Tales of research initiatives on university-level mathematics and primary historical sources.

TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources (TRIUMPHS) is a multi-year, multi-institution collaborative project funded by the US National Science Foundation aimed at developing and testing student projects based on primary historical sources related to the original or subsequent development of core topics in today's tertiary mathematics curriculum. In addition to developing a broad range of projects and supporting their site testing by instructors across the US and Canada, TRIUMPHS includes a major Evaluation-with-Research component that is studying the effects of their classroom use on students and instructors. Our goal in this article is to share an overview of our research efforts related to the student learning experience—and as importantly, the tale of how we arrived at them—with others engaged in the effort to transform instruction in the field of undergraduate mathematics education. We provide a summary of three research initiatives undertaken by TRIUMPHS: a metadiscursive rules investigation based on Sfard's theory of commognition, an exploratory study of the concepts of transgressive actions and boundary crossings (first put forth by Polish psychologist Jozef Kozielecki) within the context of student learning of mathematics, and an examination of the different views students hold regarding the nature of mathematics. Additionally, we offer methodological reflections on how we revised our research questions and analytic tools based on theoretical constructs from mathematics education and beyond as the project unfolded over the first 6 years. [ABSTRACT FROM AUTHOR]