1–322 PME28 – 2004 MATHEMATICS TEACHING AS INVISIBLE WORK

The point of departure for this research is the notion that significant features of mathematics teaching are invisible. "Invisible " refers here not only to the features of teaching that are physically invisible: these include such practices as the planning work that goes on in the mind of the teacher, or the relational work that the teacher engages as a medium for learning. But in this work, "invisible " connotes the features of teaching that are actually physically visible but nonetheless go unnoticed by observers of teaching. For example, the teacher often works hard to knit together student ideas in her efforts to build collective understandings in whole class discussions. These efforts, though physically present and easy to discern, often evade the notice of observers. Teachers likewise deploy mathematical knowledge to move a problem along or engage a particular student. Knowing what piece of mathematical information, or what question to ask at a given moment, is the essence of good mathematical teaching practice. And yet even practiced observers of teaching miss these important moves made in the flow of instruction. This research is based on data collected in an elementary mathematics method