Month: May 2009

The MV Calculus Final Projects

Last week my multivariable calculus class turned in their final projects, and made presentations. Of all my classes this year, by any metric, this course was my most successful. I loved seeing their final projects, and the amount of work and dedication they devoted to them. The best part: they were super proud of their projects too.

I made a post about coming up a list of fourth quarter final projects a while back. My big fear with these projects was senioritis. The projects are designed to be largely self-directed, and if a student got lazy, well, …, that would spell disaster. Luckily, none of the students in the class fell prey to that dreaded disease. My kids are great kids, so that helped. But also I let them pretty much have free reign on their projects and kept emphasizing they should pick something they WANTED to have FUN with. Lastly I met with them weekly to help them out and keep tabs on their progress — prodding them a bit here and there.

Without further ado, the four projects:

1. One student actually created a harmonograph (a device which draws damped Lissajous curves).

Yes, that is his video of his harmonograph.

2. One student researched Maxwell’s Equations and read A Student’s Guide to Maxwell’s Equations (Fleisch). He produced a written paper explaining the integral and differential forms of Maxwell’s equations.

3. One student created a giant wooden and wire sculpture (titled “The Visualizer”) which illustrated a lot of what we’ve learned about curves in 3-space. Namely, he illustrated arc length, vector equations for curves, curvature, and the tangent, normal, and binormal vector with his sculpture. He also wrote an associated paper which is to be used with the sculpture to examine these ideas in more detail.

4. One student took foam board and cut a whole bunch of figures (from the simple square to weird and complex shapes). He then calculated the center of gravity of these figures theoretically, and tested to see if the figures would balance at that point. Then he extended this by making figures with non-homogeneous density, calculated the center of gravity of these figures theoretically, and tested to see if the figures would balance at that point.

I mean, seriously, look at that. Amazing. These kids got into it, because it was their own thing. Because they weren’t really worried about their final grades. (I let them grade themselves.) I am going to miss these miscreants a lot next year.

Senior Classes Over; Letters Distributed

My internet at home hasn’t been functional, so I have been negligent about putting posts up. There’s a ton to tell you about (the balloon caper, birthdays, reviewing for finals, the multivariable calculus final projects, etc.) and just no internet to do it with. But I’m staying late at school to at least get this post up.

Today was my last day of classes with my seniors. My calculus students took a test yesterday so it was time to party. This was going to be their last math class of high school! Some were sentimental and had a hard time coming into the room — if they came it, it would mean the end of an era for them. My class of seven met first period and we started out having a rousing chorus of L’Hopital (I have Calculus in the Heart). Then we played a lot of “Apples to Apples.” (Best. Game. Ever.) There was a mountain of junk food we devoured. At the end of class, I gave them each a letter (see below) and let them go. I was feeling pretty sentimental. The other class 0f seventeen met last period (their last class of high school ever!) and minus being able to rouse everyone into a chorus of L’Hopital, the same happened.

And like that, it was over. The seniors are not under my charge anymore. My sentimentality is waxing.

My senior letter this year (I also included the poem/prose from my senior letter last year, put up here):

Shadowing a Student

It all stemmed from one of the weekly meetings that we 10th grade homeroom advisers have. We were talking about how little we actually knew about what it was like to be a 10th grader — and the ups and downs of going to school everyday as a 10th grader. One idea we had was inviting a panel of students to come in to talk to us frankly about their experiences. We did that. Listening to these kids — it was incredible. They were kids from all across the personality and academic spectrum, but they all were so articulate and honest and thoughtful. Their maturity, the way they think about teachers and about school and about learning, the way they handle their frustrations… let’s just say that although I usually think our student population is great overall, I don’t always get to see or remember how great they are.

I said it all got started with this 10th grade meeting. Well someone, I don’t think it was me, came up with the idea of shadowing a 10th grade student for a day. To see what it was like to run from class to class, to experience all the daily things that a 10th grader might go through.

If you know me, and probably by now you’re getting a sense of me, I jumped at the chance. I asked to be paired with a student I had never met and knew nothing about. And last Wednesday, I became her shadow. We did separate once. My student had to change for gym in the girl’s locker room.

