Teaching Conics

I'm loving this unit more and more each year. It's a chance for the students to practice their ever-waning algebra skills (hello completing the square, I love you). It's also a chance to do some hands-on stuff. AND it's a chance to see some cool applications.

One year (not this one, because ... well, just because) I saw an application that you could build a pool table in the shape of an ellipse, and then if a ball was at one focus point and you hit it, then in an ideal world, it would pass through the other focus point. I then just had to try it. I had the kids construct an ellipse (lots of string and a large piece of paper. Then I had my patient/loving husband carve this out of some wood and hollow out the inside to be the "pool table" in the shape of the ellipse. I brought it to class and we recreated where the foci were and we tested it out. It worked most of the time and was cool.

This year for ellipses, I just had them create ellipses on paper with a partner and a loop of string and 2 sharp pencils held down for the foci. Then they took their notes on this creation. Every student had 2 ellipses, one on each side of the paper, one with vertical foci, and one with horizontal. It worked well.

I'm having them do a project of searching for practical uses of each conic (circles, parabolas, ellipses, and hyperbolas). Let's see what they wow me with.

The Worst Part of Turning in Grades

Grades were due at 2pm on Monday. The previous Thursday night I was driving out of town to go to a math conference and would be out Friday. I warned the kids and told them that the LATEST they could turn in grades would be 4:16 on Thursday afternoon. I made a joke of it to hammer it home.

"Do not run after my car waving your homework at 4:30"
"Do not slip your work under my door after 4:16 and expect me to get it"
"Do not secretly slip it in my mailbox"
"Do not come to my house, please, this weekend to turn things in."

Mostly it went okay. But then there's always the special cases that I make allowances for without telling anyone else. One student's dad had recently died and she was having a rough time of it. She was also out the end of last week for FFA. She talked to me before Thursday, and I said that she could turn in late work AND work that was way past acceptable to turn in.

One student is struggling socially and familially and scholastically and has been in tears and has a hard time keeping it together. I went to school Monday and found some test corrections on my desk from him. I accepted them. He still didn't pass, but this brought his grade up.

Then there's the students that beg and plead and such after the fact and after they have slacked off ALL 6 weeks (which is 7 weeks this time, but who's counting).

Student #1. Monday morning he shows up. "I see my grades a 50%. Is there anything I can do?". Hmmmm, well, you turned in no work all 6 weeks, you barely did your late work. You didn't take advantage of tutoring or retests or test corrections. "No, there's nothing you can do. The time has passed." ... "Please, please, please, PLEASE. I'll do anything. I'll do quadruple work, I'll turn it in before 2pm (due time), I'll, I'll, I'll." .... "NO!". I mean, quite honestly, it's nothing to me if he turned in more late work. I had time to put it in. But I made the decision that that would not be beneficial to him. What would he have learned in that case. "Oh, I can always slack off and then be super polite and hang dog faced and teachers will let it slide at the end." Still it put a sour taste in my mouth and I felt horrible for the day, but ultimately I know it was the right decision.

Student #2 Basically the same story as student #1, except he came in AFTER school AFTER grades were turned in. "IS there ANYthing I can do? I need to stay eligible for band.". ... NO. This one had the extra added effect of super politeness, "yes ma'am, no ma'am, thank you ma'am", and the dipped head of sorrow. He wouldn't leave. He kept waiting around looking all glum waiting for me to change my mind. No, no, no. It may seem nicer to give in now, but it's not useful to you in the long run.

Argh. Hard decisions. I feel like "mean teacher", but I have to remember that I'm trying to do what's ultimately best for each kid.

Teaching Neatness

I just graded my algebra 1 tests over Solving Systems by Substitution. Oh my. The kids generally knew what they were doing, but their sloppiness got in their way. Some couldn't read their own handwriting and dropped negatives or made 3's into 13's and such. Some wavered all over the place and then misread their work that way.

Today we had a lesson on neatness and how part of your job as a "mathematician" is not just to get the answer but to communicate to others how the problem is done, so they can just follow along by reading your work and you don't have to be there to interpret the "doctor handwriting" as I call it. I implored (ordered) them to write each step and keep it all lined up going down the page and not all higgeldy-piggeldy every which way.

We practiced. We practiced some more. We refreshed our memory on fractions. We refreshed our memory on the fact that "3x/4" means the same thing as "3/4 x". We refreshed our distributing skills of "5 - 3(x - 2)" types of situations.

We discussed how to check our work (plug (x,y) back into BOTH equations).

"But why do I have to check both?"
"It could be right in one but your previous mistake makes it wrong in the other. Check both!"
"But I'm not going to be a mathematician. I'm going to be a doctor."
"Well, after surgery you don't just want to check ... 'did I leave the scalpel in the body? No? Good, sew him up' and meanwhile, you didn't check that you left the saw in the body."

Differentiating

Yesterday, for some strange reason, I actually had more time than my usual 2 seconds to prepare for classes, and I was giving a test in precalculus, and I have a handful of very smart kids that are polite and bored in class because it's going too slow for them.

This all adds up to a differentiated test on vectors and polars. The bulk of the class just had the standard test that asked them to:
find the angle between 2 vectors,
convert a polar point to a rectangular point and visa versa,
plot r = 3 sin theta + 2, etc.

Without saying anything to them, I handed the super-smart kids a different version of the test and kept an eye on them throughout the period to see their reaction. They did fine. It took them the whole allotted time (whereas usually they're done in less than 1/2 the time of the other students). They're aware of this fact, so periodically, one of them would look up as another student handed in his test. I wonder what was going through their minds.

Their questions were more of the variety of (and maybe I could have made them harder, but ...) :

give me 2 vectors that are perpendicular to each other and neither lies on the axes or has equal components,

plot 4 points on the polar plane that when connected form a rectangle, none are on the axes. then give me their coordinates, each in 2 ways.

vector u is <6,> find me a vector in the same direction that is 1 unit long (and we did NOT cover this in our short time with vectors). I did give them a hint by making them answer a "similar triangle" type question right before this one.

Anyway, I'm glad I could "unbore" them briefly, and hopefully I can do this again.

Polar Graphs

I'm so excited. I taught the graphing r= 4 sin(theta), r = 2 cos(theta) + 3 and such today, and I think THIS method will stick more successfully than what I've done in the past.

Two years ago at the NCTM Atlanta Conference, a teacher from North Dakota shared her strategy, and it made so much sense, and this year I adapted it and tried it.

I made up a packet where I have 12 such graphs mapped out on a rectangular coordinate system. I don't even label which ones they are. Right next to these graphs are blank polar coordinate systems. The tick marks (or angle marks) on each are divided the same (into pi/6). This ND teacher stressed to make the connection between "y = f(x)" and "r = f(theta)" and link x to theta and y to r and to keep mentioning it. Then you transfer each point from (x,y) to (r,theta) accordingly, and voila! You have your graph.

On the front page I had 3 similar ones, and after they/we graphed all three, then we refreshed our memory on what the equations were. Then we discussed what the connection was between "amplitude BIGGER/smaller than vertical shift" was, etc.

We got through 4 in class, and they have the rest for homework. I'm thinking it will work, because even I can now remember what the graphs should look like by doing such an analysis (whereas before, I had to refresh my memory each year).

Scaffolding & Storing Teaching Materials

As I was searching for "teaching polar coordinates" materials from an NCTM workshop I attended a while ago, I came across a packet that described scaffolding. I liked their 4 tier process they layed out:

1. I teach, you watch
2. I teach, you help
3. You do, I help
4. You do, I watch

I got me thinking about how I've been teaching lately, and about how different uses of these 4 steps work for different populations of students. I think lately my philosophy is more "2", then practice based on "4" with help if I see they need it. I teach preAP and AP classes that are supposed to be for students willing to try things on their own, but realistically has a whole range of abilities. I internally balk at running through all 4 steps because it makes me think of them learning math by seeing, "oh, this is THE method/way of doing things. I will memorize this technique and parrot it back when tested".

I want them to think for themselves. But then another part of me says, "well, they have to learn the basic skills first, and THEN you can throw in some harder thinking problems". And then a 3rd part of me is inundated with comments of "hard homework" and "you didn't teach us how to do THOSE types of problems". I, apparently, need to have more time to think through each lesson and map out my strategy of presenting concepts then mixing the types of problems effectively .... maybe with some warning about various problems and hints (?) and admonitions to actually put forth some effort on the more challenging ones.

Anyhow. Then that got me to thinking about how I store my teaching materials, and how my plan has evolved since I started teaching. I use those large plastic tubs (with tons of hanging files to store papers). I have 4 tubs currently: one for precalculus, 2 for calculus, and 1 I just started for algebra 1.

