A series of seven posts on major turning points in my teaching career. A study of where I was, where I am, and where I'm headed.
It is really easy to declare a lesson or unit "feature complete." The base mathematics that we teach hasn't evolved much at all. Methods and initiatives come and go, but at a certain point it's easy to decide that there really isn't a better way to teach someone about a triangle.
I admit that I grow attached to the way I approach things, but every school year I push myself to actively think about how I'm going to do things and how I will push students to do things that we never did before. As Dylan Kane put it in his TMC 16 keynote, find 10% of your practice to improve. Many years of finding the 10% have dramatically changed what I expect of myself and my students when it comes to output.
Where It Was
I started teaching academic Algebra II. As mentioned in my discussion of curriculum, I followed the book because it was available and that's what my team was doing. If you needed practice problems or homework or something, there were these workbooks you'd flip through and make 100 copies of worksheet 6B, or worksheet 6C if you felt like giving them a challenge. These things were always the same, maybe 15 problems, most of them rote level knowledge problems with a random word problem at the end. Nothing very dense, and they had a tendency to communicate to students that math was full of special cases. With only 12 problems, usually 3-4 of them existed only to present gotcha situations.
I started keeping a binder of the worksheets I'd copy alongside the tests and quizzes that were given. After all, it'd be the easiest way to pull them for copying a year later.
Eventually I added a wrinkle and would take the idea of a worksheet and have students present the work as a poster. Sometimes I'd generate the problems they were working.
It was about this time I realized that I needed to trash the binder. Keeping that binder locked me into a way of thinking about what student practice should look like. I needed the freedom to adapt to a new set of circumstances, and force myself to offer a greater challenge that even worksheet 6C could provide.
The assignment side of this was previously discussed. Moving to SBG pushed me to be better about what I taught and how I taught it. Writing my own curriculum that supported SBG pushed me to learn my content better and think about how to integrate it into more coherent narrative. The third component is raising the expectations of what a student should have to do in my classroom.
Where It Is
In 2014 I made a concerted effort to improve the type of classwork my students would do. There was still a need to practice mechanics and we still do plenty of that. What I focus on when I talk about pushing is more extensive, project-type classwork. These are assignments that combine many days of students learning and have them meet a number of specifications to demonstrate learning. Often they have to put together several mechanics and offer an explanation of their thinking or how they fulfilled the specifications of the assignment.
For example, what's better? An arbitrary 25 problem set of vectors where you calculate the magnitude and direction of each, or a scenario where a student designs 40+ vectors, does all the same calculation, and then explains scaling operations? And oh, all neatly contained in an adorable picture of a pig?
Students get a better feel for how realistic it is to run into a special case. Many students making these drawings used perfectly vertical and horizontal lines. Their calculator throws a fit when they try to determine the angle. Why might that be happening? What aspect of a perfectly vertical or horizontal line might be the cause? It takes the talking points you'd normally just tell them and turns into something they'll ask you about. In the course of making these drawings, students do just about everything I'd want them to do with two dimensional vectors. None of this happens if I don't push myself to make the assignment better, to evolve the assignment from a single task everyone completes to a rough spec sheet everyone has to meet.
Assignments like this don't exist in a binder from 2009.
Where It Is Going
These open-ended approaches have been working wonderfully in Pre-Cal and the last year I taught Algebra II. Calculus has been a greater challenge, but progress exists. While not Calculus specific, I had a lot of success (post AP test) giving kids a couple days to create Desmos art, again with very limited requirements (use 30-ish equations, make something neat):
The creativity on display was something else. Everyone had something unique to contribute to this assignment using the same set of limited requirements. All of them felt the task was accessible and that it was theirs.
There are big and small ways to push yourself. At a macro scale, you can try to never teach the same lesson twice. Limit what you reference from the year before. Approach the topic with a fresh point of view and a see if that helps improve your understanding over time. Or start small. Take one lesson that has never gone well or one that your team complains about and throw it out. Almost every subject team has some topic they don't like, but real push comes when you decide to do something about. Delete the folder from that unit off your server. Throw out the binder that has the copies of this assignment. Find a new way to do it. Put more work on the student. Find ways for them to put their personality in what they're learning. Start with that one lesson, see if that doesn't have you second guessing others.
If you want students to engage, give them a reason to engage, give them a skin in the game. But don't take your foot off the gas. If you've always wanted to students to do more writing, make them do more writing. If you've always wanted to hear them explain a concept, make them do it. Kids are way more eager to learn than we often give them credit. Don't be afraid to push.