What I expected:

  • The day would be hectic, and I would end the day at 3:10 exhausted.
  • I would be jolted as I bounced from class to class with different teachers with different expectations.
  • I would enjoy learning.

That’s it. I didn’t go in with a ton of preconceptions.

What I discovered:

  • The day was strenuous, but not overly so. Even though the student I shadowed didn’t have a lunch period on the day I shadowed her, I wasn’t dead at the end of the day.
  • It was easy to go from classroom to classroom, teacher to teacher, and deal with the changing expectations.
  • Doing any strenuous thinking (reading, answering tricky multiple choice questions, etc.) before 9:30am was tough. I had to read and re-read the passages assigned in the AP US History course multiple times.
  • I need to be given instructions twice. Because even though I try to listen, focus, and take everything in, I sometimes missed what I was supposed to be doing. Having instructions written on the board, or repeated, would have helped me out in those cases.
  • It is not a good feeling to be answering multiple choice questions and think that the rest of the class is ahead of you and that you don’t have enough time to finish them all. I resented it when I was told “Even if you aren’t done, stop. We’re going to go over these.” [1]
  • It is hard to take good notes in most teachers’ classrooms. Many don’t design their classes with notetaking in mind, or give students the time to write down notes.
  • Dodgeball isn’t as scary as when I was in high school. They don’t use the tough rubber red balls anymore.
  • Students do a lot of running around, and don’t have a lot of down time. (At least not on this day, where my student had no free periods.)
  • Taking tests is scary. I took the last-period chemistry exam on the Ideal Gas Law. Finishing it in time was scary, as well as that moment of panic when I was still on question 7 of the multiple choice and a student raised his hand and asked the teacher about the 5th short answer question. (In case you were wondering, I got a 67% on this test, which highly impressed the teacher. I would have definitely broken into the C range if I had remembered the conversion from Celsius to Kelvin.)
  • Teachers in general aren’t good at handling class discussions, or synthesizing the information from these discussions into a digestible format useful for everyone.
  • I like being lectured to. I learn a lot in a short amount of time.
  • Some classes (e.g. chorus) are like vacations from the stresses of the day. Not that work doesn’t happen there, but chorus was really enjoyable and relaxing to be an environment where everyone loved what they were doing.
  • At least on this day, there wasn’t a lot of group work. Actually, in none of the academic classes except math were students asked to talk with anyone but the teacher. Conversations were mainly between teacher and student.

It was worth doing. If you can convince your school to get you a sub so you can do this, I highly recommend it. Plus, the other kids in my shadow’s classes thought I was so cool for trying to learn what it was like to be in their shoes. Okay, not so cool. But they definitely respected me for it.

(And the best part: my shadowee and I got to invent our own special handshake.)

[1] That was especially painful, because I know as a math teacher I do that a lot. I’ll put up 3 problems for students to work on — the last one being the hardest. When I’m sure everyone has gotten the first two, and I’m running low on time, I’ll stop everyone and we’ll go over all the problems together.

 

Silent Teaching

A few weeks ago or so, the GSA (Gender and Sexuality Alliance; formerly GBSA) club at my school held a day of silence to highlight the experience of being silenced, and to show support for gay, transgendered, and questioning students. Students who wanted to participate could wear a sticker saying they were participating, and for those teens who couldn’t keep their mouths shut, there was even a sticker for “vocal supporters!”

It was great. I had a few students come to the front of the classroom and write their ideas on the whiteboard, and I made an effort to keet everyone engaged.

It made me think that next year, I would plan a class where I wouldn’t talk at all. Some classes naturally lend themselves to have the teacher fade into the background: group work/investigative activity, student presentations, etc. But I was thinking: what an interesting exercise to think what a class would look like if I was teaching something routine (e.g. logarithms, completing the square) but I couldn’t speak. Can one teach as effectively without a voice? How important is our voice to the teaching process? What are alternatives to talking? What other means of communication do we use without knowing it?

No good ideas yet, but I’ll keep on thinking. Just a gedanken experiment (thought experiment). Could be fun for a us to all try this out on the same day next year. You know, as a lark. It’s not like we have anything better to do with our time other than baffle our students with even more nonsensical actions.

Why Twitter?

