Current courses (Summer 2020):
M572: Algebra for teachers
M132 Number and operations for elementary teachers (F 2015; S 2016; F 2016; S 2017; F 2017; S 2018; S 2019; S 2020)
M429 History and nature of mathematics (S 2017)
M500 Current mathematics curricula (S 2016; S 2017; S 2019)
M510 Problem solving for teachers (F 2017; F 2019)
M572 Algebra for middle school teachers (Sum 2016; Sum 2018)
M595 Probability and statistics for teachers (Sum 2017)
M596 Qualitative research methods (S 2018)
M596 Teaching and learning in Calculus (S 2019)
M602 Teaching college math (F 2016; S 2020)
F 2017: Alternative forms of knowing in mathematics
F 2019: Rehumanizing mathematics for Black, Indigenous, and Latinx Students
Resources for Teaching college math
Resources for Teaching mathematics through problem solving
BS Carnegie Mellon University
MA Univeristy of Colorado
Ph.D. University of Colorado
My research draws on two traditions in mathematics education and the learning sciences: Realistic Mathematics Education (RME) and cultural-historical perspectives on learning. RME starts with the premise that mathematics is, first and foremost, an activity, the human activity of structuring the world. Cultural-historical perspectives on learning are also concerned with human activity. From a cultural-historical perspective, the primary features of human activity are (a) that it is productive, and (b) that it is intertwined with the products of prior activity. Thus my research examines the following big question:
“what gets produced as people engage in mathematical activity?”
In short, my answer is, activity, artifacts, community, and identity are all “productively intertwined,” with each producing and being produced by, the others:
I view all aspects of this mutual production to be at play in all mathematical activity. However, I find it productive to focus different strands of my research on particular aspects, as described in the "Projects" section, below.
Strand 1: The productive intertwinement of activity, artifacts, and identity.
As humans engage in activity, we produce and accumulate “partial solutions to frequently encountered problems” (Hutchins, 1995, pp. 354–355). These partial solutions are called “cultural artifacts.” Mathematical artifacts include the “content” of mathematics, including concepts, models, tools, strategies, representations, algorithms, and notation systems. Artifacts serve to make the accomplishments of prior activity available in the present, and human activity always incorporates artifacts. Moreover, as humans act with artifacts, the artifacts “act back,” working to produce the human actors in particular ways. For example, mathematical artifacts help to produce particular kinds of mathematical identities, including identities as “a math person” or “not a math person.”
Taken together, this leads me to study the productive intertwinement of activity, artifacts, and identity:
This strand of research is prominent in the following research projects:
- Student learning in high school algebra. In a series of design-based research studies, my colleagues and I studied how mathematical artifacts were reinvented and made meaningful in activity in a high school algebra classroom, and the implications for students’ identities.
- Teacher learning about classroom assessment. In a research-practice partnership, our research team collaborated with a group of teachers to design classroom assessment systems based on learning trajectories. This involved the intentional production of particular artifacts, and research into how these and other institutional artifacts mediated teachers’ activity.
- Infrastructures and identities in engineering school: In this field-based ethnography, my colleagues and I studied the organizational infrastructure of a prominent engineering school, and how that infrastructure worked to produce students as particular kinds of people.
Strand 2: The productive intertwinement of activity, identity, and community
Above, I described how I seek to understand mathematical activity as a cultural endeavor. I also seek to understand activity as a social endeavor. To do so, I take the perspective that in activity, humans relate to other humans and thus it is useful to conceptualize activity as a joint enterprise. As people engage in joint activity, they form communities. These communities are produced by their members and by the joint activity that binds the members together. In turn, activities derive meaning and people develop identities by virtue of their situatedness within communities.
Taken together, this leads me to study the ways in which mathematical activities, communities, and identities are productively intertwined:
This strand of research is prominent in the following research projects:
- Community and identity in Math Teachers’ Circles. In this field-based ethnography, my colleagues and I study the longitudinal development of communities of math teachers who gather together to engage in mathematical activity. We are interested in the kinds of activities the groups engage in, and the implications for the development of community and identity. This project is a multi-institution collaboration.
- Montana Models: In this study we collaborate with youth in rural communities and American Indian nations to address a community-based project that is of interest to youth, using both local practices and mathematical practices. This involves the following activities: (1) We use ethnographic methods to study the local problem solving practices in the community. (2) We use design-based research to design and study summer camps for youth that act as hybrid spaces to bring mathematical activity and local problem solving practices into contact. (3) We work with the youth to identify a community project and to address that project using both local and mathematical practices. This project is a multi-institution collaboration.
