General Ideas for the Classroom

Having your class create their own museum guide

It wasn’t my idea; I won’t take credit for it. But honest, I heard about it so long ago — maybe when I wasn’t even a teacher, even! — that I can’t give credit. But I stole it and modified it and used it.

We had to plan and execute a field trip for some location in New York City in my teacher boot camp. My group chose, after a failed attempt to quickly plan something around social action and conservation in Central Park, to go to the Brooklyn Museum for an pretend 11th or 12th grade English class. (But it could be exported to a history or art history class too.)

The Background: The class has been in the middle of a poetry unit, and haslearned to analyze poetry through a three step process. Step 1 is observational and literal, to note things about a poem without interpretation (e.g. the poem has a rhyme scheme, the poem uses a lot of ‘sh’ sounds, the poem is about an old tree). Step 2 is interpretive, to note things about a poem that are symbolic, metaphorical, emotional, thematic, etc (e.g. the poem seems to imply that the solid tree is like mankind, the ‘sh’ sounds enhance the softness of the poem). Step 3 is context, what is the purpose of the poem, why was it created, what is the larger set of debates that it engages in.

The trip to the museum is to show students that they can apply this same analytic method to art. So we’re assuming, for the sake of the fake field trip we planned, that students had been exposed to applying it to art, by us modeling it for them and then them trying it out.

The Trip: The gist of the trip goes like this. Students go to the museum and each gets an hour to just wander around looking for three or four pieces that speak to them in some way. It could be that it angered them, bored them, was generally pleasurable for them, etc. Then they meet a teacher stationed somewhere in the museum who then tells them to pick two objects to analyze. (They chose 3-4 pieces because we don’t want two students doing the same piece — first come first serve!) They have a worksheet which takes them through doing the three-step process for both objects which they have an another hour to fill out. Finally, they get extra time to wander about and enjoy the rest of the museum.

Back at School: Back at school, students learn how to do research on their artist and on their art piece. They gather some information which can help them with understanding Step 3 (context). When they are done, and they have fully analyzed the piece, they are charged with creating two podcasts for a museum goer — explaining their two pieces. They can be creative — it doesn’t have to be the dry, boring explanation of some curator. It could be funny, or a dialogue, or anything! But it should express the student’s reaction and analytic interpretation of the piece.

Finally, the teacher puts all the podcasts together and creates a museum guide for others to listen to!

It’s a big project, with lots of work for the teacher, but the end result is hopefully something that the kids will go back to the museum to listen to their friends, and that their parents will be excited to use.

Note: Of course this idea of podcasting can be used for any walking tour, not just a museum. So students could create a walking tour of a neighborhood, talking about its history, or construction projects going on, or issues and activism.

Videotaping your class

In teacher bootcamp yesterday, we each had to teach a 15 minute section of a 40 minute lesson to our peers. And did I forget to mention that there was a giant, professional videocamera following our every movement?

I haven’t watched the videotape yet. Even though I’m terrified, I think there is so much value in an exercise like this. Because even though it may be hard, and you may not want to see yourself, I know that when I do, I’ll see my teaching in a new light.

Already from my verbal and written critiques of the lesson, I have been told something that I never knew — that no student ever told me in any of the feedback I ask from them. That sometimes (but not all the time) I speak too fast. It wasn’t nervousness or fear of the video camera. I felt like I was conducting the lesson exactly as if I were in my school giving the lesson. (Once I get in front of a class, no matter who or what is observing me, I forget about everything but the math lesson.) So now I know.

I wonder what gems I’ll find from the tape when I watch it… if I can get past the horror of hearing my own recorded voice.

I hate protocols

In my school, lots of meetings have “protocols.” What, you say? Protocols?

Protocols are a highly organized, structured way to accomplish tasks which involve lots of people.

My school frequently uses two.

One protocol my school loves to do in various meetings is called “Critical Friends Group.” One person spends 5 minutes presenting an assignment (or shares some of their students’ work and the assignment that led to that work) to a group of 8-15 other teachers. Then everyone thinks about the assignment silently, with reference to one or two key questions (e.g. “what kinds of thinking skills would a student need to complete this task successfully?”). One by one, each teacher asks the presenter a question about the assignment — something like “how many days did you give students to work on it?” and “did you have a grading rubric?” Finally, after the initial questions are answered, each person makes an analytic comment about the project — with the presenter just listening. If there is enough time, everyone can make a second comment. Finally, the presenter responds to as many of the comments as he or she wants. There is no interrupting or discussion.

