the Internet, and we recalled the number of feet in a mile.

6. Then before I set them on their way, I asked that if I was 5'4", how many feet tall am I and show me on your calculator as I walk around. I heard good conversations and them correcting each other. Then I got another kid to tell her height, and we did the same thing to make sure everyone got it.

7. Then I set them on their way to find how far each of them individually with THEIR OWN HEIGHT could see to the horizon. As I walked around, I saw too many kids doing everything in feet (because "I don't know HOW TO DO IT in miles")... they converted the radius of the earth (about 3960 miles) to feet!!! We had a discussion about how these are too large of numbers.

8. I stopped the class temporarily and did a mini-lesson. Let's say I have 53", how many feet is that. What about 38 feet, how many yards is that. Okay, let's say I have 5.25 feet, how many miles is that? They caught on. Then we had to have another mini-lesson on using our store button on the calculator instead of rounding early or writing EVERY BLESSES DIGIT out on paper and then retyping it in.

9. THEN when they'd calculated the length from their eyeball to the horizon, we asked the shortest kid what their answer was, and the tallest kid their answer. And we had to fix some kids' work and computation until they did it correctly.

10. Interesting span of possibilities of how far we all could see .... which I won't divulge in case you want to try it.

Graphing Parabolas

I had really good luck with this sheet when we were practicing graphing parabolas today. I apparently haven't been doing enough graphing in class because I still got a handful of questions during class, "how do I find points on the graph". Scary. Anyway, I'm not too worried because with other topics earlier in the year that they couldn't do, now they're great at them (like terms, solving for x, ...). We only got through this front side because of all the other extra administrative stuff we needed to take care of.

What I like about having a preprinted sheet is that I can stop them at each step and have a discussion: why is it called the axis of symmetry? how do you know what x value to plug in for the vertex? what kind of shape is the axis of symmetry (a point or a line or other?), how do you know how to find the y-intercept? why? does every parabola have a y-intercept? (that brought surprising answers when I asked for thumbs up for yes and down for no) ....

Rote Memorization

I was reading this post the other day, and flashed back to my 7th and 8th grade German class where we had to memorize dialogs and play both parts with the teacher for a grade. Now, I'm not saying I'm old, but this was in the late 70's. The thing is, I still remember parts of the conversations in some of these cheesy dialogs.

That got me thinking that maybe I could make up a cheese-ball conversation for my algebra 1 students to memorize and have to perform for me. In this way maybe when they're solving a quadratic equation in the future that's not all prettied up and ready for them, they'll break into a cold sweat and remember this dialog and solve it properly.

Here's what I have (and the version I'll hand out):

Real-Life Problem

Ms. Cookie conscientiously deletes ALL memory from her calculators: RAM, ROM, RIM, ROOM, and all the excellent APPS on the "school bus yellows" for the TAKS test. Ms. Cookie saved one calculator to the side and kept the programs/APPS on there. Ms. Cookie now wants to repopulate the other calculators. Once she does one, then she has 2, then 4, etc. Each repopulation takes 12 minutes (!!!! who knew!!!!). How long will it take her to "fix" all 74 calculators?

Culturally/Gender Biased Test Questions

We were practicing problems for our TAKS test, and 2 funny incidents came up.

First problem: a baseball diamond has 60 feet between the bases. How far is it from home plate to 2nd base?

Some of the girls in my class indicated that they did not know what a baseball diamond looked like. Now we were working on the Pythagorean Theorem, so it had to be a square ... but they didn't know the layout of the bases. We discussed it. Then, being a good teacher (cough), I wanted to link it to something, so I asked if they'd heard about boys getting to 1st base, etc. But I digress; the point is that if we hadn't happened upon this practice problem, and they got it on their exam, they may get it wrong not for not knowing the math, but for not knowing baseball.

Second problem: What information do you need to figure out to know how much material is needed for a basketball? (surface area? volume? ....)

I thought this was obvious (surface area), but then a child asked me why it wasn't volume. I started to explain, and then she said, "oh! there's no stuffing inside?" I'd never thought of that, and explained that it was just air inside. Then I thought about it. There are sports balls that have stuffing inside (baseballs, softballs, ...). We could think of 3 more in addition to those 2 when we brainstormed. Anyway, ARGH sports problems and non-sports people!

TAKS helpful hints

And so starts the crazy TAKS week. I made up a sheet for my 9th graders and printed it on pretty paper and discusses each tip with them. So in addition to doing algebra/TAKS practice MTW, we will talk about calculator skills, and these test taking skills. And we will cross our fingers that everything will be okay.

One student shared with me that someone at church had walked up front and was in tears (a junior) and asked people to pray for her because this week she was taking her math TAKS. Oh my goodness, what have we come to with all this testing stress.

Anyway, here's what I handed out (on a 1/2 sheet front and back):

Movies & Teacher Talk

I went to see "City Island" with my teacher friend today - my teacher friend that still works at my old "crazy" school. Loved the movie, loved spending time with my friend. She said something that resonated with me, "sometimes I just want to go do some volunteer work or something in another country with school children who still actually appreciate their education so that I don't get too far gone and cynical about the state of things."

She's dealing with kids that:
* just come to her class because it's a part of their probation,
* come to class and don't do anything but still expect to pass,
* don't show up on the day of their oral exam for no good reason and then expect to have time to do it again at their convenience.

I wonder if there are summer programs for teachers like this - 1-3 week programs where you can travel and volunteer and do something nice/beneficial for others in this "school" way and not have it be too much of a drain on your wallet. Maybe we should come up with something - the power of teachers.

Also, I'm wondering (and worrying) about Mrs. H and hope she's okay and just taking a blog break.

Perceptions and Circles

I started to "do the math" and it basically seems that barring tests and tests and finals and reviews and other-time-vacuums, I have basically 5 or so block days left of teaching each class. Panic!

In other news I had an interesting conversation with another math teacher in the copy room today. Unlike the other 2 schools I've taught in, at my current school, everyone is expected to go above and beyond, and it's just an ordinary thing and possibly commented on in some way if you don't ... or maybe that's just our new teacher perspective of things. Anyway, we were discussing the results of the math 8th grade TAKS scores .... that were phenomenal .... for any other school, but since they were not 100% passing, there's an undercurrent of "why not?". Yeesh, the pressure.

