So I don’t claim to have figured this out yet, but I have solidified a lot more of my thoughts about how language should work in the math classroom that I would like to implement. I’ve shared my thinking about the progression of language learning: speaking → reading → writing. Each helps you become more proficient at the previous.
I would really like to more explicitly build this sequencing into my classroom when we learn a new idea. I want students to start informally with ideas by speaking about them and using vocabulary appropriately with each other. To jump to the next level of understanding and formalize the ideas I want to then get them reading, whether it is via the textbook, an article, or another book. I really would like to get students reading relevant material that is more than just the textbook, though. I haven’t done that much. I feel like reading about math helps one to see what writing about math looks like, which hopefully can break down the wall that looms in front of so many when asked to begin writing.
I haven’t really had students write in my classes much, at least in the way I want them to. It’s been mostly restricted to note-taking and reflecting. But I want them to write to connect ideas. Writing something on your own is difficult because you have to actually create, which is a huge jump from simply reading someone else’s creation. But to write about something in this way pretty much necessitates that the author makes sense of what they are writing about. I know that a student won’t always be right necessarily (am I?), but they are sifting through ideas and making connections between them. The more I do math on my own (and PCMI has really shown me this), the more I realize that I will never learn all there is to know about what I teach. This means I need to make sure that my students realize that, though there are certain learning outcomes I want from them, they shouldn’t ever expect to be “done” learning about something. That’s a life lesson, really. I think that writing will be one of the most important tools that I’ll be able to use to accomplish solidifying a learning outcome while at the same time allowing the release from thinking that you have to be done learning about the topic at hand.
I guess my question to myself becomes: How can I use writing to support students in building connections and solidifying ideas? Journal prompts? Explaining a process? What else?
I am positive that there must be a ton of research to support these ideas. I know they aren’t new ideas, but they are sort of new to me (at least in the specific context of this language learning progression). I suppose I should begin searching for some stuff to give me somewhere to go. Or I can just start on it. I’m really good at not starting something until I feel I have it down pat (like my growth mindset phrasing? I was going to say “bad at”). Yeah, I should just start on it.