Monthly Archives: October 2008

I woke up feeling under the weather today. As the day went on, I felt worse. I’m going to bed sick. Of course I would get sick for the first time this school year… the night before parents night.

We have “parent night” on Thursday and there are five things I have to remind myself to do:

1. Plan to speak for 15 minutes, even though I only have 10 minutes with them. That way you can go “oops, I guess I’m out of time” and send everyone along.
2. Integrate humor into the presentation.  
3. Talk about the content of the class, the expectations I put on students, the expectations I put on myself, and anticipating any parent questions and addressing them in the presentation (e.g. do I ever allow extra credit? no.) 
4. Do NOT let any parent ask me questions about their individual child. Politely say “I don’t think tonight is the best night to have conversations about individual children. However, I’d be happy to set up a conversation! Here’s my contact info.”
5. Don’t freak out! 

I’m being asked to write college recommendations. I have a hard time with this, because I view it as such an important responsibility. The colleges my students are applying to are often prettycompetitive and every part of the application is important. 

My strategy for dealing with this is to send students desiring a recommendation the following paragraph:

When you have all your colleges picked and the forms gathered, will you give me the forms paperclipped to stamped and addressed envelopes? It would be good to have them at least two weeks in advance of when you want them sent out. That way I can do them all in one fell swoop. Also, when I write recommendations, I usually ask students for two things: (1) things you want me to highlight in your recommendation [math or non-math related], and (2) for you to write a sample recommendation for yourself. Why? Well simply put, it is this: recommendations become strong recommendations if there are lots of specific details/specific instances/stories. And you know things I wouldn’t know — like if you formed a study group or something. Don’t feel like you need to be humble. Just write it honestly and with confidence.

I’ve talked to some teachers who have a form they give to students, questions students need to answer about their experience in the class(es) they had with the teacher.

Do any of you do something that makes writing these recommendations easier? Do you have any suggestions about how to write a strong and honest recommendation?

One weekend ago, I had the fourth cycle of the CD club I organize. It rocked. (You can read about a previous cycle here.) The general idea: a group of 10-15 people meet up at a local watering hole and bring a mix cd they’ve created around a theme. In fact, everyone brings 10-15 copies of their mix, and when we’re all gathered, we exchange them.

The end result: you get 10-15 cds filled with really good music.

The last four themes were:

1. No Theme
2. The Academic Colon: A CD About Some Aspect Of Education
3. Time Travel
4. Stages Of A Relationship 

(You can see the tracklistings for each of my four CDs here.) 

There is something really awesome about this set up: the work you put into creating and reproducing one thing comes back to you ten fold. And you get to — and want to — engage with everyone else’s work.

Is there any way to harness this model of intellectual exchange in the classroom? To reverse engineer it? 

The two key points:

The object needs to be coveted by all participants (e.g. carefully crafted CDs)
The object needs to be easily reproducible (e.g. copy CDs)

Ummm. The best example just popped in my head: VALENTINES DAY CARDS IN ELEMENTARY SCHOOL!

Or a slight variation:

Can we come up with an single large entity that students individually contribute to? So students have ownership in it?

So in the mix CD example: if every person chose a song on a theme — and we made a CD — we’d have a single CD with input from all. Or if we were making a bulletin board, we could have each student bring in one picture to contribute to it. 

Before signing off, I thought I’d share one idea that might be useful. Before a big assessment, I could ask students to each make a one-page set of study questions they created, along with their solutions. I could scan them in for students to use to study from. For students, by students. And for the assessment itself, Icould  chose some of the good problems from the study guides to be on it. 

Other ideas? Is there a good math project out there that fits this CD club model?

This year, my math department has changed radically from last year. Among the many changes is a revamping of the Algebra II curriculum. Not only are we adding new topics, but we’ve removed a whole bunch of what we traditionally taught — pushing it to precalculus, I suppose. The course is totally reordered. For our first quarter, we are covering:

Unit 1: Number Lines, Intervals, and Sets

1. Set notation and interval notation (along with union, intersection, and subset)

2. Linear inequalities –graph on a number line

3. Compound inequalities

4. Absolute value inequalities

Unit II: Algebraic Manipulation: Rational Expressions and Exponents

1. Factoring two, three, and four term polynomials

2. Review of basic exponent rules and simplification

3. Polynomial addition, subtraction, multiplication, and division

4. Rational expression addition, subtraction, multiplication, and division 

Unit III: Radical Equations

1. Review properties of radicals (integer exponents)

2. Simplifying radicals with exponents under them

3. Solving radical equations 

This seems very hodge-podgy to me, now that we’re going through it for the first time. One day we’re talking about sets and subsets, the next how to solve . We are doing a lot without the textbook (which I’m fine with), but every so often we’re turning to the middle of the textbook to cover a topic (e.g. compound inequalities and absolute value inequalities come at the end of chapter 3). It just feels fractured. Why am I concerned?

