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.

Music & Computer Work

Frequently my IED (engineering) class is on the computer all period working on the CAD program (Inventor). Several of the students daily ask me if they can listen to music while they work. I always say no. BUT it's "Pandora", they say, there's no talking, they say, it helps me concentrate, they say. Ms./Mr. So-And-So let's me in THEIR class, they say. No, I say.

I had a bunch of reasons all jumbled up in my brain, and I didn't sort it out as to the real reason I was such a grinch until the other day. Here's my main reason. More and more I see people in society all plugged in and earbudded into isolation and in their own little worlds not interacting with the people in the present and around them. I guess I want my students to see and be with the students around them at the current time and learn to interact with them - whether it's talking with them about what they're doing, chatting about various things, or learning to focus with the outside noise potentially disturbing them. You know, being part of our community.

And also because I'm a grinch.

Reviews

It's almost time for finals, and I scurried around last minute as is my nature to make a review for algebra and geometry. While I was doing so, I remembered various conversations I'd had with my algebra students this semester whenever test time rolled around.

I want them to be active learners and to take the initiative to think of what's going to be tested, go over problems of a type, come in for help if needed, etc, etc. Yea, I know, maybe it's all pipe dreams and wishful thinking, but how do you get them there. I tried with a study guide (not a review sheet), and after some tweaking, used it the few remaining times I had tests. I never went back and surveyed the students on paper to see if it changed their study habits. Maybe they just found it one more chore to do, but maybe it put a seed in their heads about how to study.

Or maybe not. Right after another test, we were discussing it in class, and some students raised their hands:
"other teachers give us a review sheet with questions to practice"
"other teachers give us points when we turn in the review sheet"

Yeesh. They think there's something magic about the extra review problems I could come up with. And THEN they want someone else to give them motivation to actually review. I said as much (in nice teacher talk words) to them in response to these questions. I don't know who I sold, or who still thinks, "meanie. give us the review!"

Treadmill Year

I teach 4 different preps this year, and always feel rushed to get done what I need to get done. I want to do a good job (obviously), and always go over and over in my mind what I'm teaching, how I'm teaching it, how it could be better, etc. Three of my preps are single classes, and one prep I teach 3 times per lesson. That's the lucky prep (algebra 1) because I can refine it by the 3rd time. Or maybe I should say that my 3rd class of algebra 1 is my lucky class, and the other 2 are my guinea pigs (squea squea). Why am I mentioning this? Because like maybe all teachers I'm a world-class self-beater-upper in that I'm always thinking I could have taught it better or given better problems or better something. I finally have started saying to myself, "you're doing the best you can. do it and move on." Who knows how long I'll listen to myself. What I am loving is my GoogleDocs account. I'm doing my lesson plans on there this year, and I like that the documents are available no matter what computer I use and where I am (home or school). What's going on so far: geometry - we just learned CPCTC. I'm following the curriculum I taught in New Jersey, and we're doing flow proofs. I think those are more logical than 2 column proofs, and it shows me and the students what statements are needed and how for what conclusions. algebra 1 - we have just covered patterns and linking them to tables, graphs, rules, and descriptions using tiles. I moved away from tiles the 2nd day, and wanted them to find rules and use the rules without drawing pictures, and I like the problems I gave them. Sample: Suppose 13 15 17 19 21 ... is a sequence of "tiles. a. Let "13" be the 1st figure in the sequence, write the rule. b. Let "13" be the 5th figure in the sequence, write the rule. c. Let "13" be the 20th figure in the sequence, without counting backwards, write the rule. d. Let "13" be the 100th figure in the sequence, write the rule. e. For "a.", suppose you have used 51 tiles, what figure number are you at? f. For "a.", suppose you have 200 tiles to use, what's the maximum figure number you can create? And for each of these (a-d), I made them write what each variable and each # represented. Then we moved on to other "tile" like problems: A cell phone company charges $29.95 per month with a 3cent per minute fee, (after a bunch of leading questions to link to tiles): write the rule. This one was interesting because of the units issue. Many kids started with b = 29.95 + 3m .... we had a discussion about units and got it to b = 29.95 + 0.03m etc. engineering - we've talked about dial calipers and statistics and geometry. Lots of good discussion about how statistics is used in engineering. TAKS math class - we've taken a LOT of deep breaths because of behavior issues and just plowed on. Today we learned how to count. After some snarky comments, they kind of got into it. I gave them 4 different colored snap cubes and we learned how to count "choosing 2 for a team" then "choosing a president and a vp" then choosing 3 for a team, etc.

