TALKING ABOUT RATES CONCEPTUALLY .2. MATHEMATICAL KNOWLEDGE FOR TEACHING

Part I of this report (Thompson gi Thompson, 1994) described the attem pts of one teacher, Bill, to teach concepts of speed to one child, Ann . We analyzed sources of their eventual dysfunctional communication, c oncluding that Bill had encapsulated his deep understandings of rate a nd proportionality within his language for numbers and operations. Par t II presents the session of the researcher, Pat, with Ann, analyzing his instructional actions in light of his agenda for having Ann build a scheme of operations by which to understand distance, time, and spee d. We contrast Pat's agenda with Bill's, focusing on the mathematical knowledge that guided their instructional decisions and actions and br iefly discuss implications for the preparation of teachers with regard to content knowledge.