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.

"69"

Argh! The dreaded number for a high school teacher. And what is it, that if you just make a problem up on the fly ... out of the infinite possible results that could come out, THIS one does.

Anyway, at my "new" school (when will I stop starting a sentence with that?), the kids are pretty well-behaved, and I don't really have many situations where I either inwardly or outwardly roll my eyes at their adolescent-ness. In one class, I have some 2 girls that are classified for special ed because of learning disabilities. Once or twice in the past when I'm making up problems on the fly, to "engage" them more in the process, I ask generally, "what is your favorite number?", and the first one to call one out, gets that number in the current part of the problem. This one particular girl shouted out as her favorite number, "69" amongst the other one digit numbers I was hearing. I didn't make a big deal of it then and just moved on, but I thought at home about an effective way I could address it.

In the past it was boys that did it, and I would just roll my eyes in front of the class and say, "high school boys!" and move on. Here .... girl yelling out .... weird. I couldn't get a grasp on whether she was doing it for effect or if she actually knew what it meant or was just cognizent of the fact that it got a reaction. Anyhow ... it happened again today, and I was ready. I turned to her and said, "you need to stop calling out this number. You probably don't realize it, but you are making yourself out to be a person you REALLY don't want to be mistaken for." or something to that effect and moved on. ... Let's see if this works in the future.

New Kid on the Block

Blach! I think last Thursday and Friday were the 1st 2 days in a row that I had a completely good day. All the other days have been filled with either snippy looks from certain students because I dared move their seats, or second guessing myself because all the other teachers seem to be clicking and I'm not chatting with them, or rush rush rushing to get all my things ready to teach my 3 different preps and not feeling as prepared as I'd like to be and semi-winging it. And just general "blahness".

On Thursday I decided to kill my students with kindness. Instead of just scanning their homework for completeness, I wrote little notes on them ... something positive: "great work", "you really get it", "your handwriting is so neat and easy to read", that sort of thing. That was in my snippy student class with the seat changes. Well, miracle of miracles, we had a good day together. They actually worked and laughed at my lame jokes, and nary a snippy look passed.

Then another teacher sat down with me and we mapped out the algebra course we're teaching and that was good and I felt like I belonged. Then I actually had time to think things through about how I'd teach a concept (the dreaded "5-2(x-3)" type of situation where they DON'T want to distribute the negative (or subtraction) in front of the 2.

Then there was teenage girl drama on Friday, and I happened to walk in on it, and I think I was part of their solution. This was with a group of friends that were clashing, and some of the girls were my snippy students, so maybe we've made progress towards forming a better relationship.

So, WooHoo, I'm on the up part of the inevitable rollercoaster.

Absent Students on Test Day

I got my first taste on how things work at my new school in the cases where kids are absent on a test day. In my old school after I'd been there a while, I found what the culture of the school was and what it would take for the kids to finally make up a test (so that a week or so hasn't passed and they then finally meander in after school to make it up). I announced firmly at the start of school and frequently after that (right before test day) that if they were absent during a test, then I would put them in the hall the next class and they would finish/take the test. This stopped people from being spontaneously sick during test day. It also stopped people from taking forever and 2 days to make it up.

Well, at my new school, I just gave my first test. To be fair, a ton of kids have been out with the flu and such. So basically I had about 2 kids per class that missed a test over the span of 2 block days. Hmmm, I was told the kids were pretty good about coming in and being proactive about taking care of business. Supposedly, they were to come to me of their own initiative and make up the tests. Did not happen. Then the next class day I asked them separately when they could come in after school. Hmmm, mumble mumble. Still did not come in. Finally, I entered a 0 in the electronic gradebook for the absentees' test columns, and it brought their averages WAY down.

Our students and their parents have access to the gradebook. The advisory classes were also to check grades today. And magically, 3 students showed up after school today to make up their tests without any extra prompting from me. Coincidence? Well, either that, or I don't have to keep nagging. If they choose to keep the zero, okay. .... Well, what if later on after TOO much time passes, THEN they want to make it up. I guess I'll wait and see what happens to see if I'll change my strategy.

