Using the Philosophy of Mathematics in Teaching Undergraduate Mathematics

Book cover

Edited by Bonnie Gold, Carl Behrens, and Roger Simons

Published as Number 86 of the MAA Notes Series

Using the Philosophy of Mathematics in Teaching Undergraduate Mathematics is a collection of mostly original essays by mathematicians and philosophers on the topic. It was inspired by Bonnie Gold’s CMJ article “How Your Philosophy of Mathematics Impacts Your Teaching.” That article (reprinted in this volume) argued that one’s personal philosophy of mathematics affects his or her teaching and students, usually implicitly and often unconsciously. It also advocated making that impact explicit by having the teacher explain to their students where they are coming from and what some other options might be.

The majority of essays in this volume are reports from colleagues explaining how they tried to implement this mandate in various courses and what successes and challenges they enjoyed. Like most good Notes volumes, it will repay the thoughtful reader with many ideas that can profitably be carried into the classroom.

The E-book is free for MAA members.

Table of Contents
  1. The Big Picture
    1. Philosophy in Mathematics Education: A Categorization of the “Whys” and “Hows”, Uffe Thomas Jankvist & Steffen Møllegaard Iversen
    2. How Your Philosophy of Mathematics Impacts Your Teaching, Bonnie Gold
  2. First-year Seminar and General Education Courses
    1. What Is Mathematics and Why Won't It Go Away? Philosophy of Mathematics in a First-Year Seminar, Susan Jane Colley
    2. Helping Students See Philosophical Elements in a Mathematics Course, Mike Pinter
    3. An Exercise in the Philosophy of Mathematics, Chuck F. Rocca Jr.
    4. Evangelizing for Mathematics, Kayla Bradley Dwelle
  3. Developmental Mathematics and College Algebra
    1. Less is More: Formalism in Developmental Algebra, James R. Henderson
    2. Using Beliefs about the Nature of Mathematical Knowledge in Teaching College Algebra, Lesa Kean
  4. Calculus and Probability and Statistics
    1. Capturing Infinity: Formal Techniques, Personal Convictions, and Rigorous Justifications, Margo Kondratieva
    2. Making Philosophical Choices in Statistics, Daniel C. Sloughter
  5. Logic, Foundations, and Transition Courses for Mathematics Majors
    1. How to Use Ideas in the Philosophy of Mathematics to Teach Proof Skills, Jeff Buechner
    2. An “Unreasonable” Component to a Reasonable Course: Readings for a Transitional Class, Gizem Karaali
  6. Geometry
    1. Developing Student Epistemologies, Brian P. Katz
    2. Helping Students Develop Conscious Understanding of Axiomatizing, Paul Christian Dawkins
    3. The Philosophical and Pedagogical Implications of a Computerized Diagrammatic System for Euclidean Geometry, Nathaniel Miller
  7. Other Upper-level or Capstone Courses for Mathematics Majors
    1. Senior Seminar in Philosophical Foundations of Mathematics, Sally Cockburn
    2. Connecting Mathematics Students to Philosophy, Nathan Moyer
  8. History or Philosophy of Mathematics Courses
    1. History Without Philosophy Is Mute, Thomas Drucker
    2. Let's Teach Philosophy of Mathematics, Reuben Hersh
  9. Mathematical Education of Teachers and Teacher Educators
    1. Philosophical Aspects of Teaching Mathematics to Pre-service Elementary Teachers, Erin R. Moss
    2. Pre-service Teachers Using Core Philosophical Questions to Analyze Mathematical Behavior, Elizabeth de Freitas
    3. A Mathematics Inquiry Course: Teaching Mathematics in a Humanistic Way, Alfinio Flores, Amanda Jansen, Christine Phelps, and Laura Cline
  10. Philosophical Issues That Can Be Related to Multiple Courses
    1. Mathematical Enculturation through Conjecturing, Jason Belnap and Amy Parrott
    2. Consideration of Mathematical Certainty and Its Philosophical Foundations in Undergraduate Mathematics Courses, Linda Becerra and Ronald Barnes
    3. Proofs That Do More than Convince: College Geometry and Beyond, Margaret L. Morrow
  11. Philosophy of Mathematics and Teaching
    1. On the Value of Doubt and Discomfort in Education, Sheila K. Miller
    2. From the Classroom: Towards A New Philosophy of Mathematics, Alejandro Cuneo and Ruggero Ferro

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