Hall Conversations

Last week was not a good week. I was crabby and in a funk to begin with (perimenopause anyone? ... or maybe I just want to place a reason to this cloud that goes by periodically lately). Then in my TAKS help class, on Thursday, I had to deal with outrageous rudeness. The kids are usually pretty good, save for the "I'd rather talk to my friends than do math" behavior. Two particular students were in the chatty mood. One had already come into class with an attitude. About 20 minutes into class, I said, "when we start our next activity, one of you needs to move tables", and I walked away to let them process that. The next activity started, and neither had moved, I asked again, and here came the craziness. One girl gets a big attitude on her face, crosses her arms and says, "I'm not moving".

Excuse me? Step out into the hall, I need to talk to you. I got the other students started on their work, and so began the conversation in the hall. She would not let up. Finally, she's all in a snit and states she's ready to come back in and work. I don't think so. I brought out a chair, and she remained in the hall doing her work for the next hour. Oh my.

Then on Friday in my last class of the day on student mentioned she left her work in another teacher's class, and could she go get it. No, not right now. She was not happy, but she continued to work. Then about 20 minutes later, she asked to go to the bathroom. I was thinking she wanted to go roam the halls and find her homework in the meantime, but she was jiggling in her seat, and she's generally a good kid, so I said, "go quickly and come back".

Twenty minutes later she shows up. Oh my was I angry. Again I started the kids on an activity, and talked to her in the hall. I mentioned why I was upset, and asked where she'd gone (to a counselor), and why she hadn't asked (you asked me in front of the class, and I didn't want to say it out loud), and how she could possibly handle it in the future (come up and whisper your request in my ear or call me over).

Anyway, she was near tears, and I was angry and yuk, not a good way to end the day/week (wooHOO for margaritas with friends after work to decompress). Today I asked the counselor if she'd been in to see her, and she said yes, she'd been having family issues and all sorts of sad things and we should be on the lookout to support her. Great! Big Ogre Teacher with the angry face berating a poor child.

Deep Breaths and Fresh Starts this week.

Algebra Algebra Algebra

Phew! That's what seems to be consuming my thoughts these days. I like teaching it for the 2nd year, and also I like that I know what's coming up on the horizon in the higher level math classes for the kids, so I can know what skills to focus on. For example, we just covered solving proportions, and I had some problems with the variable in the denominator. Well. The kids learned from 8th grade that you can just change the equation by taking the reciprocal of both sides and then solve.

So 12/5 = 7/x becomes 5/12 = x/7.

This is all well and good, and sometimes that's the simplest way to solve, but what if in algebra 2 or above you come across:

3x/(x+1) = (3x-2)/x.

Then "flipping" does not get you any closer to the answer.

Oh. Then someone mentioned "cross multiplying". Well, I didn't even want to go there because of all the misuse of that I've seen later on: OH! magically any time I see 2 fractions together involving variables whether or not there's an equal sign, I'm going to cross multiply without knowing why it works or even IF it works. Voila!

Anyway .... tons of algebra fun. I did have a discussion with my coworker, and she had this brilliant idea that I tried with solving absolute value equations ... but it can work with solving any equation. Write down the equation. On top of it, write numbers in circles in the order of operation of what would be done to x if you were to plug in a number. Then on the side I listed PEMDAS and the circled numbers in order and wrote in words what that was:
1. multiply by 3
2. subtract 4
3. take absolute value
4. add 10

Then under that sidebar, I wrote "to solve: undo in backwards order SADMEP"
4. subtract 10
3. 2 cases
2. add 4
1. divide by 3

Then the kids had a road map of what to do, and they didn't do weird things like get rid of stuff inside the absolute value symbols before taking care of them.

Literal Equations

We've moved on to solving literal equations for a variable. I like this transition because it reinforces the same skills they've been working on forEVER. One thing came up in my first of 3 classes to teach it this year that made me change tactics for the next 2 classes.

