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A Mathematician’s Practical Guide to Mentoring Undergraduate Research

Michael Dorff, Allison Henrich, and Lara Pudwell
Publication Date: 
Number of Pages: 
Classroom Resource Materials
[Reviewed by
J. W. Gaberdiel
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An Undergraduate Research Program (URP) in mathematics provides collaboration between faculty and undergraduate students in order to generate new knowledge in a particular mathematical field; i.e., students actually work on unsolved problems.  
URPs are becoming increasingly more prevalent at universities and two-year colleges, as are conferences and journals devoted to publicizing the work of student researchers.  And yet, the decision of a teacher or institution to create a URP is hindered by a multitude of myths about the difficulty of establishing such a program.  In fact, with more sources of funding and resources than ever before, right now it is easier than ever to start a URP at your institution.
This book is a comprehensive, practical 'how-to' guide for faculty who want to learn how to create, operate, and fund a URP.  The three authors have each been operating their own URPs for decades and have collectively received over 9 million dollars in funding to support their student researchers.  They make the impassioned case that undergraduate research is the ideal way to prepare students to thrive in a global market that requires workers who can craft solutions to unsolved problems, rather than traditional classrooms that simply train students to perform a skill with proficiency.  They lay out clear best practices for establishing a URP, focusing especially on dispelling the misconceptions about starting up your own URP:
  • You don't need advanced students who have already taken numerous prerequisites; you just need students who are enthusiastic and hard working.  
  • You don't need funding and numerous students to get started; you just need one student who is eager for a new experience.
  • Math research is not "hard" and only for talented students seeking PhDs; rather, it can and should be done by regular students at any college.  In fact, the students who will most benefit from this high-impact practice are students who are underrepresented in mathematics (women and minority groups: black, Latinx, Native American, native pacific islanders, first-generation college students, and students with disabilities).  
  • The main benefits to students are not just math skills; rather, students build communication skills (verbal, written, public speaking, and small group) and the ability to persevere through challenging open problems with grit, critical thinking, and creativity.  
  • It's not as hard as you think to get funding; since the 1960s, there are dozens of sources of funding for URPs.
  • It doesn't necessarily take up additional time from your schedule; you can make adjustments in how you already spend time on scholarship and mentoring.
  • You don't need to work on famous unsolved problems; students just need experience working on open problems whose solutions cannot be looked up on google, especially problems found in industry.  
Compared to other books on the market, this one stands alone as a complete 'how to' guide to create a URP from scratch, including the benefits and challenges of doing so (the only thing it is missing is an index).  Other books on the market are more limited in scope:  some simply summarize the myriad benefits of a URP as a high-impact practice; others give specific examples of open problems in mathematics that are accessible to undergraduate students; yet others help students navigate their way through the undergraduate research experiences, as well as introduce higher levels of mathematics as a 'boot camp' to help students jump in.  This book alone offers complete support to faculty in establishing a new URP, including a wide variety of useful examples and links to more information:  
  • 2 sample grant proposals that received funding
  • best practices for promoting effective group communication
  • best practices for public speaking, poster sessions, and writing papers
  • sample papers written by students
  • sample posters created by students
  • lists of journals that publish student work
  • lists of conferences that highlight student work
  • lists of summer institutes for undergraduate research 
  • steps for setting up your own summer institute, or REU (Research Experience for Undergraduates)
  • guidelines for choosing 'good' research problems, especially from industry
  • tips for thinking about the audience of your research results
  • how to assess your program, students, and self
  • a helpful list of acronyms and a bibliography
Read this book today, and you can start your URP tomorrow.  


J. W. Gaberdiel earned his BS in Mathematics at the University of Arizona, Masters in Education at Arizona State University, and is earning a Masters in Mathematics from Emporia University. He has over 10 years of experience teaching mathematics to high school and college students, and is passionate about helping students move past math phobia to math fluency. JW enjoys math research and humor, and can be reached at: