Absent.

I’m beginning to hate the word. I don’t care why you’re not here, I just wish you were.

Though I have only 13 students right now — 8 in calculus and 5 in pre-algebra seminar — I still face the problem of chronic, and sometimes acute, absenteeism. In fact I’ve got one case of each right now. I don’t know how teachers with more students keep everyone caught up.

It’s not just the keeping them caught up either. I worry about them when they miss too much school. I know they’re falling behind in other classes too. I miss them.

And I appreciate all the more the presence of my other students.

Here’s how we did it:

• I had each of my students (four today) write a blank table in their seminar journals* with time in increments of 10 seconds up to 120 seconds as the row labels and two columns, one for number of bounces during interval and one for cumulative number of bounces.
• The students took turns acting in one of four roles:
  • Ball bouncer — bounces tennis ball on ground from waist-high as many times as he can in two minutes.
  • Timer — calls “time” every ten seconds.
  • Counter — counts number of times ball hits ground, starting at 1 each time “time” is called.
  • Recorder — records number of bounces in his table for each interval.
• Then each student filled out his “Cumulative Number of Bounces” column by adding a running total of the bounces and made a graph of the results.
• I reviewed the process of finding an equation for a line using two points on the line (1. find the slope 2. plug in an x/y pair to find the y-intercept.)
• Then I had them pick two points from their line — any two points — and find an equation for the line between the two points.

What was good about it

This activity required a lot of focus of the participants, no matter which role they were assigned — and they mostly met the challenge. Some trials worked better than others just because certain students were better at certain tasks. But all of the trials were a rare case of the class working together productively to complete a task.

It was physically active and competitive — a plus for a group of four boys.

Because we had some problems during the “experiment” I got a chance to talk about what to do with outliers and missing data. I also pointed out areas on the graphs that suggested “something happened” — e.g., the bouncer dropped the ball for a few moments.

It theoretically offered the chance to think about what’s a reasonable result for an equation representing bouncing a ball for two minutes… but we didn’t actually discuss that, because the students were plenty challenged by just the basics of it. I would have liked to discuss and think about it more.

What wasn’t good

We didn’t have a decent discussion about whether it’s reasonable to pick two random points and find an equation from those. We didn’t really have any discussion about our results at all. Maybe tomorrow.

I could draw some different example graphs you might get from this experiment and ask what was happening in them: was the bouncer focused and fast? what does the slope mean here? Does it make sense to calculate an equation from just two points? How might you calculate a “line of best fit” from more than two points?

Also, the tennis balls were too tempting. They were used for juggling, for jostling the projector attached to the ceiling, and for tossing at other students. I think I may use them to ask students questions: throw a ball at them when I want them to answer.

Bottom line

Would definitely do this activity with a similar group of students again. I feel like each day I’m making infinitesimal steps with my seminar kids — whether it be getting them to really think about slope or just having them trust that I really do care whether they have fun and learn and that ideally they can do both at the same time.

Notes

* Seminar journals are composition books that I gave to each student at the beginning of this trimester. They do as much daily work in there as possible then I collect them and grade them. This keeps their work in one place and has proven easier for me than collecting individual pieces of paper. Also I have a record of what they did before and how they are improving.

My one female student was out, so I was left with four boys and as you might expect they spent some time torturing their Barbies before doing the experiment. One student approached it with unusually good attention and asked great questions. I have yet to develop any ability to lead a good discussion so I didn’t take advantage of that. Next year, perhaps.

Why was it good?

• It was physical — you had to use your hands, get up from your desk,  have the Barbie jump, attach the rubber bands, etc. Good for so-called kinesthetic learners though I’m not so sure I believe all that stuff about different modes of learning.
• It was a real-life experiment that gave rise to linear data. We’re studying linear functions this week and I like the chance to embed line graphs and slope and intercept calculations in a real-world context. (See What does the slope mean? for some related research.)
• It was goofy. The students looked at me like “you can’t be serious” when I pulled out the Barbies but they didn’t hesitate at all to do the experiment.
• It’s one of those things where I didn’t know which student would get most into it and I was surprised at the results. That’s one reason I keep trying lots of different approaches — it’s hard to know what one thing will spark an interest.

Before doing the experiment we watched a video of tree diving and I accidentally showed “Turkish bungee jumping,” which the students loved.

*Speaking of NCTM, I have been meaning to join… this is a reminder to myself to do that.

Right before winter break my Calc BC class did a short unit on parametric and polar equations. They did fine on the parametric stuff but thinking in polar coordinates doesn’t come naturally, and they stumbled on sketching polar curves and finding area enclosed by them. So I am reteaching it as we move into vector functions.

Yesterday we played Polar Pictionary, a game I designed to get them more fluent in polar coordinates. This would work for a pre-calculus class too.

Here’s how you do it:

1. Start by giving an example of a Pictionary idea “drawn” with polar equations. I “drew” a butterfly with four very simple equations: a four-leafed rose, an ellipse with major axis along the y-axis, and two straight lines for antennae (the butterfly above has some wing designs added that the students suggested). Ask students to sketch the curves and guess what they represent.
2. Each student gets a card telling them what they need to “draw” with polar coordinate equations.
3. They have ten minutes to come up with a set of equations and, if necessary, limits on the domains of those equations, that draw a picture of the item on their card.
4. Each student writes his or her equations on the white board and the other students try to guess, either by thinking in their mind of what it draws or by sketching the curves.
5. A student gets a point for guessing correctly and the student who made the equations gets a point too.

I let the students use calculators and Geometer’s Sketchpad when they were developing their equations but during the guessing phase they had to do everything by hand.

This was a great activity. Students asked questions that hadn’t come up before: “how do I draw a line in polar coordinates?” “how do I shift a polar graph?” “how do I make two short curves that look like antennae?” etc. They came up with ideas for representing their items that were really creative and very different from what I would have done. I’d like to do this every year and keep a gallery of drawings.

