The Next Alexander Calders

Back in January when our school was in intersession, one of the courses was a math class just for 9th graders. Students were selected to participate, with the goal that it would support struggling students. Of course, if you take the 20 kids who need the most help in math, they're probably also the kids who like math the least and are least interested in doing it for three hours straight every morning. Fortunately, the teachers are two of the most amazing math teachers I've ever met (and with no exaggeration, probably two of the most amazing math teachers in the country) who planned a class specifically around helping students grow their mathematical confidence and skills by providing them opportunities to engage with deep, difficult mathematics.

In addition to many other tasks and problems, the students had an ongoing art/math project that lasted for the entire month. Each student built a perfectly-balanced mobile using foam shapes. This was much more than just playing around with balance, but used some serious math that would challenge the average adult. First, students experimented to figure out the relationship between two objects of different weights and where they would have to be placed in order to maintain balance. Then they chose a theme for their personal mobiles and designed at least four pieces. The requirements stated that (1) all pieces would be built out of basic shapes (quadrilaterals, circles, triangles) and all shapes must be used at least once, (2) no more than one stick could have its string balanced in the middle, and (3) they would have to make all calculations and prove mathematically that their mobile would balance before they could actually start cutting out their shapes. Like I said, that's some serious math.

The results were amazing. The students were more creative than I could have imagined. They got really into the artistic aspect and nobody tried to "go easy" by just picking easy shapes. Some of the math they ended up using, and seriously improving at, included:
-Number sense
-Measurement
-Converting fractions to decimals
-Calculating areas
-Spatial reasoning
-Proportional reasoning (the balancing relationship is directly proportional)
-Working backwards
-Measuring area versus length
-Productive disposition
-Connecting mathematics to real-world applications

Okay, now the good part: the finished products. My mind was blown by these.

The Spider-Man mobile (the artist refused to pose with it, so I took her place):


Music theme: a radio, iPod, headphones, and a radio


Food theme: pizza, ice cream, pop, and a Hershey bar (obviously made my a growing teenage boy)


Three girls made this one as a gift for one of the teachers who is pregnant with twins


Another mobile for the twins' nursery


Clearly made by a teenage girl, but still extremely impressive in the way she used basic shapes to create very not-basic objects


Transportation theme: a rocket, a boat, and a tank (carrying Spongebob and Patrick, of course)


Lots of happy faces


This is one of my favorites (shhh, don't tell the kids). Partly because I love the Japanese monsters, partly because she used the shapes so creatively, partly because she made it for her brother, and partly because this is from a kid who I've never, ever seen excited about math (until this)


There are a couple others that are truly amazing, but I decided not to post them because my pictures include students. Email me if you want to see the girl whose theme was European landmarks.

Found: Note

Although most kids these days send their in-class communications via text message, there are still those hold-outs who pass notes in class. I guess it's less detrimental to get a piece of scratch paper taken away than it is your iPhone. And it's generally more entertaining for me, the teacher. I feel too guilty to go through text messages, but I definitely do not feel guilty reading whatever note they were passing.

So far I have two favorite lines from notes I've found.

1.
Girl 1: "I can't tell if he likes me."
Girl 2: "You should talk to him."
Girl 1: "Who are you, Dr. Phil?"

2.
Girl 1: "Guess what? Yesterday I got my geometry test and I got my first A+ and A!"

On one hand, Note #1 is way funnier (especially if you know the two girls who wrote it). On the other hand, if they're passing notes in math class, I'd much rather that they're talking about what they got on their latest tests.

Just Instructions

It's true, the worksheet I gave in class today was a little more text-heavy than usual. The first bit of text was almost four sentences long and contained important mathematical information. The general format of the worksheet was this:

-Approximately four sentences of text reminding them what we did yesterday and explaining how the picture below is a picture of what we did yesterday.
---Picture/graph---
-Problem #1, asking students to draw triangles on the above picture
-Problem #2, asking students to write down relationships they noticed between the triangles they just drew.

I am not sure exactly what was confusing about this layout (I spend a lot of time thinking about layouts and formatting that make the content more accessible), but something told the kids, "It's okay, you don't actually need to read the questions." I think that in math classes in general, kids are used to seeing problems where they just know what they're supposed to do. They see an addition problem and they add it. They see a multiplication problem and they multiply it. They see an equation and know they have to solve for the variable. So it's a paradigm shift when they see a page where numbers and processes aren't clearly laid out for them. Because my students work in groups 99% of the time, the synergy of four students usually is enough for one person to ask, "Wait, what are we supposed to do?" Then someone realizes that they could figure this out by reading the instructions. It also helps (or doesn't help, depending on who you ask) that I answer at least half of their questions with, "Well, what did you read in the instructions? What does it say you need to do? Read it back to me. What does that mean you're looking for?" I even prompt every group conversation to start by someone asking, "Who wants to read?"