So our conversation took the turn of her saying, "I can't wait until summer; I'm so exhausted." .... and, "I always walk around, and it seems everyone else has their act together, and I'm scrambling to keep up". I could contribute that I don't think everyone DOES have their act together, they're just putting on a great facade and doing the best they can (based on other conversations I've had). That got me to thinking. We make these judgment calls based on our insecurity of how we're performing by looking at others, and if they look calm or "with it", maybe we think, "ackh ... I need to work harder ... why don't I have things done and planned and thought out yesterday?". Anyway .... maybe a reason to get out and talk to more teachers in depth instead of just surface, "hello, how's it going" conversations.

Finally, we started circles today in geometry. We barely scratched the surface, and again I didn't want them to copy definitions, so I did the matching game again. My twist this time was that I did a search on the internet, and found a cool website that showed me how to make envelopes that don't use glue. So I had the kids make them out of pretty paper, and they could store their cut out matching cards there (also on pretty paper) ... AND they could write the key on the back of the envelope. Nice.

Quadratic Formula

It's that time of the year in algebra, and I'm processing the right sequence that works for me on how to teach this. I have block classes, and even though that seems like, "whoa! 1.5 hours! You can cover HEAPS." It turns out that this is still a multiday process for me. Here's what I've done so far and where I'm going.

Previously on As the Algebra Turns:
Quadratics bla bla bla
Factoring bla bla bla
Finding Zeros of Quadratics by factoring
Linking Zeros of equations to graphs of parabolas.
TEST on some stuff

START of our Program:
Day 1: start the class with reviewing one problem of finding zeros by factoring and link it to the graph. Start them on the 2nd problem of trying to find the zero by factoring, and BOOM, falls apart. Ask them if they think this means it DOESN'T cross the x axis. Show them it does but the numbers aren't "nice". Show them a slow step by step process of how to use the never-fail quadratic formula to solve. Have time for 1 "nice" problem.
HWK: can't involve simplifying of radicals (haven't done that yet). Can't have the equation in a weird form yet ... must be in ax^2+bx+c=0 form.

Day 2: now they have a reason for simplifying of radicals. Spend most of the period on simplifying (just the stuff they need for the quadratic formula). Then have time for one quadratic formula problem where they solve AND simplify. I also threw in a problem to solve that looked like: ax^2 + c = bx to get them used to this.
HWK: mixed radical problems (some with and without denominators) and some quadratic formula problems.

This is where I am so far.

Now I'm thinking, they need practice of both radicals and more quadratic formula. I still want to link it to the graph. I'd like to throw in some word problems. I'm probably forgetting something, but that seems about it. So, sheesh, 4 block days on this. Why am I stressing about that? Better to do it well than just to rush through it. .... I guess I'm stressing because I still have/want to cover: more radicals (adding multiplying...), Pythagorean theorem use of radicals and to refresh their memory, midpoint and distance formulas .... more geometry and radicals. Will I have time for rational expressions?

Stay Tuned for the Next Episode.

Quadratics Review

Woot Woot! Our school participated in a 10K today (which I think of as a 10K+ since we walked to and from our bus to the race place), and I actually ran/walked the whole thing. Oh yea! I think I'm hooked now. It was fun with the bands along the way and the various people cheering us on from the side lines. It was my 1st race, and here were my fears before hand: oh no! I'll get trampled by the faster people at the start of the race, and it'll be a tragedy reported on the news. or... oh no! I'll be so slow that there won't be any other runners in sight, so I won't know the route and I'll veer off the course and get lost. or ... oh no! what about bathroom issues? or ... oh no! my pasty white chubby legs will blind the other runners and there'll be another tragic accident from the glare that will be reported on the news. It turned out that there were runners of all shapes and sizes and ages, and I am now home safe, and if anyone was blinded from the glare, I didn't hear any cries of agony. I think of a phrase I read on another blog (crazyauntpurl? or yarnharlot?) that my "deficiencies" will make others feel better about themselves ... it's just a small service I provide to the world.

Anyway, in algebra we (and by we, you know who I mean) will have a test this week on our beginnings of quadratics, so I've created this self-checking review sheet for the kiddies that I like. Once again, the box.net preview looks wonky, but it should download nicely. Also, the "English" of the sentence is probably cringe-worthy, but I didn't want to keep using the same words over again.

EDITED LATER: no matter HOW many times I checked this sheet, there apparently was still a mistake (which is now fixed on box.net). In the answer bank, the "-4x^6" should be "-4y^6". Thank you to a student with eagle eyes.

Great Intentions, Bad Execution

As with probably most school districts we have a dress code policy (though at the other school I worked at it didn't prevent me from having to see massive cleavage and feel uncomfortable about saying something). But maybe unlike many schools, at my current school, it's mostly enforced. Today I noticed a girl without shoes in my 1st period. I asked her what was up and where were her shoes and "put on your shoes". This was sort of a "drive by" on my part because I didn't expect any grief from her.

I started class, and then noticed a while later she still didn't have on her shoes, so I was more firm with "put on your shoes". "No," she said. Ding, ding, ding, warning bells. The whole class (in my memory) quiets down to see what'll happen. I stared at her wide-eyed in disbelief and asked her to step outside, which she did. I got the class to continue moving on with their work (the thrilling quest of finding zeros of quadratics, ooh, aah), and went in the hall to "discuss".

I asked her what was wrong and why she wasn't putting on her shoes and waited. I got no sensible response. I said that her options were to put on her shoes or to go to the office, and I asked her what her decision was. She opted for the office. This was at the beginning of a 1.5 hour block class. Then I had to simultaneously teach and figure out how to get word to the office without a disruption. I sent e-mail, and thankfully (I LOVE my administration this year!), I got an immediate response that it was being dealt with.

In the last 10 minutes of class, the administrator came back with the girl, and I found out what's what. Apparently, it's "A Day Without Shoes", and this girl was participating. Did she ask me? Did she explain to me? Did she have documentation about this? No. She waited all the way (even with the administrator) until she was facing suspension for insubordination before she explained in tears what she was doing.

Oh my goodness, 14 year old minds and their logic/decision-making-skills, etc.

