This is my sixth year teaching geometry and I'm pretty much at that point where I can walk in to my classes ask them what we talked about yesterday and I can go to town. I've always wanted to be at this point in my career, where I can spend time focusing on increasing the quality of questions and researching new ways of teaching rather than taking a tremendous amount of time just figuring out what I'm doing the next day, creating problems, etc. Because I have most of the ground work laid out, I've been able to try some really cool (and some not-so-cool) things over the last few years. For some of my units I've gotten rid of tests and created projects, for some I've made them more discovery-based and student-directed, and for some lessons I've created some really involved questions that require some incredible thinking from my students to solve. This year an idea I've been toying with is the student-directed curriculum. Its got some pros and cons to it and I'm not quite sure what I'm going to do.

Our geometry curriculum used to be like almost every other math class: follow the textbook. Unfortunately, we have UCSMP which is terrible in my opinion. When I rewrote the curriculum two years ago I had one goal in mind: organize it in a way that will make sense to the students and where connections can be made. I got tired to teaching topics and having to jump all over the place to struggle to draw the lines between everything. The beauty of geometry is that is all related and our students were not seeing that. Now, even though technically we jump all over the book (although no one in our dept uses the book anymore) I've noticed student achievement go up and we've been able to create deeper questions. The students don't care that they don't have a book to follow because the way that its organized makes sense to them. They would rather reference pg. 18 and pg. 262 in the same day than have everything disorganized and all over the place.

This semester I took the first three units (basic vocab, quadrilaterals, triangles) and mashed them together as opposed to teaching them separately. Now these units include things like all of the types of angles, symmetry, trig., and more, so they're pretty heavy on material, but I wanted to have it make

*even more sense*for my students (if that's possible). As I thought about the curriculum, I realized that it could be organized in a number of different ways and still emphasize all of the interconnectedness of the world of geometry, but how could I have it be the absolute best for my classes? Or for anyone's classes for that matter?

I started the year by asking my students what came to their minds when they thought about geometry. Their response: "Shapes and stuff." Me: "Name some shapes." Them: mur mur mumble mumble shapes blah blah ...and somehow I took it from there. I took the shapes they gave me and we started to dissect each one individually, exploring all the properties until there was nothing left to talk about, making connections as we went. I never had to say "Ok, we're done with that figure. Let's move onto the next one." because the properties naturally lead to more figures. Through student questioning I was able to completely cover the curriculum, plus some more.

Because this was my first time trying this, I limited myself to just the first three units as opposed to attacking the entire course this way. I'm teaching two sections of geometry and my hope was that I would be teaching them different concepts because their questioning would lead them to different places, but they'd end up at the same place in the end. I'll be honest, it got confusing. I no longer could stand in front of them and say "What did we do yesterday?" because I couldn't remember everything we'd discussed. I found myself keeping an unnaturally large number of post-it notes on my desk reminding me of what I've discussed with each class. I'd imagine when my third block asked my second block what to expect in class, they were surprised when they did something completely different.

I noticed that teaching this way caused achievement to increase compared to other years. Now, obviously I could just have an awesome batch of students (which I do), but I believe the way I taught had some impact as well. All of this has led me to ask myself,

**what if I taught the entire course this way?**

**Teaching an entire course through student questioning: innovative or something I should've been doing all along? Either way, there are some definite benefits and challenges to this approach. I believe my students would see some great success both in learning the basic knowledge and developing some higher order thinking skills. Teaching this way allows me to easily pull all kinds of topics together and potentially create some really cool projects. It would allow my students to really understand that math is all connected; its not separated into Alg 1, Alg 2, Geometry, Pre Calc, etc. but they're all based upon each other. It would also keep my students involved in the course. They would have complete ownership over the material because they would be determining what happens next. This also reinforces my philosophy of 'teach what makes sense, not what comes next in the book.' Looking through the PACCSS, I think I could hit everything with this style.**

The tough part is that I have to almost be fully prepared to teach the entire course at any moment. Because I won't know where my students will lead me, I need to have everything ready to go on the first day. I'm sure I could predict a little bit as to where they would head, but I wouldn't know what they're going to do on a daily basis. If I taught this way I wouldn't want to push them in any direction unless they stall; I want them to be pushing me. Another challenge is keeping straight what I've covered and what I haven't in each class. If I would do this next semester, I teach three sections of geometry, that would be three different places in the curriculum simultaneously. I would be very fearful that I would forget to cover something or I'd start going over something in May that we discussed in February. While ideally this would be 100% student run, obviously there would have to be some questioning on my part to push them, which would give me some influence as to what's being discussed. My post-it note system of organization would fail rather quickly and I'd have to come up with something more efficient. I'd also need to create a new system for catching students up when they are absent. Maybe designate someone to constantly take picture of the board and post them online? There are some details to figure out.

As of now, I'm leaning towards doing this for one class instead of all three as a trial. This might help me get some of the details worked out before I push through entirely (of course, we all know what will happen if I do this: this will be the last year I teach geometry and I'll be back to the drawing board with new courses next year). It would also be fun to switch things up a little bit. I'm excited, and scared out of my mind, to try this. I'm not usually the most organized person in the world so this plan has potential to fall apart in a hurry. I'm hoping my desire outweighs any negatives that would potentially come out of this. The positives definitely outweigh the potential bumps in the road, and because of that I keep coming back to "I'd be an idiot not to do this!" I can't help but think of a quote from Mr. Pershan that I recently saw on Twitter (@mpershan), "If I'm not working really hard - if it isn't mentally exhausting, then I'm probably not getting better."

However, this style does kind of go against the 'common unit assessment' plan that my district has implemented for this year. Having common courses among teachers gets thrown out the window with this idea. Oh well... I gotta do what's best for the kids.

Do you, Mr. or Mrs. Reader, have any thoughts on this plan? Any positives or negatives that I didn't mention? Any ideas on how to overcome the negatives?

There's a great book you should read, recommended to me by Christopher Danielson (I think) called "Teaching Problems and the Problems of Teaching." I'm a couple of hundred pages into it already, and I think you'll get some answers to these questions of curriculum (and whether a student-centred problem-based curriculum works - it does).

ReplyDeleteI'd love to organize a course around problems for students to do, and spend much of the class time discussing the solutions & experiments students do around those problems.

Awesome, thanks for the book. I'll look into it.

DeleteI've been trying to come up with a database of problems to use in my courses because as of now I've been making up new ones each semester, which is getting tedious. Basing my instruction off of challenging problems has been working very well and as my colleagues try it they are seeing equal success.

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