Research

Investigations of best practices for educational experiences and broadening participation in undergraduate STEM, and best practices for departmental change aimed at implementing those practices at scale.

Departmental Change

Progress through Calculus (PtC)

RBIS in Chemistry, Math, and Physics

Social Network Analysis

Students' Mathematics

Coming Soon!


Departmental Change


My current focus in research is departmental change aimed at improving students' experiences with introductory STEM courses. Existing and ongoing research in RUME and DBER (and K-12 mathematics and science education fields) points to many pedagogical approaches, curricular changes, and program structures which can support student success and broaden participation beyond the current system. However, shifts at the individual, departmental, and institutional level toward implementing these practices and structures are fraught with difficulty and a major shift has not appeared. I believe that a systems approach is needed to understand the relationships between individual, department, and institutional factors that support and constrain interest, willingness, and capacity for instructional change.

I have worked on several projects that explore theoretical, empirical, and practical implications of and for change in undergraduate STEM departments. A selection of the resulting writing is presented here:

  • Apkarian, N. (2018). Emerging instructional leadership in a new course coordinator system. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro, & S. Brown (Eds.) Proceedings of the 21st Annual Conference on Research in Undergraduate Mathematics Education, pp. 1414-1419. San Diego, CA. [link]
  • Henderson, C., Rasmussen, C., Knaub, A., Apkarian, N., Daly, A.J., & Quardokus Fisher, K., (2018). Researching and Enacting Change in Postsecondary Education: Leveraging Instructors' Social Networks. Taylor & Francis.
  • Reinholz, D. L., & Apkarian, N. (2018). Four frames for systemic change in STEM departments. International Journal of STEM Education, 5(3), 1-10. DOI: 10.1186/s40594-018-0103-x [Enhanced PDF]
  • Apkarian, N. (2018). Transforming Precalculus to Calculus 2: A longitudinal study of social and structural change in a university mathematics department (unpublished doctoral dissertation). University of California San Diego & San Diego State University: San Diego, CA.
  • Apkarian, N., Bowers, J., O’Sullivan, M. E., & Rasmussen, C. (2018). A case study of change in the teaching and learning of Precalculus to Calculus 2: What we’re doing with what we have. PRIMUS, 28(6), 528-549. DOI: 10.1080/10511970.2017.1388319

Progress through Calculus


The Progress through Calculus (PtC) project is an NSF-funded research grant (DUE IUSE #1430540) investigating Precalculus to Calculus 2 (P2C2) programs in mathematics departments at universities in the United States. This project is run in conjunction with the Mathematical Association of America, and the PI team consists of David Bressoud (CBMS, Macalester College), Chris Rasmussen (San Diego State University), Sean Larsen (Portland State University), Jessica Ellis Hagman (Colorado State University), and Rachel Levy (MAA); Senior Personnel are Naneh Apkarian (Western Michigan University) and Estrella Johnson (Virginia Tech). This project follows the earlier Characteristics of Successful Programs in College Calculus, and information about both projects can be found at maa.org/ptc.

Phase 1: National Census Survey

The first phase of PtC involved the design, distribution, and analysis of a national census survey. The survey was sent to representatives of the university departments in the United States which offer graduate degrees (MA, MS, PhD) in mathematics. Overall there was a 68% (223/330) response rate. Analysis will continue for some time, but some results have already been presented or published:

