Chapter 13: Collaborating to Investigate and Improve Classroom Mathematics Discourse

We didn’t know whether to feel elated or to cry as we read student comments (such as those above) at the end of our first semester co-teaching a first-year algebra class. Comments such as, “I like doing group activities because if you don’t understand something it is easy to have a group member explain the problem,” and “I liked the bottle-filling activity because I learn better using visuals and actually doing it and interacting with it,” contrasted with comments such as, “I don’t like working on projects in pairs, especially when I am ‘carrying someone’! It gets annoying when people ask me to give them answers,” and “I don’t really like the projects because we spent time on unnecessary parts. I like just getting to the main point and repeatedly working problems.” These comments suggest that students’ views of what occurred in our classroom—investigations of non-routine problems coupled with sharing and assessing students’ varied solutions— were quite mixed. Our goals for the semester had been to put into practice the recommendations of NCTM (1989, 1991), with a particular focus on building mathematical understanding through discussion. We judged our success with respect to building discussion by the extent to which students became engaged in using discussion to develop their understandings of mathematics. We also collected data that allowed us to analyze our own teaching practices and answer questions such as: “Which aspects of teacher practice are critical with respect to building a classroom discourse community?” “What methods or strategies for facilitating discussion seem especially promising?” “What do students expect and how can we respond to their needs and expectations?” “What are the benefits and challenges of collaborating and sharing the roles of teacher and researcher?” and “What recommendations can we make to others who may want to engage in similar work?” In this chapter, we respond to these questions as we describe the genesis and development of our collaboration, the strategies we used to improve classroom discourse, and the results of our investigations—including students’ feelings about “learning mathematics through discussion.”