## Publications

Check out our published papers by clicking the links below!

Barnett, J. H., Ruch, D., & Scoville, N. (Editors). *Teaching and Learning with Primary Source Projects: Real Analysis, Topology, and Complex Variables*. Classroom Resource Materials Series. AMS\MAA Press. 2023.

Barnett, J. H., Can, C. & Otero, D. Tagging Opportunities to Learn: A Coding Scheme for Student Tasks. *The Mathematics Enthusiast*, **21**(1&2):225–255, 2024.

Scoville, N. The Closure Operation as the Foundation of Topology: A Mini-Primary Source Project for Topology Students, *Convergence *(May 2023).

Monks, K. M. Fermat’s Method for Finding Maxima and Minima: A Mini-Primary Source Project for Calculus 1 Students, *Convergence *(February 2023).

Clark, K. M., Can, C., Barnett, J. H., Watford, M. and Rubis, O.M. 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, 2022.

Barnett, J. H., Klyve, D., and Ruch, D. Learning from the Master: A Collection of Euler-based Primary Source Projects for Today’s Students, Part II. *Euleriana*, Volume 2, Issue 2, 94–106, 2022.

Barnett, J. H., Clark, K. M., and Can, C. 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, 2022.

Barnett, J. H. 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, 2022.

Monks, K. M. Fourier’s Infinite Series Proof of the Irrationality of *e*: A Mini-Primary Source Project for Calculus 2 Students, *Convergence *(September 2022).

Parker, A. E. Solving Linear Higher Order Differential Equations with Euler and Johann Bernoulli: A Mini-Primary Source Project for Differential Equations Students. *Convergence* (July 2022).

Klyve, D. How to Calculate *π*: Buffon’s Needle – A Mini-Primary Source Project on Geometric Probability for Calculus 2 Students, Pre-service Teachers and Others, *Convergence* (May 2022).

Watford, M. (2022). Discursive transgressive actions exhibited in a History of Calculus course. In S. S. Karunakaran & A. Higgins (Eds.), *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.

Barnett, J. H., Klyve, D., Monks, K., and Parker, A. Learning from the Master: A Collection of Euler-based Primary Source Projects for Today’s Students, Part I. *Euleriana*, Volume 2, Issue 1, 40–50, 2022.

Monks, K. M. Fourier’s Heat Equation and the Birth of Modern Climate Science: A Mini-Primary Source Project for Differential Equations and Multivariable Calculus Students, Convergence (February 2022).

Barnett, J. H., Can, C., & Clark, K. M. Learning mathematics from primary sources: Metadiscursive rules, exogenous growth and transgressive acts. In B. Pieronkiewicz (Ed.), *Different perspectives on transgressions in mathematics and its education* (pp. 293–310). Scientific Publishing House of the Pedagogical University, 2021.

Otero, D. Teaching and Learning the Trigonometric Functions through Their Origins: Episode 6 – Regiomontanus and the Beginnings of Modern Trigonometry, Convergence (December 2021).

Barnett, J. H. Gaussian Guesswork: Three Mini-Primary Source Projects for Calculus 2 Students, Convergence (November 2021).

Otero, D. Teaching and Learning the Trigonometric Functions through Their Origins: Episode 5– al-Bīrūnī Does Trigonometry in the Shadows, Convergence (September 2021).

Klyve, D. The Logarithm of −1: A Mini-Primary Source Project for Complex Variables Students, Convergence (June 2021).

Monks, K. M. Bhāskara’s Approximation to and Mādhava’s Series for Sine: A Mini-Primary Source Project for Second-Semester Calculus Students, Convergence (May 2021).

Otero, D. Teaching and Learning the Trigonometric Functions through Their Origins: Episode 4 –Varāhamihira and the Poetry of Sines, *Convergence* (March 2021).

Barnett, J. H., Can, C. and Clark, K. M. “He was poking holes …” A case study on figuring out metadiscursive rules through primary sources, *The Journal of Mathematical Behavior*, Volume 61 (March 2021), https://doi.org/10.1016/j.jmathb.2020.100838 .

Parker, A. P. Wronskians and Linear Independence: A Theorem Misunderstood by Many – A Mini-Primary Source Project for Students of Differential Equations, Linear Algebra and Others, *Convergence* (January 2021).

Otero, D. Teaching and Learning the Trigonometric Functions through Their Origins: Episode 3 – Ptolemy Finds High Noon in Chords of Circles, *Convergence* (December 2020).

Klyve, D. Babylonian Numeration: A Mini-Primary Source Project for Pre-service Teachers and Other Students, Convergence (October 2020).

Otero, D. Teaching and Learning the Trigonometric Functions through Their Origins: Episode 2 – Hipparchus’ Table of Chords, *Convergence* (July 2020).

Scoville, N. Topology from Analysis: A Mini-Primary Source Project for Topology Students, *Convergence *(June 2020).

Monks, K. E. Braess’ Paradox in City Planning: A Mini-Primary Source Project for Multivariable Calculus Students, *Convergence *(May 2020).

Otero, D. Teaching and Learning the Trigonometric Functions through Their Origins: Episode 1 – Babylonian Astronomy and Sexagesimal Numeration, *Convergence* (March 2020).

