INVESTIGATING
MATHEMATICAL LEARNING PROBLEMS FROM THE STANDPOINT OF REPRESENTATION THEORY
Sunday A. Ajose
East Carolina University
ajoses@mail.ecu.edu
Students who have difficulty in learning mathematics usually attribute their plight to certain situations which suggest that mathematical learning difficulties may, in essence, be problems of representation. Teachers are often accused of being unable to represent mathematical concepts and processes in forms which students can easily assimilate, and students sometimes cite their own inability to transform adequate representations into meaningful knowledge. Therefore, to minimize leaning problems and enhance students’ opportunity to learn mathematics, it seems prudent that all mathematics teachers should acquire rich repertoires of connected representation knowledge that they can use flexibly and effectively, especially when teaching topics like fractions, which many students find hard to learn.
The purpose of this study was to investigate the ability of a group of thirty pre-service elementary school teachers to represent fraction concepts, and translate given representations into different forms. The study was done partly to inform decisions about the kind and amount of representation experience that these prospective teachers would need.
Lesh’s (Lesh, Post & Behr, 1987) 5-mode model of representation provided the framework for this study. The participants did two kinds of tasks requiring performance of representational acts that are required to do fraction problems in two current textbook series.
The results of the study
indicate that participants were good at representing fraction concepts
involving single regions. However, many
of them were weak in making translations within and between different modes of
representation. The presentation will
give full detail of the study.
Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations. in
mathematics learning and
problem solving. In C. Janvier (Ed.), Problems of Representation in the Teaching
and Learning of Mathematics pp. 33-40.
Hillsdale, NJ: Lawrence Erlbaum Associates.