Productive Mathematical Discussions  

June 09, 2014
In a time long ago, in a land not so far away, if any of my teachers ever would have told me that they wanted me to talk MORE in class, I would have been dumfounded, flabbergasted, and confused. How many times had “Talks too much in class” been written on my report card or reported to my parents at parent-teacher conferences? I am sure that there are those even today who would agree with my teachers back then and say that “she still talks too much.” Students definitely understood that the expected behavior was to sit in silence and listen. If we wanted to respond, we had to raise our hands and wait to be called on. Sometimes a student who didn’t want to respond – maybe one who had been daydreaming that the teacher wanted to humiliate? – was called on to answer. Those who did not want to be called on to answer learned to avoid eye-contact with the teacher by covering as much of the face as possible with a book, perhaps aided by slouching down as low as possible in the seat. Speaking of seats, they were permanently bolted to the desk portion and the entire piece of furniture was bolted to a steal runner on the floor.

Today’s classrooms look very different. Desks can easily be rearranged to form groups, or have been replaced by tables where students can sit together and engage in conversation. Although the furniture has changed and is arranged differently, how much has really changed, especially with low income and English language learners (ELLs)? In one study, Arreaga-Mayer and Perdomo-Rivera (1996) found that ELLs spent only 4% of the school day engaged in school talk and 2% of the school day discussing focal content of the lesson. Nystrand et al. (2003) found almost no effective dialogue in low-track eighth- and ninth-grade classes.

More effective teachers are not as concerned with students talking too much as they are with the quality, depth, content, complexity and the level of critical thinking shown in the talk. Knowledge alone is not enough. It is what students do with the knowledge that counts. Knowledge is a problem solving tool, not an end in itself. Problems are to be solved with others reflecting the real work world.

-Rosemary Cervantes, English Language Coordinator