Modeling the process of learning common fraction operations: designing an Internet-based integrated learning environment for knowledge construction

The aim of this study is to model a learning process for construction of subject matter knowledge. An Internet-based fraction-learning integrated learning environment (IFILE) has been designed to model the learning process. The IFILE models the domain, teaching and learner´s knowledge in the form of a learning situation, the graphical partitioning model (GPM) for meaning making; an affordance model for learning fraction equivalence, the prerequisite knowledge for learning fraction addition/subtraction; and a model of learner´s knowledge for fostering the production of cognitive residue. The design of the GPM is originated from the nature of the subject matter. An affordance model for learning fraction equivalence is derived from an earlier evaluation study of the authors´ GPM prototype. The IFILE is then built by integrating the GPM, the affordance model and a model of learner´s knowledge for developing learning properties of the constructivists´ view such as constructiveness, cumulativeness, self-regulatedness and reflectiveness.