We were all about "isolating the variable" and "undoing what's done to the variable you're solving for" and such. Then as I'm walking around, lo and behold, a student was actually moving the variable. She wanted to get it to the other side. What was she doing?! Don't touch that variable!

That led to the following in my next 2 classes. Suppose the problem is
Solve 3A = 2w + 4p for w.
I first made them get out another colored pen/pencil, and then identify the variable they were solving for. Then they had to write that variable in a DIFFERENT color:

3A = 2w + 4p

Then I made them draw an arrow to the w and write in their notes, "DON'T TOUCH THIS" while humming the M.C. Hammer song of the same name. We continued on, and most everyone successfully colored the "solve for" variables and left them alone in the remaining problems.

"Subtracting or Negative"

In the course of getting my algebra 1 kids up to speed on solving equations and inequalities, they have to combine like terms, and I'm getting the above question too often for comfort. Sometimes after they combine the terms, they'll squish them all together and instead of something like 6x - 5, it will be 6x-5, where that's a teeny tiny negative sign and not a subtraction sign. I hadn't clued into this until a kid wrote "7x4" instead of "7x + 4" because in her mind, it was a positive 4 that remained after combining the like terms, and not an adding of the 4.

So I'm trying to be careful to say things like: you're keeping track of all the steps you're doing, for example subtracting 5 and then adding 18, so at the end of the day, you haven't seen all the intermediate steps, and if you had just done it in one step, you might as well have just added 13 (and not "positive 13").

Also, in my continual attempt to bring in problems in context, I had interesting conversations with the kids about this problem I gave them:

1. Two cell phone plans Verizon offers are as follows. You can have a monthly fee of $40 and pay $0.20 per text message, or you can have a select plan costing $60 and unlimited texting. Consider the inequality
40 + 0.20t > 60
a. What does the t represent (give units)?
b. What is the person trying to find out by solving this inequality?
c. Solve for t and explain what this means in the context of the problem.
d. Cell Phone Sally has tons of friends and wants to see if her texting habits would be too expensive under the 1st plan. If she texts about 10 messages per day, what would her bill be per month under the 1st plan mentioned?
e. How many texts do you send per day? What would that be per month?
f. What would your monthly bill be under the 1st plan?

I had gone online to the Verizon website, and got that accurate information. I was very careful to have them do only a couple of problems and stop them. Invariably they answered "text messages" for a. Then we had to have a discussion about "what about the text messages? their length? their time? what?".

Then for problem b, practically everyone got it wrong. They said: they're trying to find out which plan is cheaper. So I asked them, okay what is your answer going to look like when you solve the inequality, and THAT'S going to tell you which one is cheaper? We held off on answering b until they did c.

Now note, my coworker and I decided to clump topics: solving equations and solving single variable inequalities one after another, because it would give the kids a chance to practice the same skills. Also note that we have not discussed linear equations and graphs and rates of change yet in the sense that they would not know how to set up the 40 + 0.20t if just the words were given to them.

So, my students solved c. And the answer is t > 100. So we had to have a discussion about what this means. Some kids had $100, some kids said "this means the left plan is more expensive", etc. We finally got to: if someone sends more than 100 text messages, then the first plan is more expensive. I asked what the t values were the solution to this problem, and they said "all t greater than 100", so I asked, would t = 101.3 work? and they said, no, it has to be an integer in this case. good.

d was also a problem that started discussion. There were kids that just started working it without asking me how many days in a month, so that was a good check of their careful reading.

And the last two were GREAT big eye-openers for me. I don't have a cell phone, so silly me, I knew "10 messages a day" was low, but I didn't know HOW low. Some of my students reported out that they sent anywhere from 100 - 500 - in one case 1000 text messages a day? Hmmmmm, I had to ask how many hours a day they were doing this, and we had to do the math to see if this was even physically possible. Holy Moly.

Duties and Conversations

Most likely, just like other schools, I have extra duties and guilt that sometimes makes me volunteer for EXTRA one time duties. And, just like other teachers, there's probably a fair bit of grumbling under my breath about how I don't have TIME for this and I need my time to prepare and on and on.

On the other hand, there are some nice perks that go along with my morning duty. The 2 other teachers I share it with teach different subjects and different grade levels, and I never see them other places. So my 15 minute morning duty allows me to chat with and get to know them and feel more connected to our school's "family".

