How Do We Learn Mathematics? A Framework for a Theoretical and Practical Model

Abstract

The purpose of this paper is to propose an effective learning environment for the initial stages of mathematical learning. Basic numerical skills and the objects and actions that trigger those skills are conceptualized as a mathematics-learning environment. We discuss numerical learning mechanism and the basic skills and environments we use to learn numbers briefly within the human cognition system. The three subsystems of number, i.e., exact number system, approximate number system and access to symbol system, are explained with reference to basic number competencies. They are discussed within the framework of "number sense” by drawing evidences from the neuroscience and mathematics education literature. Finally, how to manipulate the components of these subsystems for an effective learning of number is exemplified in a proposed model of mathematical learning environment.