Looking at the development of mathematical knowledge from the perspective of the framework theory approach to conceptual change: Lessons for mathematics education

The chapter describes the framework theory approach to conceptual change and explains how it is applied to the development of rational number knowledge. Unlike existing approaches that emphasize continuities between natural and rational number, the framework theory approach to conceptual change focuses more on discontinuities. We argue that understanding these discontinuities is critical in order to explain students’ difficulties and the formation of misconceptions. The empirical evidence that supports the application of the framework theory approach to the development of rational number is discussed. The chapter also outlines some of the principles for the design of mathematics instruction that arise from this perspective with an emphasis on rational number learning.