Resources for Using Historical Projects

Websites, Articles, and Books on Using Primary Sources in the Teaching of Mathematics

TRIUMPHS Society General Resource List

Selected Online Resources

Annals of the TRIUMPHS Society

The flagship publication of the TRIUMPHS Society, related to the Society's goals of promoting the use of primary historical sources in the teaching of mathematics. Toward that end, the Annals publishes Primary Source Projects (PSPs) ready for classroom use, artifacts and documents related to the development or that support the implementation of such projects, and articles on the scholarship and learningThe Annals is peer reviewed and fully open-access to readers.

TRIUMPHS (TRansforming Instruction via Primary Historical Sources)

Provides access to the TRIUMPHS (Transforming Instruction in Undergraduate Mathematics via Primary Historical Sources) database of classroom-ready PSPs (Primary Source Projects) and mini-PSPs; site-tester information; and allied publications and presentations.

Learning Discrete Mathematics and Computer Science via Primary Historical Sources

Information connected to the 2008-2011 NSF grant project which was the “parent” of TRIUMPHS, with similar but more focused curricular goals; includes 20 classroom-tested Primary Source Projects.

Teaching Discrete Mathematics via Primary Historical Sources

Information connected to the 2005-2006 NSF grant project which was the “grandparent” of TRIUMPHS, with similar but more focused curricular goals; includes 16 classroom-tested Primary Source Projects.

Teaching With Original Historical Sources in Mathematics (aka “David Pengelley’s webpage”)

Motivations, origins, and two sets of book materials for teaching with primary historical sources that predate the “primary source project” approach; the “great-grandparent” site of TRIUMPHS.

Books Based on Primary Sources for Students

R. Laubenbacher and D. Pengelley, Mathematical Expeditions: Chronicles by the Explorers, Springer-Verlag, New York, 1998.
A. Knoebel, R. Laubenbacher, J. Lodder, and D Pengelley, Mathematical Masterpieces: Further Chronicles by the Explorers, Springer-Verlag, New York, 2007.

PSP Volumes for Instructors

Note: All PSPs is these volumes can be downloaded free to share with students from one of the above websites. The incentive for instructors to acquire the volumes themselves lies in (a) the introductory chapters on advice for instructor use and/or providing an historical overview of the mathematical topics addressed by the volume and (b) having all the PSPs related to the courses in question in one place!rite your text here...

Barnett, J. H., Bezhanishvili, D.G., Leung, H., Lodder, J., Pengelley, D. and Ranjan, D. (2009). Historical Projects in Discrete Mathematics and Computer Science. In B. Hopkind (editor), Resources for Teaching Discrete Mathematics: Classroom Projects, History Modules, and Articles (pp. 163–274), MAA Notes Series, Volume 74.
Barnett, J. H., Bezhanishvili, D.G., Leung, H., Lodder, J., Pengelley, D., Pivkina, I., Ranjan, D. and Zack, M. (2013). Primary Historical Sources in the Classroom: Discrete Mathematics and Computer Science. Convergence. DOI:10.4169/loci003984.
Barnett, J. H., Ruch, D., & Scoville, N. (Editors). (2023). Teaching and Learning with Primary Source Projects: Real Analysis, Topology, and Complex Variables. Classroom Resource Materials Series. AMS\MAA Press.

Select Papers on the Use of PSPs and Primary Historical Sources as a Tool for Instruction

