Investigating transgressive actions undertaken by students while studying mathematics via primary sources

Mark Watford; Kathleen Michelle Clark

doi:10.29333/iejme/15477

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Mark Watford ¹ ^* , Kathleen Michelle Clark ²

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¹ School of Teacher Education, Florida State University, Tallahassee, FL, USA² School of Education and Human Sciences, The University of Alabama at Birmingham, Birmingham, AL, USA^* Corresponding Author

Abstract

We describe an exploration informed by transgressionism and supported by data collected from students’ report of learning abstract algebra via curriculum materials where primary historical sources are central to their design, namely Primary Source Projects (PSPs). PSPs require students to actively engage with primary source texts written by historical mathematicians and counter students’ more traditional mathematical learning experiences. We explore the components forming transgressive triads consisting of outcomes of transgressive actions taken to overcome boundaries encountered in students’ study of mathematics. Particularly, we focus on transgressive actions undertaken by students and provide exemplars identified from data to empirically support our theoretical conceptualisations. We end with a discussion by proposing research that draws upon transgressions in both learning mathematics via PHS in particular and with regard to other approaches in undergraduate mathematics education which may place students in contexts in which their familiar is made unfamiliar.

Keywords

transgressions
primary historical sources
undergraduate mathematics education

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 19, Issue 4, November 2024, Article No: em0794

