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.