Barnett, J. H. Learning Mathematics via Primary Historical Sources: Straight from the Source’s Mouth. (2014). Problems, Resources and Issues in Mathematics Undergraduate Studies (PRIMUS). Special Issue on the Use of History of Mathematics to Enhance Undergraduate Mathematics Instruction, 24(8):722–736. DOI:10.1080/10511970.2014.899532.
Barnett, J. H. 2012. Bottled at the Source: The Design and Implementation of Classroom Projects for Learning Mathematics via Primary Historical Sources,. HPM 2012 Conference Proceedings History and Pedagogy of Mathematics Quadrennial Meeting, vol. I, Daejeon, South Korea, 335–347.
Barnett, J. H., Bezhanishvili, D.G., Leung, H., Lodder, J., Pengelley, D., Pivkina, I. and Ranjan, D. Designing student projects for teaching and learning discrete mathematics and computer science via primary historical sources. (2011). In V. Katz and C. Tzanakis (editors), Recent Developments on Introducing a Historical Dimension in Mathematics Education (pp. 187 – 198), MAA Notes Series, Volume 78.
Barnett, J. H., Bezhanishvili, G. Lodder, J. and Pengelley, D. (2016). Teaching Discrete Mathematics Entirely Primary Historical Sources. Problems, Resources and Issues in Mathematics Undergraduate Studies PRIMUS 26(7):657–675. DOI 10.1080/10511970.2015.1128502.
Barnett, J. H., Clark K., Klyve, D., Lodder, J., Otero, D., Scoville, N. and White, D. (2017). A Series of Mini-projects from TRIUMPHS: TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources. Convergence.DOI:10.4169/convergence20170601.
Barnett, J. H., Klyve, D., Monks, K. and Parker, A. (2022). Learning from the Master: A Collection of Euler-based Primary Source Projects for Today’s Students, Part I. Euleriana 2(1):40–50.
Barnett, J. H., Klyve, D. and Otero, D. E. (2025). Advances in Using Primary Historical Sources to Teach Mathematics: A Special Issue Introduction and Invitation The Mathematics Enthusiast 22(1). Article 1.
Barnett, J. H., Klyve, D., and Ruch, D. (2022). Learning from the Master: A Collection of Euler-based Primary Source Projects for Today’s Students, Part II. Euleriana, 2(2):94–106.
Barnett, J. H., Lodder, J. and Pengelley, D. (2016). Teaching and Learning Mathematics from Primary Historical Sources. Problems, Resources, and Issues in Mathematics Undergraduate Studies (PRIMUS) 26(1):1-18.
Clinkenbeard, J. (2023). Primary Source Projects and Reading Apprenticeship in Mathematics History. Convergence. DOI:10.4169/Convergence20231101
Davis, T. (2025). Team Teaching with Primary Historical Sources. The Mathematics Enthusiast 22(1). Article 3.
Duffee, A. (2025). From Geometric Intuition to Arithmetical Rigor: Teaching Analysis with Bolzano’s Original Text, The Mathematics Enthusiast 22(1) Article 5.
Edwards, A. (2025). Trusted Together: A Commognitive Perspective on a Primary Source Project in Multivariable Calculus. The Mathematics Enthusiast. Article 8.
Edwards, A., Klyve, D. and Monks, K. M. (2025). Inclusive Pedagogy in Mathematics via Primary Source Projects. The Mathematics Enthusiast 22(1). Article 6.
Kent, D. and Lorenat, J. (2025). Situating the Statistical Legacies of Galton and Fisher: Multi-layered discussions in the Mathematics Classroom. The Mathematics Enthusiast 22(1). Article 7.
Klyve, D. Stemkoski, L. and Tou, E. (2013). Teaching and Research with Original Sources from the Euler Archive - Introduction: Teaching, Research, and Primary Sources. Convergence. DOI:10.4169/loci003672.
Laubenbacher, R. and Pengelley, D. Mathematical Masterpieces: Teaching With Original Sources. (1996). In R. Calinger (editor), Vita Mathematica: Historical Research and Integration with Teaching (pp. 257–260), MAA Notes Series, Volume 40.
Lodder, J. (2025). The Figurate Numbers: From Verbal Expression to Algebraic Symbolism. The Mathematics Enthusiast 22(1). Article 4.
Muldoon Brown, T. (2025). Becoming a More Effective Instructor Using Primary Source Projects. The Mathematics Enthusiast22(1). Article 2.
Pengelley, D. Teaching with primary historical sources: Should it go mainstream? Can it? (2011). In V. Katz and C. Tzanakis (editors), Recent Developments on Introducing a Historical Dimension in Mathematics Education (pp. 1–8), MAA Notes Series, Volume 78.

Research on This Approach to Teaching and Learning

Primary Sources and Meta-discursive Rules \ Commognitive Theory

Barnett, J. H. (2022). Primary source projects as textbook replacements: a commognitive analysis. ZDM – Mathematics Education (Special Issue: Exploring the Significance of the History of Mathematics in Mathematics Education: Recent Developments in the Field), 54:1569–1582.
Barnett, J. H., Can, C. and Clark, K. (2021). Learning mathematics from primary sources: Metadiscursive rules, exogenous growth and transgressive acts. In B. Pieronkiewicz (editor), Different perspectives on transgressions in mathematics and its education (pp. 293–310). DOI 10.24917/9788380846678.17.
Barnett, J. H., Can, C. and Clark, K. “He was poking holes”: A case study on figuring out metadiscursive rules through primary sources, Journal of Mathematical Behavior, Special Issue: Advances in Commognitive Research 61, March 2021. https://doi.org/10.1016/j.jmathb.2020.100838.
Barnett, J. H., Lodder, J. &Pengelley, D. (2014). The pedagogy of primary historical sources in mathematics: Classroom practice meets theoretical frameworks. Science & Education: Special Issue on the Philosophy and History of Mathematics in Mathematics Education 23(1), 7–27.
Bernardes, A. & Roque, T. (2018). History of Matrices: Commognitive Conflicts and Reflections on Metadiscursive Rules. In Clark, K. M. et al, (editors), Mathematics, Education and History: Towards a Harmonious Partnership (pp. 209–228), Springer, Berlin.
Güçler, B. (2016). Making implicit metalevel rules of the discourse on function explicit topics of reflection in the classroom to foster student learning. Educational Studies in Mathematics, 91(3):375–393.
Kjeldsen, T. H., & Blomhøj, M. (2012). Beyond motivation: history as a method for learning meta-discursive rules in mathematics. Educational Studies in Mathematics, 80(3):327–349.
Kjeldsen, T.H., & Petersen, P.H. (2014). Bridging History of the Concept of Function with Learning of Mathematics: Students’ meta-discursive rules, concept formation and historical awareness. Science & Education 23:29–45.

