Thursday, December 29, 2011

Math Lesson Formula

Okay so, seven years in, and I feel I am finally cracking this nut: how do you make any math lesson work for most kids under most circumstances? Throughout the year I have been tweaking most of my lessons to follow the same basic formula. Not that we do the same boring thing every day - there are infinity variations to make it work for me or a particular group of kids. Not that I'm saying teaching doesn't require a whole mess of skills besides knowing how to set up a lesson. Anyway.

I will illustrate with the most frustrating of topics : log laws. I can't think of a topic that seems more boring and pointless to most math teachers and students. I know their virtues as well as you, but let's be honest, 99% of your kids don't really need to know them for anything they are likely to do for the rest of their lives. I posted about it last year, but there was a piece missing, and now it really sings. To believe this works, you have to believe that the one doing the work is the one learning. Nobody gets much out of Miss Nowak doing dramatic performances of math problems and proofs other than Miss Nowak learning how to do dramatic performances of math problems and proofs under the withering attention of 24 bored and irritated teenagers. I don't want to give the impression that I'm giving them a worksheet and being all like, "You're on your own, kids! Time for me to kick back and drink coffee." Because I'm running around, scanning for common questions or points of confusion or missed connections, re-capping with the whole group every five to ten minutes, encouraging and validating, etc. But if you believe "teaching" = "lecturing" then you are not going to see the validity of this approach, and I can't help you.

Phase 1: Productive Struggle
Hook the new thing to something they already know or know how to do. Then make them do it. A few times. Let them discuss and work together. No reason this has to be done in silence. Whether calculators are allowed depends on whether the calculator will let them avoid the things you want them to remember and see. (This particular lesson is no-calculators.)

Phase 2: Generalize. Make them write whatever they have been doing with letters. This is harder for most kids than you'd probably expect, especially if they've never been asked to do it before.



Phase 3: Use it. Presumably this new thing you've discovered is good for something. Even if that something is obviated by ready access to a shmancy calculator.


Phase 4: Prove it. The hardest part for kids, and the hardest part for me to figure out how to get them to be the ones doing the work. I have had some success with this approach of setting up an organizer and basically telling them what to write. But they still need lots of hand-holding. But at least they are doing more than watching/copying a dramatic performance.


Phase 5: Lots and lots of practice. I want them to understand, but I also want mental automation of relationships and procedures. Because later they are going to use this stuff to learn something new.



I would like to say Phase 6 is apply it to a novel and interesting problem, but I'll be real, I'm not there yet with log laws. Though I am there with good projects on some other topics that lend themselves to applications. Give me another seven years.

Friday, December 16, 2011

All I Really Need to Know about Teaching

Dave started it. Here's mine: It's been on a bulletin board at eye level at my desk for seven years. It's a little embarrassing to share because it's more than a tad hubristic. But I think it helps me be better. I don't really need to have it hanging up because I can recite it from memory. Like a mantra. But it's comforting to have it there. Like a talisman.
“I have come to the frightening conclusion that I am the decisive element. It is my personal approach that creates the climate. It is my daily mood that makes the weather. I possess tremendous power to make life miserable or joyous. I can be a tool of torture or an instrument of inspiration, I can humiliate or humor, hurt or heal. In all situations, it is my response that decides whether a crisis is escalated or de-escalated, and a person is humanized or de-humanized. If we treat people as they are, we make them worse. If we treat people as they ought to be, we help them become what they are capable of becoming.” ― Johann Wolfgang von Goethe
(There is a teacherified version floating around by Haim Ginott. I like the original better.)

I don't take away from this "it's all about me." The take away is more like, "There is a ton that is in my control, and that makes all that happens here my responsibility." Which is maybe a little oppressive and maybe a little "duh." But I still like reading it every day.

Monday, December 12, 2011

In Which Ben Articulates My Reasoning Better Than I Could

...and then some.

Read.

#takethetest

#passiton

I'll add, since I didn't provide much in the way of explanation. The NY Algebra 2/Trig test is a horror show. It tests many things. Notation. Vocabulary. Procedures. Graphing calculator button sequences. It is not a test of mathematical understanding. I am pretty sure any reasonably mathematically-literate adult would sit down to take it, and within twenty minutes be all like, "What the HELL is all this CRAP? And WHY are we inflicting it on our young people? Get me the Governor! Oh wait, I am the Governor!"

I just want the guy to know what his organization says is important for college-bound kids to know. Thats all. I'm not even totally anti-test. I'm anti horrible, very-bad, no-good test.

Sunday, December 11, 2011

"Favorite No"

Just a quick share - I have tried this a few times this year, because I was looking for ways to more frequently but still quickly assess a whole class. It works really nicely. I don't have anything to add - Lea covers it all. Just watch.

Saturday, December 10, 2011

This Journey to Wherever...

...is about to get slathered in chimichurri. If you keep up with me on Twitter this is old news, but everyone else: I accepted a position at an International School in Buenos Aires for 2012-2014. Reactions fall into two camps: 1) Awesome! 2) WHY IN THE WORLD WOULD YOU DO THAT? so, here goes. While a young pup Navy officer I spent great chunks of time overseas, predominantly Italy and Bahrain (which seems like an odd pairing only if you've never been a Med/Gulf Sailor,) and hearted it. I like being a stranger in a strange land. I like navigating mysterious cultural waters. I like spending twenty minutes of gesticulating to communicate the idea "I think this thing is awesome but I am not willing to pay 20 dinars for it." "Okay fine you can have it for 15." "10." "12." "Fine."


