The University of Montana
Department of Mathematical Sciences

Technical report #6/2013

Theories of Learning Mathematics

Richard Lesh
Indiana University

Bharath Sriraman
The University of Montana

Lyn English
Queensland University of Technology, Australia

Abstract

According to Karl Popper, widely regarded as one of the greatest philosophers of science in the 20th century, falsifiability is the primary characteristic that distinguishes scientific theories from ideologies or dogma. For example, for people who argue that schools should treat creationism as a scientific theory, comparable to modern theories of evolution, advocates of creationism would need to become engaged in the generation of falsifiable hypothesis, and would need to abandon the practice of discouraging questioning and inquiry. Ironically, scientific theories themselves are accepted or rejected based on a principle that might be called survival of the fittest. In this article we examine developments of learning theories in mathematics education through the lens of four essential Darwinian functions.

Keywords: Complexity; Learning Theories; Models and Modeling; Models versus Theories; Theories of mathematics education.

AMS Subject Classification: 97

Excerpt of article to appear in S. Lerman (Ed), The Encyclopedia of Mathematics Education, Springer Reference Works. Full article unavailable due to publisher embargo. Pdf (176 KB)