Despite the importance of mathematics in our educational systems little is known about how abstract mathematical thinking emerges. Under the uniting thread of mathematical development, we hope to connect researchers from various backgrounds to provide an integrated view of abstract mathematical cognition. Much progress has been made in the last 20 years on how numeracy is acquired. Experimental psychology has brought to light the fact that numerical cognition stems from spatial cognition. The findings from neuroimaging and single cell recording experiments (...) converge to show that numerical representations take place in the intraparietal sulcus. Further research has demonstrated that supplementary neural networks might be recruited to carry out subtasks; for example, the retrieval of arithmetic facts is done by the angular gyrus. Now that the neural networks in charge of basic mathematical cognition are identified, we can move onto the stage where we seek to understand how these basics skills are used to support the acquisition and use of abstract mathematical concepts. (shrink)

Several authors have hailed intuition as one of the defining features of expertise. In particular, while disagreeing on almost anything that touches on human cognition and artificial intelligence, Hubert Dreyfus and Herbert Simon agreed on this point. However, the highly influential theories of intuition they proposed differed in major ways, especially with respect to the role given to search and as to whether intuition is holistic or analytic. Both theories suffer from empirical weaknesses. In this paper, we show how, with (...) some additions, a recent theory of expert memory (the template theory) offers a coherent and wide-ranging explanation of intuition in expert behaviour. It is shown that the theory accounts for the key features of intuition: it explains the rapid onset of intuition and its perceptual nature, provides mechanisms for learning, incorporates processes showing how perception is linked to action and emotion, and how experts capture the entirety of a situation. In doing so, the new theory addresses the issues problematic for Dreyfus’s and Simon’s theories. Implications for research and practice are discussed. (shrink)