PSA project idea

In our city once a year about this time, the art of the students from our school district is displayed in a building downtown. Apparently, the people that work in that building say it's something they look forward to every year. All grades from K-12 are showcased. I went to see it last Friday and was inspired by all the creativity. I'm even thinking of taking some art classes this summer.

There were all sorts of techniques, and being an art know-nothing, I don't know (shocking) the names of the styles. But. There were things made with aluminum foil and blackened; there were things painted on cloth. There were pictures and then an overlay of an overhead slide with another component to the drawing. Very fun to browse. One technique intrigued me, so I thought maybe I could incorporate it into a project for my kids.

They could create a PSA (public service announcement) for some things you never want to do in math or always want to do in math. For example, (x + 3)^2 = x^2 + 9 OBVIOUSLY in many of my students' minds. My thinking is that if they spend time making the PSA, and they're hanging up around the room and other students look at them, then maybe the correct thing to do will be triggered in their minds when they need to use/perform the math task.

Anyway, I made a mock up of an example today. I guess I'll think through the specs and see if it's something feasible.

Factoring Trick

I don't know if I mentioned this before last year when I taught algebra 1, but it worked so well this year, that I have factoring geniuses in class - even kids who have trouble elsewhere.

We just finished learning how to factor trinomials of the form axx + bx + c where a is not 1. My retired math teacher friend had taught me this trick (over chips and salsa and margaritas last year), and I tried it out with my class. I had to first prep the period with the following statements:

* I'm going to show you a trick today that's going to be your new BFF in math.
* First I'll predict how the class will go.
* You'll take notes on the process while we slowly go through it with an example and you take notes carefully like you're taking them for your best friend who's absent.
* You'll whine and say, "I'll NEVER like/use this trick. It'll NEVER be my BFF".
* After the 2nd problem you'll say, "okay, it's not so bad. I can be in the same room with this trick."
* After the third problem, you'll quietly wait for the 4th after you finish this current one a little faster.
* After the 4th problem, you'll be ready to marry this trick. Your NEW BFF.

We laughed and got down to business. And yes, I had to make fun of them for each of my predictions coming true. And yes, 2 or 3 classes later, when I came back to this kind of factoring, they almost all of them remembered it.

Miscommunication

Wednesday in algebra 1 we were exploring parabolas on the calculator. We're just getting into our groove with the calculators, and I'm slowly trying to introduce more capabilities of it. The question was, "when does the rocket reach 528 feet", and after we'd graphed the equation, I was showing them how they can put y2=528 and then find the intersection with the original rocket equation.

I tell them to press 2nd TRACE (though I always say, 2nd calculate, ... whatever), and go on to show them the intersect capability. Many kids ooh and aah, and move on to the next question.

One girl calls me over, "it doesn't work", and she's all frustrated and pushing 2nd and TRACE over and over. I walk up behind her and ask her to do what she's doing slowly. Then I couldn't help myself, I laughed. She was pushing down on the "2nd" button with all her might and annoyance and holding her finger there in the down position while simultaneously then pushing the TRACE button.

I'd never come across this before, but now that I think about it, why not? Never have I said, "push 2nd and release and THEN push TRACE". Aaaaaaah, good times.

Prisms & Polyhedrons

We started out unit on polyhedrons this week, and are learning first about volumes and surface areas of prisms. I know they've worked out volume and surface area with a vengeance in middle school, but I know they didn't do the "hard" problems. With all this in mind, I started with the information that is shown in "Discovering Geometry" about how the lattices of different substances that are made up of the same elements (carbon) can have way different properties (diamonds vs. graphite), and can behave counter intuitively (water expands when frozen and other things don't).

Then, instead of giving them definition upon definition to copy down (edge, vertex, lateral face...), I handed them 2 blue sheets, and we had a race of cutting out the squares (otherwise, la la la, I'll take my own sweet time to trim VERY neatly and NEVER get done). Then they had to match the cards. I didn't answer any questions (what's oblique mean?), and just said that they should use process of elimination. And, "why are there more than one hexagonal prism cards?" .... you'll figure it out. Here are the sheets. (note: for some reason, the "preview" on box.net comes out all wonky formatted, but it downloads nicely. I'm not sure why that happens.)





At the end, I gave them a key and let them keep these to put in a plastic baggy. I plan to do the same with pyramids, cones, cylinders, on different color paper. I also made sure we had a discussion about correctly describing right and oblique prisms.

Ways of Asking For Things

A student came in after school concerned about her algebra 1 grade. This 6 weeks, she was absent for maybe 2 days in one stretch, and then she basically never got back up to speed turning her in stuff (in any of her classes). Then, thank goodness for good parenting, she's now concerned about her grade because her birthday is coming up soon, and if her grades are stinky, well mom won't be too much in the birthday mood.

So I love how she tried to turn in some late work. First of all, she turned it in during class a while ago claiming it was absent work - about 3 week old work, so I gave it back to her and said it was too late (as is our school policy) (thank you sane administrators). Then she tried to turn in stuff after school today. Hmmmm, one had 2 problems out of 8 done, and another had 6 out of 8 done. She tried to do the "air quotes" thing with me claiming that she'd tried to turn them in earlier, but I wouldn't accept them so they were "air quotes" too late "air quotes".

Now I just have to laugh. I asked her why she hadn't done the work. "Well I didn't get it, so I thought I'd just turn it in for some credit (2 of 8 problems)". Then I asked why she hadn't come for tutoring. "Well .... excuse, excuse, excuse". Then I quickly disabused her of her air quotes and said, "hopefully you'll be in school for another 7 years (she's a freshman), and you'll have many teachers. Most likely when you're asking them for a favor, it probably won't do too well if you just come with an attitude, and ESPECIALLY if it looks like you're not even interested in learning the material. A better thing would be to say, 'well, it may be too late to turn this in, but can I still have help on knowing how it's done, and I can practice'".

So somehow, magically she could stay for tutoring on the spot, and we worked through some of the problems. She was a quick learner and showed improvement. Her funny statement then was, "why do I get it when I'm working here with you (she's NEVER been to tutoring), and I can't get it at home?". I asked if she was distracted at home when she was doing her homework. BINGO. "Well, I guess so, but don't tell my mom." We discussed that math was hard, and you had to think about things as you were doing them, and not just half pay attention to your homework.

Maybe she's seen a wee bit of light? Or .... most likely, this is the upswing of the see-saw that is a teenager's personality .... and her birthday incentive will be gone soon. ... I'll take what I can get.

