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Instructional Practices Guide

Guide to Evidence-Based Instructional Practices in Undergraduate Mathematics

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Success in mathematics opens opportunities for students. A wealth of research literature exists on how mathematics instructors can facilitate rich, meaningful learning experiences and on what instructors can do to improve teaching and learning at the undergraduate level: Effective teaching and deep learning require student engagement with content both inside and outside the classroom. This Instructional Practices Guide aims to share effective, evidence-based practices instructors can use to facilitate meaningful learning for students of mathematics. Professional associations in the mathematical sciences along with state and national funding agencies are supporting efforts to radically transform the undergraduate education experience; it is truly an exciting time to be a mathematics instructor!

With that big picture in mind, this guide is written from the perspective that teaching and learning is a force for social change. Beyond the confines of individual instructors’ classrooms, beyond their decisions about what mathematics to teach and how to teach it, there are societal forces that call upon all mathematics instructors to advocate for increased student access to the discipline of mathematics. Inequity exists in many facets of our society, including within the teaching and learning of mathematics. Because access to success in mathematics is not distributed fairly, the opportunities that accompany success in mathematics are also not distributed fairly. We in the mathematical sciences community should not affirm this inequitable situation as an acceptable status quo. We owe it to our discipline, to ourselves, and to society to disseminate mathematical knowledge in ways that increase individuals’ access to the opportunities that come with mathematical understanding.

Some of us have become reflective instructors over the course of our careers, and our classrooms have changed and improved as a result. But if we truly want to effect change, then we are compelled to extend the reach of our efforts beyond our own students in our own classrooms. It is our responsibility to examine the system within which we educate students and find ways to improve that system. It is our responsibility to help our colleagues improve and to collectively succeed at teaching mathematics to all students so that our discipline realizes its full potential as a subject of beauty, of truth, and of empowerment for all.

Such a sea change will require transforming how mathematics is taught and facing our own individual and collective roles in a system that does not serve all students well. It is tempting to guard access to mathematics as an exclusive club – there is an underlying self-interest that makes appealing the default belief that only special or gifted individuals can do mathematics. We in the profession of teaching mathematics must look inward and determine if we hold that underlying belief. If this introspection reveals instructional practices affirming we subscribe to this belief, practices that exacerbate restricted access to mathematics, we must discard those practices.

All instructors can facilitate student success in mathematics, and we cannot underestimate the power of the environment in our classrooms, departments, and institutions to positively impact student learning. Changing teaching practice is hard. But those of us who do mathematics recognize the hard work required to learn and understand it and we choose to do that hard work. We can likewise choose to do the hard work required to teach our beloved subject. 

Mathematics instructors stand at a crossroads. We must gather the courage to take the difficult path of change. We must gather the courage to venture down the path of uncertainty and try new evidence-based strategies that actively engage students in the learning experience. We must gather the courage to advocate beyond our own classroom for student-centered instructional strategies that promote equitable access to mathematics for all students. We stand at a crossroads, and we must choose the path of transformation in order to fulfill our professional responsibility to our students. This Instructional Practices Guide can serve as a catalyst for community-wide transformation toward improved learning experiences and equitable access to mathematics for all students. Society deserves nothing less.

The MAA Instructional Practices Guide (© 2017 The Mathematical Association of America, Inc.) is an open access publication distributed in accordance with the Creative Commons Attribution Non Commercial (CC BY-NC 4.0) license, which permits others to distribute, remix, adapt, build upon this work non-commercially, and license their derivative works on different terms, provided the original work is properly cited and the use is non-commercial. See

Conference Presentations about the Instructional Practices Guide

Please feel free to download and use any of these presentations for your local discussions on pedagogical practices. Each presentation below is in PDF format, but the authors are happy to provide editable formats upon direct email request.

Leadership Team

  • Martha Abell, Georgia Southern University
  • Linda Braddy, Tarrant County College
  • Doug Ensley, Mathematical Association of America
  • Lew Ludwig, Denison University 
  • Hortensia Soto-Johnson, University of Northern Colorado 

Steering Committee (Lead Writers)

  • James Alvarez, University of Texas, Arlington
  • Benjamin Braun, University of Kentucky
  • Elizabeth Burroughs, Montana State University
  • Rick Cleary, Babson College
  • Karen Keene, North Carolina State University 
  • Gavin LaRose, University of Michigan
  • Julie Phelps, Valencia College
  • April Strom, Scottsdale Community College

Advisory Board

  • Matt Ando, University of Illinois
  • David Bressoud, Macalester College
  • Marilyn Carlson, Arizona State University
  • Annalisa Crannell, Franklin and Marshall College
  • Tara Holm, Cornell University
  • Dave Kung, St. Mary's College of Maryland
  • Rachel Levy, Harvey Mudd College
  • Francis Su, Harvey Mudd College
  • Uri Treisman, University of Texas, Austin
  • Paul Zorn, St. Olaf College

Contributing Writers

Scott Adamson Aditya Adiredja Spencer Bagley Randy Boucher
Derek Bruff Joe Champion Beth Cory Jessica Deshler
Jackie Dewar Jess Ellis Hagman Angie Hodge Brian Katz
Elizabeth Kelly Klay Kruzcek Brigitte Lahme Rachel Levy
Luis Leyva Guadalupe Lozanoa Bill Martin John Meier
Victor Piercy Mike Pinter Chris Rasmussen Christine von Renesse
Jack Rotman Behnaz Rouhani Ayse Sahin Milos Savic
Kimberly Seashore Mary Shepherd Robert Talbert Diana Thomas
Laura Watkins Claire Wladis Phil Yates Maria Del Rosario Zavala

Support for this MAA program is provided by the National Science Foundation (grant DUE-1544324).