Month: February 2010

The Unfolding of a Non-Intuitive Problem

Below is a problem that one of my calculus classes tried solving (unsuccessfully) so we banded together and walked through a solution. The problem is this (from here):

If you have two flies on a deflated spherical balloon — one on the equator and one on the north pole — and the balloon inflating at a rate of 5 cubic centimeters a second, how fast are they moving apart from each other at some time t_o?

What I like about the problem is that it is looks as simple as all the other related rates problems they’ve done, but it actually gets pretty complex. And it gets tricky figuring out what you’re trying to solve for, unless you keep yourself organized. What I love most is that you’re given almost nothing, but you end up with an answer I’d call beautiful because it is so ugly. You start out with practically nothing and can get something so ugly out as answer? Awesome. Welcome to math, neophyes!

So we walked through the solution together — after they had a good amount of time a couple weeks ago to try to solve it. I gently asked a few questions prodding them and kept the information organized. What you see below is how the problem unfolded on the whiteboard.

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Students write comments on ME

Sometimes I feel like a doctor who doesn’t take his own medicine. I spend a lot of time writing narrative comments on my students — in the hopes that students know that I do care about them and pay attention to who they are and what they do well. But also so they know places they can work to improve themselves.

I ask my kids to write narrative comments on me, and every year I am a total wuss about reading them. First I put them aside on my desk at school, and when I realize I’m never going to read them at school, I bring them home and put them on my desk, letting them sit there. They get bigger and bigger as they sit there. I don’t know what I expect to find in them — but each year I’m so critical about myself and my teaching that I expect these to be as critical. [1]

As an adviser, I sit down with my kids and we read their narrative comments together. We highlight the good in one color and the weaker areas in another, and look for trends within classes. I encourage my kids to read these and use them to improve. I would never let my any of my advisees not read their comments for a couple weeks while they prepared themselves.

But look at me, total wuss. I did.

But right now, as I type this, I have the unread stack next to me. What I’m going to do is to go through it, and publicly make a list of all the things that I do that students say are places of weakness / areas for improvement.

BIG BREATH.

Okay, let’s begin.

Algebra II

  • “I enjoyed the small group tables we used to do… I think bringing back the group work at the tables would be effective and good.”
  • “at times you tend to move rather quickly”
  • “Sometimes [Mr. Shah] moves very quickly through the smart board slides, which sometimes leads to a bit of confusion, but I am generally able to catch up”
  • “I feel that at times you expect us to do a lot of work with little time and without a calculator [on tests]”
  • “One thing that does not work for me is group work”
  • “Sometimes I struggle to keep up with my notes, and then understanding as we go is also hard since I’m trying so hard to take down the right notes”
  • “I do not like the binder checks, since I have a different way to organize myself”
  • “Every once in a while I wish we would move a little more slowly through the material”
  • “My one complaint is the binder check. I do not think we should be graded so harshly on our organizational isues. I end up spending valuable math studying time redoing old assignments that I lost”

Calculus

  • “I do find that [class] can be pretty slow at times, simply because we go through every problem step by step as a class”
  • “Every once in a while I feel the homework takes a little too long but overall it’s a good amount”
  • “I feel [] at times it would be better if you spent a little more time explaining the concept behind how to do problems, rather than simply doing the problems themselves”
  • “I think that you should give more partial credit on tests, because often we understand things but make simple mistakes which really should warrant more credit than given”
  • “I do feel that homework should be counted more than 10% because that’s what I put the most time into”
  • “One thing that makes class difficult for me sometimes is the pace that we move. Sometimes it goes a little fast and I don’t have time to digest everything that you say”
  • “[I]t is really hard to have to learn new things the day before we take a test. If I have questions about the new topic it doesn’t always give me enough time to work out my problems.”
  • “Sometimes his unyielding energy can be annoying, but that’s probably because I’m living on 4 hours of sleep every night”
  • “[T]here isn’t as much in-class review for assessments as I would like, but I know that as seniors it is expected of the class to do a lot of studying on their own”

Okay, so guess what? That wasn’t bad at all! Basically, I feel bad for you because you didn’t get to read all the supergreatawesomethings that were said, which now makes me feel like “hey, I’m not a total failure!” And now I have a list of things that I get to sort though, decide if it is a generally valid point, and if so, what (if anything) I can do to change it.

A few things that immediately come to mind for Algebra II

1. A few of my students feel like I’m moving too quickly. Already I’m thinking “we’re like 3 weeks behind where I was at this time last year!” — so finding a solution won’t be easy. But I think doable. I think it calls for redesigning the routine of the class a bit.

2. One thing I wanted to do last year and earlier this year (but never did) was to design and put a little “WRITE THIS DOWN” icon on the smartboard slides that I thought students should take notes on. Students have difficulty taking notes in a class which uses SmartBoard, because the text is already up there… so unlike when a teacher is writing on a whiteboard and students are copying it, with a SmartBoard students don’t have this lag time

3. I want to bring back more group work in Algebra II! I somehow stopped doing it regularly. The desk configuration in that room is all weird, and I tried something last quarter which didn’t work (groups of 4 are never a good idea), so I think this quarter we’ll institute groups of 3.