My hanging file folders used to be: "chapter 1", "chapter 2", .... because I shortsightedly thought I'd ALWAYS be teaching out of the same book and the same school and the same topic. Then I think I moved to large groups of topics in each hanging folder. I'd have to paw through all the papers each year when the time came to teach concepts. Then, for some reason, I moved to "first 6 weeks", "2nd 6 weeks", ... (what was I thinking). Maybe I was a masochist or liked to take tons of time to sift through the whole pile every time I had to teach something.

I finally wised up (at least it's working MUCH better for me) and added manila folders inside each large hanging folder, and the manila folders have concept titles: "vectors", "triangle area", "graphing lines". I've also used large sticky notes attached to lessons to make my reflections about how a topic went after I taught it the current time and possible suggestions for the future teaching of it. MUCH more convenient and time-saving for me.

Fresh Starts

One thing I love about teaching high school is that you're forced to start every day fresh no matter what happened yesterday with the kids. Last semester I had a rash of cheating and some student crying and bad behavior and the usual drama of day-to-day high school life. Teachers usually don't have the luxury of banning the students from our vision/life/class, so we have to make the best of the situation.

This is good because it forces me to see beyond black and white to the gray: "cheating student = bad person" vs. "cheating student = bad decision and potentially a person that has other great qualities".

Today was another such day. I have a student in BC Calculus whom I had (ooh pompous-sounding "whom") in precalculus last year. He's a football player, smart as a whip, lazy as a cuss, funny as all get out. He struggled 2nd 6 weeks because of various life things and football things and laziness things, and didn't pass, but has since made up some grades and keeps coming to class and plugging away. Anyway, this morning (he's my aid in another class ... so that I can force him to spend 1.5 hours on his calculus homework) he looked to be in a foul mood, and he was texting and I was "put away your cell phone" in a grumpy voice. We didn't talk much the rest of the period as I was teaching vectors in precalculus.

Later on in calculus he comes in and asks how my day had been so far, and I mentioned that it was not good at all, and he commiserated with how crappy his day was and recalled this morning and how he almost lost it with me because of the "cell phone incident", but he thought better of it. Anyway, we had a good "grown up" discussion about horrible days and various other things.

These are the fun parts of teaching.

Mish Mash

As someone else has probably said before, when your mind is consumed with how bad things are at work (crazy decisions from "above", bullying of new teachers called "mentoring", being tested ad infinitum, ...), you have less to give your students (reflecting about the lesson, making sure in a positive way every kid is doing okay, developing new ways to teach concepts). This is the position I find myself in.

It's a never-ending loop in my mind about what I'd really like to say to so and so, what should be done in regards to being a successful math department, how you could make kids succeed. Copy room conversations with other math teachers revolve around the nightmare of this year and what/where they/we will do/be next year. Already 2 teachers have quit midyear. More are planning to leave at the end of the year. I'm sad and frustrated.

On a positive note, I've read some quotes lately that resonate with me, that I find myself referring to repeatedly:

When dealing with yourself, use your head.
When dealing with others, use your heart.

People first, paper second.

Great people talk about ideas. Average people talk about events. Small people talk about others.

And from my phenomenal teacher friend from the northeast when dealing with bad situations: Here is where you grow a little.

Accumulation Functions (Calculus)

I'm so excited. I think I found a more effective way (for me) to explain a certain part of Accumulation Functions in calculus. These are functions defined by

f(x) = integral (from some number to x) of r(t) dt

where r(t) is a graph. The graph can be (say) from -4 to 8 and the lower bound of f(x) could be 1, so: f(x) = integral (from 1 to x) r(t) dt.

Anyway, if r(t) is ABOVE the x-axis to the right of 1, then f(x) is accumulating "things" and getting larger, and if r(t) is BELOW the x-axis to the right of 1, then f(x) is losing "things" and getting smaller.

Well, everything is "reversed" in this example if you pick an x value to the left of 1. Say, f(-2) = integral (from 1 to -2) r(t) dt. Then if the graph is ABOVE the x-axis, between -2 and 1, then this defined f(x) is getting smaller.

This always confused the kids, and I hadn't a effective way to explain it. This year I tried: Suppose you took a movie of how f(x) is changing from start to finish on the SHOWN graph (regardless of the lower bound of your integral), so in this case, the movie would run from -4 to 8.

Now if f(x) = integral (from 1 to x) r(t) dt, you start this movie at "1" and show it either forward (for x>1) or backward (for x<1) and you see what is happening to f(x). This seemed to make sense to them, since ABOVE the graph r(t) means you're accumulating, and so if you show the movie "backwards", then you're doing the opposite.

Anyway, it looks kind of confusing written out here, but it was a small joy of my day to see their looks of comprehension.

I asked for it...

It was good to be back with the students today. I ignored the administrative silliness and just concentrated on the kids. My new mantra this semester will be asking myself, "what's best for my students at this time?"

For example, today what was best for my students was to not go to a department meeting that was slated for 30 minutes, but that I heard lasted (not surprisingly as it always does) 1 hour. It was also a meeting that sounded not purposeful. It was also a meeting scheduled after we'd proposedly spent 3 hours in a math meeting the day before during our "work day". Anyway. Today it was best for my kids (and my sanity) to skip the meeting during my one planning period and to concentrate on thinking through the best way to teach the next 2 lessons of this day.

One funny thing happened in class. I was going over calculus problems with my kids, and I was modeling the stream-of-thought way I work through the problem and how I ask myself questions about what is needed or what is to be done at each step.

I said to my students, "you could do this. Just pretend you have a little Ms. Cookie on your shoulders asking you these questions while you're working through a problem." And I put my thumb and forefinger together to mimic a small me and put my fingers near my shoulder. Then out of the corner of my eye I see one funny kid swat his shoulder to get rid of the nuisance.

Happy New Year

I have no idea how reasonable an idea this is, but what the heck. I was looking through my "teaching closet" at home and realized I had all these teaching books that are just sitting there gathering dust. I culled through the ones I wanted to keep and found many I'd be willing to share with someone who may get more use out of them.

I'll mail any of them to you on a first come first serve basis on the following condition. You will send a check to me made out to the charity of your choice for whatever amount you think is reasonable, and I'll pass the check along when I get it and mail you the book. If you're interested, please send me e-mail at math_mambo@yahoo.com indicating which book(s) you want. We can continue the conversation there. I also have favorite charities in town I'm willing to suggest (food banks and "safe places" and such).

Here's the list in "pulled out of the closet" order:

"The Passionate Teacher", Robert L. Fried
"Ordinary Children, Extraordinary Teachers", Marva Collins
"Among SchoolChildren", Tracy Kidder
"Small Victories", Samuel G. Freedman
"Escalante", Jay Mathews
"Why I Teach", Esther Wright
"36 Children", Herbert Kohl
"The Classroom Crucible", Edward Pauly
"Mentors, Masters and Mrs. MacGregor", Jane Bluestein
"Hot Tips for Teachers", Harrison and Spuler
"Teaching and the Art of Successful Classroom Management", Harvey Kraut
"Nothing's Impossible", Lorraine Monroe
"Growing Minds", Herbert Kohl
"In Code", Sarah Flannery
"Ed School Follies", Rita Kramer
"Positive Discipline: A Teacher's A-Z Guide", Nelsen, Duffy, Escobar, Ortolano, Owen-Sohocki
"Improving Schools from Within", Roland Barth
"Positive Discipline in the Classroom", Nelsen, Lott, Glenn
"Teaching Matters", Whitaker & Whitaker
"The Teacher's Almanac", Patricia Woodward

Holy Cow! What a book hog.

Winter of Discontent

Phew, a few days into the holidays, and I think I've finally caught up on sleep. It's lovely to nap when you want and to sleep past 5am. My mind keeps returning to how down and sour and stressed out I've been for this past semester. Most of it comes from policies "from up above" that are not sitting well with me.

For example, we have a huge tardy issue at school. They've tried various things with no great success, and "they" have to get the numbers lower. What do they do now? Let's ring the 6 minute warning bell as usual, but then let's start school and ring the "late" bell 1 to 1.5 minutes AFTER it should ring. Voila! Number of tardies has magically decreased (for now). And in response to teachers' indignation and concern about this bad precedent? "Teachers should trust the administration".

Another example, not-too-newish teacher is at her wits end with disruptive students and goes to administration for some extra suggestions on what to do. Response? Let's put the teacher on a "growth plan", which I think is akin to warning the teacher about possible teacher consequences, ultimately.

Another (biggest) example, let's make all the math teachers implement a disruptive TAKS remediation/pre-emptive teach-to-the-test strategy where students practice the 1st part of class and the last part of class and get taught the regular class material in between. Let's not test this process out for bugs or to see if the timing is appropriate. Let's not be open to any suggestions.

Arghhhh. In the past I've strongly believed in the public school system since it seemed most democratic (sorry I know that sounds judgmental about private and charter schools). But lately I can see the draw to teach at non public schools. I'm wondering if policies are implemented more sanely there and administration and teachers are not as badgered by the NCLB mandates.

