Publications

Selected papers

Rangkuti, M. A., & Karam, R. (2023). Encouraging students to understand the 1D wave equation. Physical Review Physics Education Research, 19. https://doi.org/10.1103/PhysRevPhysEducRes.19.020161

Karam, R. (2020). Schrödinger’s original struggles with a complex wave function. American Journal of Physics, 88(6), 433–438. Featured. https://doi.org/10.1119/10.0000852

Karam, R. (2020). Why are complex numbers needed in quantum mechanics? Some answers for the introductory level. American Journal of Physics, 88(1), 39–45. https://doi.org/10.1119/10.0000258

Karam, R., Uhden, O., & Höttecke, D. (2019). The “math as prerequisite” illusion: Historical considerations and implications for physics teaching. In Mathematics in physics education (pp. 37–52). Springer International Publishing. https://doi.org/10.1007/978-3-030-04627-9_2

Karam, R. (2019). O que diferencia as Feynman lectures de livros tradicionais? Revista Brasileira de Ensino de Fisica, 40(4), 1-11. https://doi.org/10.1590/1806-9126-RBEF-2018-0071

Karam, R. (2015). Introduction of the thematic issue on the interplay of physics and mathematics. Science & Education, 24(5), 487–494. https://doi.org/10.1007/s11191-015-9763-9

Karam, R., & Krey, O. (2015). Quod erat demonstrandum: Understanding and explaining equations in physics teacher education. Science & Education, 24(5), 661–698. https://doi.org/10.1007/s11191-015-9743-0

Karam, R. (2014). Framing the structural role of mathematics in physics lectures: A case study on electromagnetism. Physical Review Physics Education Research, 10(1), 010119. https://doi.org/10.1103/PhysRevSTPER.10.010119

Uhden, O.*, Karam, R.*, Pospiech, G., & Pietrocola, M. (2012). Modelling mathematical reasoning in physics education. Science & Education, 20(4), 485–506. * Both authors contributed equally. https://doi.org/10.1007/s11191-011-9396-6

Complete list

Refereed Journal Publications

Palmgren, E., & Karam, R. (2025). A glimpse of matrix mechanics via the harmonic oscillator. American Journal of Physics, 93(1), 21-27. https://doi.org/10.1119/5.0141573

Weber Pereira, R., Karam, R. A. S., Heidemann, L. A., & Veit, E. A. (2025). Grounding analytical mechanics in statics: a didactic emphasis on the principle of virtual work. European Journal of Physics, 46(1). https://doi.org/10.1088/1361-6404/ad9c02

Souza, D. S., Lima, N. W., & Karam, R. A. S. (2024). A gênese da interpretação probabilística em livros didáticos de mecânica quântica. Revista Brasileira de Ensino de Fisica, 46. https://doi.org/10.1590/1806-9126-RBEF-2023-0238

Rangkuti, M. A., & Karam, R. (2023). Encouraging students to understand the 1D wave equation. Physical Review Physics Education Research, 19. https://doi.org/10.1103/PhysRevPhysEducRes.19.020161

Rangkuti, M. A., & Karam, R. (2022). Conceptual challenges with the graphical representation of the propagation of a pulse in a string. Physical Review Physics Education Research, 18. https://doi.org/10.1103/PhysRevPhysEducRes.18.020119

Lima, N., & Karam, R. (2022). Schrödinger’s equation from Snell’s law. European Journal of Physics, 43(3), Article 035402. https://doi.org/10.1088/1361-6404/ac5635

Oktarisa, Y., & Karam, R. (2021). From a central force to Kepler’s area law: Student difficulties and preferences with two derivations. European Journal of Physics, 42(1), 1-23. https://doi.org/10.1088/1361-6404/abbf3d

Lima, N., & Karam, R. (2021). Particle velocity = group velocity: A common assumption in the different theories of Louis de Broglie and Erwin Schrödinger. American Journal of Physics, 89(5), 521-528. https://doi.org/10.1119/10.0003165

