So, what does this have to do with teaching math? Earlier this summer, I had posed the question "What does your math class look like?" I am at a point where I am ready to make some changes in my classroom and how I teach math on a daily basis. I guess I'm asking myself the same question that we were asking about our bathroom - do I totally need to start from scratch and revamp what I am doing, or can I make some changes and keep some of what I've done in the past? Between my twitter twin @druinok and myself, we posed the question a couple of times on twitter - trying to see how other people structured their math classes other than the rather common "bellringer activity, go over homework, teach new lesson, do problems on new concept, and maybe an exit slip as students head out the door" process most math teachers use. Most of the answers that were different involved flipping the classroom. To be honest, I'm not really certain that's the way to go. First of all, not all of my students have access to the internet. We have about 50% on free or reduced lunch. Secondly, getting students to do outside class work is a struggle on many fronts. Finally, I'm just not buying it. My skeptic's radar is up with this one. I can't really explain it beyond that. I just don't feel like it jives with how I feel about teaching.
When I left to head to Orlando for the Institute on Reasoning and Sense Making, I was still very much of a mindset that I needed to gut my teaching structure. I wasn't really sure how I was going to make that happen, but I felt like that's what needed to happen. I attended two really great sessions Dan Meyer presented and I was still thinking I needed to gut my classroom. Maybe trying to find as many real world connections and bringing in great visuals was the way to go. The next session I attended was presented by Henri Picciotto. I had picked his session based on the title, that he was a classroom teacher, and I remembered that @cheesemonkeysf had said some good things about him. Picciotto's session was different than Dan's. It was based on more "traditional" types of activities, although he did bring in the use of manipulatives which is somewhat unusual for Algebra 2. I left his session somewhat confused. The two gentlemen's sessions were somewhat on opposite ends of the spectrum ("current" vs. "traditional") for me. But yet, both were at an institute touting reasoning and sense making. I was struggling with making sense (pun intended) of this. On the last day of the conference, I attended two more breakout sessions, one by William Thill, and the other by math faculty of Adlai E. Stevenson High School in Illinois. Like with Piccotto's session from the day before, both sessions used more "traditional" activities. So by the end of the institute, I was rather confused. What exactly was I supposed to be doing in my classroom?
Well, although I cannot exactly pinpoint when in the last couple of days it has become clearer to me, I feel I have a more definite direction to head. When I attended William Thill's session in Orlando, there were a couple of things that caught my attention: I was engaged so much throughout his session I barely took notes and Bill wasn't that much younger than me (although I misjudged a little...) and was using a more traditional approach. We had two brief conversations in Orlando, one immediately following his session when I had let him know that I would be blogging about his session and later on Saturday about blogging and Park City Mathematics Institute before the closing keynote. As I reflected on the Institute as I headed home, I thought that Bill might be able to help me with my gutting dilemma. Bill and I exchanged a couple of emails where I asked him some rather lengthy questions about incorporating reasoning and sense making into the classroom as well as about a "typical" day in his class. Through our exchange and really taking the time to read and digest what was said, I believe I finally have an answer.
Part of my answer came from this tweet:
This tweet was in the middle of a discussion about Khan Academy and the flipped classroom. The previous evening (I think), there was a lengthy discussion about applied mathematics and pure mathematics. What I took from that twitter discussion was that we have lost some of the beauty of mathematics when we try to find an application for everything we do. Although there are a lot of applications of mathematics, that is not all of its value. Between that discussion and the @Vvelasquez2 tweet. I think it all finally clicked in my head. I don't need to gut my class structure. I need to make some changes, but I don't need to completely and totally change everything. I had started to realize this as I digested what Bill was sharing in our email exchanges and this tweet helped me to put it all together in my head. There is a time and a place for what we do in the mathematics classroom.
Vvelasquez2 Vincent Velasquez
So, what am I going to do? I am going to have structure with my bellringers as I had blogged about in July. I am going to work on getting students to the board as we go over homework problems. This will be new for me. I think I will choose specific problems for students to put up from the previous assignment and have them share how they solved the problem. I think from there, I will take another homework question or two if we didn't get them answered from the problems that were put up on the whiteboards. In the new lesson portion of my lesson, I am going to try some new things. One suggestion Bill offered in our email exchange was to select a two-four key problems to have students work through with little guidance and stop them at key junctures. His suggestion was to" have students make decisions first at those key junctures, compare with their peers, discuss what makes the most sense mathematically, and reach a shared resolution to a mathematically appropriate conclusion." I definitely want to start this with the earlier lessons first, which is material they should be more familiar with and evaluate how it goes from there. I also will work on incorporating rich tasks into my classes. The advice I have received from both Bill and Eric Robinson (he is the chair of the Task Writing Group for NCTM) was to start slowly and I intend to follow that advice. More importantly, as I do these reasoning and sense making tasks in my classes, I will blog about them so that I can adequately reflect on how it went and learn from my experiences.
In an odd twist, my remodeling experiences will begin at about the same time. I will meet with the owner of the company doing our bathroom remodel next week to finalize decisions on our bathroom. During the next couple of weeks, I will begin planning the first lessons of the new school year. Even though I am making only what may appear to be minor changes to what I am doing in class, it feels like some pretty big changes to me right now. I have done things basically the same ways for the last nineteen years. Change is not easy, but I believe that it is necessary so I can be a better teacher. It should be an interesting couple of months around here.