That’s an example of a protocol. It’s a highly structured method to elicit specific feedback on a particular project or assignment.

Another example of a protocol is something called a “chalk talk.” There are one to four questions or statements on various boards around the room. Everyone gets a marker and writes their comments down on each of the boards. Then everyone makes a second pass and writes down comments on the already written comments. No one is allowed to speak — this is done in total silence.

And I tell you, when I first heard about protocols, I thought: hey, an efficient way to get very specific information back from a group of people. The concept of the protocol is good.

I’ll even admit that the information gathered from some of the protocols are good.

But I don’t care. I hate them. And here’s a list of the reasons why:

1. It’s infantalizing. I really feel like the formal procedures treats its participants like young children the way they’re set up. It’s hard feeling to explain. Maybe it’s the markers that are put out to write with, or the too-rigid environment that’s set up. But I don’t feel like a capable, intelligent adult.

2. I don’t feel like my voice is being heard. With the “chalk talk” for example, I often feel very strongly about some of the questions asked. They will ask, for example, “what can we do for professional development next year?” and I have a lot of very specific ideas. I am given only 5 or so minutes to write it down in marker (or pen if I’m lucky) — and I usually haven’t thought about the question beforehand, so I feel like my thoughts aren’t yet fully formed. My ideas are now ill-formed, poorly-written, and scrawled on a giant sheet of paper with about fifty or sixty other comments. The worst part is that people feel obligated to write — so something I’m passionate about, something that I care deeply about, is often sitting next to statements written by people who write because they have to. They don’t care (I’ve talked to them; I know) and they wouldn’t put anything down if they could. But they do and now my contribution is floating in a massive sea of detritus. It forces fake engagement. (Plus, let’s be honest, I doubt that anyone seriously looks at these pages. If anything, they glance at them, take a few notes, and make a memo.)

3. It stifles dialogue. And actually, I think that’s what they’re designed to do. They are structured to have a very specific goal. So, for example, the Critical Friends Group protocol will engage with one or two specific questions. And the “discussion” is centered around them. But the problem is that there is no “discussion” really. Everyone gets to speak while everyone else is silent. Only the presenter gets to respond, and then only to a few people. It’s a bunch of sound bytes, with serious discussions about teaching ripe for the having, yet never had.

4. It doesn’t account for the individual being smart. Critical Friends, for example, is used to help a teacher improve an assignment. However, here’s my issue. Let’s say you do an assignment and it doesn’t go so well. You do Critical Friends, making, say, 8 people spend 50 minutes analyzing your assignment. You improve the assignment. Great. But here’s where my problem is.

If you had initially critically thought about your assignment and come up with ways to improve it the following year, I’d say that chances are, you’d come up with some pretty insightful ideas. And then you do Critical Friends, and you get, say, a few more good ideas that aren’t already on your list. Is it worth it? You’ve spent 50 minutes of 8 other people’s time to get a few different ideas/perspectives. But I contend that having a few informal conversations with other teachers about your assignment would have given you those few additional ideas/perspectives that you hadn’t thought of. In a cost-benefit analysis, it just doesn’t seem worth it. You can get the same result, I’m guessing, without spending all this time.

5. I get the feeling that it’s a safety net for meeting leaders who don’t know how to lead a meeting. Certainly this is not universally true. But I think I’ve become so jaded that I hear this advertisment: “Don’t know what to do with this meeting? Don’t have a way to get everyone involved and engaged? Make everyone miserable with a protocol! Force them to think, write, and ‘discuss’ so you can say you are engaging everyone, without truly engaging anyone!”

Of course, I go on this diatribe, knowing full well that leading a meeting is hard work and I don’t have a lot of answers. You have a lot of different people with a lot of different ideas and strong opinions that you need to rally together. You need to make sure everyone’s voice gets heard. You have to strive to engage your audience, without making them resent spending their time with you. You have to come to some sort of closure at the end. And that’s hard work. Moreover, there are a lot of people at my school who say they find immense value in them. (Though I wonder how much true take-away value these meetings have had; has anyone come out knowing how to advise their advisees or teach their students better? Probably, but I’m betting the number is few, and that there are a heck of a lot more people who feel their time was completely wasted.)