I don’t know. I can’t articulate it. It’s just a whole bunch of thoughts running through my head…

We haven’t started graphing, and that makes me nervous. I’m now feeling like we’ve cut out too much of the curriculum in quarters three and four to cover this stuff. I don’t see the natural flow in this beginning material, as I saw the natural flow in our old curriculum (functions and lines; quadratics; polynomials; rational functions; exponentials and logarithms; trigonometry).

However I’m hoping that the past month and a half — which seems like a lot of vamping before we get to the good stuff — is worth it, because it does force students to practice their basic algebra skills. 

If there are any other Algebra II teachers out there: how do you start the course? And do you like it (equivalently put: does it work)?

In non-AP calculus — since I get to cover what I like at the pace I like — I focused the past month and a half specifically on the skills that my students last year had difficulty with: visualizing basic functions including logs and exponents, solving logarithmic and exponential equations, solving trigonometric equations, and knowing trig values at special angles. This too is totally different than what I did last year, where as a new teacher I just forged through our book. But let me tell you — unlike with Algebra II — I am certain that all this review is going to do some good, because I remembered some of the wounds my students suffered last year, and I am applying extra padding in those same areas to my students this year. 

Today was a tough day. The toughest so far this year.

Fielding parent calls, communicating with administrators, getting questioned by administrators, having issues with my computer, not having a lunch. Yargh. My classes were awesome, though, but even that wasn’t enough today, when I felt boxed in from all sides.

All I wanted was a giant hug, and someone to tell me that I’m good at what I do, and they respect and support me as a teacher.

In my multivariable calculus class yesterday, I was introducing spherical and cylindrical coordinates. These students didn’t take precalculus, so they didn’t have a ton of practice with polar coordinates. So I thought it was going to be a tough class to teach. To compound that, the smartboard wasn’t working, so I couldn’t show them some great demonstrations (here and here).

We had to do things by hand.

And I wanted to spend the entire period working on deriving the conversions:

Given a point in rectangular coordinates, how do you find the cylindrical coordinates?
Given a point in cylindrical coordinates, how do you find the rectangular coordinates?
Given a point in rectangular coordinates, how do you find the spherical coordinates?
Given a point in spherical coordinates, how do you find the rectangular coordinates?

And we went through it all. It wasn’t easy, but they “saw” it. They came up with the conversions. I just guided them.

I had two favorite moments in this class:

(1) At one point, when dealing with spherical coordinates, one student discovered an equation for the angle made with the positive z-axis. The equation wasn’t the one in the book. I suspected the two were the same, but decided I wasn’t going to pursue it. A student said we couldn’t leave it hanging, we HAD to figure it out. So we did, together. That 7 minute aside was awesome.

(2) The school clocked stopped at one point, and of course, it was noticed by a student. (Do my students wait with hungry eyes for the course to end?) Apparently the clocks in the school do that occasionally. And somehow, in a fit of impulsivity, I got onto an aside about standardizing time, Einstein’s work in the Patent Office in Switzerland, and his original 1905 paper on special relativity. (See Peter Galison’s Einstein’s Clocks, Poincare’s Maps if you want a lengthy version of what I told them.)

Teaching seniors is a mixed bag.

With college admissions, you often get students suffering from a Dr. Jekyll-and-Mr. Hyde complex. The first semester has seniors constantly stressed out, with SATs and SAT IIs, writing college admissions essays, with soliciting recommendations, and deciding where to apply. Many seniors also — at least in my school — tend to fill their plates to the edge. Some have crud oozing off the edges of their plates.

They’re overextended and stressed. And I feel for them.

And then, once college admission decisions have been made, you get seniors falling victim of the most ugly and heinous of all diseases: senioritis. Grades, the traditional motivator, have little curative effects. Their corporeal bodies might be in chairs, but their spirits have flown yonder. The stressed out blobs of nervous energy have become sedate lumps. 

Right now I’m dealing with the blobs of nervous energy.

And quite a few of them are even more nervous.

A good number of seniors who sign up for regular (non-AP) calculus specifically for colleges. And this then becomes the rub. Because it’s about at this time of the year when students start to realize that they actually are getting graded in calculus. That it’s more than just the name of a course for college admissions. It’s — you won’t believe this — actually a course.  

All I can say to them is that I’m here for them. And that it’s never Me Vs. Them, but always Us Vs. Calculus. But I suspect that this distinction will get blurred in their minds as the admission season gets underway.

