Problem-Based Learning Associated by Action-Process-Object-Schema (APOS) Theory to Enhance Students’ High Order Mathematical Thinking Ability

Abstract

The research has shown a model of learning activities that can be used to stimulate reflective abstraction in students. Reflective abstraction as a method of constructing knowledge in the Action-Process-Object-Schema theory, and is expected to occur when students are in learning activities, will be able to encourage students to make the process of formation of new mental objects, new processes and new schemes through the construction process in the form of generalization, interiorization, encapsulation, coordination and reversal. Problem-based learning that is presented through eight steps of learning has been able to enhance the mental action in students even though there is no doubt that it cannot possibly know the whole picture of a person's mental activity. All steps in the problem-based learning approach can reflect on the problems of mental action in students. Problem-based learning is appropriate to be used to improve students’ high order mathematical thinking ability because of it has been able to condition the reflective abstraction related mental actions, mental processes, mental objects and schemes in students. Computer assistance and scaffolding techniques can be further stimulus for students to take place in their mental action which corresponded to expectations.