Getting back to today's worksheet, in 6th period (Lettuce) I came across one group that had skipped drawing the triangles and trying to answer the question about the triangles. Although I cannot say for sure, I'm pretty sure they skipped the reading part too. I checked in with them, asking how they could notice relationships between the triangles when they hadn't actually drawn any triangles on their paper. All three students in the group stared at me blankly.

Student: "What are we supposed to be drawing?"
Me: "What did you read? What does it say you need to draw?"
Student: "Where does it say we need to draw something."
Me: "In question 2. What did question 2 say?"
Student: "Oh, we skipped that. We thought it was just instructions."

Interesting. The fact that the text in question 2 was "just instructions" was exactly the fact I was trying to point out to them.

London, you've got to do better

All signs pointed to disappointment. First, the nanaimo bars I so desperately tried to make turned out too lumpy and too gooey at the same time. Even my sugar-loving roommate pronounced them "cloyingly sweet." Then, in search of Canadian beer, the guy at BevMo had never heard of Labatt's or Molson and led me to the European section. I know I'm no longer living in a state where Canadian pennies mix with American and no one takes second notice, but come on. Then, of course, there was the death of the luge-er (luge-ist?) that Brian Williams just couldn't help but show on a seemingly endless loop.

But despite such omens, I had high hopes for that favorite event of mine that comes only once every two years: the Olympic opening ceremonies. I love the opening ceremonies more than I love the actual Olympic events. The parade of nations makes my heart melt. I get that nervously excited knot in my stomach when the torch enters the stadium. I like the imagination of the IOC that French is somehow the most sensible language to conduct business in.

But this opening ceremonies... blah. I get that Canada is not the most exciting nation ever. And I get that it's pretty much impossible to live up to an army of synchronized drummers recruited from a pool of 1.3 billion. I even get the hope that three hours of dancing First Nations people could be the beginning of an apology for a history of attempted genocide. But fiddlers? A poetry slam? A weird child running over digital wheat fields? I just think there could have been something else. The whales were cool. As pointed out by a savvy Slate blog-reader, kd lang's all white ensemble was reminiscent enough of a cake-topper that the world was indeed reminded of Canada's progressiveness around gay marriage (take that, USA). But I think I would've preferred floating state-sponsored health care or something to really showcase what Canada has to offer. Nelly Furtado's heels just didn't do it for me.

To be honest, my continued disappointment in the Olympics thus far really stems from NBC. Just because you were projected to lose $200 million on all of this is not a legitimate reason to only post half-hearted clips of nothing on your website. Thanks for spoiling the excitement of competition--do I want to watch Jacobellis' unforgettable silver (and her creepy pale hair) or Kearney winning the first US gold? What I actually would've liked to watch is something where I didn't know the outcome, but I guess that's out. Not to mention that the closest thing I can get to watching live is reading the live blogging comments. Looks like this year will be just like the Olympics of my childhood where I turned to CBC for any real coverage of Olympic events.

Somehow, Canada pulls it out in the end.

Lions, Tigers, & Bears, Oh My! HELP!

One thing I really like about my school is the rotating periods. Rather than having my classes and prep periods in the same order every day, they rotate each week. For example, there's a class that I'll see 1st period in an A week, 3rd period in a B week, and 5th period in a C week. On first glance it's kind of confusing, but it's definitely worth it. Seeing kids at different times of days means I get to see them in different state of mind. The kid who's late to 1st period EVERY day doesn't end up missing as much from my class. The kid who's asleep after lunch is awake in the morning. I don't have to end every day with the same crazy 6th period group. On the more instructional side, I don't have one group who are always my guinea pigs for a lesson. I really like it.

As a teacher, it's crucial to keep track of your different classes. Most teachers do this by period number, but I can't really call one class "fifth period" when I only see them in that time slot 1/3 of the time. Most teachers end up choosing section names for their classes. The natural inclination is to name them after famous people or themes from your subject area. One math teacher has classes named !, ∞, Σ, and Θ. The physics teacher named his classes Faraday, Newton, Gallileo, and Tesla. In the first semester, I decided against that option. For the symbols, I name my table groups after Greek letters, so that takes out a lot of good math symbols (at least ones that kids are going to use in their high school math careers). When I tried famous mathematicians, I got stuck between on one hand not wanting all my classes named after white men, and on the other hand not being able to understand the mathematical contributions of the more famous female and/or non-white mathematicians. To be honest, I don't understand the math behind 99% of the contributions listed when you google "famous mathematicians," so that seemed a little disingenuous.

For simplicity's sake, I chose to name my classes last semester "Lions," "Tigers," "Bears," and "Oh My!" It was easy to go through the classes in my mind because they roll off the tongue so nicely. Sadly, most of the kids didn't even realize that the names fit together, even when I had them listed on the board (in order). Do people not say that anymore?

This semester, my classes are getting mixed up. I don't want to use the same section names because I've gotten in the habit of mentally organizing kids by what section they're in (and the corresponding color for that section) and it's just too confusing to figure out whether a kid was "Oh My!" this semester or last. So, dear readers, I'm looking for your suggestions on what four things I can name my classes. I imagine that between the eight of you, we should be able to come up with something.