Spring Break Almost Over

I remember how in the past someone had mentioned to me, "Students like routine. They want to have a sense of comfort of what to expect and such." I don't remember the context of the conversation, but I was thinking about it over break. I apparently like routine, too.

Break's all well and good - I slept about 8 or 9 hours every night, delicious; I got to go to bookstores during the day and browse and come upon great new books to read (hello, "Little Bee"). I went rollerblading 3 times in the afternoons (goodbye fish-white pallor ... almost), etc. But. I miss my routines. I missed my 2 favorite yoga classes for various reasons; tap dance class follows the school schedule, so it was canceled. I didn't run at 5am MWF, well, because, who in their right mind would get up at 5am if they didn't have to, I miss my Thursday morning treat of having breakfast out at a 24-hour diner before school and reading the paper and doing the puzzles. I miss the free exercise of being on the go all day and not having easy access to my refrigerator (hello tighter pants).

Waa waa waa. All that is to say, that though I won't like the stress, I'll be happy to go back on Monday and get back to my well-tuned-and-familiar routine. Then pretty soon I can start my finger countdown of weeks until summer .... and then I have to find other ways to resist the fridge and the sitting all day.

Differentiation Chapter 2

A key point of chapter 2 of the differentiation book I'm reading is that you can differentiate in one of 3 areas:
* content
* process
* product

Her examples are not from math classes (wait! there's one at the end of the chapter), so I have to brainstorm about how to differentiate content. Let's say I'm teaching solving inequalities in 2 variables. Maybe a content differentiation would be to have separate groups of kids: one with basic line inequalities (y=mx+b set-up), one with point-slope inequalities, and one with standard, point-slope, and basic all mixed. Or maybe a group with line equations given where there is some thinking involved to graph the line (the y-intercept is not an integer, or the "easy" point is off the grid I've given them). So then my thinking goes to: when do I separate them into groups? At the outset? After my initial spiel? After a day together? How do I gather them back at the end of class and make sure they learned? Do they have an opportunity to advance to another level if they mastered the basic ones? Is there enough time, or will we move on to the next topic?

Continuing on with the same example for process differentiation: this would be how they're originally learning the information (among other things). Maybe they could listen to me speak, or separate off and learn from the book, or maybe I have a sheet pre-typed out that goes through the process and prompts them to learn the concept.

For the product differentiation: hmmm, this always smacks of "project" to me, and I know it shouldn't. If I get away from a paper and pencil test, how will I allot the time to assess them orally or in other ways? How will I stop from giving them hints either with my body language or with actual words? How do I know they really know the material?

She does discuss starting your differentiating small and adding to your bag of tricks each year.

The Book...

Ode to Freshman Test Takers

Nine Questions. Blank blank blank blank, scribble times four, blank. Partial credit does not compute.

Let me practice writing my name. All over the paper. Curly, squirrely, poorly Q's. First and last name. Oops, ran out of time to complete many problems.

Week-long note on the board: TEST! solving by elimination, solving systems of inequalities, graphing inequalities in two variables. This was not code for DON'T STUDY.

Earnest note at the bottom of a half blank test, "do not understand this part. will come in for tutoring on Friday."

Many practice problems involved integers. Or. GASP. Minor fractions. One Half. GASP GASP. Negative one half.

Thus, my befuddlement at your "23/67" for an answer. And your gumption at following through and plugging in to get y - 2 and 17/93. Yay. Boo. Joy and Sorrow.

Checking Your Answer. Outrageous. Don't Fall For It. She's Tricking You Into Doing Needless Work. Mwa ha ha, Teacher Lady. I will NOT be fooled!

Blank Math Joke Sheet

I started thinking that is would be convenient to have some blank "joke sheets" ready to make a quick practice assignments for various math skills. I took my last geometry sheet and reworked it so that it's ready for a quick altering. In this one, I guess I'd have to find 12 problems that each have 2 parts, or I ask 2 different things, since there's an a and a b component. I guess I could easily rework it to make 24 problems, but I would have to reformat it. Let's see if it works.

Here's the downloadable version. And here's what it looks like:

Grading Projects

Some things I've come away with on my geometry project:

* Even if you don't get around to grading them immediately (say in a week or so), glance through them all and count them. If any students haven't turned the project in, notify them and their parents. I had one child inSIST she turned it in 1 day late in my mailbox - swearing up and down to her parents. I never saw the project. Luckily, the parents were supportive, and the child is turning it in WAY late, but turning it in .... well I say that, it's supposed to be tomorrow. We'll see.

* I like the "wow factor" component. I purposely left it vague, and just said, "wow me", and not everyone, but MANY students went beyond what I would have imagined.

* Put EVERY child's poster up if you're going to hang them .... and don't put them up in waves, do it all at once, or you'll hear about it.

* Don't assume they know how to draw "tilted rectangles" on a coordinate plane. Some just eyeballed the 90 degree angle, and didn't use slopes to force the 90 degrees.

Other than that .... spring break after tomorrow. Woo HOOOOOO. Sleep at last and movies and books and more sleep. I've also assigned a "castle project" to my IED (engineering class), and I have to build my castle on the Inventor program over break since I told them I'd do the project with them. ... Just got home from "Alice in Wonderland". Phenomenal. The creativity of people is very inspiring. It makes me want to go meditate and ponder on doing all sorts of fantastic things. The sky is apparently not the limit.

System of Inequalities

We just finished our unit on inequalities, and my students have a test next class. I'm thinking of putting the following question on it to gauge their understanding of what the solution graph really indicates. (sorry can't figure out a nice way to embed the document directly onto this page ... does anyone have a tried and true method?)

LATER: Thanks to a wonderful commenter, I learned a new skill of "screen shots" (after I asked him how to do it ... and then thought of "Google University"):

Special Triangles

We are just finishing up trigonometry and special triangles in geometry and moving on to areas, but as with all skills, they need to revisit the topic a few times. Here's a sheet I made up that I'll be giving my students next week.

EDITED LATER TO ADD: Well, after I made the sheet, I thought about how much I like the puzzle sheets with answer banks, so I improved it to make the following puzzle geometry sheet.