https://doi.org/10.29333/iejme/15477

Publication date: 15 Oct 2024

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Article Downloads: 13

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References

Barnett, J. H. (2018a). Otto Hölder’s formal christening of the quotient group concept. https://digitalcommons.ursinus.edu/cgi/viewcontent.cgi?article=1004&context=triumphs_abstract
Barnett, J. H. (2018b). The roots of early group theory in the works of Lagrange. https://digitalcommons.ursinus.edu/cgi/viewcontent.cgi?article=1002&context=triumphs_abstract
Barnett, J. H., Can, C., & Clark, K. M. (2021). “He was poking holes …” A case study on figuring out metadiscursive rules through primary sources. The Journal of Mathematical Behavior, 61. 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, 23(1), 7-27. https://doi.org/10.1007/s11191-013-9618-1
Barnett, J. H., Lodder, J., & Pengelley, D. (2016). Teaching and learning mathematics from primary historical sources. PRIMUS, 26(1), 1-18. https://doi.org/10.1080/10511970.2015.1054010
Bernardes, A., & Roque, T. (2018). History of matrices: Commognitive conflicts and reflections on metadiscursive rules. In K. M. Clark, T. H. Kjeldsen, S. Schorcht, & C. Tzanakis (Eds.), Mathematics, education and history: Towards a harmonious partnership, ICME-13 Monographs (pp. 209-227). Springer. https://doi.org/10.1007/978-3-319-73924-3_11
Can, C. (2019). Primary sources and professional growth: A phenomenological study of university mathematics instructors [Unpublished doctoral dissertation]. Florida State University.
Clark, K. M., Can, C., Barnett, J. H., Watford, M., & Rubis, O. M. (2022). Tales of research initiatives on university-level mathematics and primary historical sources. ZDM – Mathematics Education, 54(7), 1507-1520. https://doi.org/10.1007/s11858-022-01382-2
Clark, K. M., Kjeldsen, T. H., Schorcht, S., & Tzanakis, C. (2018). Introduction: Integrating history and epistemology of mathematics in mathematics education. In K. M. Clark, T. H. Kjeldsen, S. Schorcht, & C. Tzanakis (Eds.), Mathematics, education and history: Towards a harmonious partnership. ICME-13 Monographs (pp. 1–23). Springer.
Clark, K. M., Kjeldsen, T. H., Schorcht, S., & Tzanakis, C. (2019). History of mathematics in mathematics education – An overview. Mathematica Didactica, 42(1), 3-27.
Duda, J. (2020). Mathematical cognitive transgressions of gifted students enhanced by information technology. In B. Pieronkiewicz (Ed.), Different perspectives on transgressions in mathematics and its education (pp. 253-269). Wydawnictwo Naukowe Uniwersytetu Pedagogicznego Kraków.
Fauvel, J. (1991). Using history in mathematics education. For the Learning of Mathematics, 11(2), 3-6.
Glaubitz, M. (2010). The use of original sources in the classroom: Empirical research findings. In E. Barbin, M. Kronfellner, & C. Tzanakis (Eds.), Proceedings of the 6^th European Summer University (pp. 351-361). Holzhausen Publishing.
Goldin, G. A. (2020). Beauty, insight, power, and connection: The conative domain of mathematical engagement. In B. Pieronkiewicz (Ed.), Different perspectives on transgressions in mathematics and its education (pp. 61-71). Wydawnictwo Naukowe Uniwersytetu Pedagogicznego Kraków.
Handley, K., Clark, T., Fincham, R., & Sturdy, A. (2007). Researching situated learning: Participation, identity and practices in client-consultant relationships. Management Learning, 38(2), 173-191. https://doi.org/10.1177/1350507607075774
Hersh, R. (1991). Mathematics has a front and a back. Synthese, 88(2), 127-133. https://doi.org/10.1007/BF00567741
Huygens, C. (1657). De ratiociniis in aleae ludo [Of the reasoning in the game of chance]. In F. van Schooten (Ed.), Exercitationum mathematicarum (pp. 521-534). Johannis Elsevirii. https://doi.org/10.1016/B978-1-4933-0404-2.50058-2
Jahnke, H. N., Arcavi, A., Barbin, E., Bekken, O., Furinghetti, F., El Idrissi, A., da Silva, C. M. S., & Weeks, C. (2000). The use of original sources in the mathematics classroom. In J. Fauvel, & J. van Maanen (Eds.), History in mathematics education: The ICMI study (pp. 291-328). Kluwer. https://doi.org/10.1007/0-306-47220-1_9
Jahnke, H. N., Jankvist, U. T., & Kjeldsen, T. H. (2022). Three past mathematicians’ views on history in mathematics teaching and learning: Poincaré, Klein, and Freudenthal. ZDM–Mathematics Education, 54, 1421-1433. https://doi.org/10.1007/s11858-022-01376-0
Jankvist, U. T. (2009). A categorization of the “whys” and “hows” of using history in mathematics education. Educational Studies in Mathematics, 71(3), 235-261. https://doi.org/10.1007/s10649-008-9174-9
Jankvist, U. T. (2014). On the use of primary sources in the teaching and learning of mathematics. In M. R. Matthews (Ed.), International handbook of research in history, philosophy and science teaching (pp. 873-908). Springer. https://doi.org/10.1007/978-94-007-7654-8_27
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. https://doi.org/10.1007/s11191-013-9641-2
Kozielecki, J. (1986). A transgressive model of man. New Ideas in Psychology, 4(1), 89-105. https://doi.org/10.1016/0732-118X(86)90062-0
Lakoma, E. (2016). The concept of mathematical cognitive transgression in exploring learners’ cognitive development of nondeterministic thinking. In L. Radford, F. Furinghetti, & T. Hausberger (Eds.), Proceedings of 2016 ICME Satellite Meeting (pp. 465-471). IREM de Montpellier.
Lappa, E., & Nikolantonakis, K. (2018). The teaching of logarithms in upper secondary school from a historical perspective. In E. Barbin, U. T. Jankvist, T. H. Kjeldsen, B. Smestad, & C. Tzanakis (Eds.), Proceedings of the 8^th European Summer University on History and Epistemology in Mathematics Education (pp. 331-341). Oslo Metropolitan University.
Lave, J. (2019). Learning and everyday life: Access participation and changing practice. Cambridge University Press. https://doi.org/10.1017/9781108616416
Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge University Press. https://doi.org/10.1017/CBO9780511815355
Mauntel, M. (2018). A case study of the implementation of primary sources in undergraduate mathematics. In E. Barbin, U. T. Jankvist, T. H. Kjeldsen, B. Smestad, & C. Tzanakis (Eds.), Proceedings of the 8^th European Summer University on History and Epistemology in Mathematics Education (pp. 463-480). Oslo Metropolitan University.
Melhuish, K., Dawkins, P. C., Lew, K., & Strickland, S. K. (2022). Lessons learned about incorporating high-leverage teaching practices in the undergraduate proof classroom to promote authentic and equitable participation. International Journal of Research in Undergraduate Mathematics Education, 10, 284-317. https://doi.org/10.1007/s40753-022-00200-0
Pieronkiewicz, B. (2015a). Affective transgressions in learning mathematics. In K. Krainer, & N. Vondrová (Eds.), Proceedings of the 9^th Congress of the European Society for Research in Mathematics Education (pp. 1259-1265). Charles University (Prague), Faculty of Education and ERME.
Pieronkiewicz, B. (2015b). Affective transgression as the core objective of mathematics education. Philosophy of Mathematics Education Journal, 29.
Pieronkiewicz, B., & Goldin, G. (2020). Affective transgression and meta-affect: An exploration of processes for belief change in mathematics education. In B. Pieronkiewicz (Ed.), Different perspectives on transgressions in mathematics and its education (pp. 73-90). Wydawnictwo Naukowe Uniwersytetu Pedagogicznego Kraków.
Poincaré, H. (1905). Science and hypothesis (W. J. Greenstreet, Trans.). The Walter Scott Publishing Co. (Original work published 1902).
Semadeni, Z. (2015). Educational aspects of cognitive transgressions in mathematics. In A. K. Żeromska (Ed.), Mathematical transgressions and education (pp. 25-42). Wydawnictwo Szkolne Omega.
Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourse, and mathematizing. Cambridge University Press. https://doi.org/10.1017/CBO9780511499944
Sfard, A. (2014). University mathematics as a discourse–Why, how, and what for? Research in Mathematics Education, 16(2), 199-203. https://doi.org/10.1080/14794802.2014.918339
Wachtel, P. L. (1991). The role of “accomplices” in preventing and facilitating change. In R. C. Curtis, & G. Stricker (Eds.), How people change: Inside and outside therapy (pp. 21-28). Springer. https://doi.org/10.1007/978-1-4899-0741-7_3
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). http://sigmaa.maa.org/rume/RUME24.pdf