Field of Study
Peer reviewed publications
Peck, F.A. (in press, to be published in the July 2020 issue). Beyond rise over run: A learning trajectory for slope. Journal for Research in Mathematics Education
Peck, F. A. (2020). Towards anti-deficit education in undergraduate mathematics education: How deficit perspectives work to structure inequality and what can be done about it. PRIMUS (online first). https://doi.org/10.1080/10511970.2020.1781721 [full text]
Renga, I.P., Peck, F.A., Feliciano-Semidei, R., Erickson, D. & Wu, K. (2020). Doing math and talking school: Professional talk as producing hybridity in teacher identity and community. Linguistics and Education, 55, 100766. https://doi.org/10.1016/j.linged.2019.100766 [full text]
Peck, F.A. & Sriraman, B. (2017). Breaking the constraints of modernist psychologizing: Mathematics education flirts with the postmodern. Interchange, 48, 351-362. https://doi.org/10.1007/s10780-017-9306-1 [full text]
Peck, F.A., Erickson, D., Feliciano-Semidei, R., Renga, I. Roscoe, M., & Wu, K. (2017, October). Negotiating the essential tension of teacher communities in a statewide Math Teachers’ Circle. Proceedings of the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Indianapolis, IN. [full text]
Peck, F.A. & Matassa M. (2016). Reinventing fractions and division as they are used in algebra: The power of preformal productions. Educational Studies in Mathematics, 92, 2, 245-278. https://doi.org/10.1007/s10649-016-9690-y [full text]
Peck, F. A., O’Connor, K., Cafarella, J., & McWilliams, J. (2016, October). How borders produce persons: The case of calculus in engineering school. In M. B. Wood, E. E. Turner, M. Civil, & J. A. Eli (Eds.), Proceedings of the 38th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1079–1086). Tucson, AZ: The University of Arizona. [full text]
O’Connor, K., Peck, F.A., McWilliams, J. & Cafarella, J. (2016, June). Working in the weeds: How do instructors sort engineering students from non-engineering students in a first year pre-calculus course? Proceedings of the 2016 American Society for Engineering Education Annual Conference and Exposition, New Orleans, LA. [full text]
Briggs, D. and Peck, F.A. (2015). Rejoinder to commentaries on Using learning progressions to design vertical scales that support coherent inferences about student growth. Measurement: Interdisciplinary Research and Perspectives 13, 3-4, 206-218. https://doi.org/10.1080/15366367.2015.1104113 [full text]
Briggs, D. and Peck, F.A. (2015). Using learning progressions to design vertical scales that support coherent inferences about student growth. Measurement: Interdisciplinary Research and Perspectives 13, 2, 75-99. https://doi.org/10.1080/15366367.2015.1042814 [full text]
O’Conner, K., Peck, F.A., and Cafarella, J. (2015) Struggling for legitimacy: Trajectories of membership and naturalization in the sorting of engineering students. Mind, Culture, and Activity 22, 2, 168-183. https://doi.org/10.1080/10749039.2015.1025146 [full text]
O’Connor, K., Peck, F.A., & Cafarella, J. (2015). Constructing “calculus readiness”: Struggling for legitimacy in a diversity-promoting undergraduate engineering program. Proceedings of the 2015 American Society for Engineering Education Annual Conference and Exposition, Seattle, WA: ASEE. 26.397.1-26.397.17 [full text]
O’Connor, K., McWilliams, J., Peck, F.A., & Cafarella, J. (2015). Ideologies of depoliticization in engineering education: A Mediated Discourse Analysis of student presentations in a first-year projects course Proceedings of the 2015 American Society for Engineering Education Annual Conference and Exposition, Seattle, WA: ASEE. 26.880.1-26.880.17 [full text]
Matassa, M. & Peck, F.A. (2012). Rise over run or rate of change? Exploring and expanding student understanding of slope in Algebra I. Proceedings of the 12th International Congress on Mathematics Education. Seoul, Korea. 7440-7445.
Webb, D.C., & Peck, F.A. (2020). From tinkering to practice — The role of teachers in the application of Realistic Mathematics Education principles in the United States. In M. van den Heuvel-Panhuizen (Ed.), International reflections on the Netherlands didactics of mathematics: Visions on and experiences with Realistic Mathematics Education (pp. 21–39). Springer. [full text]
Helen and Winston Cox Educational Excellence Award, Univeristy of Montana
William Stannard Award for the Teaching of Undergraduate Mathematics in Montana, Montana State University.
Best Should Teach award, University of Colorado
Chancellor's Fellow, University of Colorado
2015-Present: Assistant professor of Mathematics Education, Department of Mathematical Sciences, University of Montana
2013-2015: Instructor, School of Education, University of Colorado
2006-2012: Math teacher, Centaurus High School (Lafayette CO)