Quadrilateral Project

Holy Cow, my kids are awesome. Out of about 23 students in geometry class, 8 turned in amazing projects, and the rest (barring 2 late assignments) did great stuff (but not with the "wow!" factor of the first 8). Here are 6.

Here's "super man". You can put it in front of your chest and strut your stuff.


Here's a purse. All the math equations and essentials are on strips of paper inside.


Here's a camera, taking a picture of the world.


Turtle Soup. The "recipe" is awesome.


Surfer Dude (had an incident with a shark).

Monster in the closet.

Differentiation Chapter 1

Maybe this will motivate me to actually get through the differentiation book. There are 18 chapters, and I like her writing style and attitude. Invariably, though, for me, with all good ideas I read about, I'm all "Great Idea!" and then it's a crap shoot as to whether I implement it. So maybe if I talk/blog it out, it'll have a better chance of going into action.

The first chapter can be summarized as "there were no good old days of teaching". Way back in the late 1800's only a teeny percentage of boys went to and completed high school. And it seems the debate was always on about the purpose of high school and what should be taught and such. Here's a site with one synopsis.

So what does this have to do with differentiation? I guess in the early days only a select type of kid went to high school and only a few graduated. Now we're trying to get everyone to be successful, so that means we have all levels of kids in our classroom, not just the select few. And not everyone learns the same way.

She has one statistic that by 1990 only 38% of the nation had graduated from high school. Wow. Page 11 of this document breaks down graduation rates by state in 1990 and 2000. Too many percentages in the 60's and 70's. So I guess if kids weren't cutting it in school or the school wasn't serving them, then off they went. These days, I'm guessing most schools would not make "adequate yearly progress" if these were the numbers, and the school would be a potential candidate for closing.

So, this sort of makes the case for differentiating for students who need more/different ways of learning instead of just listening and notes. It's not making a case for the "fast learners" and how to differentiate for them. We have to keep both in mind.

Algebra Epiphany

I'm apparently a slow learner. I just realized the other day that I'm treating my algebra 1 preAP students like "gifted" kids, or "true preAP" students. I show them 1-3 examples (they work at least 2 of them by themselves in class) of a particular topic, and then invariably the bell rings MUCH too soon, and I send them off with homework. I also provide them with my school website in which I've linked various videos and sites that help for that topic.

I give about 10 problems of a type, and then the next class starts and we move on to a new topic after we've gone over homework. About 25% of the class (very rough estimate) is fine with this and can self assess and readjust their thinking and learn from their mistakes. BLACH! That means I'm not serving 75% of my students. They need MANY more examples, they need more hand-holding, they need more time in class to process new information.

Then there's always the war raging on in my head: Ackh! I'm going too slow, we won't learn everything we need to know for algebra. Eek! I'm molly-coddling them too much, when will they learn to stand on their own. Oof! what about the kids that get it, what will they do when we're practicing more in class when they already GET it. Yeesh! This is a preAP class, step up to the plate, kiddies.

Yes ... the "D" word ... differentiation. I had started to read a good book about it a while ago, and then as always seems to happen, other things got in the way, and I only finished 3 of 18 chapters. Then just the other day, I started reading it again. I'm on chapter 3. MUST. READ. BOOK. Must reflect on another way to do things.

Textbook Skills

I had a major scare yesterday after school during tutoring. My kids had a test the following day, and the homework I assigned was 1/2 odd problems (answers in the back) and 1/2 even on all the skills they needed for their test. One of the students was working an odd numbered problem, and then asked me if it was right. I told her to check the answer in the back. This was a total revelation to her. She didn't know the odd numbered answers existed, and after I told her, she couldn't track them down.

Then another student asked me how to do another problem. I asked her what the directions were and had her read them to me. Then I asked her to flip to the start of this particular section of problems. She didn't know what to do. We figured that out. Then I asked her to find an example they work through that is similar to that problem. We struggled to do that, too.

So, their homework tonight is a Textbook Scavenger Hunt (we use the Holt book).

New Math Game Addiction

So what do you do on your weekend when you are procrastinating doing your work? Well, you play this, which I found out about from her, (who is also the source of other game addictions).

Geometry Polygon Project

Inspired my Mrs. H and by the cool graph separation of a grid from Mr. K, I designed this geometry project for my kids after we've covered all things polygon. I'm going to pass it out next week and see what I get back.

A Valentine for "sticky notes"

I love the versatility and color choice and usefulness of sticky notes. Especially for returned homeworks.

Line Project Finale

Well, all, okay most of the projects have been turned in, and now comes my grading fiesta (ay yi yi yi) which I solemnly do swear NOT to put off until forever and a day (p.s. I dread grading projects). I love the creativity of the students, and was impressed with some of the facts they found that they thought interesting. Here are a few of them (with no mention yet of whether they are accurate or not).









Things I've learned and would change for next time:
Be more specific about what you want on the poster (data, what work, the sentence of the prediction, the fact that the prediction has to be from using the line equation and not just the slope).
Be SUPER HAND-HOLDY on the step by step procedure of finding the equation of the line of best fit.
Grin and take Deep Breaths because even though some projects are not exactly what you were expecting, everyone still learned something about how lines are used in "life".

Lines Project Continued

My students are still working on their Line Project, and I'm glad I assigned it because various things have come up that I think are good learning experiences for them and for me. I had separated their completion of the project into 3 successive class periods, and for the 1st one they had to turn in a set of data points and a computer-generated scatter plot to show the linear correlation. Well!

Most kids were fine, but others had a variety of issues:
* "The spreadsheet won't make a scatter plot of my data!" (the student was entering data of height vs. weight, and the heights were typed in as 4ft 5in, 4ft 6in, ...)
* "Here's my data ... SEE! Linear" (the set of points was EXACTLY linear since the student found a site that said that every 1 second ___ kids drop out of school, and the student had used that to create 5 coordinate points)

The 2nd class period, they had to turn in their own hand-created scatter plot and best fit line and equation and idea for a prediction using their line equation. Issues:
* Some kids used rise/run to calculate their slope, but the scale of their graph wasn't in "1's".
* Some prediction ideas were: I predict the cost of a loaf of bread will rise 31 cents every 7 years (they used their slope instead of their equation)
* Some just connected the data points, forgetting the example we worked on in class for best-fit line.

