Constructivist Teaching Experiment: Constructivist Research and Constructivist Teaching

The aim of the discussion is twofold: first, we formulate and present examples of the creative bisociativity inherent in teaching-research TR/NYCity model (Section 1). Second, we bring the creative model of teaching-research as the precise solution to the difficulties experienced by Common Curriculum Standards in Mathematics (CCSM). Section 2 analyzes the reason for extraordinary difficulties in successful introduction of the curriculum into practice, which manifest themselves among others, by the necessity of scripted lessons telling teachers exactly what to do in all different moments of the lesson time. The root reason for the contemporary difficulties is the absence of teachers involvement in the design process It is in contradiction with the irreducible presence of teaching within the central constructivist instrument of research- constructivist teaching experiment of Cobb and Steffe (1983).

The Constructivist Researcher as Teacher and Model Builder

The constructivist teaching experiment is used in formulating explanations of children's mathematical behavior. Essentially, a teaching experiment consists of a series of teaching episodes and individual interviews that covers an extended period of time—anywhere from 6 weeks to 2 years. The explanations we formulate consist of models—constellations of theoretical constructs--that represent our understanding of children's mathematical realities. However, the models must be distinguished from what might go on in children's heads. They are formulated in the context of intensive interactions with children. Our emphasis on the researcher as teacher stems from our view that children's construction of mathematical knowledge is greatly influenced by the experience they gain through interaction with their teacher. Although some of the researchers might not teach, all must act as model builders to ensure that the models reflect the teacher's understanding of the children.