Anyway, bla bla bla. Grumperina must go out now and spread her cheer on the human race during this last-minute-shopping time of year.

Finals Week

Tuesday we'll be into the 2nd day of finals. That's one of the (many) things to love about Texas. We consistently get 2 weeks off for Christmas break. Thursday is our last day with the kids, and Friday is just a minimal "check grade print out" sort of morning.

This year, I did something different for my precalculus final. In the past, at this school, it's been all multiple choice. Mostly because that's what the tradition had been and also because we are in such a rush to finish grades and turn them in. For example, our last test ends on Thursday at 1:10, and ALL grades are due by 3pm that day. Whew. Also, the finals are worth 25% of the semester grade, for however THAT fits into the equation.

Anyway, it never sat right with me, this multiple choice test, and this year, I made it a "fill in the box with your answer and show your work on a separate sheet" sort of test. This way, the kids are not overtly guessing at answers, and I can see more of what they know (or don't know as the case may be). I guess a time comsuming part of tests in general is hunting through all their work to find their answer, and even if they box it on regular tests, the boxes are all over the place. On my final, I placed the boxes, and there were only answers to dig through, and the grading went very fast. I finished up one set (33 tests) while I was monitoring another final ... and by monitoring I mean I was walking around and looking up every 10 seconds and answering questions and such.

Anyway, I'm REALLY looking forward to this break. It's been a stressful semester, and I've had to work with people I don't respect and whose focus is the ever-dreaded TAKS test at the expense of lots of other important issues. It's so bad, I'm wavering about coming back next year. Stress, stress, stress. Come ONNNNNNNNNNN holidays.

New Things On the Radar

It's been a busy year, and I don't know if I've mentioned yet (to everyone I know and strangers on the street) that I have 4 preps this year. So maybe it doesn't seem too surprising that unlike the past, I haven't found the time to make new seating charts and change the students' seats every 6-8 weeks or so. Finally, they were getting SO chatty and comfortable with each other, something needed to be done.

I made little slips of paper that I handed to them as they walked into class, and I made them choose their seats. These slips basically said:

You are (mostly) in charge of your seating destiny.
Pick a NEW seat by following these rules:

1. Sit in a new section of the classroom.
2. You may NOT sit by anyone you’ve sat by before (front/back/side).
3. Find a seat that will allow you to learn effectively.
4. Be flexible and willing to move (a wee bit) if doing so allows someone else to satisfy these conditions.

Good Luck, and Go to it.

I was nicely surprised, and only had to move a few seats after they were all settled. Some kids moved themselves after class started and they noticed their chosen seat wasn't effective. Anyway. Whew. That chore done for now.

The second thing I think I'll start trying has to do with implicit differentiation in calculus. ONE of the issues the kids have is incorrectly slapping down "dy/dx" in the wrong places and wrong times or forgetting it all together.

I noticed one student was always successful, and when I looked at her work more carefully, I noticed she did the following. When taking the derivative of an "x" terms she adjoined "dx/dx", and with the "y" terms, "dy/dx". Then she later canceled out the "dx/dx" term since it equals 1 and it's always multiplied. This way, she puts everything in the right place, and she doesn't forget that she has to use this "extra" appendage. I think this is the way I'll start teaching implicit differentiation now.

Spread the Warm Fuzzies

Last year a teacher started something at our school that I thought was so cool, I had to do it to. I've done it a few times, and this last time I got a great response from one of my students.

I've done it in advisory (we meet once a week for 30 minutes), but I've also used it when I've had an extra 5-10 minutes in math class. I ask my students to write a thank you note (on paper I provide, with markers I provide) to a teacher in school which I then put in the appropriate mailboxes. I mention that it shouldn't just be, "thank you". It should be genuine and indicate something they appreciate about the teacher, and it doesn't have to be "saga long".

Anyway. This last time I did it in advisory, a couple of students were balking. I tried to persuade them with, "it really feels good when you get an unexpected positive note or compliment or such from someone. Think about how you're making someone feel." One student finally, grudgingly wrote a note.

The next time in class, he talked to me about it and said (with a grin on his face) that that teacher had come up to him and said she was having a horrible day, and then she got his note and it cheered her up immensely.

Laws of Sine & Cosine

We've recently worked through those laws in precalculus. This is my 5th year teaching them at this school, and I think I've finally settled on a way to present the "ambiguous ... A.S.S. case" for the Law of Sines.

This I've done before and this year: I present a sheet that has 3 situations drawn in which I have a partially made ASS case but ask them to use their rulers to complete the triangle with the last "S". For example, for triangle ABC. I've drawn a long line for the "base" of the triangle representing side b. I've measured and drawn in angle A of 31 degrees and side c of 5 cm. B is at the top of the triangle, and they're to draw segment BC of length 3 cm to complete the triangle. I eventually get them to see that there are 2 triangles they could draw. Then we see how this plays out without drawing and why there are 2 triangles mathematically.

I also do this for the cases where there is one and zero triangles.

In the past, I used to make a big case of how you could tell there was a 2nd triangle by looking at the given information and if the 2nd "S" in ASS info given is longer or shorter than the 1st "S" then you make some decisions. Hmmm, made sense to me, and that's how I still do it myself, but the students weren't always successful.

This year, I just said: after you solve for your 1st angle, try for the 2nd option of that same angle and "see if it works" (you can add up to 180). That seemed to work for more students.

We also just did Law of Cosines. I had everyone create their own scalene, non right triangles and measure all sides and angles. Then we plugged into the formula to see why it may work (instead of just proving it to them or just showing them the formula). I always hesitate with this measuring thing because the numbers never work out EXACTLY. But I figure, it's a good opportunity to discuss human error and measurement tools and degrees of accuracy and such. I make a game out of it and make my own triangle and ask if they can beat my "closeness". Depending on the class, I was off by anywhere from 0.3 to 1.5 units when the 2 sides should have been equal. I blamed my aging eyes (cough cough).

Cheating

Ackh! It's a few weeks until the students have to start thinking about and studying for (cough cough) finals. For the past couple of class periods in precalculus I haven't really gone over new material since they were getting ready for a test on graphing all the trigonometric functions. Instead of not assigning homework, I decided to assign OLD topics and grade on accuracy instead of just completion like I normally do.

The first assignment was on function notation, and the current one is on function composition. I gave them the stern teacher face of "don't show up and say you don't know how to do it. Look at your old notes and look at the book examples and look at the web, but LOOK and recall and do something for yourself." Gee. My face is expressive.

Anyway. I was giving the graphing test on Friday, and the homework was due, but I didn't collect it until after the test. Some students finished early and were doing various things. Two friends started to look suspicious. I saw one pass back a paper to the other. Then I saw the other surreptitiously copying her paper. Crap. I walked over and quietly said, "do not do that! That is a zero for both of you. Do your own work.". I was so mad. First for her doing it, and equally for thinking that I'm so oblivious, that I can't notice what's going on.

I debated talking to both after class (I didn't). I had the whole speech prepared in my head about how once you lose someone's trust, it's very hard to gain it back. But I settled for the unhappy glances their way and the ignoring of them and a total change of my demeanor towards them after the test was over, and we were going over other concepts. I'd had a hard enough week, and I didn't want to deal with more stress.

November Slump

Sheesh. I forget this happens every year. I get super depressed and down on various kid behavior and teaching and the stress and all the whole bundle every year at about this time. I think I should make a cross-stitch sampler to remind myself that this will pass, and things do get better SOON.

It's been especially bad this year. We are mandated from above to have meetings up the wazoo that suck the life out of our planning periods. Then we are dictated to teach to the "exit exam" in a specified way and eat into our regular curriculum to do this. Then .... then .... then.

I think I have enough seniority to say "phhhphflt" and do what I think is best for the students: a type of don't-ask-don't-tell policy. My rationalization is that if questioned, I'll have a valid reason for why I think what I'm doing is the best for my kids.

On a positive note. My students are mostly great. Highlights:

One shared with me her way of remembering the sine and cosine graphs. She's Hispanic, and "sin" in Spanish means "without", so that's the one that is zero at zero. And "con" in Spanish means "with", so that's the one that has a value at zero.

A day or so ago we were doing the ambiguous case of "Law of Sines", and for the "no triangle case". I wanted to show them that in the A.S.S. case when they're first solving for the angle, the ratio of sides is 1._____. So I asked what happened on their calculators when they tried to solve sin x = 1._____. They said, "ERROR". Then I said, okay, close your eyes and picture the graph of y = sin x. My goal was to get them to see that the largest it could be was 1. So I asked, after they were thinking for a while on what the graph looks like, "what do you see?". One kid answered, "ERROR".

Anyway. Some of us got together tonight as a math department and went out for a drink after work and destressed and laughed and such. That will go a long way to making the rest of the 6 weeks livable.

