Originally, I figured I would write one post per class for this “A Day In…” series. But then something strange happened in Honors Precalculus: this week.
So even though I have an Honors Algebra 1 post (or two) burning a hole in my brain, I need to process the goings-on of another day in Precalculus.
4th Period, Thursday, April 4, 2013
Honors Precalculus with Trigonometry
How Things Went Down
The bell rang. Kids graded homework (two hard copies of solutions handouts per table of four kids) while I walked throughout the room. Most students begin grading a few minutes before the bell, so we finish pretty quickly and they get detailed feedback on each assignment (and I don’t spend 2+ hours grading every day after school).
We then played SET. Next, students signed up for their CSU Fresno Math Field Day events—or wrote down why they could not attend. This took approximately 300% longer than it should have, and I have more kids opting out this year than ever before, both of which were a little frustrating. (Formerly, I’ve required my honors students to participate, unless they have an unavoidable conflict. But I’m growing tired of the tension this policy creates so I’m making it optional from here on out.)
So there we are, moving forward quick-as-molasses, finally ready to begin the lesson. Using this handout (an exploration from Paul Foerster’s Precalculus textbook) students were supposed to graph polar curves on their calculators in order to determine which of the apparent points of intersection were “true” points of intersection (and therefore solutions to the system).
Several times over the past five or six years my students have worked their way through this exploration. And with some wandering about the room, listening in on conversations, offering a bit of guidance where appropriate, and so forth, my students have been successful. With that prior success in mind, I didn’t really prepare for this lesson.
That. Was. A. Mistake.
If the lesson was a train, then it pulled slowly out of the station, flew off the rails, crashed into something big and destructive and flammable, and burst into flames. At least there was no ambiguity. It was undeniably horrible.
When I realized the depravity of our situation, I called for everyone’s attention in order to make an announcement:
Hey guys, this isn’t going well, and it’s my fault. I didn’t prepare for this lesson as well as I should have. I want everyone to stop working on the handout and find something else to do. You can work on something from another class or just relax and chat with your friends. I’m going to sit down to rewrite the handout. If I can fix what’s broken in 5 or 10 minutes, we may resume. If not, we’ll pick things up tomorrow.
The subtext (which I didn’t verbalize to the kids): I value your time and effort too much to waste it with some half-baked lesson primed for disaster.
I then spent the next 20 minutes (yep, we didn’t resume the lesson) rewriting the handout. The bell rang, I invited them to have a great rest of their day, and that was it.
What I Liked
There’s some cool stuff that is supposed to happen in that lesson, and Foerster’s handout has been great in the past at helping my students wrestle with these ideas.
Aside from those potential good things, there wasn’t a whole lot I liked from that class period. I suppose I could score my students’ response to my abandoning ship on the positive side of the ledger. They were gracious and forgiving, though probably only because they were in a good mood after 20 minutes of relaxation.
What I Didn’t Like
I’ve already addressed most of what I didn’t like about my lesson above, but I will add more detail for why I think the handout didn’t stir up its former magic. The handout was designed for the TI-84. None of my students have TI-84s anymore. A few years ago we made the shift to TI Nspire handhelds, and the first group of kids who made the switch are now in Precalculus.
So why did the lesson come to a screeching halt? There was a total mismatch between (1) the guidance provided and the demands made by the handout, and (2) the technology students had access to. Granted, the TI Nspires are newer, shinier, and (at least in my opinion) better than the TI-84s. But a handout written for another device doesn’t care about newness or shininess.
How I’ll Get Better
That 20 minutes (with my students sitting around, happily chatting with one another) was the most productive (and professionally enjoyable) 20 minutes I’ve had in the last three months. I can think of a few reasons why:
- I knew what was broken, and I had some ideas for how to fix it.
- I felt the pressure of the clock. Class was ending soon, and I wanted to at least get the lesson rewrite well on its way while my ideas were fresh.
- I’ve been digging through dozens of amazing teachers’ lessons via Twitter and blogs, so I had a few more ideas floating around my head than I usually do.
- I was excited to try my hand at writing a lesson in a way that would allow me to move off center-stage in order to let the students take on the most active roles.
So I wrote feverishly for 20 minutes during the last bit of fourth period. Then for another 15 minutes during lunch. Then for another 30 minutes after school. Then for another 30 to 45 minutes before I went to bed.
I ended up with this handout. And a gen-u-ine teaching buzz. I was so excited for the next day to roll around so I could bring what I created (really, what I modified; for better or for worse my new handout owes its existence to Foerster’s lesson/handout) to my students, to see how they would respond, what they would learn, what questions they would have afterwards, etc.. I haven’t had this sort of feeling for quite a while, and I quickly identified the reason why: I haven’t spent this much time thinking about and writing (or re-writing) a lesson in a number of years. It’s not that I don’t spend time preparing for my classes these days, but a lot of what I do now consists of reusing last year’s lessons, with or without some minor tweaks. In years past I would spend hours and hours getting ready for a day, sometimes just for a single class. That investment of time often led to decent returns (that is, decent lessons), which in turn led to an I-can’t-wait-until-tomorrow vibe.