And guess what? That’s teaching. Leading a meeting requires almost all the skills that a good teacher must possess. And I often complain about the meeting formats at my school. But at the same time, I am always wondering: how could I have led the meeting differently? [1]

The answers are few and far between, but I know they exist. I’ve come up with a few ideas — some which involve straight up, good presentation. I’m okay not “dialoguing” and just getting the information I need. Also, I’m okay with an informal small group dialogue led by a facilitator which is allowed to veer in different directions of conversation, depending on the interests of the participants.

Does anyone enjoy any of the meetings at their school? Are any of them not a waste of time, as determined by a cost-benefit analysis (how much take-away value have I gotten versus how much time I’ve spent getting that take-away value?).

The catalyst for this post after the fold.

[1] The answer to that would probably partially be the answer to how to keep a class of 10th and 11th graders with varying ability levels and interests engaged in math class. It’s not easy (at least not for me), but I believe it’s possible, and that’s what I striving for. It takes a lot of preparation beforehand. And I only really succeed every so often.

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Senior Letters Made of Sap

Everyone is bringing food, and we’re going to play Apples-to-Apples. Monday will be the first time my calculus class will be doing something almost-totally non-mathematical (except for the one time we watched “Numbers” before winter break). I’m convincing myself that this is okay because I have the deluxe edition of Apples-to-Apples with blank cards; we’re going to be throwing in some calculus terms.

I work them hard, and they’ve met the challenge. So we’re celebrating on Monday, and we’re going to hear presentations of everyone’s calculus projects on Tuesday and Wednesday. And then: it’s over.
I didn’t think I’d be maudlin, but I am pretty much all sap at this point. I decided to write a letter to each of my senior students thanking them. (Well, ahem, actually I wrote one letter to the whole class.)

We often expect to hear thanks for our work. But as you well know, teaching goes both ways, and I wanted to thank my students for their work. Not just for their mathematical work in class and at home, but for their positive attitude and humorous good-nature as we fought tooth-and-nail against the beautiful beast that is calculus. Being a new to a school, and being a new teacher, was made so much easier because of them.

In the envelope with that letter, I’m including two additional things.

  1. Their first day’s homework assignment — this form which they filled out (stolen from dy/dan).
  2. A juxtaposition of two quotations about Nature and Wonder. Many of my students have their grillzs all up in the humanities. I am not trying to convince them to be mathematicians and scientists. But I want them to see that the two are not mutually exclusive. So I will be giving them the poem and quotation below the cut.

I wouldn’t let them get away with having no homework. So I’m leaving them with one final homework assignment, playing on the theme of “the letter”: write a 1-page letter to yourself a year ago, giving your “old” self advice on how to succeed in this course.

After the next three days, they’re gone.

Sigh.

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True or False: Smartboards are an Expensive Distraction

On the blog On The Tenure Track, Benjamin Baxter asks in a recent post:

Why the hell would you want a SmartBoard in a classroom? What ways could you use a SmartBoard in ways that don’t make it an expensive distraction?

But, in fact, I agree with most of what Baxter says about technology:

Who cares about LCD projectors if students have just as much trouble remembering how the Balkan Wars and The Great War are related, or have just as much trouble remembering why the powderkeg that was Europe at the turn of the 20th century is important historically, and in our own lives?

Technology adds many desirable things, but these benefits will only be felt once it’s in good hands. That should be our priority

I certainly am not on the “let’s explore new technologies in the classroom and then figure out what we’re doing with them” cart-before-the-horse bandwagon. I also don’t think that foisting technology on teachers works well. (You shouldn’t force a teacher who has been successfully teaching with a chalkboard and worksheets to switch to SmartBoard just “because it’s technology.” That’s doing students and the teacher a grave disservice.)

My opinion — surely held and written by others — is to support teachers who want to pick up technology and figure out an effective way to use it. Then other teachers get others on board because they want to be, because they’re inspired by the possibilities of applying it to their own teaching, because they see how it can enhance their students’ understanding. [1] That’s the way to have a technological culture shift at a school. Don’t force, do inspire.

When I say effective above, I will be explicit: it will have to enhance student understanding in some way. (We get the horse before the cart.) So students would have to come away knowing how the Balkan Wars and the Great War are related better than if they had learned it without the technology.

Now onto to my paean to the Smartboard in my classroom, at my school. (Where every classroom has a SmartBoard, and every student has a laptop.)

At worst, the Smartboard in my classroom is a replacement for a whiteboard, but a whiteboard where the markers are multicolored and never stolen or dry. At best, the smartboard provides me the opportunity to create better lesson plans by making me think more carefully about flow, allows me to have a design aesthetic and put up graphics up that I never would be able to draw by hand, gives me a lot of time in class where my back isn’t to my students writing a problem or definition down, and provides an archive of notes for students who need that extra help at home.

