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Recent drafts are now placed on my downloads page, and are denoted by letters at the end of the alphabet (z, y, x, ...) until they are submitted and accepted for publication and are then denoted by a, b, c, ... in order of publication.
My book on How Humans Learn to Think Mathematically has recently been accepted for publication by Cambridge University Press to appear sometime in 2013. The first chapter outlines the whole framework and is available from my downloads page.
Previous drafts that were not published are as follows:
An Example of the Fragility of a Procedural Approach to Solving Equations (with Rosana Noguera de Lima). (We withheld the paper because we refused to rewrite it as specified by the editor of a well-known journal. I place it here in draft form to let others form their own opinion.)
(with Tony Barnard) Cognitive Units, Connections and Compression in Mathematical Thinking. This paper is a seminal paper that is the foundation of the ideas of ‘thinkable concept’ and ‘crystalline concept’ that are essential concepts in the book How Humans Learn to Think Mathematically.
(with Mercedes McGowen) Flexible Thinking, Consistency, and Stability of Responses: A Study of Divergence.
(with Anna Watson) Schemas and processes for sketching the gradient of a graph.