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On November 18th, I decided to give Twitter a try. I wrote:

So I’ve decided there is possibly a vibrant teaching community that I’m not familiar with, because I had decided to ignore Twitter while getting the year in order. So here I am, going to take the plunge. […] I found a whole bunch of blogs by math teachers that I follow regularly. Let’s see if I can find the same on Twitter. 

It is now May 10th. I have made 741 tweets. I follow 71 people. And I check twitter multiple times a day. 

On November 18th, I didn’t “get” it. No one could explain to me why twitter was worth trying. But people on the blogs I read were talking about it. Before writing it off as inane… I mean, why do I care what a math teacher in Northern California had for lunch?… I gave it a shot. My goal for this post is to share with you how I use twitter, and why I continue to use twitter. 

One: I joined twitter to be involved with the math teacher blogger community. Turns out, most of the people writing the blogs I follow regularly have twitter accounts. I didn’t know that so many people were on twitter before joining. So these people, who I sporadically communicated with by commenting on a post here or there, have become people I communicate more regularly with. I solicit ideas from them and I share my ideas with them. The dialogue, short and sweet, is continuous. Like a bird chirping in the electronic zeitgeist.

Two: I get to solicit advice and share frustrations. And I get to give advice. 

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Three: I don’t know much about the people I follow, but I do know we share a set of values about teaching math. We love what we do. Why else would we want to talk with others who are the same. Not that I don’t have great colleagues in my school, but I am the only teacher for three of my four classes. I like to have someone to hash out ideas with. These people on Twitter are those people.

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Four: Links, links, links! I post links relevant to the post I’m writing on my blog. But I tweet lots of random math links that don’t seem to fit in what I’m doing now. Cool things that I think other math teachers might find useful. And others do the same. When I first started twittering, this was hands down my favorite benefit. Plus I get links about non-math related things too. Like when someone linked to the entire 5 seasons of Angel which were on sale for $57 at Amazon for one day.

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Five: I actually like hearing about the ordinary, math and non-math related things that my twitter friends post. Ummm. Okay, I know that these people aren’t my friends. And that I’m not ever going to meet them in real life, for the most part. But I’ve actually come to care when someone’s kid is angry at them or when someone’s husband was in the hospital. It brings the people behind the blog posts to life. Picture 7Picture 8

Six: I didn’t used to do this, but I have started doing this: when I write a blogpost, I tweet about it for other people to learn about it.

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Seven: I have discovered new math teacher blogs out there by looking at the followers of some of the people I follow.

Eight: This doesn’t apply only to Twitter, but also the blogs I read. I’ve noticed that having other people care about what they do makes me care about what I do. I want to do well that much more because of them. I honestly can’t say that I would have the drive for continual improvement and spend the time thinking through things as much if it weren’t for this little community.

And that’s my story with Twitter. I can see how someone wouldn’t find it useful. But to the nay-sayers out there, I will say this: I went in thinking I probably wouldn’t find Twitter useful/interesting/fun. It was only after I was following math teachers and joining in the conversations did I actually say “hey, this is actually pretty rad.”

To visit my Twitter Page, click here.

Bright Student Doesn’t Do Homework

Wow, my post title reads like an Onion headline. But in fact, I didn’t read it in the Onion. I read it on Twitter.

Jackie Ballarini asked:

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The question is worth thinking about, because it gets to the heart of some pretty deep issues. What is a grade, what is homework, and what is our role as teachers? I’m afraid my opinion will be in the minority and I’m okay with that. Just don’t be too harsh in the comments.

I personally am a fan of homework. I assign it. This year, in my second year, I’m assigning less of it than last year. But it allows me to focus on concepts in class, and has students practice more skills at home. We spend about 1/2 the class learning concepts and building up to being able to solve problems. The other half is solving these problems. Then I assign homework to have students try things on their own, individually, away from their desk partners and with some time between when they first saw the material and when they see it again. Why homework?

1. It forces students to naturalize the skills they’ve learned in class. I think there is something valuable about doing the same problem, but with different numbers, five times over. It drills home basic procedures. Some of my students can’t see something once and remember it. They need time to work through it on their own. And doing it again and again actually does help them.

