Research in mathematics education: What can it teach us about human learning?

Among the diverse domains of human knowing, mathematics stands out as a hothouse for insights about teaching and learning in general. This chapter summarizes the ways that research on mathematics learning contributes to our understanding of how people learn. We begin with a brief historical overview, which explains what it is about mathematics that has made it the content area of choice for the study of human learning. We then focus our attention on two distinct approaches in education research, the acquisitionist and the participationist approaches, which have influenced our understanding of learning and the practices of teaching in all content areas. Mathematics education research is particularly important to the learning sciences, because it challenges the first approach (which is still dominant in much education research) and it has helped to introduce and develop the second approach. Mathematics Education Research - A Historical Overview Mathematics education is an applied discipline aiming at improving the practice of learning and teaching mathematics. It became established as a full-fledged academic discipline about 50 years ago. However, various scholars began studying mathematical learning at the end of the 19th century, when the currently popular idea of evidence-based pedagogy first came to the fore. The first half of the 20th century saw numerous experimental and quasi-experimental studies (see Campbell & Stanley, 1963, for a review) in which researchers endeavored to compare and evaluate the effectiveness of different teaching approaches. That research, conducted mainly by mathematics educators, attracted the attention of professional mathematicians, whose concern for the teaching of mathematics was accompanied by puzzlement over the question: "How does it happen that there are people who do not understand mathematics?" (Poincaré, 1929/1952, p. 47). These early studies by mathematics educators proved unable to answer the mathematicians’ query, in large part because they focused on an "input-output" model that examined causal relations between teaching methods (inputs) and student achievement (outputs) and gave little attention to the intervening processesof learning in the context of instruction (on processes, see Chinn & Sherin, Chapter 9, this volume).