Karam, R. (2020). Schrödinger’s original struggles with a complex wave function. American Journal of Physics, 88(6), 433–438. https://doi.org/10.1119/10.0000852

Karam, R. (2020). Why are complex numbers needed in quantum mechanics? Some answers for the introductory level. American Journal of Physics, 88(1), 39–45. https://doi.org/10.1119/10.0000258

Karam, R. A. S. (2019). O que diferencia as Feynman lectures de livros tradicionais? Revista Brasileira de Ensino de Fisica, 40(4), 1-11. https://doi.org/10.1590/1806-9126-RBEF-2018-0071

Karam, R. (2018). Fresnel’s original interpretation of complex numbers in 19th century optics. American Journal of Physics, 86(4), 245–249. Editor’s Pick. https://doi.org/10.1119/1.5011366

Assis, A. K. T., & Karam, R. A. S. (2018). The free fall of an apple: conceptual subtleties and implications for physics teaching. European Journal of Physics, 39(3), 1-14. https://doi.org/10.1088/1361-6404/aaa91d

Karam, R., Kneubil, F. & Robilotta, M. (2017). Forces on a current-carrying wire in a magnetic field: the macro-micro connection. European Journal of Physics, 38(5). https://doi.org/10.1088/1361-6404/aa75a0

Kneubil, F., & Karam, R. (2017). Keyhole: Equal signs as bridges between the phenomenological and theoretical dimensions. Revista Brasileira de Ensino de Física, 39 (2). https://doi.org/10.1590/1806-9126-RBEF-2016-0216

Kneubil, F., Karam, R., Gurgel, I. & Robilotta, M. (2017). Electromagnetism as a world view: implications for the teaching of energy. Revista Brasileira de Ensino de Física, 39 (4). https://doi.org/10.1590/1806-9126-RBEF-2017-0119

Coelho, R.; Borges, P.; Karam, R. (2016). Atwood and Poggendorff: an insightful analogy. European Journal of Physics, 37(6). Selected for the 2016 Highlights. https://doi.org/10.1088/0143-0807/37/6/065003

Krey, O., Karam, R. (2016). Mathematik in der Physik – Muss das sein? Und wenn ja, warum und wozu? Naturwissenschaften im Unterricht Physik, Bind 153/154, 7-13. www.friedrich-verlag.de/shop/mathematik-im-physikunterricht-513153

Karam, R., Uhden, O., Höttecke, D. (2016). Das habt ihr schon im Mathe gelernt! Stimmt das wirklich?: Ein Vergleich zwischen dem Umgang mit mathematischen Konzepten in der Mathematik und in der Physik. Naturwissenschaften im Unterricht Physik, Bind 153/154, 22-27. www.friedrich-verlag.de/shop/mathematik-im-physikunterricht-513153

Zander, S., Dorn, T., Karam, R. (2016). Mathematik als Brücke zwischen Makro- und Mikrokosmos : Ein Unterrichtskonzept zur Thermodynamik in der Oberstufe. Naturwissenschaften im Unterricht Physik, Bind 153/154, 68-73. www.friedrich-verlag.de/shop/mathematik-im-physikunterricht-513153

Karam, R. (2015). Introduction of the thematic issue on the interplay of physics and mathematics. Science & Education, 24(5), 487–494. https://doi.org/10.1007/s11191-015-9763-9

Karam, R. (2014). Book review: Evidence and Method: Scientific Strategies of Isaac Newton and James Clerk Maxwell by Peter Achinstein. Science & Education 23, 2137–2148. https://doi.org/10.1007/s11191-014-9717-7

Karam, R., Coimbra, D. & Pietrocola, M. (2014). Comparing Teaching Approaches About Maxwell’s Displacement Current. Science & Education 23, 1637–1661. https://doi.org/10.1007/s11191-013-9624-3

