A constructive response to `Where mathematics comes from'

By Martin Schiralli, Nathalie Sinclair. 2003

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Some Historical Issues and Paradoxes Regarding the Concept of Infinity: An Apos Analysis: Part 2 (2005, methodology): “Several researchers such as Cornu (1991), Tall (1976), and Tall & Schwarzenberger (1978) have shown that many students think this equality is false.”
Metaphors and Models in Translation Between College and Workplace Mathematics (2007, background): “Their approach has been criticised from mathematical and psychological points of view, and especially for suggesting that there is just the one, perhaps overly simplistic ‘cognitive linguistic’ and in particular ‘conceptualmetaphoric’ route to mathematical constructions (Goldin, 2001; Schiralli and ”
Metaphors in mathematics classrooms: analyzing the dynamic process of teaching and learning of graph functions (2010, unknown): “This limitation was pointed out by various authors in the discussions that followed the publication of Lakoff and Nunez’s book (e.g., Sinclair & Schiralli, 2003 ).”
Drawing space: mathematicians’ kinetic conceptions of eigenvectors (2010, background): “However, unlike these authors, we focus on the conceptual roots of individual mathematicians—ideational mathematics— and less on the conceptual roots of the formal, written mathematics of textbooks and research articles—conceptual mathematics (see Schiralli & Sinclair, 2003 ) 1 . In particular,”