Month: January 2009

What can you do with this?

Dan Meyer of dy/dan fame has a series of posts titled “What can you do with this?” — where he shows a picture or video with some sort of math connection, and asks teachers how they might use it in class. (Others are jumping on the bandwagon.) I figured why not. I love the idea. What I’ve noticed is that many of the pictures deal with ratios and proportions. I wonder if we can get pictures that deal with other things — like radical equations and limits.

Michael Lugo at God Plays Dice directed me to the following picture:

img_6736

Fantastic, isn’t it! What you could do in a math class isn’t obvious at first glance. But let’s see what you come up with! For a spoiler (do NOT check it out until you’ve come up with an idea yourself), see below the jump.

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Day Three: Frustration

Today, besides waking up tired, I went through a whole range of other emotions. Frustration being the most prominent. Now that day 1 and day 2 are over, the school is slowly starting to go into full swing again. Classes are starting to put more content in them, students are becoming more engaged, jokes are being made, and I can finally smile again. Which is all really wonderful.

Still, the logistical aftermath of the tragedy is starting to unfold. We had midterms scheduled for next week, and the powers that be decided instead of changing the nature of the midterms (have teachers make them take home, or one hour instead of two, or have group midterms, or any number of other things), we are canceling them entirely. Which I can support, and will support. Sometimes top-down decisions have to be made. However, the result of this is that teachers are expected to continue teaching next week.

But no teacher, at least none of the teachers I’ve talked to, is in any way ready to start teaching our new material next week. We have a bunch of work we planned on doing during the lull of midterm week. At least, I have a ton of work — in addition to prepping for next semester. 

So things are stressful. And the fact that this is all coming out today, Wednesday, makes it hard to manage.

Clearly, you can see from this that I like order, stability, and clear expectations. When things are messed up, I get messed up.

As a last side note, I found out that I’m not even going to be in the classroom next week. I was told this after trying to figure out what I’m doing in each class, and when I’m doing it. The school is hiring me a substitute for every one of my classes, because I’m a 10th grade adviser and we have to put on gradewise community service project that was planned for midterm week. So apparently I have to leave all 4 of my classes in the hands of substitutes for a week. Which is such a waste of time for the kids. 

I hate to say this, but I think showing math movies is on the table in some of these classes.

Day Two: Stirrings

Yesterday, the key word was exhaustion. The fact that it was Monday, and when the day was over and it was still Monday, was unthinkable. Wednesday, Thursday, surely it was much later in the week. 7:45-3:10 felt much longer than 7 hours and 25 minutes. Waves of tiredness hit all of us, at various points of the day, and the thought of going home and preparing for the next day unfathomable.

I ended up having 3 cups of coffee and a can of Coke to get through the day.

As with many bad things, one of the most striking things that I noticed about yesterday was that I still had moments when I was laughing. Not the awkward, nervous laughter that comes out of not knowing what to say or do. It was true laughter at funny things. I recognized that I was going through a range of emotions, and something the school psychologist told us stuck with me. “You may, for a second or minute or a few minutes, forget what happened. You may be happy. That’s okay.” When he said it, I understood it but I did not comprehend it. I went home exhausted at 8, passed out at 10.

This morning I woke up feeling… refreshed. Like my battery had been replaced and I had a fresh supply of energy. I had rested away the sheer exhaustion that yesterday brought on. I wasn’t sad or happy or anything — except functioning. And this, my friends, was nice.

As I approached the school, the heaviness started to set in again. But at least today I had the restedness to deal with everything. Today people were figuring out not how to cope, comfort, and deal with the shock and tiredness, but how to move forward. This wasn’t all people — but I saw smiles and laughter, overheard some normal conversations instead of yesterday’s hushed whispering and muffled whimpering. I saw hustle and bustle instead of trudging and robotic-front-stare-walking. Not that it was all roses, or roses at all. A sadness and heaviness blanketed the school, but underneath this weighty shrowd, stirrings. Stirrings. That’s when the school psychologist’s statement really was highlighted:

“You may, for a second or minute or a few minutes, forget what happened. You may be happy. That’s okay.”

And I did forget, too. Not all the time, not even a majority of the time, but there were moments when I realized I hadn’t thought about the death of our student for the past three minutes. It was initially scary — because I wondered if that made me unfeeling. I don’t think that’s the case. I think that I’m in the initial stages of moving on. Not forgetting — this students’ death will be with me for years. But moving forward. Being able to function.

Not all my students are at that point, nor should they be. Some seem to be able to function. One of my classes carried on fine. Another one was quieter but students weren’t incapacitated. The last was the hardest, because it is populated with students the grade of the student who passed away.