And so on. This seems to have taken them out of their comfort zone of how our math class has been going, so I'm glad they're being "mathematicians in action" and learning extra skills. I'm also glad I broke it up into 3 days of checkpoints since I'm guessing I saved myself (and them) the agony of incorrect or NO final products. While I was walking around critiquing their graphs this past class, I gave them THIS to work on.

On a side note, after my hectic week of various extra tasks added on to the already busy schedule, I went out for drinks with my friend, and we had an interesting discussion about the difference between "unethical" and "immoral". What types of things would fall into each separate category? Would some things be both? What's the distinguishing characteristics of something that is one or the other?

Lines Project

In algebra 1 we've covered most line topics I think are important:
* calculating slope from a graph and from 2 points without a graph
* looking at a graph and finding the line equation in all 3 ways (standard, pt-slope,slope-int)
* being given either 2 points or a point and a slope and calculating any of the 3 equations.
* looking at any of the 3 line equations and graphing
* looking at any of the 3 line equations and finding 5 points on the line (and the intercepts)
* seeing that if you have a graph and it's line equation in any form, that you can plug in any point on the line and it will "work" and plug in any equation not on the line, and it won't work in the equation.
(I've probably missed some, but this is what I remember)

We still have to talk about parallel and perpendicular lines, but soon we'll move on to systems of equations. Before we do that, I thought that this would be the perfect time to assign a line project to my students. In all their later topics and math courses, lines will just be an aside where it's already assumed they have learned about them.

We had a discussion about positive and negative linear correlation and no correlation and correlation that is not linear. We went through the process of creating best fit lines and using that line to make a prediction for another point that is not represented by your data. Then I discussed that in real life, people collect data, and if they all fell on a straight line, the mathematicians/scientists would faint from the rareness of this occurrence, and that usually, if the data seems to be linear, it'll look like our scatter plots that have a linear correlation, and THAT'S how this is used in real life. People make a model and then use that model to make predictions.

Then I assigned this project that I will collect in a succession of 3 class periods. I already have had one student send me her data that was interesting. She found information about teacher pay from the 40's to the 2000's, and you can see that it looks linear until about 1980, and then there's a BIG leap of the points and then it looks linear again. After a back and forth e-mail discussion, she found that some site stated that there was a 400% increase in pay in 1980 .... hmmm, haven't verified that, but I remember some of my older teacher friends mentioning their super low pay in the 70's.

Visual Clues

Three Day Weekend

I went to Chicago for the nice 3-day weekend, and had a fun time walking around and people watching and freezing and sight-seeing. Here's the cool Water Tower Building:



This is "The Bean" in Millennium Park.




This is a river cutting through town and gives a nice idea of how cold it was:



I loved the ease of the subway (CTA) system and my old-styled hotel (thank you, Expedia.com and yelp.com reviewers). I loved trying out their many vegetarian restaurants and knit shops and independent bookstores (thanks again yelp.com reviewers). This will tide me over until my next adventure.

Near Miss

Yesterday at the start of geometry class I had the homework answers projected from the document camera, and was silently reviewing in my mind what we would be doing that day while my students checked their answers. I was ready to perfunctorily ask if they had any questions before we moved on to "the real learning". Okay, I'm not that robotic, but on hindsight, that's what it feels like because I almost missed a great learning moment.

On one particular question a bunch of students raised their hands. The question was something to the effect of: In a pentagon, the angles are consecutive multiples of 4. Find the measure of each angle. Instead of simply putting up the answer, I put my work down also since I thought there would be several confused students that would want it broken down: 4x + 4(x+1) + 4(x+2) + 4(x+3)+ 4(x+4) = 540 and then went from there.

The students with their raised hands weren't confused, they were chomping at the bit to show how they did the problem. Oh my goodness were there some clever kiddies there. They love to come up to the overhead and present (note to self: stop being a projector hog), and one by one they showed us what they did.

1st student: well, I divided 540 by 5 and got 108. That's a multiple of 4. The angles couldn't all be 108, but I thought they'd hover around it, so 108 was an angle, then for 2 other angles, I added and subtracted 4 and had 3 angles: 104, 108, 112. Then I added 4 to 112 and subtracted 4 from 104 to get my angles: 100,104,108,112,116.

2nd student: well, I started with 100 degrees for each angle (a multiple of 4), and with 5 angles that adds up to 500, so I had 40 degrees left to play with. Then I tried to break down 40 into 5 consecutive multiples of 4. 4, 8, 12, 16, 20. I added these up, and they were more than 40, so I just used 4,8,12,16 and it worked.

3rd student: well, I divided 540 by 5 and got 108. I divided 108 by 4 and saw that 108=27 * 4. So I then I found the consecutive numbers around 27: 25,26,27,28,29, and those were the consecutive multiples of 4, so I multiplied by those and got the answer.

4th student: well, I knew they were consecutive multiples of 4, so I set up an equation:
x + (x+4) + (x+8) + (x+12) + (x+16) = 540 and solved that.

I was very impressed and humbly reminded that there are teaching moments quite available to me even when I'm not "teaching".

Rates of Change & Slope

As school started back up again, in algebra 1 we started our unit on equations of lines by talking about rates of change. Last year I just jumped right into slope first, and verbally mentioned some applications (if I remember correctly), but this year I thought I'd give them a context first. I started with a worksheet on rates of change and had them work through the first 2 problems with not much prompting. Then we discussed their answers. I made sure they used units. I made sure we saw ALL ways of writing the numbers. My classes (everyone's?) seem unsure that 9/4 and 2.25 and 2 1/4 can all be correct answers. They still look at me like they don't QUITE believe I'm not pulling a fast one on them.

Then they did the next two, and we discussed, and so on. I made sure to mix up the units, I have some with negative rates of change on the back. After a few, if it didn't come up, I discussed and made them write their calculations on the side as (y2-y1)/(x2-x1) using the appropriate numbers. If it didn't come up, I made sure to investigate what would happen if you used different points or a different order.

In my block class, we had just enough time to do this and then to have a discussion about rates of change and slope and how they're the same (barring units).

I'm thinking this went well because on the second day, when we discussed rise/run and started graphs to y=mx+b equations, they were pretty good and quick on calculating slope. Also, when I stepped back and asked them to identify positive and negative slopes, they had a picture of water levels increasing or decreasing and were pretty accurate.