How to cite this article

APA

Watford, M., & Clark, K. M. (2024). Investigating transgressive actions undertaken by students while studying mathematics via primary sources. International Electronic Journal of Mathematics Education, 19(4), em0794. https://doi.org/10.29333/iejme/15477

Vancouver

Watford M, Clark KM. Investigating transgressive actions undertaken by students while studying mathematics via primary sources. INT ELECT J MATH ED. 2024;19(4):em0794. https://doi.org/10.29333/iejme/15477

AMA

Watford M, Clark KM. Investigating transgressive actions undertaken by students while studying mathematics via primary sources. INT ELECT J MATH ED. 2024;19(4), em0794. https://doi.org/10.29333/iejme/15477

Chicago

Watford, Mark, and Kathleen Michelle Clark. "Investigating transgressive actions undertaken by students while studying mathematics via primary sources". International Electronic Journal of Mathematics Education 2024 19 no. 4 (2024): em0794. https://doi.org/10.29333/iejme/15477

Harvard

Watford, M., and Clark, K. M. (2024). Investigating transgressive actions undertaken by students while studying mathematics via primary sources. International Electronic Journal of Mathematics Education, 19(4), em0794. https://doi.org/10.29333/iejme/15477

MLA

Watford, Mark et al. "Investigating transgressive actions undertaken by students while studying mathematics via primary sources". International Electronic Journal of Mathematics Education, vol. 19, no. 4, 2024, em0794. https://doi.org/10.29333/iejme/15477