On another note. One of my classes was getting TOO chatty, and I was crabby in class because of it. New seating today. Poof! Quiet class (for now!) and poof poof: happy teacher that could actually crack some jokes because she wasn't monitoring their rude behavior. I even threw in some off-topic math that they actually found cool (who knew). I was making up problems and asking for numbers, at one point someone called "6". Then I had to say, "you know, 6 is a perfect number". Then went on to tell them what the definition of a perfect number is. Then shockingly (I guess it shouldn't be, but remember, this was my trouble class), they started to wonder out loud about other numbers and their perfectness. Ahhhh, I'll take this one bright spot with this class as it was our best time together since the start of school. Hopefully, it will happen more often.

Algebra 1 Surprises

This is only the 2nd year I've taught algebra 1 as a one-year course (in New Jersey we had a slower paced 2 year course of which 1 taught the 1st year). Recently, some interesting things have come to my attention that I'll be aware of the next time I teach it.

We've just started "baby graphing" ... I give them an equation, and x values, and then they find the y values and plot the points. They're still at the stage where they don't know if they should connect the points or not. When I prompted them on a linear graph as to whether they should connect them or not, I got "yes because they go up at a constant rate" or "yes, they follow a pattern". We'll fix that later. But here are some more immediate things that I need to address.

On the 2nd day we were doing this, I then did NOT give them x values. Oh HOLD THE PHONE! What should we do???? Oh no!!! We got that straightened out with the "rule of thumb" (then I had to tell them the origin of that phrase). Then here's the problem, sometimes I had given them a preset grid, and OH NO, the points they chose did not fit. They didn't figure out that they could change the scale, or NOT plot that particular point. So ... new buggaboos that I'm learning to address in the course of this unit.

Then, here's the more interesting one. I saw with alarming frequency that apparently, 10 divided by 20 is 2. I know. Who knew?! Then I realized, they did not know that if they saw "10 div 20" (where the div is the division sign) that that was the same as 10/20 or 20 into 10 (under the long division symbol). They didn't know what went where.

And finally, I'll have to come up with a clever way to make stick that if you're given: y = -x^2, and you plug in x=3, then that's NOT (-3)(-3). or similarly, if you plug in x=-5, then that's not (--5)^2 or 25. I'm thinking "x box": put a box around the x physically and follow PEMDAS. ... Another teacher today said that a student of hers suggested, "oh! y=-x^2 can just be written as y = 0 - x^2". Then they would follow PEMDAS more easily. Maybe I should try that.

Sitting at Tables

This is the 1st time in my teaching career that the students sit 4 at a table. I've always had desks that have been arranged in groups of 4 (facing forward). Now the kids are 2 on each side facing each other, and the tables are angled towards the front, so that everyone can see the board.

Well, this past week I gave my 1st quizzes, and I was pondering what to do about wandering eyes. I didn't have enough time to make a big table divider, and doing nothing didn't sit well with me since I can't monitor all students at all times. So I remembered what I'd heard about manila folders propped up in front of each student.

I was passing out the folders to my 9th graders, and some of them started to act offended. I don't know if it was a show or real offense, but the comments were, "we haven't done this since the 6th grade", "this is so childish", etc. Hmph. I've SEEN 9th grade eyes wandering. I presented it as, "humor me. This is so I don't wrongly accuse you of cheating, and it makes me feel better." But seriously, the seats/papers are too close together to not have issues. I wonder what other people do? I guess I'll ask at my school.

Answer Banks

Still loving the new school, but not loving the last minute scrambling to get everything together. Guess I'll figure it out soon (or it will be June and a moot point). The school philosophy sort of discourages the use of textbooks for homework problems, and we're to create our own thing. I'm fine with that because mostly that's what I do, but this year with basically 3 classes to get materials ready for, it's a challenge.

Anyway, wa wa wa. What I am pleased about is how my algebra 1 homeworks are going. I know when I'm learning something new, I like to have immediate feedback on my correctness. At the same time, if I'm a high school student that may quickly look at the answer without struggling with the problem first, that wouldn't benefit me. Therefore, I've been giving about 10 problems per homework and then putting an extra box on the bottom of the sheet with all the answers in mixed order. So they have to do all problems and cross them all off and will know soon if something is amiss.

I had feedback today as I was handing out the next assignment. One girl looked at the sheet and whooped, "YES! Thank you for the answer bank!".

