How does a teacher feel when a classroom lesson turns students into mathematicians? When such a transformation occurs—usually not as often as most teachers would like-thoughts arise of bottling this inquisitiveness and releasing it at times when students are not so inclined. This wishful thinking can turn into a more realistic reflection on the characteristics of the learning environment—the content, the process, and the assessment—that mark certain memorable lessons. Many such lessons share two points. First, the students are genuinely interested and engaged in the activity. They act independently, as if they have chosen the activity themselves and the teacher is just a more seasoned coexplorer. Second, they use powerful tools, notably computers, to help them solve the problems they encounter. This second aspect can be a key to generating the first—if it is used in powerful ways.
Ihor Charischak is involved in helping teachers use technology in their mathematics classrooms.
Robert Berkman interests include concept development, technology in education, and detracking mathematics classes.
Edited by George W. Bright, University of North Carolina at Greensboro, Greensboro, NC 27412-5001