Articles
  • Rasmussen, C., Apkarian, N., Hagman, J. E., Johnson, E., Larsen, S., Bressoud, D., & Progress through Calculus team. (2019). Characteristics of Precalculus through Calculus 2 programs: Insights from a national census survey. Journal of Research in Mathematics Education, 50(1), 98-112.
  • Apkarian, N., Kirin, D., Gehrtz, J., & Vroom, K. (2017). Math department concerns: Working to bridge the gap between goals and first steps. MAA FOCUS, February/March, 35-37. Available online.
  • Voigt, M., Apkarian, N., & Rasmussen, C. (2017). Diverging from the standard fare: Variations in the calculus curriculum. MAA FOCUS, February/March, 32-34. Available online.
Technical Reporting
  • Apkarian, N., Kirin, D., & Progress through Calculus Team. (2017). Progress through calculus: Census survey technical report. Mathematical Association of America. Available: http://bit.ly/2xcbZTV
Conference Papers
  • Voigt, M., Rasmussen, C., & Apkarian, N. (2017). Variations in Precalculus through Calculus 2 courses. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro, & S. Brown (Eds.) Proceedings of the 20th Annual Conference on Research in Undergraduate Mathematics Education, 1001-1008. San Diego, CA. [link]
  • Bragdon, D., Ellis, J., & Gehrtz, J. (2017). Interaction, activities, and feedback: A taxonomy of GTA professional development. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro, & S. Brown (Eds.) Proceedings of the 20th Annual Conference on Research in Undergraduate Mathematics Education, 502-510. San Diego, CA. [link]
  • Rasmussen, C., Apkarian, N., Bressoud, D., Ellis, J., Johnson, E., & Larsen, S. (2016). A national investigation of precalculus through calculus 2. In T. Fukawa-Connelly, N. Infante, M. Wawro, & S. Brown (Eds.), Proceedings of the 19th Annual Conference on Research in Undergraduate Mathematics Education, 1245-1251. Pittsburgh, PA. [link]
Phase 2: P2C2 Case Studies at 12 Departments

The second (ongoing) phase of the PtC project is the careful study of the P2C2 programs of twelve departments, selected using the census survey data to have a range of program features, priorities, institution types, and success rates. These departments will be visited and surveyed by the PtC project team over a span of two academic years to develop a detailed understanding of how each program and its constituent parts function as a system, and which aspects appear to particularly support student success in the P2C2 courses.

As part of the ongoing analysis of PtC data, we have identified four themes which stand out across multiple sites for further investigation. These four themes are (1) structural course variations; (2) attention to diversity, equity, and/or inclusivity; (3) course coordination systems; and (4) the process of change.


RBIS in Chemistry, Math, and Physics


The full title of this project is "Collaborative Research: Evaluating the Uptake of Research-Based Instructional Strategies in Undergraduate Chemistry, Mathematics, and Physics." It is a collaborative project funded by the NSF (DUE #1726328, 1726379, 1726281, 1726126, 1726042), with PI's Charles Henderson (Western Michigan University), Marilyne Stains (University of Nebraska-Lincoln), Estrella Johnson (Virginia Tech), Jeffrey Raker (University of South Florida), and Melissa Dancy (University of Colorado at Boulder). I am currently a postdoctoral research associate on this project. The interdisciplinary focus of this project is supported by interdisciplinary background of the project team: Henderson and Dancy come from a Physics background, Stains and Raker from Chemistry, Johnson and Apkarian from Mathematics.

Research-based instructional strategies (RBIS) are strategies which have been shown to improve students' experience with their coursework, including learning, affinity, retention, confidence, and persistence. However, RBIS are not in as common use as one might expect. This project aims to investigate why some instructors use RBIS in their courses and others do not, to inform ongoing and future efforts to increase their usage across the country. We focus on three of the major gatekeeper courses for STEM majors: general chemistry, single-variable calculus, and introductory quantitative physics. The primary aims of this research project are to (1) build capacity to document changes in the implementation of RBIS; (2) estimate the importance of individual, departmental, institutional, and disciplinary factors in shaping instructional decisions to implement RBIS (or not); and (3) test a set of hypotheses about how and why instructors use RBIS.

Phase I: National Survey

The goals of this phase of the project are (a) to better understand the extent to which postsecondary instructors in chemistry, mathematics, and physics use research-based instructional strategies in their teaching of major gatekeeper courses; and (b) to identify factors which have significant impact on instructors' decisions to use (or not use) RBIS in these classes, with consideration given to disciplinary, institutional, departmental, and individual level factors. To this end, we have developed a survey that asks questions about instructional practice, institutional/departmental context, and instructors' experiences. This will be administered to faculty teaching the target courses at two-year colleges, four-year colleges, and research universities.

Phase II: Case studies

Following the completion of Phase I, certain respondents and sites will be selected for closer investigation. Participants in Phase II will be interviewed to get a richer understanding of themes emerging from analysis of the survey data.


