Transforming Instruction in Undergraduate Mathematics via Primary Historical Sources (TRIUMPHS)

Daniel Otero – 11 Feb 2019

Daniel Otero is an Associate Professor at Xavier University, Cincinatti ( He is visiting the School of Mathematics and Statistics at the University of St Andrews until early April, as one of their Visiting Fellows in the History of Mathematics.

This talk outlined the approach of the TRIUMPHS programme ( to the teaching and learning of undergraduate mathematics. TRIUMPHS contributors design and deliver ‘Primary Source Projects’ in particular topics of mathematics, aiming to supplement or even partially replace, traditional teaching of those topics.

Projects are based around historical sources, including examples such as (an image of) a Bablyonian tablet illustrating their system of numeration (base 60). Students engage with the documents and take an active approach to discovering and learning about the topic. The aim is to encourage group work, moderated by the instructor.

Each project is designed to take anywhere between two or three class periods, and a whole semester, to deliver. The Bablyonian example covers two classes, while a unit on trigonometry is designed to take the first 4-6 weeks of a traditional module on the subject, then allow a faster track version of the same module to continue in the remainder of the semester.

These projects seem to be especially successful at engaging students who are not already strong mathematically, but are very challenging to ‘better’ students, who are sometimes uncomfortable with the active group style.

Further information about Danny:

Danny’s scholarship focuses on ways in which the history of mathematics can be used to improve the teaching of the subject at the tertiary level. He has designed three undergraduate modules for his own students that teach maths through engagement with primary sources. Since 2014 he has been co-PI on a National Science Foundation grant project titled Transforming Instruction in Undergraduate Mathematics via Primary Historical Sources (TRIUMPHS), and he is also a member of the MAA Spectrum series editorial board. While he is in St Andrews he is going to be working on completing his book, A Smoother Pebble, that aims to teach the basic concepts of calculus to students of the humanities through primary sources that exemplify the history of the development of its underlying ideas.


Leave a Reply

Your email address will not be published. Required fields are marked *