So when I started teaching in 2005 the idea of an International School really appealed, but at the time, the reputable schools wouldn't consider teachers with no experience. I hear that's not always the case these days, but at the time, it was off the table for a few years anyway. Cut to seven years later, and you'd be right to wonder what took so long. I wonder that, too.


It took me about the past three years to Get Serious about making this happen. There was comfort with the known and fear of the unknown. There were two boys who captured my attention for a time but things just didn't go that way. I had to improve my math teacher fu. I had to gain and lose fifty pounds. Would that it had all not been so painful but it was all probably necessary. There were excuses but once I Got Serious I realized my excuses were really no thing. 


For instance, I was all concerned about What Would Happen with the Cat, but here is what my point of contact at my new school said when I asked if it would be reasonable for her to join me: 
YES!!!! Bring Kitty! (what is his/her name....that is very important for me to know!) I came here many years ago with 2 young German Shepherds and an old grumpy cat!  So you KNOW I understand bringing your little furry friend! 
So yeah, excuses loom large in your mind but sometimes go poof when exposed to daylight. And they are just that, excuses, i.e. not the real reason you are hesitating. I think my real reasons (mostly fear) were alleviated by meeting and talking to and reading the blogs of teachers currently working at International Schools. These are real people not that different from you and this is their life. I have to especially thank Mimi who spent lots of time patiently answering my questions at PCMI and afterward, and offered lots of good advice.


So when I finally Got Serious I was looking for three things in a placement: 1. a non English speaking country so I could become fluent in another language 2. a stable, reputable school committed to supporting and developing their faculty and 3. a major urban center, for all the reasons people like living in cities. Beyond that I wasn't even particularly concerned about what continent I would end up on.


I joined Search Associates and joyjobs. Search Associates turned out to mostly be useful for demonstrating to potential employers that I was "serious" - since I interviewed and accepted an offer quickly, and never even had to go to a job fair. Joyjobs is a source of lots of good information, and frequently updated vacancy postings, and worth the small fee in my opinion. 


In conclusion.... I'm ridiculously delighted with the way things turned out, and I can't wait to get there. This placement has lots to be excited about - the probability of teaching IB or AP, a block schedule, much smaller classes, no fire drills, no Regents nonsense...not to mention I won't have to scrape ice off my car any more. Considering that my new school hasn't hired a math teacher in five years, maybe all the delays make sense in the grand scheme. Now for a long six months of trying to learn Rioplatense Spanish and find new homes for all my stuff. (But not the cat. She's coming.)

Tuesday, December 6, 2011

f(t) is having a moment

Hello, faithful readers.

I need you all to do something for me.

I never ask you for anything.

I need everyone.

EVERYONE.




Just go toot my buddy Governor Cuomo about how he should take the exam that decides whether my cherubs are college-ready. That's all. Here's a template you can follow. Heck you can just re-tweet me.

If you really, REALLY, TRULY want to have an impact? Repost this on your Facebook and your Twitter and etc. We are about to get exponential on his ass.

It'll just take a sec. Then you can go back to watching My Drunk Kitchen. Promise.

 xoxox k8

Saturday, December 3, 2011

Still Relating Those Rates

First I have to express an obscene amount of gratitude to Bowman Dickson for illuminating what will be challenging for students learning related rates, and sharing how he deals with it. I basically just took his post and reorganized it into a lesson that will work for me. This post will probably make more sense if you read his first.

Second, I have been thinking this morning about what this lesson has to do with the recent discussion at dy/dan. There's probably a way to turn these into a problem we could pose without words through the cunning use of video production skills I don't have. It's really fun to think about.

Here's what I'm giving the kids. Here are relevant documents: handout for the kids, smart notebook file, ggb's that I made.


Update: Mimi Yang, a.k.a. thebomb.com, revised the cone tank ggb to reflect a constantly changing volume. That file is in there too.

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SUPA Calc Lesson 4-6 : Fold this paper in half to hide the bottom half. Please don’t look at the example problem while we are doing the investigation. It will just get in the way of your learning.

1. Blow up a balloon!

2. Go here: http://bit.ly/calcballoon

3. Figure out everything you can about rates with the balloons. Record your observations below… (there is no one right way to do this. Make it make sense to you.)

4. Which one is more like inflating a real balloon and why? Write about it.

5. What is going on with the other one? Write about it.

Air is being pumped into a spherical balloon so that its volume increases at a rate of 100 cm3/s. How fast is the radius of the balloon increasing when the diameter is 50 cm?

(Here, we'll set up a solution with a diagram, givens, equation, etc, in a very structured way.)

6. Go here: http://bit.ly/calclad




7. The model depicts a 10-foot ladder leaning against a wall. If the bottom of the ladder slides along the floor at a constant rate, what happens at the top of the ladder? Why? How did you figure it out? Write about it below.

A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 ft from the wall?

8. Go here: http://bit.ly/calccone



9. A conical tank is filling with water. Use the slider to change the height of the water in the tank. How are the height and radius related? How are the height, radius, and volume related? Write about it.

10. Imagine you are standing in a municipal pumping station, watching this tank being filled with water. What do you think is more likely: (a) the height of the water is changing at a constant rate, (b) the radius of the water is changing at a constant rate, or (c) the volume of the water is changing at a constant rate? Why?

A water tank has the shape of an inverted circular cone with base radius 2 m and height 4 m. If water is being pumped into the tank at a rate of 2 m3/min, find the rate at which the water level is rising when the water is 3 m deep.