Monthly Archives: August 2009

So I’m just going to throw it out there.

Sometimes blogging makes me feel like a fraud.

Here’s why. I’m not an amazing teacher. Most of my lesson plans aren’t exciting. I have lots of ideas but often no follow through to implement them. I plan almost 100% of my lessons the day before I teach them. I don’t use group work effectively. I rarely teach problem solving skills and don’t do honest investigation in anything other than my multivariable calculus class. I keep a teacher-centered classroom. My kids all have laptops and I never use them in class. I pretty much follow the same teaching pattern every day (warm up, homework questions, lecture, stop to practice, lecture, stop to practice). I’m afraid to give up control of the classroom to my kids.

Which are — frankly — all things I’m totally okay with, at this point. Some things I don’t want or care to change. Other things I wish I were farther along in my own personal development. And there are a number of things I know I do really well too. But there you are. That’s where I am at the moment. I’m pretty good, but I’m not amazing. (My own personal assessment, anyway.)

But here’s where feeling like a fraud comes in. Did you really think I led a teacher-centered class every day? Would you have expected me to describe myself as I did above? In other words, if you came to watch me teach, would you see what you expected?

I’m 100% certain (bets, anyone?) that the answer is no.

Two years ago, 328 posts ago, when I started blogging, I was blogging for me alone. But it struck me recently that in the past two years, I had inadvertently been constructing this online persona, post by post. Like: my online blog self is one person and my real life self another? Is it just me? Prolly.

But it’s bothering me that this online persona is so incomplete, possibly a idealized version of what kind of teacher I am in real life.

I honestly do write for me. This place has always been for me, but I know that as opposed to when I first started and I was my only reader, there are now like 5-10 people (oh! kind souls!) who read this blog in addition to me and my super awesome teacher sister. I don’t want to be a fraud to you as I continue to write here. So for you 5-10 people, in case I had somehow drawn myself into some sort of caricature teacher costume, let me just put it out there straight:

I’ve had two years in the classroom. I’m okay at what I do. I love what I strive to do.

At the end of the calendar year we make (and quickly break) new year’s resolutions. But as teachers, I thought it might be fun to make — at the end of the summer and the end of the academic calendar — some resolutions. Okay, geez guys, maybe “fun” isn’t the right word. But inspirational maybe? Okay, okay, maybe just a lark.

In order for them to be effective, I’m throwing down three simple rules.

• You should come up with at least 1 but at most 3 resolutions. This is so you don’t get overwhelmed.
• They have to be easily doable and sustainable throughout the year. This is so you don’t get overwhelmed.
• You need to publicly announce them – whether it be on your blog, on twitter, on the comments here. This is so you have some external accountability.

I will make mine here:

1. I read on someone’s blog (forgive me for not searching to find and link to it) an idea to keep students engaged. If students point out mistakes that I make, I will visibly tally them somewhere in the room. The student who caught the mistake will hopefully feel good about themselves and students will hopefully always be second guessing me. And after 30 mistakes are pointed out, the students get to have a “candy day” or something where I bring a little treat for them. I will do this in my Algebra 2 and Calculus classes.

2. I will do this random acts of kindness thank you card activity again in my Algebra 2 and Calculus classes.

3. I will decorate the classroom that I will be teaching 3 of my 4 classes in so it will be colorful and kitchy, but not elementary school-esque. I will have this done by… no, not the first day of school… by the end of the first quarter.

Signed,

UPDATE: I am going to have to nix goal 3. Even though one day I would like to do this, apparently this year my rooms have been switched beyond recognition, so instead of teaching in 2 rooms, I’m teaching all 4 classes in 4 different rooms. I will be running around the school like a chicken with my head cut off. And although I’d like to decorate all 4 rooms, I honestly don’t have the energy to create and maintain something in 4 different rooms, and I won’t have “priority” in these rooms because other teachers will probably be teaching in them more and want to do something.