The Power of Off-The-Cuff Words

Just recently, my memory was refreshed as to how seriously students take what we say. Things I just sort of blurt out because I think they're the right thing to say seem to make a difference.

For example, I have this incredibly smart and hard-working student in BC Calculus this year. Last year I had her for precalculus preAP. Back then she was talking about her math choices for the next year, and I mentioned that she should definitely take BC calculus as opposed to AB because she had such a great work ethic and cared about really understanding topics and such. I think I also said something to the effect that it would be a waste of her time to take AB which would not challenge her as much. I did truly believe this, but I didn't know how much weight this would carry. Well, several times this year as she's bemoaning the fact of how hard it is (in a good-natured I'll-still-muddle-through sort of way), she kept mentioning the fact that I made her take BC calculus. Hmph.

I have another student in AB Calculus. I also had him in precalculus preAP last year. He's an interesting, intense, strange, slow-working, self-stressing type of person. I really did not think he could manage the pace of calculus with how much he frets over EVERYTHING. He asked last year if he should take calculus, and I hate to discourage students/people, because, really, what do I know, maybe they will surprise themselves and me and if not, then the experience will be a learning one one way or another. So here he is in AB calculus this year. He is struggling and stressing and such all along. He came to me after school one day and said he wanted to drop out of the class. I said that well, the decision was his, but I think it would be a shame if he did because then if anything hard came up in the future then his first idea would be just to quit because it was too hard. I also said that he was smart enough to handle it, and personally I would stick it out. (inside, I think he can do it, and he just has to approach it in a different way, but I DEFINITELY know that if he dropped, he'd be WAY less stressed than he is now). Well, anyway, he decided to stay, and later wrote me a note thanking me for believing in him and in his ability.

I guess the point of all this is to err on the side of pushing the kids to do their best and to do things they don't think they could do or think possible. Maybe it will open up opportunities for them and make them think of themselves in ways they didn't in the past.

Foreign Exchange Students

At my school we seem to get a lot of foreign exchange students. Every year I've had at least one; always from Germany; and last year I had 3. Phew! This year I again have 2 girls from Germany, and lo and behold one boy from China.

Well, a while into the school year, I saw that he wasn't interacting with the other students, and they weren't talking to them. I don't think it was a rudeness thing on either part. My sense is, that the girls (and boy) from Germany in the past and present were so cute and approachable and maybe "looked more like them", that they naturally talked to them and became friends. That's my guess, and now that I put it down in words, it seems kind of wrong somehow (the situation). Why hasn't anyone struck up a friendship with this boy? Maybe I'm just misreading the situation, and it's only in my class that this phenomenon occurs.

Just yesterday I asked the boy from China (He's cute: when he first arrived, he said, "My American name is Eric" ... I finally asked him his real name, and he mentioned it, and I've been practicing it, so now I use it when I talk with him). Anyway, I asked him to talk to the class about how school differs in China from our school. Sheesh. That was a cultural wake-up call for my kids.

He said they start school at 7am, and have 4 classes until 12pm. Then they have a 2 hour lunch break, and at 2pm until 7pm, they have 4 more classes. Then they have 2 hours of studying. They have a month off in the spring for a sports festival. Every year (?) they take off one week for each of the following activities (?) working in the factories, farms, and army. The sports they play are tennis, running, ping-pong, and badmington (for some reason, that got a titter from my students). I guess I was surprised there was no soccer.

Anyway, hopefully, he's getting a chance to interact with students and such and not having a lonely existence of a day.

9th graders

I'm teaching one section of algebra 1 preAP this year, and I feel like I take extra care of them ... because they're "young uns", and they're learning the foundation for everything else that comes, and they're just so darned cute most of the times. With that said, there are still some "young uns" issues.

There's one whiney child that grates on my last nerve, and I have to work extra hard to not show it. Everything we do, her response is (insert whine), "I don't get it. I don't get anything." She needs to be hand-held through every step. It got to the point where she snapped back at me in class one day because I told her to get to work when she was chatting (because she JUST didn't get it and was waiting for me to do things as opposed to getting help from her more capable group mates).

I was super frustrated last week, so I sent e-mail to her other teachers to explain the situation and to see if it was just me and my class or if these issues came up elsewhere. Two other teachers responded and mimicked what I said about her neediness. They mentioned that she either has a capable friend sitting by her to help or the teacher literally DOES break things down into baby steps. This made me feel better and gave me an idea of copying extra "reteach" sheets for each topic so that she'll have extra practice to look at while the rest of the class is "zooming" along.

She was better in class this last time, but had to leave, so I didn't get to test out my extra-sheet idea yet.

I'm also dealing with a large portion of the class (4-6 out of 28) not turning in ANY homework. I think they're still used to middle school where you magically pass no matter what. I've made some calls home, so hopefully that will produce some late work this coming week.

Passing Kids Along

I know some of our math teachers at the high school level (mostly for algebra 1) are urged to do what they can to make sure a student passes. So if a kid has a 68%, .... "well, can't they just come in and do some make-up work and make it a 70% (which is passing in TX)?"

Now, teachers I know help the students in any way they can, and it's REALLY possible to pass class if you do your work and turn in homework and ask for help and get tutoring if you need it and pay attention in class. So I'm guessing that if the student has a 68%, then more often than not, it's because the student just REALLY doesn't get it (content) or REALLY doesn't get it (work ethic). Passing this kid along to the next level is not doing ANYONE any good: the student, the next teacher, the students in the next class this student would go to.

Then I was thinking about the students that were coming to us from the middle school. There are some kids that REALLY struggle with the math. They should not have passed their middle school classes. And in fact, this was supposed to be the first year that if they didn't pass the mandated NCLB test, then they would be retained. Hmmph.

We have a new teacher at our high school that taught at the middle school last year. This is what she relayed to me. All year long the teachers told the kids that they needed to pass the test, or they'd be retained. They drilled it into them. Then kids failed. Then the administration put them in extra tutoring and let them test again. Then if they failed, they had to take summer school and take the test again. Then MAGICALLY, all the kids passed. Poof. Let's move them on to high school and continue their struggles in harder classes when they haven't mastered the basics. Grrrrrrr.

Okay, just a big vent. I don't know what could stop this "passing along". Maybe we need to track the students in high school who are not successful and probe them about their middle school experience and see how many of those were passed along and how they're doing now. Maybe we could take that data to the middle school pass-along-ers. Would that help? I don't know.

Algebra 1 Skills

I'm loving teaching (a 1 year course of ) Algebra 1 for the first time. It's fun to be the first person to show the kids all the stuff I take for granted they know later on.

Recently, we started solving one-step then two-step equations. Maybe everyone does this, but I found it helpful to start with a goofy story. I told them I bought them a special present (it was just some random object in the room), and I wanted to give it to them, but I first had to wrap it up. So I put it in a box, then I put the lid on the box (some plastic tub I had laying around), then since it was see-through, I wanted to wrap it up (I had an old sheet laying around), and then I had to put a bow on it (some random string I cut up). Then I asked them what were the steps to what I had just done. They repeated them. Then I asked them, if they wanted to get the present out, what specifically did they have to do and in what order. So we went through untieing the bow, unwrapping, opening the lid, and taking the present out of the box.

Then I linked this to a 2 step equation on how you have to undo what's being done to x and in the opposite order that you had "wrapped up" x. This seemed to work (so far).

A few days later we worked on combining like terms and "challenging" distributive property types like:
5 - 2(3x - 4) = 20. YEESH! That distributing the negative was a challenge. I explained it 3 different ways, and different ways seemed to work for different kids. One kid was okay with: okay, cover up the "5" and just look at the "-2(3x-4)", what would it become? Then it's just "adding 5 in front of that operation".

I'll see how they did on homework tomorrow.

Teaching a Class vs Tutoring one Student

In precalculus we recently learned how to solve triangles. This involved such equations as sin 20 = 5/x, or tan 35 = x/7, or cos (theta) = 6/11. From past experience I know there are students that forget how to solve things. Once you throw "sin 20" or "tan (theta)" into the mix, all their algebra knowledge goes out the window. So I carefully walk through and remind them of how to isolate variables, and assure them that "sin 20" is JUST a number, and warn them that, "no, you are not multiplying 'sin' by '20', you must keep them as a unit". And then, WHOA, stop the presses, x is in the denominator?? Well, why don't I just take 'sin 20 = 5/x, and divide by 5 and POOF, an x is left in the numerator on the right hand side.

Anyhow, we walk through this, and most kids get it. But then I see one student struggling and struggling and getting more frustrated when I'm going through the different types of examples because he doesn't know why things change up and why I'm "solving differently" for the different situations. Well, he came in for tutoring this past morning, and by probing his mind, I see that he never internalized the algebra steps: what's being done to x? how do you undo it? do the same thing to both sides of the equation.

