Teaching
Tasks as tools for Assesment and tools for change
Laurie Cavey
North Carolina State
University
Ma (1999) emphasized the importance of acquiring a profound understanding
of fundamental mathematics (pufm)
and how lesson planning facilitates its development. Ratio and proportion
concepts, in particular, are fundamental to many Algebra I concepts and
historically have been difficult to master. While simultaneously focusing on
practical and theoretical implications, as suggested by Schoenfeld (1999), I searched for ways to assess and develop teacher
knowledge in the context of a ratio and proportion lesson-planning task.
Through naturalistic methods for data collection, sophomores, majoring in
mathematics education, age 19-20, while enrolled in their first “methods”
course at a large public university, were interviewed, given a lesson-planning
task and then interviewed again. I constructed a theoretical framework that
blends some of the perspectives of the cognitive (Strike & Posner, 1992) and social (Vygotsky,
1986) sciences. Specifically, I am assuming that signs of
cognitive conflict regarding a concept imply that a particular concept is in a
prospective teacher’s zone of proximal development (ZPD). Analysis of the data
involved PUFM coding and sorting, and looking for evidence of cognitive
conflict and metacognitive thinking. Preliminary results show that the interview-task-interview process gives
access to each prospective teacher’s zpd
and can serve as a tool for change in the development of teacher knowledge,
which will enable teacher educators to plan future tasks to enhance the
development of teacher knowledge.
References
Ma, L. (1999). Knowing and teaching elementary mathematics.
Mahwah, NJ: Lawrence Erlbaum.
Schoenfeld, A. (1999).
Looking toward the 21st century: Challenges of educational theory and practice.
Educational Researcher, 28(7), 4-14.
Strike, K. A., & Posner,
G. J. (1992). A revisionist theory of conceptual change. In R. A. Duschl &
R. J. Hamilton (Eds.), Philosophy of
science, cognitive psychology, and educational theory and practice .
Albany, NY: State University of New York.
Vygotsky, L. (1986). Thought and language (Alex Kozulin,
Trans.). Cambridge, MA: MIT.