I knew they were not sleeping — a student told me that no one in that grade has been able to sleep well. We spent only 15 or 20 minutes learning new material, and it was very basic stuff. Almost no one raised their hands to answer my questions. When I gave them the remaining 25 minutes to work on a worksheet covering some of the same material, I told them: you can work on this if you feel you can focus, you can work alone or with friends, you can not work on this if you don’t feel you can focus, whatever. I expected students to get with their friends and maybe work on the worksheet or maybe talk. Or if they were sick of talking about the death of the student, they would at least talk about math.

But the level at which they were affected was so enormous that literally, for those 25 minutes, no one said anything to anyone. I encouraged students to work with each other, but no one moved. Teenagers, not wanting to talk. Let me say that again: Teenagers, not wanting to talk?! The only voice in the room was mine. All students worked alone on the sheet, and they worked pretty assiduously. And quietly.

In the last four minutes of class, I had to ask them if they thought us doing a small bit of lesson and some worksheet work (and no homework) was helpful. Again, silence. Quiet. One mumbled something about it being fine, and then another two said it was good.

I could have asked them if the moon was made of cheese and gotten a similar response.

It’s hard to see this class so deeply affected — because all teachers want to protect their students. But we can’t. And we’re all grieving in different ways and at different paces. I wish I could neatly tie today up in some summative way. But every hour was different, every class was different, every interaction was different.

So with that I’ll stop. I’m exhausted again. Maybe more tomorrow.

Day One: Triage

Today was day one after the tragedy. For the sake of respecting the student who passed away, I don’t feel comfortable sharing any details here. Still, for me personally, many things have come into stark relief in the past 36 hours. Between bouts when my chest tightens and my eyes start to water, those moments when potential sobs get suppressed so that I can be strong for my students and colleagues, I’ve had all sorts of thoughts about teaching and our roles as teachers, as well as the awesomeness (in the great and terrible sense of the word) of the human condition. 

All day my mind keeps running to — of all things — a comic I read ages ago. It’s from xkcd.

secret_worlds1

On the first day of every class, I show this to my students. We talk about what it means. Everyone is special. Everyone is flawed. Everyone is unique. Everyone has depth.

On this day, a day of triage where everyone’s emotions are all over the place, you start to see these secret worlds start to become exposed. Students were sharing their feelings, they were crying together, they were empathizing and being compassionate. They were exposing their own inner worlds, in some small way, with others. And we saw on this first day that everyone — students, teachers, and administrations — that everyone is complex, inscrutable, beautiful, flawed, great, and very, very small. 

Today I saw such sadness in in the sunken eyes of students who hadn’t sleep, who had been crying, who spent the day looking down and were too stunned to have anything to say. As I type this, I start to see their faces, and my eyes are watering up again. I know that with time things will get better. But knowing that doesn’t make anything easier right now. 

With that, I’m out for the evening. If I have any energy, I’ll post again soon with my thoughts about teaching and the role of the teacher that this incident brought up.

Tragedy

I got a call today. A student tragically passed away this weekend. I haven’t processed it but I — as surely is my entire school — is devastated. Getting through Monday is going to be a trial for everyone. I will write about it later, because I think I have a lot that I want and need to say about this, but for now I’m going to try to forge on with some semblance of normalcy. I’m going to focus on other things so I can get out of my own head for a while. I probably won’t make reference to this until I figure out what I want to say, so expect more math and more teaching in the interim.

Mathematics in Context

I have a bit of teacher-musing, and then I want to share a funny story that happened in calculus class yesterday.

MUSING

Everyone is always saying “make math relevant for your students!” Well, great. Sure. Okay. Will do. I think that’s a bunch of hooey. It’s not about making math relevant, but making math into problem solving skills [1]. I don’t care if students will ever have to use what they learn in my class in the “real world” (what world are they living in now?). But I do care that they can see a problem and break it apart into its component pieces. That they can go down dead ends without getting frustrated. That they can see that there are often multiple ways to solve a problem. Sure, sometimes one solution is more elegant than another, but that can be okay… because sometimes problems don’t have elegant solutions at all!

All this being said, I’m terrible at doing this. At least, I’m terrible at doing this in my non-accelerated classes (which are my Algebra II and Calculus classes). I stick close to the basic skills and concepts, we don’t do too much investigation; I’m focused on making sure they can do basic skills. That they can verbally explain the concepts. Which is unfortunate, because after students learn basic skills, they should be given the opportunity to draw connections, hit dead ends, and all that good stuff I just listed above.

As a teacher, it’s so easy to make excuses (we have a fast-paced curriculum, the class period is only 50 minutes, my students are working on so many different ability levels, there isn’t enough time in the day to design these classes) of why not to do it. I also think that investigative work doesn’t go well in the non-accelerated classes.