He would look at an equation like 3x - 7 = 5, and reason it out in his head: well, something minus 7 is 5, so that something must be 12. Then 3 times something is 12, so that something, or x, must be 4. Great reasoning, but then he never had to learn or practice: add 7 to both sides. divide both sides by 3. And now when he sees: sin x - 7 = 11/3 (or something like that), his old methods don't serve him well. I believe we got him to the point where now he can do it. I'm so glad he came in for tutoring, so I could take the time to probe deeper as to where his difficulties lie (lay/laid/???). I don't have that luxury in class with 33 other students of all levels waiting for "teaching".

Graph Savvy

I've had former students come back to visit lately and they talked about the expectations of their college professors. One student who's in calculus says that the professor expects them to have a solid, quick-recall grasp of basic graphs (what does the sine graph look like? the square root function? the tangent graph?, etc). Yeesh, note to self on not just teaching that for one week but reinforcing and recalling it periodically.

Then that reminded me of a dream I had the other night. I like memory tools, and I dreamt that one way for the kids to remember the square root of x graphs is that, "SEE, the graph LOOKS like the square root symbol". Nerd alert. I'm going to try that this year.

Then I also started thinking of how to make all these graphs become second nature to the kids. Maybe periodically, and consistently, I can pull out "cards" with (say) pink cards graphs and yellow cards the functions, and maybe they can have a running contest with themselves and keep track of the time it takes them to match them up, and eventually (months? weeks?) we can have a "beat the clock or teacher" contest of a match up game.

I also want them to have the quickness of thought as to, "okay, I don't remember this shape, but hey! let me quickly make a table and plot the points to help myself (without the teacher prompting me or just sitting there and not doing anything)". Hmmmm, how to teach this skill. ... Maybe also a periodic and consistent "game" of "here's a weird function on the board, quick like a bunny, find 5 points on the graph or plot 5 points or something".

Burning Questions

What is it with high school boys, the insides of their noses, and their index fingers?

How fast does a teacher shudder at night when they see a full moon, wondering how the next day will go?

Why do I get less work done when my last period is a prep period as opposed to periods when I'm rushing to be ready for my next class?

Who is the hobgoblin that comes and strews papers to be graded and dealt with and sorted all over my classroom the very next day after I clean up the last mess?

When is the timing right to drink large amounts of water (to stay healthy) during the school day?

Out of School Etiquette

This Saturday my husband and I went to "the fields" to watch our school's rocket science class students launch their first-attempt rockets. There were a mix of students and teachers there, and I introduced my husband to the 2 teachers, but then while I was talking to the students (many that are also mine), I didn't introduce my husband. I always feel goofy (and maybe not quite adult even though I'm in my 40's) and the words don't seem right:

"Student A, this is my husband Mr. ___" (seems stuffy) or
"Student A, this is my husband _____ _____" (I guess this would have been the best option: first name last name) or
"Student A, this is my husband ____" (first name only seems "wrong")

So like any goofball, I just didn't introduce him at all to any students. Then that feels wrong now, like he's just this shadow following me around while I talk with the students. Okay. In the future, first name last name. Do It!

Piecewise Function Success

Every year as I teach piecewise functions in precalculus, there are students who get it and can successfully graph and understand them, but there are too many students that struggle. I've tried various things, but nothing with consistent success. Well. Last week after school I was helping a struggling student, and as I was looking over her old test, I saw that the mistake she seemed to make on the "3 piece" piecewise function was that to graph it, she made a big table with the same x values and used the same x values for all 3 pieces. I started to say what her mistake was, but then it struck me that if she reworked the idea, it could be very useful.

It worked for all the struggling students I had a chance to try it on, so I think this is how I'll start next year, and then show them the "other" way for those that "get it" and don't want to make such a big table.

The Week, The Wiki-stix, & The Web

I went to another workshop this Thursday, and the algebra 1 information was very useful. What was NOT useful was the handful of people sitting at my table blatantly grading huge stacks of tests and totally disregarding the presenter and going so far as to discuss with each other about how to allocate points. Oh my.

What was ALSO not useful was my understanding of just how broken our "mentoring system" for new teachers is. One of our new teachers is TOTALLY struggling and crying and breaking down in class and being overwhelmed. I've heard from her mentor that she went in and gave her tips on what to do (do warmups, here are some activities, ...), and said the girl did not take her advice, and then the mentor thinks that's the end of it. Well, I sat in on the girl's class. Warm Ups are the least of her problem. There are some easy fixes that just need to be addressed and monitored and modeled and reinforced.

Anyway! After many deep breaths, I decompressed with some of my favorite "feel good" websites. Here are 2 examples:
DarynKagan.com (here are some old good ones)
http://darynkagan.com/heroism/stories/he_080324_computerfairygodmother.html
http://darynkagan.com/kids/stories/ki_080414_oneboyandaredwagon.html

smittenkitchen.com (yummy looking recipes) ... for example:
http://smittenkitchen.com/2008/08/chocolate-peanut-butter-cake/

Also, I found yet another use for the wiki stix. We started radians in precal today, and my first question was how many radii did they think fit around a circle. They drew circles and the radius, and then with a small piece of a wiki stix (stick?) they marked out the radius along the circle. It was easy to manipulate and curve.

And the funny joke I read in a book this week:
knock knock
who's there
little old lady
little old lady who
I didn't know you could yodel.

Life's Surprise Pop Quizzes

We are being judged and evaluated all the time, and we may not realize it. In fact sometimes we may think we're getting away with things when really we're not. This past week seemed to be full of those "pop quizzes", and now my outlook on a variety of people has altered.

test1: I gave my first test in precalculus this week. As I walked around the room, I noticed the continuously wandering eye of one boy. I stood near him after that and asked him to keep his knees forward (instead of turned towards a "smart" student). Then he turns in his test early indicating he had troubles with one problem (he left blank). Trying to promote his perseverence, I said, "you're a smart kid, keep looking at it and maybe you can work something out". I realized my mistake once he picked his test off the pile of "done" tests, when he walked back to his desk and I saw him erase another problem's answer immediately and put down what I'm guessing he saw on the pile. Now none of this was provable, so I didn't snatch his test up, but this was the 1st "life quiz" he failed. Even though he thinks he got away with things, I will no longer see him in the same way, and he will forever more be the "cheater" to me.

test2: For the nth and (n+1)st time one of our math teachers was basically bad-mouthing other people. In the first instance she was talking about a new teacher that was struggling, and after she recounted the struggles, she mentioned that this person was ONLY hired because we were desperate, and the new teacher must not have had strong interviews because she was not snatched up by other schools in the district. Her second mouthing incident was about a teacher at another school that our new AP wants to hire. She recounted 2 or 3 bad things about her personality and her teaching ability. I wasn't part of the 1st conversation (came in on the tail end), and for the second, I tried to say something nice about the other teacher, and basically I didn't say anything to this lady. BUT now I think of her as the bad-mouther. I wonder what she may say about me or about other people even though she's nice to me/others to their face.

test3: I park a ways away from the grocery store entrance in order to get some free exercise. I was walking back to my car and it looked like someone else with a cart had the same idea. After she was finished unloading into her trunk, I wondered if she would make the uphill trek to return the cart to the right place or just leave it willy nilly to bang into other cars. I was betting on the latter, but she surprised me and restored a bit of my faith in people by conscientiously walking it back to the "right" place.

test4: I walked my (cute little puppies) algebra 1 9th graders over to get textbooks this past week ... after I discussed hallway behavior and such. I also walked my precal and calculus classes over (older kiddies). When we got to the book room, the "manager" seemed surprised I was trusting the 9th graders with textbooks since apparently they don't have good reputations of caring for them and returning them. He even added an extra spiel that he didn't for my older kids about the cost of the books and such. Well, after they went through the checking out process, he told them all they were the best behaved 9th graders he'd ever seen. And I have to agree since out of my 6 classes, they were the best behaved through the whole process. Go Them!

Math Workshop Already!

During the 2nd week of school I had to get a sub for Friday to attend a 2-day math workshop. Oh my, whine, whine, whine: too early in the school year, too hard to leave students with meaningful work when we just started, sets a bad precedent, .....

Okay. It was a great workshop. I learned so many things that will be BIG payoffs in the long run, so can I take back my whining? (except for the fact that now in 2 weeks time I'm basically mandated to miss another day to go to another workshop).

Here are some things I learned:
* a way one teacher gets her kids to remember the divide by zero and zero divided by something rule: 0/K = 0 means it's "okay to have a zero in the numerator". N/0 = undefined means "NO! you cannot have a zero in the denominator".

* which reminded me of the way I learned a long time ago to help kids remember the no slope and the zero slope of vertical and horizontal lines: "No" starts with a capital "n" and when you're writing "N", the first line is a vertical line, so vertical lines have "no slope". "Zero" starts with a capital "z" and when you're writing "Z", the first line is a horizontal line, so horizontal lines have "zero slope".

