Learning Mathematical Flexibility in a Constructivist 5E Model
ABSTRACT
Flexibility is a key dimension of creativity. Classroom discourse which promotes mathematical flexibility has been highly valued. Past studies have established evidences that learning mathematical flexibility, e.g. by attempting and discussing alternative solutions to multiple-solution tasks, leads to enhanced mathematical learning and performance. However, few studies have addressed how such learning should take place systematically for an optimal result. This preliminary study explored the learning of mathematical flexibility in an adapted constructivist 5E learning model. Conceptual variability in nine purposively sampled A-Level participants’ solution strategies for solving three multiple-solution tasks pertinent to Quadratics were qualitatively examined and compared before and after the 5E intervention. The findings generally revealed the participants’ enhanced flexibility and accuracy in producing conceptually-varied solutions to the quadratic tasks upon intervention. The constructivist 5E learning of mathematical flexibility provides a guide to classroom discourse as to how the learning of mathematical flexibility may systematically take place.
KEYWORDS
Mathematical Flexibility, Constructivist 5E Learning Model, Conceptually-Varied Solutions to Multiple-Solution Tasks