Twyla Tharp says in her book The Creative Habit:

Poems come in many forms, from sonnets to villanelles to pantoums and sestinas. Some forms confine the poet, others make him or her sing.

Does our school culture confine me or make me sing?

Tharp distinguishes between the sestina, “more of a parlor trick than a deeply felt poem” and the sonnet, whose “length and rhymes make it pleasing to the ear, and provide room for linguistic and thematic invention.”

She says:

Creating is all about playing and innovating within familiar forms. It’s natural to want to establish as many ground rules as possible about form before we get down to work, but you have to choose the form that’s not only appropriate for you but right for your particular idea.

I find myself wondering, is my school’s culture and administrative approach more sestina, confining in restrictive and arbitrary ways, or sonnet, releasing creativity by establishing rhyme and consistency and a beginning and end to my work?

For now it feels like a sonnet, though I chafe sometimes at the expectations and restrictions.

Are you wondering if teaching is creative anyway? I think it is — from making lesson plans to performing them (it is a performance and that is the part I really need to improve) to figuring out how to make meaning… teaching is an exercise in creation and maybe that’s why I love it so well.

[Thank you Merlin Mann for suggesting Tharp's book.]

When I start to think things like that, I remind myself that I should take a growth mindset with regard to my teaching, just like I try to instill a growth mindset into my students. It doesn’t matter if you get an F this trimester or if you were the worst, most boring, and least energetic teacher ever. Figure out what you need to do to improve. Check what other more proficient students/teachers do. Reflect on your results. Get better.

So here are some reflections on what seemed to work this past trimester with my algebra support class. Did they really work? I dunno — it’s not feasible to run a controlled experiment on my five students. But I know what engaged them and what seemed to promote improvement even if almost infinitesimal. And I know what was boring and disengaging to all of us.

What worked:

• Linear vs. exponential growth sticker activity — I had the students use stickers to explore the difference between linear growth and exponential during their unit on linear functions. Okay, they didn’t need to know about exponential growth; it’s not on the standards. But I want them to start realizing that the world isn’t made of nice linear processes even though people tend to think linearly. Population growth, compound interest, infectious disease — all these things require an understanding of exponential growth. Having to peel off 64 stickers and put them on a page vs. say, 8 stickers,  demonstrates how exponential growth gets crazy fast. And the kids like having their hands busy. I didn’t have to do anything to motivate them to put on the stickers. They just did it with zero complaints.
• Make-your-own tangrams — they’re starting geometry today and I wanted to get them in a geometric mood. So they did a paper folding/cutting activity in which they made their own tangram set. Then they explored the Pythagorean theorem with it. Again, it was good because it got their minds and hands engaged at the same time. My student who did worst on the trimester final made his tangram set the fastest and with the most accuracy — does he have some hidden geometro-spatial abilities I need to tap into? After we put out the squares to show the squared sides and hypotenuses of a right triangle one of the students yelled out, “I get it!” and her eyes were lit up like I’ve never seen.
• White board drills with gate problems — right before the final I drilled the kids hard on topics I knew would give them trouble on the exam. I told them that once they showed me they knew how to do a particular kind of problem they could work on their homework. One student pressed me for extra problems to make sure he had mastered them. It was like being in the calculus class — he genuinely wanted to learn. That’s where I want to get with these kids. I’m not starting from scratch: they come to class; they do their work; they want to succeed. Yet sometimes they need help finding that inner spark that drives them to really want to understand not just pass the class.
• M&M proportions — I don’t want to buy the kids off with sugary treats, but we did use M&Ms to calculate percentages and proportions and it’s an activity I’d definitely do again. They were so motivated to eat the candy that they jammed through the percentage calculations.
• Multiplication mad minutes — Most of us need help on our 12 times tables and my algebra students are no different. I saw them get steadily better at multiplication through the semester as we did weekly mad minutes focused on 8s, 9s, and 12s time tables. Next step I think is to do division because they could stand to improve their speed on that.

What didn’t work? A lot of things: letting them have unstructured time to work on homework, allowing disruptive students to derail the class, reteaching things in boring ways instead of hooking them up with new ways of experiencing math, moving slowly instead of quickly, generally following the last teacher’s recommendations instead of finding my own way with this group.

I want to write — I’d like to blog about my experiences teaching and more generally about education — but I think I’d rather do it at another site. This has been a great experience for me here, but it was really about getting up to speed on the world of web technology after being away from it for a few years. I did that, and I realized I want to deal with web technology only as a sideline to some other grander purpose. I love teaching; I love learning; I love how they feed upon each other in a virtual cycle of knowledge and (I hope) wisdom. I want to know more about education. I want to write about charter schools, online learning, and remixing educational content. I want to write about economics too. I want to write about mathematical models in the social sciences, because those models and the insights they give into the human condition are why I’m fascinated with math. I want to write about how calculus suggests that the happiness research on kids is wrong.

I want to write about how my 12-year-old son wanted to be a writer when I was writing a book and now thinks he might want to be a math teacher. He’s excited by my TI-89 Titanium calculator (so am I). And his math teacher this year is awesome. I want to be like her.

I want to write about how in a week we’re getting a new dog, and it makes me miss Sally so much.

I want to start tweeting again too but it seems weird to start out of nowhere just like it was weird to stop out of nowhere. And doubly weird because I stopped when Sally was diagnosed with cancer and now I’m going to start just as we get a new dog?

I want to write about what happened last January and how I fixed myself and why I never want to go through that again but I fear it’s inevitable. But I don’t have enough courage (or maybe I should say foolishness) to write about that.

Maybe in January a new January I will find myself in a place where I can connect again online.