Arcavi, Kessel, Meira, Smith (1998), Teaching Mathematical Problem Solving: An Analysis of an Emergent Classroom Community, Research in Collegiate Mathematics Education, III, CBMS series on Issues in Mathematics Education, vol. 7. AMS, 1-70.
Chazan, D. (2000), Formulas in Mathematics and Teaching, Dynamics of the High School Algebra Classroom, Teachers College Press, New York.
Conway, J., Guy, R. (1996), The Book of Numbers, Copernicus, New York.
Descartes, R. (1925), The Geometry of Renee Descartes: translated by Smith and Latham, Open Court Publishing, 1925. — Translation of Descartes's geometry.
Hutchings, P. (1998), Introduction, in The Course Portfolio, How Faculty Can Examine Their Teaching to Advance Practice and Improve Student Learning, Hutchings (Ed.), American Association of Higher Education, Washington, pp.1-5.
Hutchings, P. (2000), Approaching the Scholarship of Teaching and Learning, Opening Lines - Approaches to the Scholarship of Teaching and Learning, American Association of Higher Education, Washington.
Klein, F. (1939), Elementary Mathematics from the Advanced Standpoint: (vol. 1 & 2): Dover, 1939 (translation from 1907,1908). — These are the translated lecture notes of Klein for his capstone. They cover much more than the material from my course. They also provide a nice way of thinking about the process of bringing mathematics to the prospective teachers.
Lakatos, I. (1976), Proofs and Refutations: the logic of mathematical discovery, Cambridge, 1976.
Lampert, M. (1990), When the problem is not the question and the solution is not the answer: mathematical knowing and teaching, American Educational Research Journal, Vol. 27, no. 1.
McLeod, D. (1985), Affective Issues in Research on Teaching Mathematical Problem Solving, in Teaching and Learning Mathematical Problem Solving : Multiple Research Perspectives, Silver (Ed.), Laurence Erlbaum Assc., Hillsdale NJ, pp. 267-279.
Persell, C. (2001), Personal communication of Carnegie project report 2001.
Polya, G. (1957 ), How to Solve It, Doubleday, New York.
Rudin, W. (?), Principles of Real Analysis,
Schifter, D. (1996), Constructing meaning for the rhetoric of mathematics education reform, in What's happening in Math Class?,
Schoenfeld, A. (1985), Mathematical Problem Solving, Academic Press.
Schoenfeld, A. (1983); Problem Solving in the Mathematics Curriculum:
Schoenfeld, A. MAA Notes 1983. - Schoenfeld includes a bibliography and a lot
of commentary and suggestions. A good read for the comments and quotes about
how mathematics is taught/understood.
Shulman, L. (1986), Those who understand: knowledge growth in teaching, Educational Researcher, 15(2), 4-14.
Shulman, L. (1985), Insert title, in Teaching and Learning Mathematical Problem Solving: Multiple Research Perspectives, Silver (Ed.), Laurence Erlbaum Assc., Hillsdale NJ, pp. 439-450.
Swetz, et al. (1995), Learn From the Masters, MAA, Washington. - This book contains articles on using history in teaching of mathematics.
Yakel, E., Cobb, P. (1996), Sociomathematical Norms, Argumentation, and Autonomy in Mathematics, Journal for Research in Mathematics Education, v. 27 (4), pp. 458-477.