I’ll elaborate. (I’ve been anticipating counterarguments to each of these [how one could achieve these same effects with an overhead projector, scanner, more experience as a teacher, etc.], but in the spirit of being non-defensive, I’ll just write.)

When I started designing lesson plans before SmartBoard, I did an okay job. I had the general topic I wanted to present, some sample problems, and I would go in and talk. But using the SmartBoard did something great for my lesson planning skills: it got me to think like a student. A good presentation won’t have 18 ideas on a slide. In my math class, I try to keep it limited to 1 math idea per screen. But being forced to break down every idea into it’s most basic components led me to think in depth about each step of what I was showing them. (And doing this let me realize: oh, here’s where a student will make a mistake. And then I’ll make a big text slide saying: DON’T DO THIS!) The flow and thoughtfulness of my lessons has improved, big time.

In my math classes, also, we do a lot of graphing. Having SmartBoard, with the ability to have blank graph paper up there, or to show a virtual TI-83+ calculator, helps a bunch. Also, I like to throw up some random images to keep things fresh and keep their attention piqued. So they’ll see a picture of Sanjaya (from American Idol) every so often. A 5 second Sanjaya distraction will get them back to the task at hand. Continuing on with the idea of the visual aspect of it: if the slides are designed right, the student can be presented with the information in a way that’s infinitely more effective than if I were up there writing on the whiteboard.

Because of the SmartBoard, I’m spending a lot less time writing at the board. I’ll often throw an easy problem up there and have students solve it as a quick way for me to see if they’re getting it. I don’t need to spend time drawing a graph or writing out an equation.

Lastly, the ability to save SmartBoard files is a godsend in terms of archiving. I save a blank copy of my lesson, for me to draw from next year. But I also post a copy of the SmartBoard that we marked up in class for the students to access online. This is useful for kids who are absent, obviously. But it’s also useful for kids who didn’t quite get it all the first time around, or who missed something, or who spaced out. They just open the pdf and look at the steps we went through. It’s a good resource for me. In one of my classes, I have 16 students. About 5-6 of them look at the smartboard each night. (Often times not the same 5-6.)

How do I know it’s working for my students? I asked them for an anonymous narrative evaluation about my teaching at the end of the first semester. I wanted to know about my teaching, but I also asked them to write a paragraph about SmartBoard. I honestly wanted to know, because I spend a lot of time creating the SmartBoard presentations for class, and if my students weren’t getting a lot out of it, I would have stopped using it and cut my lesson planning time in half. (I remember thinking that if they weren’t positively glowing about SmartBoard, if they were “it’s okay,” I would have stopped.) But my students did have glowing things to say about it.

So yeah, I’ll be the first to praise SmartBoard. I’ll also be the first to admit that if I didn’t have SmartBoard handed to me on a silver platter at my school, I probably would have found ways to do things just as well as I do them now. But when it comes down to it, SmartBoard is helping me become a better teacher, and it’s helped my students with the material. So for me it’s definitely not an “expensive distraction.”

PDFs of some of my Algebra II Smartboards here:

  1. population-growth
  2. rational-functions
  3. rational-inequalities
  4. direct-and-inverse-variation
  5. interest
  6. inverse-functions
  7. logarithms
  8. logarithm-rules
  9. log-and-exponent-equations
  10. logarithmic-scale-history-of-life
  11. trig-opener-and-refresher
  12. trig-on-the-coordinate-plane
  13. radians-again
  14. linear-and-angular-velocity

[1] Recently I presented a project I had my Algebra II students work on (to be blogged about in a future post) to the other tenth grade advisers. A few came up to me afterwards and told me that they were really excited by the project and saw how it could fit in with their curricula — whether it be art or English — with some adaptation.

UPDATE: Turned off comments. For some reason this page was getting a lot of spam comments, everyday. Yeesh.

Students teaching students

In the past few weeks in my seventh grade pre-algebra class, we’ve been working on some hard problems involving inscribing circles in squares and squares in circles and, sometimes for good measure, playing around with equilateral triangles too. Radicals abound. And for the most part, I see them getting it.