Oh, one funny thing. I like to give them memory tools to keep things straight, and on "rise over run", I said, well what goes on top? the y's, and y's rhymes with rise. Then I told them I couldn't think of a memory tool that links run with x's, so I put it to them. Maybe these have already been done before, but I forgot, so I really liked some of the ones my kids came up with:

you run from your ex
you run from T-rex
you run cross country (x)
you run on a flat surface, and x is on the horizontal axis.

Silliness

I got a much-needed laugh today from a student. In my quest to drink more water and to stay caffeinated, I bring two 1-liter bottles of water to school every day. One (the BLUE one) I use with my electric water boiler to make tea (for normal days where you got enough sleep) or with my single-serving coffee maker to make hazelnut coffee (for the oh my god wake me up days). This water allows me 2 large (20 oz) cups of hot beverage (and I might add that it's very hard to find good, 20 oz reusable hot beverage cups. Thank you Starbucks). Add a little non-sugared soy milk and I'm in heaven. The other bottle (the YELLOW one) is to just drink straight. Of course there's the bathroom vs. class time issue, so usually I drink 1/2 of it during lunch time, and then the other half at the end of the work day.

Today, I had a mixture of chalk or dust in the throat and/or an on-coming cold and/or allergies, and I desperately needed a sip of water while I was teaching, so that I could continue without turning into a sputtering mess. I did something I'd apparently never done in class before. I got the yellow water bottle and took a few sips.

A girl looks at me for a bit and then says, "why would anyone drink water out of a yellow water bottle?"

After I finished laughing, I came back with, "I'm recycling". Ew.

New Year's Teaching Resolutions

Okay, so New Year for teachers is really August/September, but it's never bad to reflect on how the year has gone so far and what things I could work on for the 2nd half of the school year. Also, by now I have some sort of groove going with the kids (good or bad), and that gives me more to work with.

1. I'm still not happy with my homework I assign. Ideally I would like it to be 80% or so new material, and 20% mixed review. That's always in the back of my mind, and it seems to have taken up permanent residence there. My issue is that I'm scrambling to create or assign homework at my favorite minute - the last one, so ... Now I'm old enough to know that this is the way I work, so I need to think of something I can do within my limitations.

Idea: While I'm creating the current homework or while I'm entering it in GradeSpeed, jot down 2 similar problems to that night's homework along with topic covered while it's fresh in my mind. If I do this for a while, then I'll build up a store of problems ready-made, and then in my future last minute, I can hunt and peck around this list and just add them to the homework. Better yet, type in or scan in the problems onto my school website, and then just point the students in that direction and tell them which additional problems to do each night.

2. At the end of each class, I really only have a good sense of how a portion of my students understand the current material. There are still too many ways in class to pretend like you're listening and comprehending, but really tuning out in the myriad of teenage ways. I'd like to have a quick easy take on everyone, and have them understand if they get it or not. Problem: I'm usually bell-to-bell, and feel 5 minutes of something else won't happen without squeezing out important content.

Idea:

Hmmm, no immediate ideas. My original idea was to have them do a problem by themselves similar to what they just learned (with? without notes?), but then I'm sitting here thinking about how I learn best, and maybe like everyone else, part of the process is to go back over what you just learned and try to rephrase it or think about it a piece at a time: what were the important points, what did this or that mean, what would happen in such a situation, etc. Maybe a starting idea to see how it works would be to force myself to stop class 5 minutes early, and have a standard set of prompts related to my thoughts above, and the kids have to silently go over their notes and work and brains and answer the questions/prompts about the topic, not solving a problem, but thinking about what was learned. No talking to others, because then I wouldn't know what they know (even though you learn by discussing, but I see this short 5 minutes as not amenable to this).

3. There are still some students who I basically never talk to. You know how it is. A handful of students in each class seem to dominate the time or attention or are the boisterous ones that always engage you in conversation. Then there are the quiet ones who sit there and behave and, well, are quiet. Sure I'll call on them, and they'll answer the question, but that's the extent of our interaction.

Idea: List such kids, and make it a point to engage in conversation with them before class starts at least____ times a 6 weeks. I don't know, I'd have to make a list of all such kids and cross them off or "check" them when I converse with them, then I could probably engage, say 2 per class, so 4-6 per week (block schedule), and then see how many such cycles I could go through. Hmmm, seems calculated. Well I guess it is, but that's what I've got.

Okay, those are not my only concerns, but let's not get carried away and have too much on our plates and end up doing nothing. Happy last day of the year to all of us. Hope 2010 holds all sorts of joy and hope and an enjoyment of at least parts of every day.

Winter Trip

Just this past weekend we went to Santa Fe and stayed at a nice B&B just south of town. We also went snowshoeing for the 1st time, and now I'm a convert. It was easy to rent equipment from REI and fun to trudge through the snow for a couple of days. We lasted about 2-3 hours each day, with much resting on the way up, and a quick scurrying downhill with the promise of lunch to spur us on. I liked the partial packed snow better than the much-trampled on road/paths that were available. I also liked hanging out at the Santa Fe Baking Co. & Cafe and people watching and checking my e-mail and blogs. Here are some pictures of our outing and of our B&B place and of a funny bird that was snuffling around in the snow on one of our breaks.

Discussions About High School

Ahhhh vacation. Time of 9-10 hours of sleep a night, of eating too much, of drinking more than needed, of talking with various people about high school.

Today I had lunch with another math teacher that I used to work with. We were discussing kids who didn't persevere and didn't have a good work ethic .... you know, "kids these days". Then we started talking about when we were in high school, and she mentioned that she wasn't such a hot student back then. Then I mentioned that as a student I wasn't that "student-y". I did what I needed to do to get good grades, but I don't remember really being engaged about topics or thinking hard or being any of the things I want for my students these days. Then I look at how we turned out as adults. My friend is a conscientious teacher who really thinks about what and how she teaches, and I want to believe I'm the same way, and I didn't really learn how to be a good student until I was in grad school and saw how other students worked. So, really, in the end, even though our high school performance wouldn't have predicted it, we turned out okay.