* with calculator usage for calculus and showing a function and its derivative function at the same time ..... put one in y1 and one in y2 and in MODE change the graph style to "simultaneous", and then you can start and stop the graphs at will and have a rich discussion about positive and negative slopes and + & - derivative values throughout the whole graph.

* I never remember which one of the "ON" or "ENTER" buttons on the TI=84 stops or pauses the graph, so I always end up pushing both. Well! The "ON" button stops the graph, so you can get "ON" with your life.

* Which reminds me of what I shared in the same session regarding calculators and limits to infinity. I have my kids look at just one of the polynomials of the numerator or the denominator in a rational function, say 4x^3 - 2x^2 + 100. I ask if you plug in larger and larger numbers, will that evaluate to basically the same or different value than if you plugged in the same large number to 4x^3 (the dominant term). They are convinced they'll be different. So we put 4x^3 - 2x^2 + 100 into y1, and in the main window do "function notation" of y1(5) and compare it to 4(5)^3. Then we start comparing the 2 things by typing in larger and larger numbers. They're eventually the "same" on the calculator. I tell them that the highest power term is like the ocean and all the other stuff is like spit, and if you spit in the ocean, it doesn't change the volume much, so you can basically ignore it when you are calculating limits at infinity.

More Games and Such

I decided to add 2 new links to my homework website for games since these are ones I love love love. The first is ABC pureisu. Basically you place the letters A, B, & C (and sometimes D) so that every row and every column has exactly 1 of each. You can click around the buttons to get different sizes and difficulties of puzzles. By clicking in the box, you can place your letter.

The second is a "squiggly" sudoku site. I love the different variations of sudoku, and this one also has different difficulty levels. A different puzzle appears every day. This one you have to print out.

I had put a "notes" section on my website, but ultimately knew I wouldn't keep up the copying of the notes, and I didn't know how helpful it would be. So I decided just to sum up the topics of the day/week and mention what would be important to know how to do, and then I will provide web links to various sites that show/quiz/video/tutor/etc the same topic. That way the students have a different way of learning the same thing, and maybe a different explanation will make things click for them or just let them review more. It also gets them in the habit of searching the Internet using the topic name, and they can find other help.

Testing Scribd

I gave the following quiz today in Algebra 1, and I've had "Scribd" on my radar for some time, and then I saw it used on the "f(t)" blog, so I thought I'd test it out here to see what's what.

http://www.scribd.com/doc/5267432/graphing-points-quiz

Hmmm, not exactly perfect, but I'll work on it.

My Book Love Affair

I have passionate feelings for this resource and turn to it whenever I need great ways to ask questions or great real-life examples. I got my copy at an NCTM workshop, and am doing the happy dance ever since. For example, in precalculus today we were talking about function notation, and after we did some "math" graph and table and equation examples, I pulled 2 context examples from the book. One was a table having to do with NFL revenue for a number of recent years, and one was a velocity vs. time graph for a man going to the store.

They both generated discussion about the amount of money NFL made (billions!) and interpretations of the velocity graph and why it may be so "wiggly" going up and down and such and how you knew when he reached the store. The questions were worded such as: find v(24) and interpret the meaning. So they had to think about what "24" meant in this problem and what the "y" value meant and put it all in a coherent sentence.

We also started a discussion on graphs such as y = abs(f(x)). We first refreshed our memory on abs(x) (much needed for some folks). Then I had them make a table for f(x) = x*x - 2 and graph it. Then I had them hold up their hands in the shape they thought y=abs(f(x)) would be .... some, of course, held up "V" hands. So we made the table values and graphed JUST the points, and then I showed them the visual of "flipping" all the negatives "up". Ooh, ahh. That was a good segue into doing the same table/graph thing with f(x) = x ..... then doing y = abs(f(x)).

On a whiny note, my 6 class sizes so far are: 31, 22, 17, 26, 39, 34.

I'm just saying. .... but maybe that's the norm in other schools. BUT, I rember my math teacher friend in another state complaining that she had LARGE classes one year .... "26".

Wikki Stix & Me

A while back I was first introduced to Wikki Stix at a calculus workshop where the presenter showed how she taught slope fields by having large pieces of graph paper around the room, and each group had a differential equation and each person in the group had a point or 2 or 3, and they were to calculate the slope and stick the piece of wikki stix on that point in the appropriate slope. Super cool.

I was at a teacher supply store the other day, and found 48 for $5.95, and bought them thinking I could find some use for them. Well, now I have 2 things so far. On the first day of school, I will review functions and lead to function notation and how to read f(x) and find f(3) and find x such that f(x) = 6, etc, by first handing out premade graphs/grids/coordinate planes to each student and one wikki stix (stick?) to each kid. I'll first instruct them to plop down a "graph", and maybe have them decide if they're functions or not and maybe have themselves walk with their graphs and separate into 2 camps of functions and non functions. They can then self correct by glancing at others and discussing it amongst themselves. Then I'll say find your f(3), and separate yourselves into like groups (how to deal with non integers .....???). Anyway, you get the idea. I could do more.

My second idea is what I think is an improvement on an old activity I've done with precal in the past regarding learning the sine and cosine graphs. But my teacher friend (who I first learned to teach with/from) in another state basically does the same activity but with Wikki Stix. She has them do the measuring of the angles and the heights, not with a string, but with the Stix. Also, once they measure the "height", they snip the Stix into that length and "stick" it down on their graph. So ultimately, later on you have a Wikki Stix sine curve graph. Way cool and something I'll try this year .... though with 3 precal classes of (current sizes) 37, 32, 30ish, how much will that cost?

New Skills

I was at a math workshop today, and from a participant I learned a great calculator skill that left me saying, "where have you been all my TI-83/4/silver edition/titanium life?".

Suppose you're graphing, and suppose you simultaneously want to see the graph and the table screens. Well: mode > G-T, and poof, when you hit graph, voila, split screen. Then you can toggle between the 2 parts by hitting the "table" or "graph" button, and then you can do whatever you want on that part of the screen.

Also, you can split the screen horizontally (mode > horiz ...) and then you can show the graph and either the main window or the lists or a table, etc.

Ooh, aah.

First Day Back Haiku

Inservice Monday
Meeting, meeting, lunch, meeting
Where did summer go?

Addiction

Ackh! In the process of updating my homework website further, I thought I'd add a "games" link that showed some fun thinking/math/logic games. Well, of course I had to try them out to see what I was linking. .... Too many hours later, I'm addicted to 2 I found at http://www.coolmath-games.com/ : "walls logic" and "bloxorz". The first has you building diagonal walls on each of the tiles in a grid, and you can't form loops, and you have to follow "# of walls rules" for certain intersections. The second has 33 levels, and you basically move a brick around to get it in a hole. ... Okay, must stop playing and go do other things.

On a side note, as I was trying the new games, I found myself getting blurry eyed just reading all the instructions, and I just wanted to jump in and test the waters instead of reading about it. Hmmmm, sounds familiar. So now I'll try to think of each school lesson in a new way: how can the students get started right away doing something and then learning what they need to know about it at various stages of the class.

First Day Algebra Activity

It looks like on 8/25 we're starting right away with 1.5 hour block classes when school starts (as opposed to meeting all classes and having an "alpha" period with about 40 minute classes). I need about 40 minutes to call roll and ask for pronunciation corrections, have them fill out a seating chart (I like them to sit where they want the first time, so I see who can/can't sit together when I soon make a seating chart), take pictures of groups (so I can memorize names), and talk about the syllabus. While all this is going on, I like them to be doing something. Here's my something:

They'll work on it quietly while I'm calling roll, and then I'll prompt them to check and work with their group and meet everyone in the group while I'm snapping pictures. Section "A" prompts them about "PEMDAS". Section "B" has orders-of-operation problems with 2 answers to circle, one for the common mistake and one correct answer. Section "C" has a fraction/decimal/percent table with one column filled out where they fill in the other 2 with equivalent expressions. Section "D" has four "4"s and an answer, and they're to fill in operations to get the right answer.

Here's part of their first assignment (and parent homework):

This is a math autobiography and asks questions about past classes and school experiences and such. It also asks their parents to indicate "I am proud of my child because" ....

This will tell me many things about the student: if they do work on time, if they are neat/verbose/last-minute/thoughtful. They also get to see their parent's bragging comments (and sometimes if there are no comments, I'm sad for the kid). I also have a good opportunity to get their parents' e-mail address for future grade sending.

Then I have about 50 minutes left. I'm thinking of a "box plot" activity and a "meet and greet" activity. ... still in the planning stages, though.

Whew! Two tasks done.