But that’s probably a function of me not knowing how to do it right — how to design and implement these sorts of lessons without spending too much time at home or in class working on them.

FUNNY STORY

So back to what I was saying… the mantra “make math relevant” actually took a funny turn after my calculus class yesterday. To set this up, I have to remind you that I teach at an independent school. Tuition is high and students tend to come from wealthier backgrounds. It’s a different world [see my post about that here]. Anyway, after school, one of my calculus students said “Mr. Shah, I have a math question for you. It’s not related to what we’ve been learning in class.”

Turns out, he found out that he and one of the other seniors both resort at the exact same place in the summer. And after thinking about what a strange coincidence it was, he wanted to know “what are the chances that two seniors at this school both resort at the same place?”

So that’s math in context for my students, apparently. 

(These are the sorts of moments that I realize that this world is so different than the world I grew up in. But I really like these kids.)

If you care, my answer was that we can definitely figure it out together. I then told him about the birthday problem (how many people do you need in a room before the chances that two of them have the same birthday reaches 50%?), and how we could use that as an analogy to solving our problem.

In the birthday problem, you have n people in a room, and each of these people have a birthday from the calendar year (each person could have one of 365 birthdays). In our problem, we have 80 seniors, of whom “only “n resort. Each person who resorts goes to one of a certain number of places (we’d have to do a back of the envelope calculation/Fermi problem to find an approximate number of resorts that people from my school could go to).

Then the analysis would be the same as the analysis for the birthday puzzle.

If you’re curious, you need about 23 people in a room to have a 50% chance that two people in the room have the same birthday. Of course, you’re going to need 366 people in a room to guarantee that two people in the room have the same birthday. (Do you see why?)

[1] That’s not to say that I don’t think the the content is unimportant. The content is always my primary focus. And I guess when I say “relevant,” I mean specifically “real world applications.”

Blog Review of “Wild About Math”

Sol Lederman, at the blog Wild About Math, had an idea of a blog-review-exchange (he writes reviews of math-related blogs, in return for math blogs reviewing his) [see his post here]. I like this idea, if for no other reason that I get introduced to new math blogs through reading his reviews. So here I go.

Wild About Math has been in existence since October 2007. His first post clearly articulated the goal for starting his blog: “This blog is the expression of a life-long passion that I’ve had for all things mathematical. My sincere desire is to share articles, reviews, and links to products, services, and web-sites that inspire people of all ages to enjoy Math.” Sol is uncharacteristic in that he was able to continually maintain the original intent of his blog for months (to the present!), without giving into laziness or devolving into a forum for personal screeds (although I do have a soft spot in my heart for the blogs with the latter).

My favorite aspect of Sol’s blog is the Monday Math Madness competition, which is alternates between Wild About Math and Blinkdagger. [The current MMM problem is here.] In recent months, besides the mini-blog-reviews, most of the blog posts on Wild About Math are related to Monday Math Madness. The problems are easy to state, range from easy to difficult, but always are engaging. The best part is that one (usually) doesn’t need more than precalculus to solve the problems, and usually less. Some of the best questions take forever to think through, even though they don’t require higher level mathematics. Those are the best kinds! I have even gotten one of my high school students hooked — and he is sending in solutions to the competitions when he has time!

Although the original intent of the blog has been maintained, the nature of the content has shifted. As I noted, in recent months, Sol has focused on nurturing his (wonderful) Monday Math Madness contests. However, before this contest started, Sol had frequently posted about everything and anything math, like neat websites about fractals or speed multiplication. To see the nature of these posts, some of Sol’s favorites in fact,  you can check them out here. And I don’t know if this is still happening, because I am not a subscriber and didn’t know about this until looking through the back-blog-posts, but Sol offers (or used to offer) a supplemental periodic email called “Math Bites”.

Some of my favorite posts:

  1. Experience With Math Camps? (which inspired me to write my own recollections! [1])
  2. Uncountably Many Errors in In Texas Math Books (the type of information that I’d miss if I didn’t read this blog)
  3. Review: Numbers Juggling (a review of a math website which goes in depth – we need more reviews like these)
  4. A Hard But Fascinating Puzzle (a problem which got me thinking deeply!)
  5. TI-Nspire Inspires Math Students (a review of the TI-Nspire)

Overall, this is definitely a blog worth keeping in your reader (or putting into your reader if it’s not there yet) for the Monday Math Madness contests. I do wish, however, that at least once in a while Sol would continue to post same types of posts — the great reviews of books, math resources, and calculators, the “for fun” math puzzles, for the math news — that defined the blog before Monday Math Madness came into the picture.

[1] You can read it here.