I guess for algebra (not the line graphing) it'll be pretty easy to keep this up, but the geometry ... hmmmm, will have to think about it.

Psychology of Pricing

I had an epiphany the other day about how much each homework was worth. In our grading program we can assign different weights for different types of things: homework, tests, projects, etc. I have a totally independent category for homework and it was worth 25% of their total grade. Now since this is the only type of object in this category, it doesn't matter what each homework is worth if they're all worth the same: each 2 points, each 100 points, etc. It all comes out in the wash. My homeworks were worth 2 points each, and I deducted points (or partial points) as needed, so you could still earn 100% or 80% or so on on an assignment.

I don't know why the 2 points always worked for me. Maybe I fell prey to the psychology of pricing, too, and subconsciously I thought that tests were where you really showed your stuff, so those were worth 40 or 50 points or what have you, so the homeworks should be worth 2 points.

Anyway, at my new school, all the 9th grade classes have to have the same percentages: 45% homework/classwork and 55% tests/projects. There was some extra wording about deducting 5 points for various homework infractions, and so being new on the block and wanting to at least try things the way everyone else is doing them, I'm deciding this year to have each homework be worth 100 points. Again it shouldn't matter because it's in its own category.

So here was my epiphany. In my old school maybe part of the reason why kids were lacksadaisical about turning in their homework was because, "hey, it's only worth 2 points. no biggie if I don't turn it in." When in reality, it was a big deal because those 0's started to add up. I'm wondering if they would have had a different attitude if I'd assigned each homework 2000 points, just to mess with their minds or to get them to think about how the math all works out.

In other news, how's my new school going? Well, I think all the staff I've encountered have come from a different planet: the planet of graciousness and kindness and hard work. Oh my goodness, I can't tell you how many nice e-mails or cards or words I've gotten from other staff just to welcome me (and other new teachers, I'm sure) and check to see if I'm okay and to see if I have any questions or need anything. I'm so blessed this year. WootWoot.

Creating Your Own Thing

In this crazy week of prepping for the start of school, I've been in a few situations where I keep thinking about the book "Why We Teach", well really about one essay in particular. The teacher described her growing up years and the need for her to find her own voice and opinions. She got to the point where she didn't want to have a discussion with others or listen to other people's opinions on something before she had a chance to digest things and form her own opinion or method of doing something. Otherwise, she felt that she was just going along with the crowd or that her thoughts would either be stifled or not formed or swayed by what others thought.

So I periodically thought about this as I was coming up with a syllabus or a first day activity or how to decorate my room or procedures I want to put into place. Maybe it's not a "la la la la I don't hear you" type of situation where I think "it's my way or the highway, baby", but more of a reminder to think my own thoughts, then gather other opinions, then go back and reflect about how I think things should be done that carry my personality stamp.

Here's one new idea I'm trying, and who knows if it'll work. For the past many years I have taken a picture of each group of students on the 1st day of school and during that 1st class I had them fill out a seating chart AND print their names on a small sticky note. Then that 1st night I go print the pictures, and with double-sided tape I put their sticky notes on their picture. This helps me learn their names, and I also put all the pictures up in the room. They love to look at them at odd times during the semester.

Because I've seen that they SO love to go up and glance at all the pictures and discuss things and point certain things out (ooh, I just realized one reason why ... this helps them also to see who everyone is). Anyway, because of this, I'm going to ask them to bring in a favorite picture of themselves that 1st week (that I'll return to them later), and I'll use the awesome stikki clips to put them up as a border around either the blackboard or a bulletin board.

New Toy

I was recently at training and learned about fun ways to present information such as:

A Movie I Made (I see a side job forming)

I could see it getting old, but it's a nice thing to throw in the mix.

I've also met amazing people at my new school. It's only been open for 2 years, so they're still inventing who they are and what they are capable of doing. They seem genuine and smart and committed. BUT.

Information Overload. I'm totally at the stage of, "I'll never remember to do all this", and "Argh, what if I screw up, and they secretly shake their heads at the mistake they made hiring me", and "Oh My GOD, I'll never be ready come Monday". You know, the usual jitters (and don't forget: they have only HOW MANY copiers? What, no work/eating/microwave room?, etc.)

