So I didn’t have this blog up when PCMI Round 1 came about last summer, but as I am in the midst of Round 2 as I write I thought I’d write on the experience now since I’ve had the chance to go through a year and reflect. First of all, if you haven’t heard of the Park City Mathematics Institute check it out. Here is the gist of last summer for me:
- I came hungry for change in my practice and to learn more about what I taught
- I was overloaded with wonderful tools and ideas to achieve these goals
- I had to sift through this good stuff and try to decide the best place to start
At the end of the three weeks we were left to choose one big change to make in our classrooms. This was an enormously difficult task because of how much mind-blowingly awesome stuff there is to take from PCMI. This post is basically meant to think through things I’ve started doing as a result of this.
I chose to focus on establishing and maintaining classroom norms. I honestly didn’t do a very good job of establishing norms and maintaining them. I felt good about our conversations at the beginning of the year when we created them, but I just didn’t follow through regularly reminding students, nor was I able to get them to help each other out on them very well. It started out pretty strong in these areas, but as they year went on it faded away and I just didn’t pick it back up. So this year I plan to do that from the start of the year by creating group protocols, posting norms in the classroom, and referencing them regularly.
This was my first full-blown year having my students in groups , and it surprised me how much just that one thing opened up my classroom. It wasn’t this magical change and now all of my wildest dreams are coming true thing, mind you, but it was a step in the right direction! It has really given my lessons freedom as they have transitioned from very structured and rigid to much more fluid and dynamic over the course of the last few years. I’m thinking back to Andrew Stadel’s NCTM Ignite talk about my classroom clock, and that really hits home with me! I do, however, plan to try and be more purposeful to choose classrooms tasks that elicit a real need to work with others. Too often I felt that I asked students to work together when most didn’t really need to, nor would it really have been all that helpful for them to do so.
My focus this year: Writing. I have become more and more interested in students’ acquisition and use of mathematical language lately. To the point where I feel it is a make-it-or-break-it issue for the access of many into the discipline. Part of this was spurred in some conversations with some colleagues in our English department. We were speaking about the level of writing students do as they progress through school. The natural language progression seems to be speaking first, followed by reading, and then writing. This simple process itself follows a structure of increasing complexity and creativity, reminding me again of Bloom’s Taxonomy. I have experienced this myself as an adult learning a second language and have really noticed how important all three of these steps are to language acquisition and true understanding. Speaking is the foundation, and once you learn to read your speaking improves and you can better articulate yourself. Then learning to write will impact your reading strength and in effect will compound with that to improve your speaking immensely. And even more, writing is so much more of a cognitive, complex, and creative act than speaking and reading are that it is the culmination of language acquisition and a true test of one’s understanding.
So with this said, it seems to me that students come to me at widely varying stages of language acquisition growth as applied to mathematics. I need to help students be comfortable speaking about mathematics, then build from this to get them making sense of what they read (difficult with such condensed text), and culminate this process with writing about what they have learned. Since this recently dawned on me, I have convinced myself that a crucial component in my students’ learning of mathematics has been missing. When new language is to be learned (i.e. with new concepts), I need to step them through this process, and I need them especially to be writing about it since that gets left out so often but it’s so important to drive ideas home.
Does anybody have good suggestions for any books or articles on this? I’m also open to various ways that students can keep a journal or have writing prompts in class that you have seen be effective. I am really looking for as many different ways as possible to incorporate writing (both informal and formal) into my curriculum. I’ll be sure to put stuff up that I create as I go through this next school year that helps students express their learning through writing.