Welcome to the HOME page of my website.
As of May 2019, I continue to take an interest in Mathematics Education and am working on new ideas relating to making sense in long-term mathematical thinking. This includes astonishingly simple observations of how we speak mathematics and use our eyes to read text and follow moving objects with completely new ways for making sense of arithmetic, algebra, calculus and other mathematical topics. Because of health problems I am only writing up these ideas slowly. Drafts will appear on my downloads page from time to time. See also latest news.
Feel free to use information about my research as a resource, or download a paper. Several earlier unpublished drafts are available. There is news about recent changes on this site (made on
News: A list of information on updates to focus on the most recent additions, including new papers, information on books including Fermat's Last Theorem (3rd Edition with Ian Stewart) and Intelligence, Learning and Understanding: A Tribute to Richard Skemp (ed. with Michael Thomas). Subsequent books include How Humans Learn to Think Mathematically (also available in Japanese and Italian), The Foundations of Mathematics (2nd edition with Ian Stewart), also available in Polish, Japanese), Complex Analysis (2nd edition with Ian Stewart).
David retired in September 2006 and is now Emeritus Professor of Mathematical Thinking at Warwick and Visiting Professor at Loughborough University.
His first foray into something different is the book Memories of Wellingborough Grammar School, with brother Graham, a social document remembering the school they attended in the 1950s with its focus on academic and sporting excellence. Two new books in the series were published on December 11th 2012: Mr Woolley and the War Years, Letters to Mr Woolley in the War Years, followed by Mr Wrenn's School in 2013.
His current interest is in extending the framework of long-term learning to incorporate the ways in which the human brain makes sense of information. For instance, the way in which we articulate speech lays a foundation for understanding the meanings of arithmetic and algebraic symbolism and the way in which the human eye tracks a moving object by locking on to it and following it smoothly enables us imagine the number line with points which can be fixed and points that can vary. This provides the foundational idea of a number line with points that may be constant or variable. This offers an alternative vision of the number line including infinitesimals.
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