I’m really proud of this graphic design. Click on it and see it in full size glory!

I wasn’t pleased with any of the planners out there, because they didn’t take in to account the strange and rotating schedule we use. So I’m going to get 40 or so of these pages professionally bound at lulu.com or some similar self-publishing site.

So I have a awesome idea (toot toot)[1], but if I know me when the school year starts, I won’t actually follow through on it. But maybe someone out there in the great Internet cosmos will follow through on it.

Kids like Pizazz sheets. I have a bunch of them for calculus. There is a great payoff because when the kids solve the worksheets,  solutions to the world’s corniest riddles are revealed. It is a self-checking homework sheet, because if students mess up, the answer to the joke is garbled.

My idea is to make my own Pizazz worksheet, but the solution will be… well, lemme just whip a sample one up.

Of course this can be done with vimeo or even any url shortner. I had at one point a grand ambition to make a giant internet web puzzle for my students, that we’d spend the year trying to solve. Each unit brings us another clue, which brings us to another page… But you know, grand ambitions get foiled at every turn, by my own laziness and the exigencies of life as a teacher.

And no, I won’t give you the answer to the puzzle. Figure it out!

[1] That’s me tooting my own horn.

In my last extended post, I wrote about how I was modifying our Algebra 2 curriculum. In this post, I’m going to briefly outline my ideas for my non-AP calculus course. The course as of right now is only decent. I haven’t put in the really huge amount of time and energy that I need to, so that the course is super fly. Unfortunately, this summer I won’t be able to do that either. I’m just incrementally improving the course (hopefully), instead of doing a wholesale rewriting. At this stage, I’m still okay with that.

So what changes will we see in this upcoming year? There are only two major ones.

First, we’ve finally given up Anton — that huge, dense textbook which is inappropriate for high school students and college students alike. I did a serious looking at a number of other books last year, but decided that all roads led back to Rogawski. The best part is that with Rogawski, there is something called “CalcPortal” which students are going to subscribe to. They will get access to an e-book — which is the textbook, but with interactive applets, and other goodies — but also I will be able to use WebAssign for online homework.

Yes, that’s right ladies and gentlemen, I will be using online homework at least once a week. It will be graded for correctness, instead of just completion, and will provide immediate feedback for students to know what they get and what they don’t get!

(My fingers are crossed that setting up CalcPortal and administering this online homework will be easy.)

Second, I am going to finally address head on the problem I’ve had with my calculus students for the past two years: they can’t do algebra. So I’ve made a list of all the algebra skills that students need for each unit. Will students need to know their 30-60-90 triangles? Holes of rational functions? Vertical asymptotes? Instead of doing over a month of precalculus review at the beginning of the year, at the beginning of each unit, I am going to put my students through an algebra boot camp which covers only the algebra skills needed for that unit. They will be tested on these skills. Then we’ll transition to calculus, and use these skills to solve problems.

What I’m hoping will come from this is an ability to do serious calculus work, while recognizing that calculus ideas themselves aren’t really difficult. In fact, if you can get past the notation and the algebra anxiety, calculus is actually pretty simple.

And that’s it — the major changes for my calculus class.

Below are working drafts of my course expectations for next year. Most things — in terms of wording and text — haven’t changed, although the grading breakdowns have. In case it wasn’t glaringly obvious, I’m all about having super clear expectations for my students. Anyway, you can see that aspect of my teaching come through in these.

Algebra II Course Expectations, 2009-2010

Calculus, Course Expectations, 2009-2010

Multivariable Calculus, Course Expectations, 2009-2010

Feel free to steal anything, if you like anything.

So factoring is super useful, yes. But at the Exeter Conference, one of the keynote speakers was making an impassioned, clarion call for CAS in the classroom and threw up an image. It was of which quadratics are actually factorable, and which aren’t. I tried to make my own 15 minute version of that to show you below (where and are non-negative, just because I got lazy). Apologies if there are any mistakes.

