The Legacy of Felix Klein

William G. McCallum is a University Distinguished Professor of Mathematics and Head of the Department of Mathematics at the University of Arizona. Born in Sydney, Australia in 1956, he received his Ph.D. in Mathematics from Harvard University in 1984, under the supervision of Barry Mazur. After spending two years at the University of California, Berkeley, and one at the Mathematical Sciences Research Institute in Berkeley, he joined the faculty at the University of Arizona in 1987. In 1989 he joined the Harvard calculus consortium, and is the lead author of the consortium's multivariable calculus and college algebra texts. In 1993-94 he spent a year at the Institut des Hautes Etudes Scientifiques, and in 1995-96 he spent a year at the Institute for Advanced Study on a Centennial Fellowship from the American Mathematical Society. In 2005 he received the Director's Award for Distinguished Teaching Scholars from the National Science Foundation. In 2006 he founded the Institute for Mathematics and Education at the University of Arizona. He was Director of the Institute until 2009 and now chairs its advisory board. In 2009 - 2010 he was a lead writer for the Common Core State Standards in Mathematics. His professional interests include arithmetical algebraic geometry and mathematics education. He has received grants and written articles, essays, and books in both areas. In 2012, he won the American Mathematical Society's Award for Distinguished Public Service.

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Marta Menghini received her degree in Mathematics from the University of Rome "La Sapienza". She is associate professor in the Department of Mathematics of the same University. She produced papers in the field of combinatoric geometry, of mathematics education, of the history of mathematics education, and of the history of mathematics. In this latter field she worked on the development of projective and algebraic geometry in the last century: a paper published in 1986 in Historia Mathematica concerned a correspondence between Luigi Cremona and Max Noether, a further paper published in the same journal with G. Israel was devoted to the different philosophic and scientific visions of Henri Poincaré and Federigo Enriques relative to qualitative analysis. The role of projective geometry in Italian education and institutions at the end of the 19th century is described in a paper appeared the first volume of the International Journal for the history of mathematics education, in 2006. In 2008 she edited, together with F. Arzarello, F. Furinghetti e L. Giacardi, the volume The First Century of the International Commission on Mathematical Instruction. Reflecting and Shaping the World of Mathematics Education, published on the occasion of the centennial of the International Commission of Mathematical Instruction by Enciclopedia Italiana. Together with F. Furinghetti. and J. M Matos., she wrote the chapter “From Mathematics and Education, to Mathematics Education” in the Third International Handbook of Mathematics Education, published by Springer in 2013, concerning the historical development of mathematics education as an academic field. With E. Berbin she wrote the chapter about “History of Teaching Geometry” in the International Handbook on History of Mathematics Education (Springer, 2013). In the Encyclopedia of Life Support Systems (EOLSS), published by UNESCO-EOLSS Joint Committee, she wrote the chapter on the History of Mathematics Education in Italy http://www.mat.uniroma1.it/persone/menghini

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Michael Neubrand is a professor emeritus at the Department of Mathematics (IfM), Carl von Ossietzky Universität Oldenburg. Michael does research in Teaching and Learning Mathematics. He was formerly a member of the PISA research group in Germany. He researches into math teachers' knowledge and education, and Higher Education. His most recent publication is 'Conceptualizations of professional knowledge for teachers of mathematics.'

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Gert Schubring is a retired member of the Institut für Didaktik der Mathematik, a research institute at Bielefeld University, and at present is visiting professor at the Universidade Federal do Rio de Janeiro (Brazil). His research interests focus on the history of mathematics and the sciences in the eighteenth and nineteenth centuries and their systemic interrelation with social-cultural systems. One of his specializations is history of mathematics education. He has published several books, among which is Conflicts between Generalization, Rigor and Intuition: Number Concepts Underlying the Development of Analysis in 17th–19th Century France and Germany (New York, 2005).

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