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EducationPh.D. (1964) University of Wisconsin Research Area: Educational mathematicsThere is a huge crisis in the teaching and learning of mathematics in the world — this crisis is affecting the future of mathematics. My work on mathematics is having an impact on this crisis by stressing that teachers (and thence their students) learn and experience ways of thinking that are as close as possible to the ways that mathematicians think, but yet simultaneously paying attention to the cognitive development of students and teachers and the underlying meanings and intuitions of the mathematics. Only a mathematician with mathematical research experiences can do this work. My main thesis is that we should enliven our conception of what "proof" is and that proofs should be a central part of mathematics teaching at all levels, where my definition of "proof" is: A convincing communication that answers — Why. This part of my work on mathematics (as it relates to teaching and learning) I am now calling Educational Mathematics. In addition, I am currently involved in extensive mathematics curriculum innovation projects. My first book, Experiencing Geometry on Plane and Sphere (1996), has appeared in an expanded and revised third edition: Experiencing Geometry: Euclidean and Non-Euclidean With History (with Daina Taimina; Pearson Prentice-Hall, 2005). My second book, Differential Geometry: A Geometric Introduction (1998) has appeared in a Revised Second Edition (2005) and a new Self Study Edition (2006). In 2005 I accepted an invitation to join the high school curriculum development team for Robert Moses’ Algebra Project and am the lead writer for the geometry portions of the Algebra Project high school curriculum.Selected PublicationsExtended hyperbolic surfaces in R^3; in the Ludmilla Keldysh Memorial Volume, Proceedings of the Steklov Institute of Mathematics, Vol. 247, 2004, pp. 1–13. Experiencing Geometry: Euclidean and Non-Euclidean With History (with Daina Taimina), 3rd Edition, Pearson Prentice-Hall, 2005. (pp: xxx + 402) How to use history to clarify common confusions in geometry (with Daina Taimina); Chapter 6 in From Calculus to Computers: Using Recent History in the Teaching of Mathematics (A. Shell and D. Jardine, eds.), MAA Notes 68, 2005, pp. 57–73. Experiencing Meanings in Geometry (with Daina Taimina); Chapter 3 in Aesthetics and Mathematics (David Pimm and N. Sinclair, eds.), Springer-Verlag, 2006, pp. 58–83. Alive mathematical reasoning; a chapter in Educational Transformations: Changing our lives through mathematics; A tribute to Stephen Ira Brown (L. Copes and F. Rosamond, eds.), Bloomington, Indiana: AuthorHouse, 2006, pp. 247–270. Is all course-based mathematics special?, A response to Ann Watson’s “School mathematics as a special kind of mathematics”, For the Learning of Mathematics 28 no. 3 (2009), 9–10. Last modified: July 27, 2010 |
