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Drafts of Papers currently in Progress
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Since my retirement, I have continued to write as I build on my developing theory of three worlds of mathematics. A book on How Humans Learn to Think Mathematically has recently been completed and submitted for publication. Two sample chapters are available from here: 1. about this book, 9. blending ideas in the calculus. e-mail me if you would like to see a full draft.
Drafts of new articles are now given in my full list of publications but with an x after the year to indicate that they have yet to be published.
Other papers currently available in draft are as follows:
(with Rosana Noguera de Lima) An Example of the Fragility of a Procedural Approach to Solving Equations. (An important paper because it shows how a procedural approach to solving equations can collapse in subsequent study. Regrettably, the editor of a well-known journal wishes us to dramatically rewrite according to his views in order to publish it. 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.
(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.