This image struck me so hard I can’t even tell you. Because although we teach the quadratic formula, in reality, most of our assessments which come after the quadratics unit give factorable quadratics. But in one powerful image, we are reminded that most quadratics are not factorable (at least, over the rationals). And we all know why we give factorable quadratics all the time — and it’s nothing to be ashamed of. We don’t want to have students spend all their time using the quadratic formula (and possibly generating incorrect answers) when we’re trying to teach an unrelated skill.

Still, the implicit lesson we’ve taught our students, by always giving nice, factorable quadratics is that most things are factorable. I mean, how many times have you been asked “is there a mistake in this question?” when you’ve given students a non-factorable quadratic on a test not on the quadratic unit? I thought so.

So next year I vow to show my students this chart, and remind them that most things in this amazing universe are NOT factorable. Heck, most quadratics that come up in engineering won’t even have integer coefficients, I will say, while showing ‘em a picture of a falling cow and the equation governing its vertical motion in metric units. And that I tend to give more factorable quadratics than unfactorable quadratics because I want to save them computing time, not for any other reason.

At the beginning of the summer, I went to a conference at Exeter, and vowed to blog about some of the things I learned from it. Which I haven’t made good on, yet. There were a few gems, and I thought I’d write about ‘em briefly in a series on mini-posts.

The first is a simple way to get kids to think about the meaning of a derivative or an integral conceptually, before they’ve formally been introduced to it. It’s a  Gedankenexperiment (thought experiment) and the presenter said they actually do it on parent visitation day, so the parents can think too.

You’re in a car with three things: a speedometer, an odometer, and a clock. Everything is going along dandy, until suddenly, your speedometer breaks. Can you tell how fast you’re going? You don’t want to get pulled over by the cops, after all.

That’s it. Can you imagine how fun that conversation would be to listen to, as a proverbial teacher-fly on the wall? And then to get to lead that discussion? Obviously, most students are going to talk about the problem as if you are going at a constant speed. Getting them out of that mindset will be awesome.

Of course, the natural second question is what happens if not the speedometer, but the odometer, breaks. Can you tell how far you’ve gone?

I dig this thought experiment. I mean, it’s so simple I don’t know why I hadn’t thought of doing it to motivate our work. Heck, you can have students talk in groups and present their ideas. Good stuff.

On Twitter, in the last day or two, teachers are returning to their schools for the requisite start-of-the-year-teacher-meetings. I have three weeks before that happens (phew), and I’m now ready to buckle down and set my sights on the start of the year. I found out officially what I’m teaching for next year, and it’s the same as what I taught this year.

1 section of Algebra II; 2 sections of non-AP Calculus; 1 section of Multivariable Calculus

My goals for Algebra II and Calculus are ambitious [1], so tonight I’ll briefly outline just one of them: Algebra II.

Algebra II: The History

For those who have followed my blog from the beginning, you’ll know two years ago when I started teaching Algebra II, the curriculum was kind of insane. We were doing so much — rational functions and the rational root theorem, a heck of a lot of trigonometry, and who knows what else — that the kids were simply following the motions. It was too much. Plus the textbook was written at way too high a level for where our kids were at. With the entrance of a new department head, we reviewed the curriculum and recognized that were were duplicating half of what students covered in precalculus.

So last year we took a hacksaw to the curriculum and asked what our kids needed to know, what they were going to see in precalculus, what was crucial and what was extra ballast. There was blood, lots and lots of squirting blood from every section of the curriculum. Nothing was safe! But out of the massacre, we came up with what I think was a tight curriculum — one that was paced well, one that allowed our kids to really understand ideas instead of procedures. The only regret I have from this year’s curriculum is that we required our kids to buy the old textbook, since we barely referred or worked out of it. (I work at an independent school, where the students purchase their own textbook.) I created and/or provided most everything we did.

Algebra II: The Future

Next year, we’re going to take this course to the next level. There are three ways we’re going to try to do this.