In fact, while reflecting on all of this I thought back to what I now consider my favorite season of teaching: the spring of 2008. That was the semester during which I wrote and taught a trigonometry unit to my Honors Algebra 2 students as part of a masters project. The lessons were all student-centered and (as I recall them, anyway) fairly engaging.
I’m convinced that this season was enjoyable for a number of reasons, but foremost among these is the fact that during that time I was creating content like a madman. Saving and reusing curriculum is healthy. In fact, for many of us (myself included with four to seven preps and four kids under four) it’s 100% life-saving-necessary. But if I want to remain satisfied in this profession, I know this: I have to continue creating. If I don’t, my interest will vanish like wind-driven mist.
So whether it’s the revamping of a single lesson, an entire chapter, or a whole course… Late at night, on a weekend, or over the summer… I know the key to keeping my heart in the classroom: Create. And create some more.
I’m writing this post on Friday night. (No time to blog last night; I was too busy drawing up a new lesson/handout.) I won’t go into a lot of detail, but I will say that fourth period was a lot of fun today. Because of my extra hard work the day before, I got to step aside during class and let the kids do the heavy lifting of thinking, arguing, and drawing conclusions. Students also got to work through the lesson at different speeds, which is totally appropriate considering that students think at different speeds.
I’d be very interested to know what you think of the my experience in Precalculus this week, as well as my semi-newfangled handout. In particular:
- Is there too much scaffolding? Too much hand-holding via handout?
- Are the lesson goals (solving polar systems via graphing, learning about auxiliary Cartesian graphs) worth exploring? I became so focused on making this old lesson work that I didn’t stop to think until I was done: Is this something we should even be studying? I think it’s cool stuff, and certainly was healthy exercise of the brain for my students, but is it essential or trivial, useful or useless? (I obviously need to rethink why I teach anything in Precalculus—or any course, for that matter. I have some serious work to do over the next couple of years in making my courses stronger, more well thought out, etc.)
- Are the directions and questions clear?
- Does the format help or hinder the lesson goals?
Joshua Zucker shared some great thoughts in two comments almost immediately after my post when up last night. (Check ’em out below.)
His first comment inspired me to tweak the handout a bit further (namely, the coordinate planes provided). The latest version of the handout is here.
Let me know what you think of the changes to the coordinate planes. (Hooray for Adobe Illustrator!)
Also, while making the polar grid for the handout I decided it wouldn’t be too much trouble to throw six small copies on a sheet and one large copy on a second sheet to share with my students for other activities. You’re welcome to use whatever you want from this Dropbox folder. The initial inspiration for the graph paper came from this, though the final version was improved (in my opinion) by a student comment that “It would be swell if every fifth circle used a heavier line stroke.”
I blog to reflect on my teaching. That alone makes it all worth it. However, more often than not someone asks a followup question that forces me to think even more critically about my teaching experiences. And it’s not at all uncommon for this person to be named Michael Pershan. Exhibit A:
@mjfenton I would love to read some analysis of what you felt the deficiencies of the original worksheet were, what you improved.
— Michael Pershan (@mpershan) April 7, 2013
I decided to respond to Michael with an update here rather than on Twitter or in the comments because I think it’s incredibly relevant to my entire reflection. With that said, here’s my reply:
I don’t think the original worksheet has any deficiencies. I love Paul Foerster’s materials, especially his explorations for Precalculus and Calculus. (In fact, Foerster was one of the first people on the list.)
The reason I revamped the handout was that it no longer worked in my classroom with my students (with the technology we’re using). My lack of planning that led to the fiery train wreck was about 90% not accounting for the changes needed in light of out shift from the TI-84 to the TI Nspire. Beyond that, I ramped up the “wordiness” and “handholding” of the lesson/handout because, frankly, my students needed it this year. Some of the wordiness is due to my poor skill as a writer, and some of it is entirely by design.
So what did I improve? Mathematically, I would say nothing. But I created a handout that worked with my students and the technology available to us. The original handout (again, see train wreck), despite its quality in other settings, was no longer functional in mine.
Joshua Zucker again, this time in response to my question of whether the activity included too much scaffolding:
There’s some handholding and some room for discovery, so thinking about some of the schools I’ve taught at (among the top in the country, where my honors precalc class is not unlikely to have some 10th grader who is taking the USAMO or something) it would be a bit too handholdy, but overall it seems reasonably balanced. You know your students better than I do.
Talk about a classy and affirming response that still dishes some helpful critique. Here’s how I read it: “Yeah, there is some handholding there. But depending on your situation/students, that may be entirely appropriate, especially if it allows for the discovery to happen.”
So I began wondering what this handout would look like if I was designing it for a group of students who were mathematically more proficient or more familiar with open ended questions (or both). Here’s my answer. It would be another “train wreck day” with my current practice and students, but maybe one day… Let me know what you think.