But recently (for a number of reasons) I’m being a “teacher centered” teacher. I’m at the whiteboard explaining things or doing problems. I call on them from the whiteboard. I let the kids work and I walk around and check to see how they’re doing. But their eyes are always on me or their work [1]. Partly it’s because I know it works. And it doesn’t take a lot of time. (These kids pick up what we’re doing quite quickly… you can actually see their initial struggle, and their breakthrough… sometimes you more than see it… you hear it… “OHHHHHHHHHHH, Mr. Shah! It’s sooooo simple!”) [2]

But today I had an extra 10 minutes and so I had a student come up and take over the classroom. She was presenting the solution to a problem, and I gave her total control. She could call on students, or be at the board, or do whatever she needed to to explain the solution to the class. And with great poise, she strode up there and started asking good questions (“How do we know what that side length is?” “What’s the area of a circle?”) and adroitly led her classmates through the solution. The other students were into it: their hands waved in the air, eager to answer her, as they are eager to answer me. [3]

The cherry on top of the sundae? Once she finished, about 75% of the kids had their hands up wanting to present the next problem. They want to be teacher. Which made me happy to be their teacher. I’m sad I’m not going to be teaching seventh grade next year.

[1] Okay, that’s not entirely true. They are a collaborative class; they work with each other answering questions, running ideas of each other, and comparing answers to see if they’re on the right track.

[2] Of course, on the other — less happy — side, you’ll get to a topic where a few kids will proclaim their hatred for the subject at hand, at which case I feign (do I feign? or is it real?) pain that someone could say something so awful about something I’ve devoted my life to, and how I want to curl up in a corner and cry.

[3] I noticed that her teaching style was a lot like mine, which means that I’m rubbing off on them.

Birthday Polynomials

A few days ago, JD2718 wrote a post about “Birthday Triangles” — having students create three coordinates out of their birthdate and then analyzing the triangle that these coordinates make.

Even though it’s just a bit of fun, and you could have students work with any sets of points you give them, there is something great to be said for students creating their own problems that they feel ownership of. As JD2718 writes:

Best evidence, (and mind this, please) almost every class, when they first plot their own birthday triangle, there is one or two sad looking kiddies (it’s not come to tears, but I’ve seen the quivering lip) who thinks their own triangle is ugly. “Nooo” I say “Yours is obtuuuse. Does anyone else have an obtuse triangle that looks as nice as Anna’s?” (it’s usually a girl)

I thought that this idea could work in calculus too, creating “Birthday Polynomials.” My first thought was exactly JD2718’s: take the three birthday coordinates and find a quadratic that would fit them. But that would be a precalc assignment. (With bonus question: With what birthdays could you not create a quadratic?)

But I wanted more. I wanted to come up with something awesome. Something calculus. Something that would knock my students’ socks off. I initially thought something like this… if I was born on April 21, 1978, the birthday polynomial could look like: f(x)=4x^3+21x^2+19x+78 [1].And questions could be: where are the local maxima and minima? where is it concave up and concave down? where is it increasing and decreasing? And of course you could do things with integration too…

But there’s something unsatisfying about that type of question. It’s nice, but I want to wow! my students. I want to knock their socks off. Show them something elegant and unexpected. So I thought…

I want them to create a polynomial using their birthdate which would have an inflection point that was their age.

I was planning on using this amazing property [if there’s a cubic equation that hits the x-axis three times, then there’s a point of inflection, and it will be the average of these three x-intercepts] they would have to discover.

So if my birthday were January 25, 1980 (it is not), and we evaluated this polynomial on March 30, 1980 (after I celebrated my birthday), a birthday polynomial might look like this:

f(x)=(x+1980*3)(x-2008*3)(x)+1x+25.

f(x)=(x+year born*3)(x-2008*3)(x)+month born*x + date born

[Note that the month and date play no role when finding the point of inflection… they are red herrings.]

But there are many annoying problems with this… First of all, that 3 is annoying. Second of all, that 2008 gives some of the fun away. I guess multiplying it by 3 and writing it like 6024 would help disguise it, but not much. Third of all, if I worked the problem on January 5th (or anytime in the year before January 25th), it would get my age wrong by a year. Fourth of all, it’s not elegant.

I’ve spent a little time tweeking it, and thinking of ways to rework it… but I haven’t anything elegant or clever yet. For now, it’s going to have to go on the backburner. Spring break is over and school is starting tomorrow and I have too much on my plate.

I’ll post an actual, good, interesting way to come up with a birthday polynomial with some amazing property (that somehow magically spews out your age, perhaps) when I have time…

[1] Of course I had to do a google search on “birthday polynomial” to make sure I wasn’t reinventing the wheel. One calculus teacher in Texas did something similar.