My Summer Vacation

Just last week I went to an aerobatics contest my husband was in. It's small, so EVERYONE is wrangled into volunteering somehow.
I got to be a boundary judge and learn the skills of how to read a sequence card and how to call the ins and outs and how to survive blistering heat and curious cows and carcas sightings. First my partner and I (another wrangled wife) had to drive 10 minutes to the location.


Here is an actual corner boundary that the pilots would see from the air.

This is the other wife sitting in position ready to call outs/ins. The contraption is uber cool and thought up by an engineer/pilot who used a compass and his brains. AND there's math involved (what else).
There are 2 sets of 2 strings lined up perpendicular to the other set, and you line up the strings of one set with your eye and .... since 2 lines form a plane, you can determine when the aerobatic planes cross the boundary or not. We were at the "southeast" boundary, so our job was to call "out south", "in south", "out east", "in east".

Boy were we stressed about doing it right. We're not pilots, and we had to figure out what squiggly lines on the cards matched what things the pilots were doing in the air. Eventually, we mastered it as a team. Here are some things that kept us company each time we went out.

Website Goals

Well, I am glad I started my homework website last year, and I'll continue it this year. I found many benefits:

* I made one of the 1st homework assignments be for parents to look at the site and send me an e-mail. This gave me their address for sending home grades, and it also made them aware.
* It gave me a place to post extra worksheets and solutions where they could download them (I didn't do this too much, but maybe will increase it this year)
* Students had an easy way to find homework assignments for whatever reasons.
* Parents now had a place to see/check whether their children had homework or tests coming up.

This year ... (with my 4 PREPS!) I'll continue it, and I want to enhance it:

* I want to somehow incorporate quick easy-to-make-&-upload videos showing various math techniques (I'll film them).
* I potentially want to link to videos from TeacherTube (since YouTube is blocked at our campus).
* I want to post notes for students that are absent (this one I'm iffy about for a variety of reasons: difficulty, space issues, student accountability, ...)

All in all, I'm happy with weebly.com. Hopefully, it will continue to be free or even cheap, and hopefully they'll resist putting ads on their/my page since that was a big draw for me.

Passive Learning

I picked up the AP Calculus exam scores for my students, and while I had a good number pass, there weren't as many passing as I expected or knew that COULD pass. This made me reflect over the school year and day-to-day activities and behaviors of the students. For the ones that didn't pass (but that could have), I see a pattern. They were seemingly attentive in class. They did their homework. They did reasonably well on tests. However, they did not pass. I think a big key is the "seemingly" attentive in class. They learned to play the game and knew to make the "paying attention" actions, meanwhile, maybe for a large portion of class, their minds were elsewhere. (this also goes for my other, nonAP classes).

I've never consistently had daily assessments at the end of class (of some form or another) to see who's getting it, and who's not. Yes, I've walked around class and they practice the skills. Yes, I know who's struggling. Yes, I suggest they come in for help. BUT. There was no consequence to them whether they followed up or not. My tests were structured in such a way that they could do corrections and earn back some points, and that was enough of a safety net for students.

On the plus side. Many (all?) of my students care about their grades, so I've started thinking. There are 6 weeks in a marking period. On block schedule, that means I see them roughly 15 times. Each day I could have a quick assessment (5 minutes?) at the end of class. Everyone getting a different problem (or at least everyone in one group of 4 getting a different problem) ... or 2 problems ... based on the day's topic. This could be worth 1 test point and so by the end of the 6 weeks, totally, this would add up to approximately 1/2 a "normal" test. They'd get 100% if it's correct. If anything is wrong, they have the option of coming after school to make it up. Each time it takes them to make it up (to 100%), their grade goes down to a B then a C, etc. Their tests are weighted about 75% of their total grade, so this would be significant enough to make a difference.

This way, they'd have more of an incentive to ACTUALLY focus and learn during class time because they'll be held immediately accountable for the information.

Possible "cons":
1. more paperwork (though it's only 1-2 problems per student and maybe I can have a limited # of total problems and put the problems on the overhead so they just have to have paper).

2. Would it have the desired affect? (well, I think so, and won't know until I try it) ... maybe I have to incorporate other things, too.

Differentiating Instruction in High School

I know it's a good idea. I know it's what we're supposed to do. Maybe I'm even doing it sometimes (most times?) and don't even know it. BUT. There's always a part of my brain saying, "too many kids, too little time, not enough resources specifically for math or for high school ...". Everything I have read in the past seems to be, "give projects!" and that seems to be the bulk of what I got from their suggestions.

This book (http://www.amazon.com/Differentiating-High-School-Classroom-Strategies/dp/1412917166/ref=sr_1_1/105-4459711-7881269?ie=UTF8&s=books&qid=1216748751&sr=1-1) seems to be different (from my glance and quick read through at the bookstore and through reading the 1st 5 pages and looking at the bulk of what each topic is about). I like the fact that the woman is (was?) a high school teacher. She has taught not just the "cream of the crop". She's not a PhD researcher who only knows theory. She talks about many obstacles and how to overcome them. She talks about the fact that, yes, we do have lots of things that get in the way. AND. The best part. It's geared to high school. Hopefully, I'll absorb the material and be able to use it as a springboard to make some progress this year on my differentiation.

Cumulative Knowledge

I've been batting an idea around in my head for a while to deal with the following problem. Students in AP Calculus need to remember information from (say) August on when they take their exam in May, and students/people have a very hard time recalling information they haven't seen in months even though it may have been "easy" for them in the past.

I don't want to give cumulative exams because I believe:
1. either the students will just shrug their shoulders and give up those "past" problems for lost points,
2. it seems more punative even though it's for their own good
3. I won't be able to cover ALL old topics every time
4. it would only be a (possible) review for students (say) every 2 weeks or so

So my thought is that I want to assign cumulative homework basically every class, and as we are on a block schedule, I'll give them "2" homework assignments each class, one for new material, and one for old. I don't want to have to scramble for old material every time, and I want it to be accessible to the students, so that the review process is not so painful. Here's my germ of an idea:

Have a designated folder on the computer for cumulative work. Have a pre-mapped idea of what we're learning for the whole year (and its timeline) and how many assignments I roughly need. Each time I teach a new topic, I'll have some notion of how many times I want it to appear for all the documents and I want to spread it out, so that day/week, I'll just take the basic problems (?) and cut and paste them into all the appropriate files with an "answer bank" (in some form) on the bottom of the page. It's fresh in my mind since I just taught it, so I don't have to waste time coming up with new problems for them to review. Also as time goes on, the assignments will either be completely filled with problems, so I'll just touch it up and print it out, or it'll need just a wee bit of extra work. I believe I'll also put the date(s) we learned the topic near the problem, and since they'll date their notes ("hey baby, want to go to the math movie tonight?"), then they'll be able to easily flip back and brush up. Also, since the answers will be there, they'll have immediate feedback if they remember the process correctly or not.

I'm also thinking that at the beginning of the year, it'll be slim pickings on "review" material, so I may assign things like (along with a brief tutorial on the page) finding equations of lines given various information, fraction work, factoring work, ... the basics that seem to need extra gentle and not so gentle revisits every year.

Volume of Revolution Project

This past year I tried something new with my calculus students for the "volumes project" in the oh-my-goodness-what-to-do-after-the-exam phase of the year (closely linked to the eek-I-hate-giving-class-time-to-do-projects-and-can-they-waste-any-more-time phase of teaching calculus).

I did the project with the kids to see what was involved, and I told them it was the first time I'd done this, so we'd learn the pitfalls and tips and such together. I also was vague on how they should display the projects at the end. I said, "wow me" and "whatever you do, have a good reason for it" and "think of the best way to display it to use as a learning tool".

The general idea was that we'd all have the same starting 2-dimensional region (y = 4 - xx), and we'd each revolve it around a different axis of revolution, and thus each have different solids at the end.

She wowed me with her final presentation:
This is mine (I now realize I took the picture upside down). Hmmm, spaghetti/math-tool ... probably not too long lasting:


Before she started, she kept saying, "I want to make it into Saturn", so I guess she continued with her space theme:

He was so funny, "tell me what to do. tell me what to do." Me, "no. no. NO.". He finally came up with it himself:

Hand Holding vs Solid Examples

I feel like a flippy-floppy fish on this whole topic, but I guess I could "spin it" as I'm readjusting my attitude as I gather more data. For the last few days, I've been studying statistics for the N.B. exams I had to take today. I went right to the source and bought a prep book for AP Statistics. Since it's a prep book, they don't TEACH every topic in depth, they just review it and do SOME examples and then give practice tests. ... Maybe not the best way for me to review something I haven't seen in ... oh my ... 16+ years.

I found that as I was learning one of the topics, they kept describing each piece/terminology of it in many ways and then building on and then redescribing each piece/terminology, and I found myself saying: JUST SHOW ME A SOLID EXAMPLE FOR THE LOVE OF GOD. And then I had to laugh and say, "oh what, you want them to HAND HOLD YOU through the stuff? can't you piece it together yourself for the joy of learning?"