Other History and Pedagogy of Mathematics

Barnett, J. H., Can, C. & Otero, D. (2024). Tagging Opportunities to Learn: A Coding Scheme for Student Tasks. The Mathematics Enthusiast, 21(1&2):225–255.
Barnett, J. H., Clark, K. M., and Can, C. (2022).Transforming mathematics instruction via primary historical sources: A study of influential factors on implementation of a curricular innovation at the tertiary level. Implementation and Replication Studies in Mathematics Education, 2(2):208–240.
Clark, K. M., Can, C., Barnett, J. H., Watford, M. and Rubis, O.M. (2022). Tales of Research Initiatives on University-level Mathematics and Primary Historical Sources. ZDM – Mathematics Education (Special Issue: Exploring the Significance of the History of Mathematics in Mathematics Education: Recent Developments in the Field), 54:1507–1520.
Clark, K. M., Kjeldsen, T., Schorcht, S., Tzanakis, C., and Wang, X. 2016. History of mathematics in mathematics education. Recent developments. In L. Radford, F. Furinghetti, and T. Hausberger (editors), Proceedinsg of the History and Pedagogy of Mathematics ICME Satellite Conference (pp. 135–179), IREM de Montpellier, France.
NOTE: This comprehensive annotated bibliography “concerning research on the relations between History and Pedagogy of Mathematics” is a technical list and an invaluable resource, but possibly not the best place to begin.
Glaubitz, M. (2010). The Use of Original Sources in the Classroom: Empirical Research Findings. In E. Barbin, M. Kronfellner, and C, Tzanakis (editors), History and Epistemologyin Mathematics EducationProceeding of the Sixth European Summer (ESU-6/HPM) Proceedings (pp. 351–361), Verlag Holzhausen GmbH, Vienna.
Jahnke, H.N. et al. (2002). The use of original sources in the mathematics classroom. In Fauvel, J. and J. van Maanen (editors), History in mathematics education: The ICMI study (pp. 37–381), Kluwer Academic.
Jankvist, U.T. (2009). A Categorization of the ‘Whys’ and ‘Hows’ of Using History in Mathematics Education. Educational Studies in Mathematics, 3:235–261.
McBride, J. C. & Rollins, J.H. (1977). The effects of history of mathematics on attitudes towards mathematics of college algebra students. Journal for Research in Mathematics Education 8:57–61.
Watford, M. (2022). Discursive transgressive actions exhibited in a History of Calculus course. In S. S. Karunakaran & A. Higgins (editots), Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education (pp. 692–699). The Special Interest Group of the Mathematical Association of American (SIGMAA) for Research in Undergraduate Mathematics Education.
Watford, M., Clark, K. M., Can, C. (2025). New Methods of Capturing Students’ Experiences with Primary Source Projects: Pioneering a Transgressive Lens. The Mathematics Enthusiast, 22(1). Article 9.
White, D., Carruth, N., Eastes, J., Klyve, D., Otero, D., Scoville, N.A.(2019). Using Primary Source Projects to teach undergraduate mathematics content: analysis of instructor implementation and perceptions, International Journal of Mathematical Education in Science and Technology 50(7):987–998.
Witzke, I., Clark, K.M., Struve, H. & Stoffels, G. (2018). Addressing the Transition from School to University: Evolution of a Seminar Emphasizing Historical Sources and Student Reflections. In Clark, K. et al. (editors), Mathematics, Education and History: Towards a Harmonious Partnership (pp. 61–82), Springer, Berlin.

General Active Learning and Inquiry-Based Learning

Braun, B., Bremser, P., Duval, A., Lockwood, E., and White, D. (2017). What Does Active Learning Mean for Mathematicians? Notices of the American Mathematical Society 64(2):936–941.
Freeman, S. Eddy, S., McDonough, M., Smith, M., Okoroafor, N., Jordt, H., & Wenderoth, M. (2016). Active learning increases student performance in science, engineering, and mathematics, Proc. Natl. Acad. Sci. 111(23):8410–8415.
Kogan, M .& Laursen, S. (2014). Assessing Long Term Effects of Inquiry-Based Learning: A Case Study from College Mathematics. Innovations in Higher Education 39:183–199.
Yoshinobu, S. & Jones, M.G. (2012). The Coverage Issue. Problems, Resources, and Issues in Mathematics Undergraduate Studies (PRIMUS) 22(4):303–316.

Other History of Math Societies

British Society for the History of Mathematics
Canadian Society for the History and Philosophy of Mathematics
History and Pedagogy of Mathematics (HPM) International Study Group
HOM SIGMAA (MAA Special Interest Group for the History of Mathematics)