We had an opportunity to welcome Dr. Kevin Feldman to our school district last week. He presented a day-long session on “Narrowing the Lexical Divide: The Critical Role of Vocabulary & Academic Language in Improving Secondary Literacy Across the Curriculum.” His focus on academic vocabulary was of great benefit to the teachers in attendance.
One thing that really caught my attention in his presentation was the discussion about where we find Academic English – that Hayes and Ahrens (1988 ) used a measure of “rare words per 1,000” to evaluate the frequency of word use. They found that the everyday adult speech of college graduates is at approximately the same level as preschool books, and that most informational texts are at a level comparable to newspapers and magazines.
This reinforced my belief that we have to talk about math before we write about it, and also supports the notion of developing formal spoken language as one path to formal written language (see Pimm (1991)). It also made me wonder about the level of spoken English in math classrooms, both by teachers and by students. Then Dr. Feldman showed us this website, which will analyze passages to determine rare words per 1,000.
Those who know me will likely guess what I’m thinking: research. This should be fun!
I’ve been thinking and talking about communication in math quite a bit lately. For elementary teachers, it’s a common language that opens the door for further mathematical conversations. For secondary teachers, it’s a critical component (a standard, in fact) that is too often given lip service. As a result of all of this thinking and talking, I’ve come to a couple of conclusions.
- It’s about discourse. I recently received my new issue of Mathematics Teacher from NCTM. The focus of this issue is discourse: what it is, how to improve (or begin to use) discourse in the classroom, and some of the obstacles that discourage effective discourse. Like inquiry, discourse ranges from being very teacher-directed to very open and student-centered. It’s about student needs and scaffolding instruction to meet those needs.
- Model, model, model. If we do not give students good models of talking and writing in math, then they’re not going to learn it. They won’t get it at home, and they’re not likely to get it from other sources. We can’t turn kids loose on a problem, ask them to talk or write about it, and expect effective communication if they don’t know what it looks like. Pretty simple, but something that’s easy to forget. Talking and writing about math is different than any other content; although the strategies are universal, the terms and the discussion are often different. When you’ve done this, model some more. It takes time for students to reach the formal level.
- Don’t expect perfection. One of the biggest mistakes I made as a teacher was showing a group of students an example of a “good” paper that I had written. They were so discouraged that none of them believed they could write about math the way I wanted them to. In hindsight, they really needed to see the process of writing, not just the finished product. The fact is, students are not going to write fluently about math until they’ve done it for a while. In a recent post, Dan Meyer summarized this thinking: “It got me writing regularly, an essential precursor to writing well.” Don’t expect perfection to start with. If we can get kids writing, the writing will improve. It might take three or six months, or it might take two or three years. Just get kids writing about math and keep them writing about math.
The bottom line is that it’s not enough to ask kids to write. We have to support them as they begin to write; we have to model throughout the process; and we have to be patient as they develop the ability to write about math the way we want them to write about math.