Please stick to a few criteria:
-Keep it positive. For example, I've already vetoed naming them after the Four Horsemen of the Apocalypse (mostly because it would be too difficult to choose which section is Pestilence).
-Keep it relevant, both to me and the students. I don't really care about the Beatles, so John, Paul, George, & Ringo are out (also, see comment above re: white men). Similarly, my students don't share my affinity for New Zealand, so sadly I am passing on Auckland, Wellington, Christchurch, & Dunedin.
-Keep it in fours. There are many wonderful things in this world that come in larger or smaller packages, but I need a group of four that I can easily run through in my head. If I named my sections Zack, Slater, Kelly, any Screech, I'd only end up trying to figure out what happened to Jessie and Lisa (and probably Mr. Belding as well).

You have your mission, now find me those fours.

Almost Normal

My school, being a charter, makes some creative decisions about, well, pretty much everything. Take, for example, our calendar. Like most schools, our academic year is broken up into two semesters. During that time kids take five classes (math, science, English, social studies, and Spanish) and a study hall. For the elective portion of their high school experience (art, music, things that they might look forward to) we have two month-long intersession periods at the end of each semester. Kids choose one elective to focus on, and then spend the whole month just doing that. For example, they might have dance class from 8:30-2:45 for 4 weeks. Our first academic semester ended in December, so we are now right in the middle of our first intersession.

You may be wondering (as am I), what do the teachers do during this time? Unfortunately it is not time off, nor is it time when we can teach elective classes. Instead, we spend time in "professional development," which means anything from traditional workshops about various teaching topics, to spending hours upon hours talking about and voting on proposals to improve the school, to community building. I am withholding judgment at this point.

What I will say is awesome about intersession is that I'm not teaching. Not that I don't love teaching (?), but it's really nice to arrive at school at 8:15, to leave before 6pm, to not plan lessons, to actually devote a reasonable amount of time to planning lessons, and to go to the bathroom whenever I need to. The best part, by far, is that when I leave school for the day, I'm actually leaving school. I'm not doing more work at home, I don't have to eat dinner while checking school email and typing a worksheet, I don't carry around a giant bag of grading. It reminds me of the good old days of office work when, at 5pm, I could stop whatever I was doing, go do things that normal people do, and not think about work until I returned the next morning to pick up where I left off. I don't even know what to do with all this time on my hands. The other day I went to the grocery store, we've finally watched and returned the Netflix DVDs we got last March, and I think I've been to the gym more in the past three weeks than in the past three months put together.

What will happen come February 1 when I have to actually teach a class again? The responsible person inside of me says that I should spend some time now preparing for the upcoming semester so that I won't have to spend quite so much time in quicksand mode. The realist says that there are many, many episodes of The Office that could use some re-watching.

The Pythagorean Leash

One of the most important things I think that I can train kids to do in geometry class is to draw pictures. Any time they come across a word problem, they need to be able to translate it into a picture because 90% of the time, word problems aren't that challenging if you can get the picture right. Furthermore, translating word situation into a mathematical model/equation is a skill that will be legitimately useful for them long after they've left school (just ask the history teacher who came to me the other day trying to figure out how many points his final exam should be worth).

I'm also a huge fan or word problems because I love writing ones that will elicit awesome drawings. I get a sad when I have to write ones like "Point A is the midpoint of BC and angle JKL is bisected by ray KM and WU is the perpendicular bisector of XY such that WU is the altitude of triangle WXY..." because those pictures just end up being shapes with a lot of letters on them. The good problems are ones like I put on a recent quiz. The gist is that Julian/Karla (obviously I always use student names and weirdly, the kids--even in high school--still LOVE it) is walking his/her pet spider/pig and I give dimensions about the height that Julian/Karla is holding the leash and how far the pet is in front of its owner. It's just a simple pythagorean theorem problem, but the pictures are the good part.

The pig in this first one looks so happy and carefree. Maybe because he is out for a lovely walk instead of taking a geometry quiz.

 

My favorite part of this one is that the pig is explaining all of the answer. I wonder whether the speech bubble was planned in advance or a last-minute add-on. Either way, brilliant.

 

Here, I can't figure out if this student named the pig because (1) she had too much time left and got bored, (2) she was killing time trying to figure out the problem, (3) she really needed to have a name for the pig in order to make the problem feel accessible, or (4) she knows more details about Karla's pets than the rest of us do (this student is one of Karla's good friends).

 

Not to judge students' artistic skills, but this is the least pig-like pig I saw on anyone's paper.

 

I think I have really gotten through to this student when I've stressed the importance of labeling everything you know about a picture. I'm so glad he labeled everything because I definitely would not have known which was the spider and which was Julian.

 

This is my favorite picture out of any of them. In case you can't tell (sorry, I took these with my camera phone as I was grading them), the spider-walker's t-shirt says, "Hi! I'm Julian."

 

And I'll conclude with a kid whose math skills are doing fine (he got the problem right, at least), but who could use a little work on his reading comprehension.