Teaching & Outreach

Before I became a research mathematician I spent a decade as a mathematics educator, and teaching, mentoring, and outreach have remained central to my work ever since — from doctoral advising to K–12 teacher professional development. I have taught mathematics at every level from third grade through graduate school; in public schools, private schools, charter schools, and summer programs; with special-needs students, girls, diverse urban populations, and Ivy League college students. In addition to all of this, I have extensive experience working with both preservice and inservice teachers.

Teaching honors

  • Regents’ Medal for Excellence in Teaching, University of Hawai‘i (2017)
  • Haimo Award for Distinguished College or University Teaching of Mathematics, MAA Golden Section (2015)
  • UH Department of Mathematics Faculty Excellence in Teaching Award (2013)
  • Brown University Department of Mathematics Outstanding Teaching Prize (2006)

Doctoral and master’s students

  • Pui Hang (Donald) Lee, Ph.D. (2025) — Local fields, iterated extensions, and Julia sets.
  • Bella Tobin, Ph.D. (2019) — Belyi maps and bicritical polynomials.
  • TJ Combs, Ph.D. (2018) — Arboreal Galois representations.
  • Elliot Ossanna, M.A. (2018) — Pascal-like triangles and fractal dimension.
  • Bianca Thompson, Ph.D. (2015) — Exceptional points in arithmetic dynamics.
  • Diane Yap, Ph.D. (2012) — Degree 2 rational maps: potential good reduction and post-critical finiteness.
  • Gretel Sia, M.A. (2011) — A survey of the discrete logarithm problem.

Outreach and broader impact

Since 2023 I have been a frequent presenter at Math Teachers’ Circles throughout Southern California and have worked with AIM staff on large public events, including the annual AIM Math Fair and the AIM Public Lecture Series.

Earlier, I founded the Math Teachers’ Circle of Hawai‘i (2011–2018), growing it from about a dozen teachers per session to sixty and sustaining it through a series of grants, and I developed a model for connecting remote circles on the outer islands to a hub in Honolulu. Other work has included co-organizing “Beautiful Day of Math” events on Moloka‘i and at UH Mānoa, teacher workshops across the Hawaiian Islands through the NSF-funded SUPER-M program, and guest sessions for teacher circles in Denver and Albuquerque.

Curriculum and education writing

  • Created an open educational resource textbook, Mathematics for Elementary Teachers (2013), and redesigned the corresponding courses at UH Mānoa.
  • Senior author on widely adopted secondary curricula, including IMPACT Mathematics, Connected Geometry, and Mathematical Methods in High School (now part of the CME Project).
  • Learning Math: Geometry, Annenberg/CPB — a multimedia online geometry course for teachers of grades K–8.
  • B. Donaldson, D. Farmer, S. Koutsoliotas, and M. Manes, “AIM: Building and supporting collaborative research communities,” Mathematical Intelligencer 46 (2024), no. 4, 378–392.
  • M. Manes, “Women in Numbers: a research community,” in Count Me In: Community and Belonging in Mathematics, AMS (2022).
  • M. Manes, “Building bridges between universities and K–12 schools,” Notes of the Canadian Mathematical Society 42.5 (Oct–Nov 2010), 8–9.

A full list of education publications and curricula is in my CV.