This paper defends a conceptualistic version of structuralism as the most convincing way of
elaborating a philosophical understanding of structuralism in line with the classical tradition …

Existing evidence has revealed that geometrical intuitions develop spontaneously without
formal education. However, empirical research exploring the development of specific …

Ecological-enactive approaches to cognition aim to explain cognition in terms of the
dynamic coupling between agent and environment. Accordingly, cognition of one's …

How is knowledge of geometry developed and acquired? This central question in the
philosophy of mathematics has received very different answers. Spelke and colleagues …

Existing evidence has revealed that humans can spontaneously categorize many geometric
shapes without formal education. Children around 4 years could distinguish between …

A down-to-earth admission of abstract objects can be based on detailed explanation of
where the objectivity of mathematics comes from, and how a 'thin'notion of object emerges …

This chapter can be considered as made up of two parts, a general discussion of the notion
of mathematical practice and the limits of its use, comprised by the first three sections, and a …

There is a noticeable gap between results of cognitive neuroscientific research into basic
mathematical abilities and philosophical and empirical investigations of mathematics as a …

In a seminal study, Dehaene et al.(2006) found evidence that adults and children are
sensitive to geometric and topological (GT) concepts using a novel odd-one-out task …

We present an approach in which ancient Greek mathematical proofs by Hippocrates of
Chios and Euclid are addressed as a form of (guided) intentional reasoning. Schematically …