How Societies Develop Mathematical Expertise

  People acquire mathematical knowledge through their encounters with the world around them, through informal communities and cultural practices, and through institutions specifically designed to cultivate advanced ability. My research examines these varied pathways and how they have changed over time. I have studied, for example, how urban life in the nineteenth century provided ordinary Americans with experiences that fostered an understanding of fractions. I have also examined how the increasing presence of line graphs in newspapers in the 1930s broadened access to a new form of mathematical knowledge while helping to create a cultural divide between the “graph knowers” and the rest of society. Other work examines informal mathematical communities, including networks of largely self-taught mathematicians who gathered around nineteenth-century puzzle columns and The Mathematical Visitor, a journal founded by the self-educated mathematician Artemas Martin. At the other end of the institutional spectrum, my research on West Point traces the role of an elite educational institution in creating a new class of mathematically trained engineers while also raising barriers for the many engineers who had acquired their knowledge informally. My more recent work on gifted education considers another mechanism for cultivating expertise: the development of specialized opportunities for mathematically talented students and the gradual movement of some of those opportunities outside the public education system. Taken together, these projects ask how different forms of mathematical expertise emerge, where people acquire them, and how changes in institutions and culture shape who has opportunities to develop them.

Zelbo, Sian. 2025. Urbanization as a catalyst of fraction understanding. In C. Cornejo et al. (Eds.). Proceedings of the 48th Conference of the International Group for the Psychology of Mathematics Education. Link.

Zelbo, Sian. 2025. When line graphs were a marker of cultural status. For the Learning of Mathematics 45(2): 31-36. Link.

Zelbo, Sian. 2025. The rise of egalitarianism and the privatization of giftedness in America (1960-1984). International Group for Mathematical Creativity and Giftedness Newsletter, 24. www.igmcg.org

Zelbo, Sian. 2023. The Role of the United States Military Academy at West Point in the Formation of America's Engineering Profession (1802 to 1850). Histoire & Mesure 38(2): 217-240. Link.

Zelbo, Sian. 2022. Building an American Mathematics Community from the Ground Up: Artemas Martin and the Mathematical Visitor (1877-1887). In Advances in the History of Mathematics Education: International Studies in the History of Mathematics and Its Teaching, edited by A. Karp, 218-238. Cham: Springer. Link  (Data for this study are here.)