Relating Theory and Practice in Mathematics Education: A Historical Overview

Three instances of “theories” in mathematics education are offered and discussed, and the question is raised whether theory, or practice, should be the main driving force in mathematics education settings. That is to say, with issues associated with intended, implemented, and attained curricula in mathematics education, should theory arise out of practice or should the reverse be true. Three main cases are introduced to aid the discussion. The first case presents an overview of the historical development of the Hindu-Arabic numeration system and its applications in mathematics education; the second case summarizes the “cyphering tradition,” as it gradually came to control school mathematics in many nations during the period 1200–1900. The third case draws attention to how developments in theories associated with neuroscience are being linked to mathematics education. An issue which arises is whether teachers follow theories consciously.