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My classroom philosophy

We all learn best by doing rather than passively watching or listening.  I've watched lots of people play the piano or throw a football, but I can't do either of those things without practicing first, and mathematics is no different.  Thus, my main goal in my classroom is to have my students doing math as much as possible, rather than just listening to math!  This can be achieved in many different ways; here are some examples of what I've tried.

Flipped classrooms

In Calculus, I use a flipped classroom.  Most of the time, my students' first contact with new material is outside of class, through screencasts and readings.  Then in class they practice, solve interesting problems, and deepen their understanding together as a team where they can lean on each other and me.  We even use inquiry-style (or discovery) activities to construct some of the key concepts!  (See more about inquiry-based learning below.)

During the Fall 2014 semester my colleague John (Zig) Siegfried and I collected data on my students to try and understand how this structure affects their learning gains.  Data analysis is ongoing, but we have been speaking about small pieces of this data at meetings like JMM 2015, MathFest 2015, and JMM 2016.  We also presented a large swath of our data at the Conference on RUME in February 2016, and have a paper in the RUME conference proceedings (see below).  Another paper, encompassing all of our data, is in preparation.

Inquiry-Based Learning

I have begun using inquiry-based learning (IBL) in some of my classes.  In this classroom style, students create mathematics themselves, which embodies the doing of mathematics for students.  I've used IBL to teach Elementary Number Theory (Fall 2015) and Discrete Math (JMU's "Intro to Proofs" course, Fall 2016), and I'm excited to say it went pretty well!  Folks interested in learning more can check out the Academy for Inquiry Based Learning for an overview of IBL in mathematics, and links to lots of other blogs, resources, and materials.  You can also join the SIGMAA on IBL (a Special Interest Group of the MAA) the next time you renew your MAA membership.  If you're in the MD-DC-VA section of the MAA, you can also join the MD-DC-VA IBL Consortium or check out our events at the section meetings.

Research on Teaching

I've been doing research on undergraduate mathematics education via my teaching since 2014.  This helps me understand what's going well and why, as well as allows me to contribute to the public knowledge of how active learning affects student learning outcomes.  So far, I've carefully collected data on my flipped classroom, and I've collected some more informal data on how experiencing IBL affects future teachers.  Below are some of the publications and talks I've given about this work.

Upcoming Conferences and Presentations about about Research in Undergraduate Mathematics Education:
• MAA MD-DC-VA Fall Section Meeting, Christopher Newport University, November 2017
• MAA MD-DC-VA Spring Section Meeting, Washington & Lee University/Virginia Military Institute, April 2017

Publications

Recent Conferences and Presentations about Research in Undergraduate Mathematics Education or Teaching:
• MAA MD-DC-VA Spring Section Meeting, Workshop on using Inquiry in Calculus (sponsored by MD-DC-VA IBL), Frostburg State University, April 2017
• MAA Session on Inquiry Based Learning, JMM, Atlanta, January 2017
• MAA MD-DC-VA Fall Section Meeting, Special Session on IBL (sponsored by MD-DC-VA IBL), Johns Hopkins University, November 2016
• IBL Workshop, run by AIBL and UNYIBL, June 2016
• AMS Eastern Sectional (Invited Speaker), SUNY Stony Brook, March 2016
• SIGMAA on RUME (Invited Speaker), Pittsburgh, February 2016
• MAA Session on Scholarship of Teaching and Learning, JMM 2016, Seattle
• MAA Session on Scholarship of Teaching and Learning, MathFest 2015, Washington DC
• MAA PREP Workshop: Implementing POGIL in Mathematics, July 2015
• MAA Session on Using Flipped Pedagogy to Engage Students in Learning, JMM 2015, January 2015
• Project NExT Workshop, MathFest, Hartford, CT, August 2013
• MAA PREP Workshop: Implementing POGIL in Calculus 1, Arlington, VA, June 2013
• Project NExT Workshop, MathFest, Madison, WI, August 2012

Project NExT

I was a 2012-2013 Silver12 Project NExT Fellow (a program of of the MAA which provides mentoring and support for new professors as they begin their teaching careers).  I'm so grateful for my Project NExT experience!  I found a phenomenal network of other early career professors who share such great ideas, and have met so many inspiring professors who have provided amazing guidance and support as I strive to become a more learner-centered teacher!   If you're interested in learning more about the program, check out the link above or send me an email!

What I teach

I teach courses across the curriculum! Here's a list of the courses I've taught at JMU:
• Fall 2017:
• The Mathematics of Cryptography (topics course, semi-flipped)
• Calculus III (MATH 237, flipped)
• Spring 2017: Calculus III (MATH 237, flipped)
• Fall 2016: Discrete Mathematics (Intro to Proof, MATH 245, IBL)
• Spring 2016:
• Abstract Algebra II (MATH 431, fill-in lecture notes)
• Calculus III (MATH 237, flipped)
• Fall 2015:
• Elementary Number Theory (MATH 310, IBL)
• Calculus II (MATH 236, flipped)
• Spring 2015:
• Abstract Algebra II (MATH 431, fill-in lecture notes)
• Calculus II (MATH 236, flipped)
• Fall 2014:
• Abstract Algebra I (MATH 430, fill-in lecture notes)
• Calculus I (MATH 235, flipped)
• Spring 2014:
• Abstract Algebra I (MATH 430)
• Calculus I (MATH 235, flipped)
• Fall 2013:  Calculus I (MATH 235, flipped)
• Spring 2013:  Calculus with Integrated Pre-Calculus II (MATH 232)
• Fall 2012: Calculus with Integrated Pre-Calculus I (MATH 231)

Other teaching experiences

In addition to teaching at JMU since 2012, I taught many courses at Colorado State University while I was a graduate student (including Calculus I, II, and III, Programming in Maple, and Abstract Algebra) and at Liberty Common School in grades 7-9.