Comparison as a Social Practice in the Analysis of Chaotic Phenomena: the Case of the Double Pendulum - Hernández-Zavaleta, Jesús E.; Preciado Babb, Armando Paulino; Cantoral, Ricardo (International journal of science and mathematics education, 2024)
While scholars have proposed incorporating the study of complex phenomena such as chaotic systems in high school and undergraduate-level curricula, the literature on this topic is scant and has focused mostly on the analysis of mathematical models—and often only on certain populations, such as gifted students. We report in this manuscript an exploratory study involving 16 high school students engaged in a task-based interview. Consistent with the socio-epistemological theory in mathematics education, the task was informed by an analysis of the social practices around the historical development of the study of chaotic phenomena. An analysis of students’ descriptions and justifications revealed key features of comparison as a mathematical type of practice involved in the study of chaotic behavior, which differs from common school mathematical practices. We conclude with implications relevant to socio-epistemological theory in mathematics education and suggestions to incorporate the study of chaotic phenomena and dynamic systems in formal education.