Social Network Analysis


One of the things I've been interested in is the use of social network analysis (SNA) and theories to better understand departmental function. This is a new direction for our undergraduate STEM education research, though the techniques have been used at the K-12 level and in organizational studies for some time. In 2015-17, we received funding (NSF DUE #1550990) and set up a few workshops for like-minded researchers. That group was called Linked Educational Researchers of Networks in Undergraduate STEM or LERNUS. Our working meetings were quite successful, fostering collaborations and supporting ongoing analysis. And we wrote a book!

  • Henderson, C., Rasmussen, C., Knaub, A., Apkarian, N., Daly, A.J., & Quardokus Fisher, K., (2018). The Role of Social Network Analysis in Undergraduate Instructional Improvement. Routledge: New York, NY. (Paper and e-versions available from Routledge and Amazon; or download the introduction)

Other work that I've done using social network analysis in some capacity:

  • Apkarian, N. (2018). Emerging instructional leadership in a new course coordinator system. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro, & S. Brown (Eds.) Proceedings of the 21st Annual Conference on Research in Undergraduate Mathematics Education, pp. 1414-1419. San Diego, CA. [link]
  • Apkarian, N., Rasmussen, C. (2017). Mathematics instruction leadership in undergraduate departments. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro, & S. Brown (Eds.) Proceedings of the 20th Annual Conference on Research in Undergraduate Mathematics Education, 485-493. San Diego, CA. [link]
  • Quardokus Fisher, K., Apkarian, N., & Walter, E. (2017). Let's talk about teaching: Investigating instructors' social networks. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro, & S. Brown (Eds.) Proceedings of the 20th Annual Conference on Research in Undergraduate Mathematics Education, 1214-1218. San Diego, CA. [link]
  • Apkarian, N. (2015). Social networks among communities of undergraduate mathematics instructors at PhD granting institutions. In T. Fukawa-Connelly, N. E. Infante, K. Keene, & M. Zandieh (Eds.), Proceedings of the 18th Annual Conference on Research in Undergraduate Mathematics Education, 369-373. Pittsburg, PA. [link]
  • Apkarian, N. (2018). Transforming Precalculus to Calculus 2: A longitudinal study of social and structural change in a university mathematics department (unpublished doctoral dissertation). University of California San Diego & San Diego State University: San Diego, CA.

Students' Mathematics


The foundation of mathematics education is research investigating how students learn and understand mathematics. It was curiosity about students' understandings of mathematics that led me to this field, and this area of investigation continues to fascinate me. While the main thrust of my research is now focused on systems and improving those systems, it is research about students' understandings and learning processes that provide targets for change initiatives. My work related to students' understanding and learning has taken place primarily in differential equations and dynamical systems courses.

  • Apkarian, N., Tabach, M., Dreyfus, T., & Rasmussen, C. (2019). The Sierpinski smoothie: Blending area and perimeter. Educational Studies in Mathematics. DOI: 10.1007/s10649-019-09889-4 [SharedIt: rdcu.be/bqXod]
  • Rasmussen, C., Apkarian, N., Tabach, M., & Dreyfus, T. (in review). Ways in which engaging in someone else’s reasoning is productive.
  • Apkarian, N., Rasmussen, C., Tabach, M., & Dreyfus, T. (2018). Conceptual blending: The case of the Sierpinski Triangle area and perimeter. In Proceedings of the 21st Annual Conference on Research in Undergraduate Mathematics Education, pp. 541-548. San Diego, CA. [link]
  • Rasmussen, C., Apkarian, N., Dreyfus, T., & Voigt, M. (2016). Ways in which engaging in someone else's reasoning is productive. In E. Nardi, C. Winsløw, & T. Hausberger (Eds.), Proceedings from INDRUM 2016: First conference of the International Network for Didactic Research in University Mathematics, 504-513. University of Montpellier & INDRUM: Montpellier, France.
  • Apkarian, N., Rasmussen, C., Dreyfus, T., Voigt, M., Milbourne, H., & Gao, X. (2016). Ways in which engaging in someone else's reasoning is productive. In T. Fukawa-Connelly, N. Infante, M. Wawro, & S. Brown (Eds.), Proceedings of the 19th Annual Conference on Research in Undergraduate Mathematics Education, 518-526. [link]