I'm teaching 4 different preps this year ... well, 3.5 (one is a type of study hall). And I've agreed to be some sort of team leader and occasional yoga instructor. I must be woozy from lack of sleep. Must. Learn. To. Say. No. I practiced a bit today when an afternoon robotics team leader position presented itself: no. Whew! Go me. Baby steps.

Words to Ponder and Chew Over

I recently came across a chart that contained these comparisons, while I was searching various high school websites. (hmmm, the formatting is wonky, but ...)
Comparing Solution Building with Problem Solving
Solution Building vs. Problem Solving

1. "How did you do that?" vs. "Why did you do that?"

2. Focus on the future without the problem vs. Emphasis on past with the problem

3. Solution talk vs. Problem talk

4. Attention on what is working vs. Attention on what is wrong

5. Student is capable. vs. Student is flawed.

6. Teacher skilled at "not knowing." vs. Teacher is "all knowing."

7. If it works, do more of it. vs. Just keep using what you think should work until it, hopefully, does.

8. Change is inevitable. vs. People cannot change.

This resonated with me and it's been popping in and out of my mind for the last few days. If I scan down the list, this past year I could count 5 of the 8 where I was more focused on what was wrong at my school than just rotating my thinking and concentrating on what I could change or fix or be a part of making better.

Ooh, 7 makes me wince because in some of my classes, that's what I did sometimes. Off the top of my head: if students were having continual problems understanding, I would tell myself that I was ALWAYS available after school and they had every opportunity to come to tutoring. Yet every year, there are kids who for a variety of reasons don't come to tutoring and STILL fail to understand various topics. Maybe I need to enhance my toolbox of skills so that more kids understand more topics in class or have different avenues of seeking help other than coming to my tutoring.

Anyway, more stuff to reflect on.

Learned & Reaffirmed Things

After a slew of math workshops all crammed together in one summer, I can generate a list of things I've either learned or relearned from my experiences:

1. Your math text is NOT your curriculum. Not for what you should teach, not for how you should teach, not for why you should teach something.

2. Every workshop seems to have the same set of characters (other than perfect people like me ... cough cough):
- the know-it-all that has to shout out all the answers quickly just to show they know things.
- the on-the-sly-constant texter
- the nary-a-peeper
- the challenged learner that asks TONS of questions
- the I-know-this-&-am-too-cool-to-REALLY-process-what-you're-saying person who will probably be unpleasantly surprised when they have to actually apply this current knowledge next year.

3. I'm set in my ways. Before my 1st out of town workshop, I was stressing, "oh no, I won't have my favorite tea, my vegetarian food, my own bed, ..." waa waa waa. I *mostly* had a change of attitude and used it as an opportunity to try new things ...... mostly.

4. I love my new school-provided laptop. When I was getting homesick, I could stream our local NPR station, and I could Skype my husband, and I could send e-mail and impatiently wait for replies to feel connected to friends.

5. "yelp.com" is a great new asset in my traveling life. I could just type in a city and "thai restaurant" or "breakfast" and get tons of opinions to scroll through to find places to go.

6. "mathforum.org" has a section called "math tools" and you can enter the subject you teach and the topic you're interested in, and it returns a list of resources for you to browse through to use: applets, calculator tasks, worksheets.

Even Better Calculator Trick

We explored a "different ways of payment" problem and learned a new calculator trick to boot. Suppose plan A gives you $20 the 1st day and increases your salary by $1 per day. Suppose plan B gives you $0.01 the 1st day and doubles your salary every day.

Calculator:

{1, 20, 0.01} (to represent 1st day, plan A, plan B)

ENTER

{ANS(1)+1,ANS(2)+1,ANS(3)*2}

ENTER, ENTER, ENTER, ..... to keep seeing current day, plan A, plan B updates.

Nice. And sandwiched between 2 nice pictures of a recent trip.

Ooh Cool Calculator Skill

Today at my math workshop, I learned some new-to-me calculator skills that I believe I'll use this year.

Let's say you want to compare 2 functions at various values. They don't need to be, but for ease sake here I'll assume the x values are integers, and the y values linear, say some geometric patterns where x represents the pattern number, and y represents the number of sides. In the main window type:

{1, 3, 7} and ENTER
This would mean: 1=1st pattern, 3=#sides for one shape in 1st pattern, and 7=#sides for 2nd shape in 1st pattern.

