Chapter 11: Gesture, Inscriptions, and Abstraction: The Embodied Nature of Mathematics or Why Mathematics Education Shouldn’t Leave the Math Untouched

An essential question in mathematics education is how to improve the teaching and learning of mathematics. A tremendous amount of efforts and resources are dedicated to provide answers to this question, from curriculum planning and teacher development, to textbook design, software development, evaluation methods, and classroom dynamics. In the quest for providing answers, mathematics education, unlike other domains of teaching and learning, usually proceeds leaving the very subject matter— mathematics—untouched. Whereas other domains in education such as music, language, and literature, implicitly and naturally see the human nature of the subject matter involved in the teaching, mathematics education does not. An important factor is the widely spread view in our culture that mathematics is a transcendentally objective body of knowledge, which exists independently of human beings, or, at best, that it is the “only truly universal language.”¹ This view is endorsed—unquestioned— by many in the academic world as well as in pop culture (e.g., film, advertising, and video game industries). Thus, mathematical facts, theorems, definitions, proofs, notations, and so on, are largely taken as pre-given disembodied facts, external to human beings (e.g., Núñez, 2005). Consequently, most school mathematics is taught, generation after generation, in a relatively dogmatic form, where the very mathematical facts are rarely (or never) questioned. And I am not exaggerating. Simply think of the simple “rule” we all learn at school that “negative times negative yields positive.” We all become more or less pretty good at using the rule. But are we able to explain what is the meaning of such statement? Or, why is this rule true? Or, what makes it true? What do you, as a reader interested in education, have to say about this question? Why is the above statement true, and what does it mean?