Effective mathematics learning through APOS theory by dint of cognitive abilities

Abstract

The paper dwells on the contributions of APOS theory to the development of teaching and learning of mathematics in school. APOS is an acronym for <i>action</i>, <i>process</i>, <i>object</i>, and <i>schema</i>. The theory emerges as an extension to constructivism but with a more focused and robust learner-centered approach to the teaching and learning of mathematics. Proponents of the theory believed that learning occurs initially as an <i>action </i>or <i>activity </i>in learners’ cognitive settings, independent of learners’ environment, triggered by cognitive coherence, then it is transformed to <i>process</i>,<i> </i>where learner now waits for internalization of the earlier <i>activity</i>, preparatory to the occurrence of learning. At <i>object </i>level, learner now considers what has been learnt earlier to have been fully internalized into mathematical <i>object(s)</i>. Lastly, at <i>schema </i>level, the <i>object</i> learnt is assumed to have been embedded in the learners’ <i>schema</i>–a cognitive structure formed as a result of accumulated learning experience, and a complete mental image of what has been learnt is said to have been formed. Against the backdrop of this, the paper looks at how this theory had changed the narrative about teaching and learning of mathematics vis-à-vis the bearing of the theory to other cognitive abilities of the learner such as intelligence and creativity. In the end, the paper suggests the application of APOS theory in teaching and learning mathematics at all levels of learning in Nigeria and beyond.