Then TYPE/GET
ANS + {1, 2, 6} and ENTER
This would mean you're adding 1 to the 1st number (1) in list, adding 2 to the 2nd number (3) in list, and adding 6 to the 3rd number (7) in list.

Now you can keep hitting ENTER, and you have a nice way of visualizing what pattern number you're at without keeping track of how many times you pushed ENTER, and what the 2 other functions are, so this list would look like:

{1,3,7}
{2,5,13}
{3,7,19}
{4,9,25}, etc.

Second skill: you know how sometimes you're populating L1 and L2 where L1 is just integers and L2 is some function of the integers? Well, in the past, I would just go to L1 and physically type in 1,2,3,4,5,... then type in the equation at the header of L2. Well. In your main window you can easily populate L1 by:

seq(x,x,1,100,1)--> L1

I guess it would only be quicker this way for large amounts of integers. "seq" is found under LIST>OPS.
The first value is your expression/function,
the 2nd value is the variable,
the 3rd value is where you want to start,
the 4th value is where you want to end, and
the 5th value is what you want to increment the input by.

Now the ironic thing would be if I "learned" this in the past, and just don't remember it because I haven't used it.

preAP math ideas

I'm at a week-long workshop for "experienced" preAP math teachers (for nonTexans, preAP is like an honors course or the higher level math students). After the 1st day, I already have some good ideas on what to do differently next year. In my school district, we have to get re-professionally-developed in preAP techniques every 5 years. At first I was thinking, hmph, I do so much other professional development on my own, this is not needed. Oh contraire. Even though I've taught calculus and precalculus, it is apparently still needed and useful.

Today our instructor did various things using calculus and statistics AP questions as the basis. But. The way he did it was very useful. We worked through a calculus problem. Then we brainstormed on earlier class skills it addresses. He showed concrete ideas on how to modify the problems to address alg, geo, alg2, precal.

But what I really came away with were the LOAD of things I could do with statistics and why it's useful. For example, at the end of the day, he had a sheet with a cm ruler on it, and we all measured our hand span from outer index finger to outer pinkie finger. We got that list in L1 on the calculator. Here are some of the things we did with it besides calculate mean, range, Q1, Q3,...:

1. What if the ruler on the page had a mistake, and we were 2 cm off, so we had to subtract 2 cm from each data point. Without using your calculator, discuss what that would do to the: mean, range, median, ...

2. What if instead of cm, we wanted inches. How would you change data? What would this now do to mean, range, ...

3. What if instead of the largest span we had, that person was replaced with (name some local basketball player who's tall with BIG hand span) ... and we put in a large reasonable number. What would this now do to ....

4. What if for our data of spans that ranged from 16.5 cm to 21.5 cm, someone got a mean of 15 cm. Discuss why this is reasonable or not reasonable.

There were a ton more good ideas. I liked it because it made us think and it would make the kids think and it was in context they could understand and it had them manipulating formulas and thinking about meanings (throughout the day).

Real Life Math (as opposed to the fake kind)

We're going on multiple longer-than-a-week trips this summer, lucky us, and our outside Texas plants are begging for dribbles of water. We decided to put a timer on a drip irrigation system, and then we wouldn't have to worry about coming back to an Adam's Family set of plants.

I was hooking up the 1 gal/hour drippers to each pot, and doing the math. I usually water them every two days with a huge dollop from a pitcher. Hmmm, how many dollops in a gallon? How many minutes every other day to equal a dollop? I guess I'll see if I did my math right when I come back to either a lush plantation or a brown oasis.

Student Teacher Interactions

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

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

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

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

My New Love Affair

Dear Webcam,

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

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

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

Love,

Me (click click strike a pose)

Core Set of Knowledge

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

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

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

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

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

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

Engineering Education Workshop

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

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

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

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

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

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

Whew! Stuff to think about.

Center of Mass Fun

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

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

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

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

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

13.7" off the table edge.

Stating the (not so) Obvious

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

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

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

Alternate Finals

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

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

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

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

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

Wrapping Up the Year and School

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

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

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

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

Crabby Pants Cookie

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

Cases in point:

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

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

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

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

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

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

Post AP Exam

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

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

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

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

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

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

Surprising Gap of Knowledge

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

NCTM goodies

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

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

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

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

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

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

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

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