ABSTRACT
In this chapter, special attention is given to three-tiered teaching experiments in which a 15-week teaching experiment for students is used as the context for a 15-week teaching experiment for teachers, which in turn is used as the context for a 15-week teaching experiment for researchers. As Table 9.1 suggests, Tier 1 of such projects may be aimed at investigating the nature of students’ developing knowledge and abilities; Tier 2 may focus on teachers’ developing assumptions about the nature of students’ mathematical knowledge and abilities; and, Tier 3 may concentrate on researchers’ developing conceptions about the nature of students’ and teachers’ developing knowledge and abilities. A Three-Tiered Teaching Experiment
Tier 3: The Researcher Level |
Researchers develop models to make sense of teachers’ and students’ modeling activities. They reveal their interpretations as they create learning situations for teachers and students and as they describe, explain, and predict teachers’ and students’ behaviors. |
Tier 2: The Teacher Level |
As teachers develop shared tools (such as observation forms or guidelines for assessing students’ responses) and as they describe, explain, and predict students’ behaviors, they construct and refine models to make sense of students’ modeling activities. |
Tier 1: The Student Level |
Three-person teams of students may work on a series of model-eliciting activities. ^{a} in which the goals include constructing and refining models (descriptions, explanations, justifications) that reveal partly how they are interpreting the situation. |
Details about such problems are given in the chapter 21, this volume.