1. We have a new textbook (Holt, Algebra 2), which serves all my anticipated needs. The students can buy a hardcopy or an e-book, which is a nice option for them. (The e-book is much cheaper too! I think $15.) The best part of the book, though, is the online homework help. Check, for a moment, the homework help for Chapter 3, Lesson 1 (click the image below):

Wow – right? The videos! The text! Clear, amazing. And the problems aren’t the exact problems from the book, but almost the same problems. So students are truly getting guided practice, and not simply given the answers.

I’m going to assign only around 10-15 homework problems a night, but I’m going to expect absolute perfection, because of this additional resource which students can use to target their own misunderstandings.

(2) To emphasize mathematical communication, we’re going to institute a class blog. Mathematical communication was one of my goals last year, and I tried to include at least one “explain…” on every assessment. However, I think we need to practice more frequently. Inspired by the likes of David Cox and Darren Kuropatwa, and blog posts like Jackie Ballarini’s, I’ve convinced myself that this could be the solution.

To be clear, I’m not envisioning this really expansive web-hub for the class. It’s going to be very limited. I want student scribes (individual or in pairs) to record what we did in class each day. Record and explain. That’s all. I don’t expect and won’t require the rest of the class to read it — though they may want to as a quick review before an assessment. Honestly, I could very well ask for the daily notes to be written on paper and turned in. The online aspect is simply to make it easier for me to keep track of all these notes. Also, I want to teach my students that they can write equations and create graphs with their computer! (We’re a 1-1 laptop school, and as of last year, I learned that even my multivariable calculus kids were typing x^3 in MS Word instead of learning they had a built-in equation editor!) Details on how this is going to be rolled out will be forthcoming… like, um, when I come up with them.

(3) Homework… homework, homework, homework. I talked with the other Algebra 2 teacher, and we’ve decided — after reading over the awesome and extensive homework survey results — to really choose our homework carefully and limit the number of problems when they are coming out of the book. We had a long-ish talk about creating different “levels” of homework like some of the respondants recommended, but when push came to shove, we decided that it made a lot more sense in an accelerated class, which our class is not. So, for now, we’re assigning easy and medium level problems and expecting homework perfection on them.

However, one thing we’ve noticed is the absolute MESS that our students make of their class notes and homework. Although they are sophomores and juniors, their ability to take class notes, show clear and organized work on problems, and keep all their work together in one place, is virtually nonexistant.

Okay, okay, not for all of ‘em, but a lot of students have never learned the skills of being organize in math. So the other math teacher and I are going to require each student to have a 3″ binder (kept in their lockers, or in the classroom) and a folder. When we’re done with a unit, students will — in class — place and organize their homework and notes and assessments in this binder.

Here’s the kicker. The student’s homework grade is going to be divided into two parts: aperiodic daily check of homework (walking around the classroom and giving students a 0-3 score on their homework) and a binder check. The binder check will happen twice in the first quarter (to get students used to the expectations), and then at the end of the second, third, and fourth quarters. On the day of the binder check, students will bring in their binders and be given a list of 15 things they have to find in their binders:

Homework assigned 9/21/2009; Section 2.5, #32

And students will have to circle this homework problem and their solution in red, and then put a mini post it tab on that page so I know to look there when I collect the binders. Then the problem will be graded on correctness and work shown.

And two added bonuses of these binders? Students will have all their assessments in one place when studying for the midterm and final. And I can have these binders on hand for parent-teacher conferences and for comment writing — both of which will be a much more powerful source of information than my gradebook and scattered notes.

So that’s the plan. Now the real question is if I can pull all of this out of a magic hat before school starts.

[1] MV Calculus was such a success last year — by any metric I want to assign — that I plan on doing the same format and let the course grow organically out of the personalities of the kids in it. Last year I had 4 students in that class. This year, I only will have 2.

UPDATE: I’ve uploaded a draft of the new curriculum here. We added a few more things from what we did last year, but it is largely the same.