Reaching back to advance forward: towards a 21st century approach to learning and teaching fractions

Abstract

Besides their usefulness in practical, everyday activities, understanding fractions and operations on fractions underpins the development of proportional reasoning and is critical for learning higher mathematics such as algebra, probability, and calculus and for success in science and engineering. Nevertheless, fractions remain a problematic curricular area in which teachers and students poorly understand and perform. I propose to review literature to understand causes of learners’ conceptual difficulties with fractions and propose an underexplored an instructional scheme based on an epistemological and pedagogical approach informed by theoretical ideas of Vygotsky and Gattegno. Based on work with teachers, I will detail the phases of the instructional scheme and their theoretical and empirical evidence. Results will illustrate how teachers engage learners with manipulatives in the instructional scheme to enable students to construct mathematically sound and robust procedures for operating with fractions.

Keywords

• 4A-Instructional Model
• Cultural-Historical Perspective
• Davydov
• Gattegno
• Rational Numbers