# Freudenthal Lecture

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* Freudenthal_Lecture (dutch)

## Contents |

## General

- Organized (annually) by the Freudenthal Institute
- In honour of Hans Freudenthal

## 2013

- Professor Rafael Núñez of the Department of Cognitive Science of the University of California, San Diego
- September 17, 2013, from 14-17 p.m., Boothzaal, University library, Utrecht University
- Embodied cognition

Núñez scholarly and cutting-edge work in the area of embodied cognition, mathematical thinking and scientific thinking is a source of inspiration for us to initiate innovative research in the field of learning and teaching mathematics, science and technology.

He co-authored with George Lakoff the standard work “Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being”. Further publications of Núñez can be found at http://www.cogsci.ucsd.edu/~nunez/web/. His research includes a broad range of mathematical issues covering different levels of learning mathematics. Moreover, he addresses these issues from various interrelated perspectives: mathematical cognition, the empirical study of spontaneous gestures, cognitive linguistics, psychological experiments, neuroimaging, and cross-cultural field research.

Mathematics is a unique body of knowledge. The very entities that constitute what mathematics is are idealized mental abstractions that cannot be perceived directly through the senses. A Euclidean point, for instance, is dimensionless and cannot be empirically observed; And our finite brains and bodies, by definition, cannot directly perceive actual infinity, a fundamental concept in mathematics. Mathematics, thus, appears to be de facto “dis-embodied” — a purely abstract and formal discipline, existing independently of the human animal. But, is it?

In this talk I will analyze the concept of embodied cognition (and some of its varieties) and investigate why it is relevant for mathematics education. I will argue that mathematics is a peculiar form of human imagination whose inferential structure, transcending direct bodily experience, is largely realized via specific concoctions of everyday cognitive mechanisms of human sense-making and abstraction, such as conceptual metaphor and fictive motion. Although these cognitive mechanisms are natural and ordinary, the (mathematical) concoctions often are not, their learning usually requiring considerable cultural and educational scaffolding. I will illustrate my arguments with data from studies on the concept of “continuity” in calculus (naturalistic and controlled gesture studies, and reasoning experiments), as well as from the investigation of one of its underlying building blocks — the “number-line” (historical analysis, recent psychological laboratory experiments, and field work with the Yupno people of the remote mountains of Papua New Guinea). I will discuss implications for mathematics education.

## References

## Versions of this document

- 20130902, wikiteam