Then that leads me to think that even though some of the kids we teach these days don't do what we want them to do, they still are absorbing the lessons we teach them either formally (math math math) or informally (be a good person, do the right thing, think about what you're learning). And that ultimately, in the end, most likely they'll turn out to be productive adults that end up having a good work ethic or end up having a strong moral compass. Just because they're one way now, when they're 14, that doesn't mean that's how they're destined to be forever. And even though they don't seem to be absorbing what we're telling them, maybe they are at some level, and if not now, then maybe later.

Then this evening we were at an open house for Christmas Eve at our neighbors' home. They have 3 children that have graduated from high school and are now out in the world. I talked with one of the girls (20's) about high school, and she mentioned how she HATED it. "The kids were so mean." We also talked about whether or not we remembered teachers' names. Now even though she's been out for only a few years, she doesn't remember many. I've been out for more than 20, and I don't either. But I do remember 2 teacher's names. What made them different? One was a "public speaking" teacher. That was the most useful class I took. I guess I remember his name because the class had such an impact on me. Another was my freshman English teacher's name. He was all "cool" and wore jeans (in the late 70's), and had a shag rug (ooh aah), and our desks were in a circle, and I still remember his lessons on: effect/affect ... it's/its ... their/they're and so on.

I guess all this is to give myself a little pep talk to remind myself that how my students are today may not be the perfect indication of how they'll ultimately turn out.

Hellooooo Holidays

After the longest week ever and the most emotional, it's finally break time. And by break I mean that now I have time to catch up on my engineering curriculum, so that I have something to teach when I return in 2 weeks. But by break I also mean sleeping past 5am and not being stressed out and in a hurry all day long to make sure I do everything and do it well.

I made 3 finals up from (mostly) scratch, and I like some of the questions I came up with or adjusted from other sources. They also spawned ideas for future lessons.

algebra:

Let s=the amount of suger you ingest (in mg)
Let c=the number of cavities you have

the independent variable is ___________
the dependent variable is ____________
_____ is a function of _______
The correct function notation is s(c) or c(s) (circle one).

This got me to thinking that the next time I am at the first day of teaching functions, after we go through some like this, I'm going to have the students each come up with a scenario and work it through and then we'll share out. That way they'll spend more time processing the concept and figure out what it takes to be dependent and independent and how things relate to each other and what functions are.

In engineering, part of the test was on statistics, so one question I adjusted from something I found on line was:

In a certain neighborhood, the following are household incomes:
$40000, $46000,$54000, ... (and 4 more like this), then $250000000

Find the mean______
Find the median_____
Your engineering firm wants a good sense of the income level for marketing purposes. Which number better represents the neighborhood income and why?

The median came out as something like $51000, and the mean came out roughly $230000000. It was interesting to me that not everyone got it right. More discussion in class next time.

Stressed Out 9th Graders

Phew what a week. It was the last week before finals. Highlights included getting cussed out by a student in a "joking" manner who then subsequently skipped another of the classes she had with me. Being treated to tales of my extremely stressed out students who said they went to their rooms the previous night and started laughing and crying simultaneously without being able to stop. Watching a hugfest take place in my room comprised of various students who were trying to pacify each other. Oh my.

I guess part of it is that my freshman are the oldest kids in this school. We're "growing" a full high school and will have 12th graders at the start of the 2012 school year. At the start of one class, after I'd heard the laughing/crying story, I had a spontaneous idea. I had colored paper in my room, so I had them each take a sheet; I took one, too. I then told them that we all were going to get our stress out on the paper for 5 minutes, and I wouldn't collect their papers. It was for their eyes only, and they could write whatever they wanted to. I told them that at the end they could crumple it up or tear it to bits or take it home and burn it or whatever. I set the timer, and we all wrote away. At the end, we "put our stress away" and moved on with our review. It seemed to calm them down (temporarily?), and we were able to get some work done.

On a positive note, my cussing student was suspended for the remainder of the week, and the class she was in (my most challenging class personality-wise) went better on Friday. On another positive note, all this work stress and other related stress has brought a few of us together, and I've actually talked more with other teachers than I have in the previous two 6 weeks. Here's to finally feeling like I belong to this new school.

Checking Your Work

It recently came to my attention that there are students who don't FULLY understand how to check their work. During this past semester in algebra 1, we solved equations and inequalities and such. To force them to check their work, periodically I would assign it point value on their homework, so they could get at most 80% if they didn't check their work.

Here are various things I noticed. Sometimes students would start checking their work at the 2nd step or the simplified step of the original problem. We discussed why that was a bad idea (potential mistake at the 1st step, and even though your answer looks correct, it's not for the original problem).

Sometimes students would "check" their work, plugging in their answer, and at the end get some number that had nothing to do with the original equation, and then place a check mark at the end. CHECK. I've checked my work. Done. Not correct, but I don't get it, I think just going through the process and the ever-important check mark at the end is good.

And finally, sometimes students would check their work. It wouldn't pan out. But then they wouldn't take it from there. Oh well, it didn't work. I'm stopping. I don't think to go back and follow my work process to see where my mistake was.

Ideas for next time (or later this year?): write out various problems all worked out, and then have students analyze the situation: is the problem correct? how do you know. If the checking didn't work out, where is the mistake? Find it (and have some mistakes in the problem and some in the checking). Have some problems where everything seems to work out, and the problem has the checking occur from the 2nd step on of the problem and "look" correct but in reality not solve the original problem.

Interpreting Functions

I think the kids get functions this year. After we looked at graphs and tables and mappings and saw what functions looked like for these situations (one day) and got a formal definition of functions, the next block day, I started by giving them pairs of objects like: rainfall and tulips. I asked which one depends on the other one? Which one is the input? Which one would be "x" and which one would be "y"? And, the new one for them: which one is a function of the other one? (we discussed what that means). We did that for 3 pairs of things.

Then I noted that THAT was a ton of writing, and we assigned variables to things like r and t, and I showed them t(r) and noted that the input, r, was INSIDE the parentheses, and the output, t, was OUTSIDE the parentheses, and if you were talking to your math boyfriend over the phone, you'd say, "t of r" or "t is a function of r".

Then we got to things like B(h) where B is your tutoring bill and h is the hours of tutoring. I asked them to interpret: B(3) = 120. We did this for 4 problems or so. I liked those types of questions, and we took them to graphs and tables the next day where I made them interpret v(5) or m(10) where there was context around the problems.

Next up, studying for finals and finals and a LONG BREAK to get more than 6.something hours of sleep each weeknight.