pt. 1 The big picture. Philosophy in mathematics education : a categorization of the "whys" and "hows" / Uffe Thomas Jankvist & Steffen Møllegaard Iversen -- How your philosophy of mathematics impacts your teaching / Bonnie Gold -- pt. 2 First-year seminar and general education courses. What is mathematics and why won't it go away? : philosophies of mathematics in a first-year seminar / Susan Jane Colley -- Helping students see philosophical elements in a mathematics course / Mike Pinter -- An exercise in the philosophy of Mathematics / Chuck F. Rocca Jr. -- Evangelizing for mathematics / Kayla Bradley Dwelle -- pt. 3 Developmental mathematics and college algebra. Less is more : formalism in developmenta algebra / James R. Henderson -- Using beliefs about the nature of mathematical knowledge in teaching college algebra / Lesa Kean -- pt. 4 Calculus and probability and statistics. Capturing infinity : formal techniques, personal convictions, and rigorous justifications / Margo Kondratieva -- Making philosophical choices in statistics / Daniel C. Sloughter -- pt. 5 Logic, foundations, and trasition courses for mathematics majors. How to use ideas in the philosophy of mathematics to teach proof skills / Jeffe Buechner -- An "unreasonable" component to a reasonable course : readings for a transitional class / Gizem Karaali -- pt. 6 Geometry. Developing student epistemologies / Brian P. Katz -- Helping students develop conscious understanding of axiomatizing / Paul Christian Dawkins -- The philosophical and pedagogical implications of a computerized diagrammatic system for euclidean geometry / Nathaniel Miller -- pt. 7 Other upper-level or capstone courses for mathematics majors. Senior seminar in philosophical foundations of mathematics / Sally Cockburn -- Connecting mathematics students to philosophy / Nathan Moyer -- pt. 8 History or philosophy of mathematics courses. History without philosophy is mute / Thomas Drucker -- Let's teach philosophy of mathematics / Reuben Hersh -- pt. 9 Mathematical education of teachers and teacher educators. Philosophical aspects of teaching mathematics to pre-service elementary teachers / Erin R. Moss -- Pre-service teachers using core philosophical questions to analyze mathematical behavior / Elizabeth de Freitas -- A mathematics inquiry course : teaching mathematics in a humanistic way / Alfinio Flores, Amanda Jansen, Christine Phelps, and Laura Cline -- pt. 10 Philosophical issues that can be related to multiple courses. Mathematical enculturation through conjecturing / Jason Belnap and Amy Parrott -- Consideration of mathematical certainty and its philosophical foundations in undergraduate mathematics courses / Linda Becerra and Ronald Barnes -- Proofs that do more than convince : college geometry and beyond / Margaret L Morrow -- pt. 11 Philosophy of mathematics and teaching. On the value of doubt and discomfort in education / Sheila K. Miller -- From the classroom : towards a new philosophy of mathematics / Alejandro Cuneo and Ruggero Ferro.
Summary:
"This book is a compilation of essays proposing ways that faculty teaching (primarily) undergraduate mathematics can incorporate the philosophy of mathematics into those courses. Each chapter gives information on the level of student understanding assumed, kinds of philosopical issues are considered, materials students are given to work with, and how students have responded. The chapters were chosen to represent a wide range of course types, from first-year or senior seminars, to logic and geometry to calculus and statistics. The philosophical approaches are also very varied, from platonist to social constructivist to formalist."--back cover.
This resource is supported by the Institute of Museum and Library Services under the provisions of the Library Services and Technology Act as administered by State Library of Iowa.