Along the same lines, I volunteered to give up my lunch time to help sell t-shirts the other day. Not so bad, since I could eat my lunch at the same time, and I have the next period off, so I didn't feel too stressed. At this duty I got a chance to talk with yet a 3rd teacher I never see (new also this year) that teaches a foreign language. This conversation was super helpful to both of us. I shared with her some of the snippy behavior and struggles I'm having with a few of my students, and she mentioned that the same was happening with her. We talked about another student that's not doing so well in either of our classes, and I think we both left with the feeling of, "Whew! it's not just me.".

It's so easy to feel isolated and stressed and feel like the ONLY one that may be having certain troubles, that it's nice to commiserate with others that are going through the same thing ... not that I'd wish it on them, but you know...

Regrading Issues

Yeesh! I thought I was careful, brought on by bad experiences and lots of practice, but today ....

Way back when in the early days of teaching, when I'd grade a test/quiz/homework, and something was missing (a problem not done, a justification, some work), I learned pretty quickly to make sure to look carefully at ALL the blank space around it, and if there was, say a blank side of the page, I'd draw a diagonal mark through it to indicate I'd noted it, and also to prevent the kiddies from later on, after they'd got the paper back, ADDING something to that blank space and then claim that it'd been there all along, and then demand/request/beg more points because it was MY mistake. Ditto for blank parts of pages and such.

I know I make mistakes ... still happens ... daily ... so this marking and covering up of blank space cut down these instances dramatically. It also cut down my 2nd guessing myself that I'd missed something.

Well, we had a ton of swine flu absences a few weeks ago, and many students missed many days, and some are still making up old tests and homework. One student had come in last week to make up a geometry test. I had a meeting after school, so I put her in a windowed smaller room that I glanced in on periodically and had her work. She took forever, and it looked as if she had not studied. I think she was assuming I'd give her the same version as everyone else and not a make-up version, and she had used a friend's returned test to study the answers instead of studying concepts. She finally handed it in, and I graded it. 68/100. Ewww. On one unchanged problem, she MAGICALLY produced the answer and none of her work supported it. On another, she showed some work, but then guessed and checked an answer .... but didn't check the geometry constraints.

On a third problem, the one I had "regrading issues" with, I had made a table where students were supposed to fill in 7 cells. She left a whole column blank - 4 cells (logic symbols). I circled the whole column and put a question mark through it and graded on. Today she came to talk to me. Amongst other things, she showed me that she had written those missing answers in small letters in another column (this was a logic section, and the answers were like " p->q " and such). Hmmmmm, I didn't outright accuse her of lying, but I questioned her as to why she didn't put those answers in the right column. She had some story about how she had written them there to help her with another problem, and she didn't know what I was expecting in this problem's column titled "symbols".

I know I'm overly cynical about such things at times, and about 50% of the time I'm wrong, and I'd HATE to accuse someone of outright lying if it weren't true (it happened to me in high school with a teacher and I still remember it to this day). So, I didn't say more and gave her 1/2 the points back, but now I'll have to remember this and be more careful in the future.

Linear Word Problems

Whew! In algebra 1 I've finished the initial introducing of solving a variety of linear equations: one-step, two-step, multi-step, weird distributive action, variables on both sides. Now it's just a matter of having them practice their hearts out until most/all of them are successful. Yesterday, I wanted to have them see how these problems could be used in real life, and after scanning through books and such, I saw that a lot of people were fascinated with how many coins someone has, or how much of a certain type of mixture to use, or which 2 consecutive numbers add to another number.

Then, whew! I scanned throught he Hughes-Hallett book of "Functions Model Change" and adapted some of their ideas that were written in table form to use as linear equation problems. There's one problems about carbon-14 dating which I know is not linear, but, boom, call it a "model", and it can become a linear situation. Then there was one about weight of a person vs. calories burned doing various exercises. Finally there was one about the years since 1970 vs population of a town.