2. It allows me to have students grapple with slightly newer situations, that we don’t always cover in class. I do this more with my Calculus class than my Algebra II class. Homework has been, at times, an extension of class. (Just to be clear, this isn’t me saying “oops I ran out of time, so you have to learn this new material on your own.” I actually choose a preliminary list of problems, and then revise the list based on where we got to in class.)

3. It is an easy way for me to make sure that all students are learning. If homework were optional, I know that the students who most need to do it to practice their skills won’t do it; and for the most part, students who don’t need it as much will do it. (Note to self: definitely an important point that I should think about.) But yeah, homework is a way for me to easily make sure that students who don’t always get things immediately have time to practice them — and a consequence is that students who do get things quickly have to do some extra work which might be unnecessary.

Clearly though, there are problems with homework. The most apparent being that it is not individualized and not all students need to spend the time on it to be successful. And certainly I agree that coming up with alternative ways to assign homework might be fruitful and worth trying [1]. However that won’t be my concern here, today, in this post.

Back to Jackie’s question. Most of the responses I saw on Twitter were of the “give the kid an A!” variety. And I totally get and respect that point of view. How can one argue against the fact that the student knows the material? And if the student can get straight As without working, and can even teach the material to other students, why would we demand that this student spend the unnecessary time to do what they already understand? Why force busy work upon the student? It doesn’t seem legit.

I see all that.

And yet, I actually believe that the student should be penalized for not doing the homework.

If a grade is merely about the ability of a student to solve problems well, I say okay, give the kid an A. But I don’t see my role as a teacher as only teaching students to work problems. (That is my primary goal, though.) Even though they are in high school, my students are kids. Think to you in your classroom everyday. These kids are learning what is acceptable behavior and what isn’t. They are learning what expectations are and how to meet them (or what the consequences are of not meeting them). They are learning how to act with maturity and handle responsibility.

I mean, holding a trashcan in front of a kid so they can spit out their gum, or encouraging them to come to you for extra help, or congratulating them on doing a fantastic job at the basketball game or the school dance concert — these actions affirm implicit values that you are trying to instill in your kids. Yeah, and one of the values is accepting responsibility for your actions.

The students knows that they should be doing their homework. Even if is the most mundane, boring, piece of busy work ever assigned. But the teacher has set up the expectation. And in my opinion, even if the student gets an A+ on every exam and the most perfect angel, the student should then be asked to face the consequences. (And in my class, since homework is factored into the grade, the consequence is that the student’s homework grade would greatly suffer.)

My question is: if we don’t penalize the student, what message are we sending? And if the consequence of not doing the homework is that the student gets an F for all the homeworks that weren’t completed, so be it. The expectations were there, the consequences were laid out, so I say: follow through.

I guess by following through with the grading system that I had been using all year, I am pretty much saying to the bright kid who can’t be bothered to do homework: “Hey, sometimes in life, we all have to do things we don’t like. Things we don’t think we need. But we have to do them anyway.” And guess what? I’m really okay with promoting that value. Welcome to the larger world.

Now I have to end this with a small note. This post isn’t about Jackie’s student. I don’t know her classroom, her student, or her policies/expectations. It’s all highly individual. But if this happened in my classroom, with any of my students, and with my policies/expectations, this would be the consequence.

[1] There is something really great about Dan Meyer’s class setup, where if you know the skills, you get the grade. If you don’t know the skills, you don’t get the grade. Most notably, it allows students to be active agents in their own learning process. And if a student drops the ball and doesn’t learn something, he or she has the opportunity to pick the ball up again. In Dan’s classroom, grades aren’t punitive but encouragements and sites for individual improvement. However that isn’t my classroom (yet) and I doubt there are many around like it.

I was thinking of trying something next year more along the lines of Jonathan’s comment at the end of Dan’s post:

I assign 3 pieces: practice, regular, and challenge. Everyone does regular, and one of the others. So the stronger kids get a couple of challenge problems, and the weaker kids get a fistful of easier exercises to build up some proficiency. And since it is easier, they are more likely to do it.

Dan himself this year has started assigning homework, but just a little. It seems like he spends a lot of time in class working problems for the drilling aspect I think is so important.