4. I refuse to change my stance on the binder check in Algebra II.

Calculus is a lot harder for me to think about changing based the feedback I got, and the varied the personalities and ability level of the students I have in the class. I’ll keep mulling it over and if I have any really strong insights about changes I’m going to make, I’ll post ’em.

[1] Yes, I know, none of my kids are going to be horrible and unkind. They are a respectful and nice group. But I always tell them to be honest — that that is more important to me than them writing empty platitudes — and I have them keep ’em anonymous. So a student COULD eviscerate me.

Favorite Tweets

A list of some of my favorite tweets, chronologically listed from long ago to today…

calcdave How often do I have to slow down when writing sec x to make sure nothing distracting goes on the board?

k8nowak @calcdave one time I taught a whole volume/surface area problem about a “10 inch rod” before I noticed the whole precalc class was DYING.

samjshah one of my advisees asked me what 111,111,111 times 111,111,111. i spouted off the answer without even a second thought. all kids: IMPRESSED.

druinok Is it sad that a few months ago I scoffed at the idea of twitter, now I find it a professional lifeline?

samjshah “What kind of pole is short and floppy?” Yes, that is the question of the factoring joke sheet I’m handing out. Guesses about answers?

msgregson kids were especially loud and talkative today … i asked why … they said “because you woke us up with quadratics!!” hah, they are funny.

calcdave The most disappointing thing about presenting a lesson poorly is when the kids don’t even realize.

k8nowak It boggles my mind that geometry kids who want to use the pythagorean thm for EVERYTHING have no ideas for finding the diagonal of a square.

samjshah just started grading a calc exam, and thought “what nice handwriting.” turns out, i was grading the key i created.

samjshah why is it that when i have only 5 tests left to grade, i need to take a break. it’s like running a race, and walking the last 10 feet.

samjshah to which my friends will laugh… sam, run? REALLY? hahaha. yes, i might never have run in my life, but i hold the analogy still rings true.

calcdave How fun is the word “minimum” to write in cursive, eh guys?

SweenWSweens @calcdave What’s cursive?

calcdave @SweenWSweens It’s like recursive, but only once, I think.

alicia_anderson @pepepacha One of my favorite lines: “Twitter is like some huge, noisy teacher’s lounge, like the type I always imagined…”

misscalcul8 Student quote of the day: “This is definitely a ghetto public school; even the teachers rap.” Thank you @SweenWSweens =)

k8nowak #ilostaschoolaptopandibrokemyfingerandmykidsthinksqrt(a^2+b^2)=a+bandi’moutofcl

SweenWSweens @jbrtva @jimwysocki I hide easy extra credit randomly in the middle of directions. They usually learn after they miss it the first time.

k8nowak Spending my evening figuring out why the 7-day exponents/exponential functions unit turned into a 12-day unit in the new Alg2 curriculum.

samjshah @k8nowak your evening sounds … um … well, at least you have your health!

k8nowak @samjshah All the single ladies. Put your hands up.

samjshah @k8nowak don’t the single ladies go to the club? in their dereon jeans? or is it in the 3rd verse they analyze exponent lyrics.

busynessgirl How is it that Calculus students do not know sqrt(1) is 1 ?

k8nowak @busynessgirl You found us out. It’s a big conspiracy. We keep it a secret from them, as a fun little surprise when they get to you.

dcox21“Do I still get a cookie if I apologize?” — Aidan, 4

calcdave @dcox21 I’m sorry, too! (holds out hand)

samjshah” I’m not an English teacher! You can tell because I’m not wearing cool shoes and I don’t give hugs.” –@k8nowak (c. 2009)

amfago today one of my students brought me a chocolate ruler and a chocolate protractor…made my day!

calcdave @amfago You can have 2 inches or 30 degrees of chocolate tonight and save the rest for tomorrow.

divbyzero New Years resolution: do such a good job teaching that my students dump Gatorade over my head at the end of the semester.

k8nowak Moved the trash can next to a (totally silent) girl’s chair about 30 seconds before she threw up. I’d like to see a remote lecturer do that.

k8nowak We have a club for that. It’s called everybody. We meet at the bar. RT @dcox21: RT @shareski: Some days I feel like I suck at my job.

dcox21 .@k8nowak Problem is, I never sucked until I met all you guys. Thanks “everybody.”

CmonMattTHINK @samjshah I was afraid of that ;) Srsly though, I’m not 1/2 the content-machine that, say, @k8nowak is. I fly by the seat of my pants 2 much

k8nowak @CmonMattTHINK You should see me in action. I could open up a miles rewards card for the seat of my pants.

dcox21 Student: “Holy shift! Look at the asymptote on that mother function.” Not sure how to respond.

Fouss @samjshah Told my hubby about your e-mail. He said “Is that the guy who wears the t-shirts?” :)

cannonsr @Fouss I love that your husband knows about the wardrobes of your twitter friends.