"Gripe 2": there were SO many new vocabulary words that I'd understand in the context while I was learning it, and then when the book refered back to such a word, oh say 50 pages later, I was thinking, "yesssssss, that SOUNDS familiar, but holy cow, don't ask me to use it in a sentence other than: _____ is a word related to statistics.

All this to keep circling back to the topic of how my (any) students learn and retain math. I guess mostly I write this, so I can get over my uppity self and keep in mind that learning anything new and hard for students is, well, hard, and students should be provided with scaffolding and good-humored reminders that they're doing something hard and should pat themselves on the back between note-taking and problem doing and such. AND teachers should keep this in mind and keep spiraling back to old topics and bla bla bla.

WooHoo! The School Year is Over

The students' last finals were on Wednesday 6/4/08. We had to come in on Thursday to check out, and our graduation was held in the early afternoon. I went in on Friday to finally clean up the rest of the clutter in my classroom. And now ... I'm at home completely done. Whew. As usual, it sneaks up on you and is over before you know it. (unless you're still in school, and then it NEVER seems to be over)

I had a bit of drama (still ongoing) with a parent EXTREMELY upset because of my grading policy for the last 6 weeks. Ultimately her child got an 87% for the semester, but that's not acceptable to her, and I've ruined her child's life, and she'll be speaking to my administrator to make sure I don't have this opportunity EVER again to do this to another student. Deep breaths. I've talked with various other teachers and friends and have calmed down a bit, but obviously I'm still bitter.

In brighter news: I've started "playing" the guitar (and by playing, I mean random strumming and posing and trying to look cool while screechy sounds eminate from the instrument as my tongue sticks out of my mouth to aid in better concentration) and am self-teaching myself (that sounds redundant) via books and cds and dvds. It is so fun.

I'm also planning on making a simple big-square quilt for our guest room this week, so that when my friend visits, I won't have to subject her to the 80's style black-neon-pink-&-green-&-purple syntheticy cover.

Calculus project news. I liked how my volumes of revolution foam projects turned out. BUT. I have an idea I want to play around with for a teaching tool for next year. I'm thinking of getting card stock or laminated color paper and cutting the same shape out many times. Then I'll either cut a hole in each one or a slit in order to string all these shapes onto a circular thin wire or stiff cardstock that is curved into a circle. Then I can "fan out" the shapes or clump them together, and the students can get a better visualization of a "volume of revolution". I'll have to experiment this summer.

Note Taking

My precalculus students have recently taken a test on sequences, series, & the binomial theorem. The students run the gamut from they-could-teach-themselves-out-of-a-book to please-take-my-hand-and-do-the-problems-with/for-me-over-and-over-again. It dawned on me while I was helping this latter type of student to study that she had no concept of what might have been some good things to study and review before taking the test: formulas for explicit terms, partial sums, pascal's triangle ...

I thought over the notes they took, and I'm wondering if it ALL was so foreign and important sounding to her that she saw it as:

sdlkfoe sdoowieur sdeoe 5 = sdlfoein sdifuoeen
oeiwonewio sdf e3dof soieen sdeid nli lskejoi i9 dflk

so maybe she couldn't parse through it all and figure out what was important to know. I know when I was presenting the stuff, I had them do examples, and I had them write down the formulas and I discussed why they work and how to think about them .... but apparently, for some students, I have to stress what's important before, during, and after. And then maybe I should make them get out their red pens and BOX all the key things.

But this doesn't sit well with me. It seems that I'm doing the thinking for the students that way, and they'll never learn to sit back and reflect on what may be important to know without someone spelling it out for them all the time.

Stress City

Good riddance to a bad week. I had 3 bad run-ins with kids that left me so angry.

Run 1: I've had issues in the past with students conveniently not showing up on exam day. Then they'd take weeks to make up the test. Two tests ago I started the new policy of, "you miss the test, you make it up during class the next day". This helped. Then this past test, I had 2 students mysteriously absent on test day, last period of the day. I checked ClassXP, and, gee, mine was the only class they were absent for. I decided to use technology to my advantage and pop a quick e-mail home to mom: "is there a reason your child is absent from my class today?". This got results, and it alerted the parents without sounding accusatory (they could have had a dentist appointment). Well, it turns out one kid lied to his mom about where he was, and I found out, and thus he got a zero for that test. So, here we are Friday, and he's in my class just sitting there fuming all period. One and a half hours. Yay. So, not really a "run-in", more like a long, drawn out sit-in with teenage angst of getting caught and having to sit and take it.

Run 2: One child is in NHS, and has been slacking off on the homework department and just general character department all year (okay, all 4 years). After a bunch of stuff had happened, the NHS sponsor would only let him wear the "stole" at graduation if he got letters from his 4 core teachers that he deserved it. So he comes in to my class and tries to good-naturedly try to bully me and guilt me into writing his letter. He still didn't get that it's his actions that brought this on. He still thought/thinks that "we" are doing this to him. That left a bad taste in my mouth.

Run 3: Oh my. We're doing projects during calculus class, so it's a wee bit more unstructured as a class period than I like or am used to. Some kids are doing videos, and one kid in particular doesn't have any of his equipment at school, so just basically sits in class and says he'll work on it during the weekend. That's all a side issue for this run-in. He comes into class on Friday and does not look physically well, so I basically don't bother him much. Towards the end of the period, one student had turned to him and asked what he was doing. Apparently, he had unbuttoned his pants and unzipped them a ways because he was uncomfortable and didn't want to put pressure on his stomach. Well, okay. So I catch this interaction, and say to him, "well just put your shirt over your pants, so we don't have to see your unbottoned pants." Then he starts arguing with me. I keep asking him to just pull his shirt over and that it's just not socially acceptable to sit there like that. This goes on for about 3 rounds as he's refusing. Then he suddenly turns all creepy and lowers his voice menacingly and leans forward to me and says, "I'll decide what is socially acceptable and I'm NOT going to button my pants so you can be on your power trip and .....". Oh my god. I was livid. I told him to stop talking to me and that he was being completely inappropriate and he just needed to either leave the room or button up his pants. Holy Cow. Jerk. Excuse me while I jump off my teacherly manner and just fume about the brat. Okay, deep breath and the knowledge that I only have to see him for 2 more days.

Anyhow. WooHoo for weekends, especially 3 day ones. And only 7 more school days.

End-o-Year Calculus Project(s)

I ended up deciding to give the students a choice of 3 projects to do for the remainder of our time in class:
1. a volume of cross section project using colored cut foam that I've done before
2. a volume of revolution project again with foam (never done and I'm doing it with the kids)
3. a video or power point (never done before, and thanks, Sam, for your tips which I've incorporated).

I'm happy that 7 students picked the video project, and 2 picked the power point project. From talking with the kids, they mostly had great ideas and are working hard. One student is resisting everything and being really derisive and dismissive and coming up with every argument in the book as to why he shouldn't be doing this. Or talking about doing something sarcastic and such (because, you know, math just isn't that exciting). I'm working on setting him straight using my teacher voice as I'm simultaneously resisting the urge to vigorously shake some manners/sense/attitude-adjustment into him.

I'm excited about the volumes of revolution project. There are 6 (?) of us doing it. I picked the same region for all of us (y = 4 - x^2 , y = 0 , x = 0) and we're each revolving it around different lines. That way we can put them all together and see what's what.

One video pair is working on a video about someone getting ready for a "math party" and they have to cut eggplant and for some reason need to know about the volume (details will emerge). They wanted to know how to get a function that looked like an eggplant. One girl was really excited and happy to learn something new when I showed her how to plot the shape on paper, pick some points on the "graph", put them in L1 and L2 on the calculator and then do a Quartic Regression. Cool. It DID look like an eggplant when she showed me.

Limits

I was teaching algebraically finding limits today in precalculus. We got to the part where x --> infinity. I've tried various ways of explaining it in the past about how you only need to look at the highest power term on the numerator and denominator and make your decision that way.

I've likened it to "when you're plugging in REALLY LARGE NUMBERS, the largest power term is like the ocean and the smaller powered terms become like spit. They don't make much of a difference to the ocean volume." This stuck with some kids, but I don't know that all were convinced.

Well. I had one problem: (8x^3 + 2x - 7) / (-4x^3 + 5x + 100) or some such thing. On the graphing calculator, we entered 1,000,000,000 and stored it in x. Then we calculated 8x^3. Enter. Then we calculated 2x. Enter and compare. That semi-convinced them. THEN we calculated 8x^3 + 2x, and that really convinced them because it "was" the same output as 8x^3 by itself. And we all know that if the calculator says something, then it must be true.

If I was thinking (because what I did was on the fly and then I moved on), I should have also then (in the main window) plugged in the whole expression using the stored value of x .... or then putting in larger values of x and then "2nd entering" to recalculate the expression. Next time.