Ruch, D. Investigations Into d’Alembert’s Definition of Limit: A Mini-Primary Source Project for Students of Real Analysis and Calculus 2, *Convergence *(February 2020).

Klyve, D. Regression to the Mean: A Mini-Primary Source Project for Statistics Students, *Convergence *(December 2019).

White, D., Carruth, N., Eastes, J., Klyve, D., Otero, D., Scoville, N.A. Using Primary Source Projects to teach undergraduate mathematics content: analysis of instructor implementation and perceptions, *International Journal of Mathematical Education in Science and Technology, volume *50, number 7, 987-998, Nov 2019

Barnett, J. H. Gaussian Tale for the Classroom: Lemniscates, Arithmetic-Geometric Means, and More., In M. Zack & D. Schlimm (eds), *Research in History and Philosophy of Mathematics: Proceedings of the Canadian Society for History and Philosophy* (pp. 79–94). Switzerland: Springer International, 2019.

Otero, D. Completing the Square: From the Roots of Algebra, A Mini-Primary Source Project for Students of Algebra and Their Teachers, *Convergence* (September 2019).

Monks, K. Euler’s Calculation of the Sum of the Reciprocals of the Squares: A Mini-Primary Source Project for Calculus II Students, *Convergence *(August 2019).

Flagg, M. Teaching Linear Algebra Using Primary Historical Sources**, ***IMAGE: The **Bulletin of the International Linear Algebra Society*** ,** Issue Number 62 (Spring 2019), pp. 22-23

Otero, D. Learning Determinants from Cramer and Cauchy: A TRIUMPHS Primary Source Project, *IMAGE: The **Bulletin of the International Linear Algebra Society,* Issue Number 62 (Spring 2019), pp. 25-29.

Scoville, N. The Cantor Set Before Cantor: A Mini-Primary Source Project for Students of Analysis and Topology*,* *Convergence *(May 2019).

Klyve, D. The Origin of the Prime Number Theorem: A Primary Source Project for Number Theory Students, *Convergence *(March 2019).

Barnett, J. H. Why Use Primary Sources in a Mathematics Classroom, *Canadian Mathematical Society Notes* (December 2018), pp. 16-17.

Bolch C. and Wood B. Seeing and Understanding Data: A Mini-Primary Source Project for Students of Statistics, *Convergence *(December 2018).

Barnett, J. H. Henri Lebesgue and the Development of the Integral Concept: A Mini-Primary Source Project for Undergraduate Analysis Students, *Convergence* (October 2018).

Barnett, J. H. TRIUMPHS Turns 3! TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources. *HOM SIGMAA News*, **8**(2):6–8, September 2018.

Klyve, D. How to Calculate pi: Machin’s Inverse Tangents, A Mini-Primary Source Project for Calculus II Students, *Convergence* (August 2018).

Ruch, D. Using Primary Source Projects to Learn Real Analysis, with Investigations from Cauchy and Abel, May 23-26, 2018, Miskolc, Hungary.

Ruch, D. Euler’s Rediscovery of e: A Mini-Primary Source Project for Introductory Analysis Students, *Convergence* (May 2018).

Barnett, J. H.Generating Pythagorean Triples: A Mini-Primary Source Project in Number Theory for Mathematics Majors, Elementary Teachers and Others, *Convergence* (November 2017).

Lodder, J. A General Education Course from Primary Historical Sources, *The Newsletter of the Consortium for Mathematics and Its Applications*, 113, ISSN 0889-5392, (2017), pp. 5–11.

Scoville, N. Connecting Connectedness: A Mini-Primary Source Project for Topology Students, *Convergence* (October 2017).

Klyve, D. The Derivatives of the Sine and Cosine Functions: A Mini-Primary Source Project for Calculus I Students, *Convergence* (June 2017).

Barnett, J. H. Why be so Critical? Nineteenth Century Mathematics and the Origins of Analysis: A Mini-Primary Source Project for Introductory Analysis Students, *Convergence* (August 2017).

Barnett, J. H., Clark K., Klyve, D., Lodder, J., Otero, D.,Scoville, N., White, D. A Series of Mini-projects from TRIUMPHS: TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources, *Convergence* (June 2017).

Lodder J. Primary Historical Sources in the Classroom: Graph Theory and Spanning Trees. In: Clark K., Kjeldsen T., Schorcht S., Tzanakis C. (eds.) *Mathematics, Education and History* (pp. 305–330). ICME-13 Monographs. Springer, Cham., 2019.

Clark, K., Otero, D., & Scoville, N. A. Primary source projects in an undergraduate mathematics classroom: A pilot case in a topology course. In T. Dooley, & G. Gueudet (Eds.), *Tenth Congress of the European Society for Research in Mathematics Education* (pp. 1709-1716). Dublin, Ireland: DCU Institute of Education and ERME, 2017.

Barnett, J.H. Monsters in the classroom: Learning analysis through the works of Gaston Darboux, & Conference Proceedings of the 2016 International Study Group on the History and Pedagogy of Mathematics Quadrennial Meeting, Montpellier France, pp. 189 – 200.