I liked my adaptations because I've altered the scales on the variables, so that the kids have to think about what the numbers mean in terms of units. Also, these are in-context types of problems, not "math world" type. Also, the kids didn't need a calculator, since I made the numbers "doable". We had a discussion about estimating. For example, for the fossils, t represented time the tree had been dead in 1000's of years. An answer came up as t=3 & 2/11, and I asked them what that meant. We discussed approximating 2/11 by 2/10 and having t=3.2 and they finally got to the point to see that was 3,200 years. I also liked that in 2c below, they had to think to put in w=1.4 instead of 140, for example.

Here's an example of one problem I adapted:

2. Exercise physiologists tested many people, and have come up with an equation that shows the number of calories used per minute as a function of body weight for various activities. For walking they calculated the equation
b – 4.6 = 3(w – 1.7)
where b represents the calories burned in one minute, and w is the weight in 100’s of pounds of the person.

a. If w is found to be 1.6, what does that person weigh? (don’t solve; interpret w=1.6)

b. If b is found to be 5.4, what does that mean? (don’t solve; interpret b=5.4)

c. Suppose a person weighs 140 pounds, how many calories did they burn walking in one minute? In 30 minutes?

d. Suppose someone burns 5.2 calories a minute, how much do they weigh?

Studying for Math Tests

Blach! I'm having an inner cursing and outer cursing with lots of hand gesturing and bad facial expressions weekend as I grade my Algebra 1 tests. This was their first true test on algebra (the other one was on topics they've seen since the womb: positive and negative numbers, fractions, simple graphing). During Friday I'd started grading my 1st set of exams (with inner grumbling and outer professionalism while my 2nd set of kiddies took the exam).

Then before my 3rd class started their exam, I had a quick informal vote: how many people did problems from scratch to study for this test (thumbs up or thumbs down)? How many people started studying before last night? How many people read through their notes? Hmmmm, the number of thumbs down was heart breaking.

Maybe it's an experience they have to go through: horrible test grades to see that they actually have to study. On a positive note, the way their grades are weighted with homework and tests, it doesn't HORRIBLY bring down their grades, but it does lower it (sometimes up to 6% points depending).

With a hope of helping them in the future, I've made up a document that I'm going to hand out to them a week before their next test. It walks through the steps of how to study for a math test. Hopefully, this will work.

Memorable Classes

I started thinking about this when a *way* former student (2001-2002 school year) "friended" me on Facebook yesterday. I immediately knew who he was and what class he was in and what year and most all of the other students in that class.

Then I started thinking that this wouldn't be true with many other students and classes. Sure, some stand out and I can remember their names and faces, but ... let's see, roughly 12 years times an average of 6 classes times roughly 25 kids per class (and by "roughly" I mean I'm blotting out the recent years of 38, 40, 36, .... and 25 is easy to multiply by ... and I'm ignoring the fact that I had some students for more than one class) ... so ... 1800 students????? Is that right? Holy Moly.

So, I'm guessing it's a good bet that I wouldn't remember the bulk of them. And, I've been "attempt friended" recently by recent grads, and it feels weird, and I ignore it and move on. But back to the student in question. He's graduated from college now I guess and is working in a tech field. ...

Here are the reasons this class was memorable. It was a gifted & talented class of juniors, and they were smart as a whip. They started out kind of wary of me and the class, and were resistant, but we grew on each other. I would just throw the most obscure problems at them and put on my "game face" of "what? of COURSE I expect you to solve this .... what? you don't think you can?" and then I'd wait, and sure enough, they would come back with answers. It was also one of my smaller classes ... 14 or so. We also had a ton of laughs together over the silliest things. And ... well, after that year was over, right before their senior year started, one of the nicest, sweetest, kindest, most honorable girls from that class (and from the school) died in a car wreck on a rainy night. I'm choking up just thinking about it, and it happened, what, 7 years ago. Boy did I cry during her memorial. Their senior year was a bit more somber because of that, and the valedictorian was a girl in my former class, and her graduation speech wove that event in through her talk and about how it altered her thoughts and actions of that year.

I'm guessing that the most traumatic things are the most memorable. Like when you try to remember your earliest memory from childhood, and invariable it seems to be of some injury or something scary that happened. ...

Anyway, it's nice to see/hear about the kids that are now "adults" and having their next part of their lives. ... Maybe if I stay in one school long enough, I'll have the kids of my current kids?! Yeesh. Or at my advanced years ... maybe I'd be in dentures and Depends by then and too old to terrorize the little kiddies any more.