Coming up with math explanations for students that don’t always “get it” can be tough. You have to be thinking on your toes, and you have to make your explanations understandable. It’s not always easy to succeed.

Two Recent Examples:

How would you explain to a student in a non-accelerated Algebra II (or even non-AP Calculus class) why it is that when you solve in the standard algebraic way, you get and ? Why is it that you generate the extraneous solution, that you then have to eliminate, because it can’t “plug into” the original equation? Where does that extra solution come from?

How would you explain to a student — without using the formal definition of a limit — what a limit is? So that they understand it intuitively. Now ask yourself: would your explanation work for the constant equation ? What would you say to a student who says “Why is the limit of f(x) as x approaches 0 equal to  6? The function has already reached 6. It isn’t approaching 6.”

And for those of you who want to prove your mathematical mettle, here’s a question that recently circulated through our math department. What’s the answer, and how would you explain it to a stuck student?: 

Suppose that a function is differentiable at and . Find and .

Today I spent a good chunk of time writing my interim comments. “What are those?” you ask quizzically.

I’m glad you asked. Halfway through each quarter, we’re asked to write interim comments for students earning a C- or below, or who we have concerns about. (We also are encouraged to write interim comments for students who are doing really well, but considering doing that requires a significant amount of extra work, no one actually does.)

They’re tough to write, because it’s unclear who the intended audience is, and exactly what the purpose of these comments are. The dean gets a copy, the adviser gets a copy, and the parents get a copy. Are we writing for the dean, the adviser, the parents, the students, or even some have asked, the tutor?

My interim comments tend to be slightly more than just a litany of grades, and slightly less than a full-blown narrative evaluation. I direct my interim to the parents, informing them — frankly and honestly — of the grades the student has received. I won’t say “on the first quiz, Jane Doe earned an B-.” Instead, I will say something like “The first major quiz was on logarithm and exponents, transformations of functions, and basic trigonometry. Jane earned a 40.5/50 (B-). She was most challenged by questions involving logarithms, but also made a number of basic algebraic errors.” I then usually outline one or two suggestions to help the student. (Normally they get more specific in later quarters, when I know the student better.) 

The one thing I avoid like the plague when writing comments is making any inferences about the student. I would never say “Jane needs to spend more time doing her homework each night” because I don’t know how much time Jane does spend on homework. I would say, however, “Jane tends to come to class with partially completed homework assignments, which are often sloppily written.”

These comments are, at least for me, to keep the parent in the loop about their child. I want them to know that I’m paying attention, and that I know their child’s math work well. But these comments can also, importantly, in the independent school system, act as insurance against parents who tend to get a bit… zealous… about their children’s grades. Which happens more often than you’d think. 

I’m really fast at typing up comments, and making them comprehensive. I thank my time at UCLA for that.

When I was a TA in grad school, I began to type up long narrative comments on each of my students’ essays, in addition to marking them up for grammar, structure, tone, etc. I got good at doing it well, and quickly. I was a bit more blunt with them than I would be with my high school students. Example:

I believe that you are trying to argue that the guillotine and the steam engine effected social change, and because they were structurally different, they caused different sorts of social change. This thesis is not actually arguing much – the second bit (the type of social changes) is descriptive, and the first part (machines can causes changes in society) is not very “deep” (in the sense that I don’t think you need to prove it). So I think that is your most fundamental problem – that your thesis indicates that your paper isn’t so much of an argument as much as a description.

I wondered if the amount of time I invested was worth it. But my answer came in an email from a former student, ages ago. But I still keep it near and dear, because it reminds us of why I do what I do. The Post Script is the most relevant part of this email:

You’re probably wondering why I am emailing you two quarters after I took History 3C with you as my teaching assistant. 

[...]

Sam, you were the perfect TA for this student who initially felt lost during his first history course at UCLA. The nature of the course was definitely new and uncharted territory for me, as I’m sure that you could tell with all my random questions. I was initially unsure of how to take notes or write historically, but you were always there to guide me and set me on the right track. You were a truly awesome TA since you always provided us students with very constructive feedback (whether in discussion, on the weekly questions, or on the papers); and although the discussion sections weren’t always organized, they were always very informative and well done.

[...]

P.S. Your providing each of us students with feedback on our papers in some weird way influenced this whole e-mailing TAs thing that I’m doing. Feedback goes a long way—thanks again for helping me realize that.

And that’s it. After the aw shucks moment, after the puffed chest deflated, what I was left with was a student saying that he got something out of my feedback.

So although I’m still unclear to whom I’m directing my interim comments, and unclear of the reasons I’m writing them, I will go along believing they do some small bit of good.