Karam, R. A. S. (2010). Minha terra tem palmeiras onde canta o sabiá… Revista do Professor de Matemática, v. 71, p. 27-30. https://rpm.org.br/cdrpm/71/5.html

Karam, R. A. S:, & Pietrocola, M. (2009). Habilidades Técnicas Versus Habilidades Estruturantes: Resolução de Problemas e o Papel da Matemática como Estruturante do Pensamento Físico. Alexandria: Journal of Science and Technology Education, 2, 181-205. https://periodicos.ufsc.br/index.php/alexandria/article/view/37960/28988

Karam, R. A. S. (2007). Grandezas físicas para exemplificar a função afim. Revista do Professor de Matemática, v. 63, pp. 29-32. https://rpm.org.br/cdrpm/63/8.html

Karam, R. A. S., Souza Cruz, S. M., & Coimbra, D. (2007). Relatividades no ensino médio: o debate em sala de aula. Revista Brasileira de Ensino de Fisica, 29(1). https://doi.org/10.1590/S1806-11172007000100017

Karam, R. A. S., Souza Cruz, S. M., & Coimbra, D. (2006). Tempo relativístico no início do Ensino Médio. Revista Brasileira de Ensino de Fisica, 28(3), 373-386. https://doi.org/10.1590/S1806-11172006000300014

Refereed Book Chapters

Pospiech, G., & Karam, R. (2023). Role of Mathematics in Physics from Multiple Perspectives. In The International Handbook of Physics Education Research: Special Topics p. 18:1-28. AIP Publishing. https://doi.org/10.1063/9780735425514_018

Karam, R., & Lima, N. (2022). Using history of physics to teach physics? In: Jenaro Guisasola; Eilish McLoughlin. (Org.). Connecting Research in Physics Education with Teacher Education 3. 1 ed. Dublin: The International Commission on Physics Education in cooperation with University of the Basque Country, v. 3, p. 22-38. https://doi.org/10.5281/zenodo.5792968

Lehavi, Y., Bagno, E., Eylon, B.-S., Mualem, R., Pospiech, G., Böhm, U., Krey, O., & Karam, R. (2016). Classroom evidence of teachers’ PCK of the interplay of physics and mathematics. In Key competences in physics teaching and learning: Selected contributions from the International Conference GIREP EPEC 2015, Wrocław, Poland, 6–10 July 2015 (pp. 95–104). Springer International Publishing.

Conference contributions

Karam, R. (2026). The complexification of physics: Historical episodes and educational implications. Invited talk, Research at the Interface of Mathematics and Physics Education, Topical Group on Physics Education Research. APS Global Physics Summit 2026, Denver, March , 2026. https://summit.aps.org/events/APR-H78/1

Karam, R. (2025). Original sources in physics teaching? Invited contribution to the Symposium Using Historical Cases to Bring Students Into the Practice of Theorizing in Physics. ESERA Conference 2025 – Copenhagen, Denmark, August 25-29.

Karam, R. (2025). Should the Cauchy-Riemann equations be named after d’Alembert? The Teaching and Learning of Calculus Across Disciplines, Milan, Italy, 16-20 June (pp.132-135).https://matriccalcconf3.sciencesconf.org/data/pages/Pre_proceedings_2.pdf

Branchetti, L., Feudel, F., Ho, F., Karam, R. & Munzón, N. (2024). Mathematics and other disciplines: Epistemological issues and their impact on teaching practices at tertiary level. Invited contribution to plenary panel at INDRUM 2024, Barcelona, Spain, June 10-14 (pp. 33-55).https://indrum2024.sciencesconf.org/data/pages/Proceedings_INDRUM2024.pdf

Karam, R. (2024). On the roles of complex numbers in the birth of quantum mechanics: Heisenberg vs. Schrödinger. Invited contribution to Symposium Complex Numbers in Quantum Theory, Philosophy of Science Association (PSA) conference, November 14-17, New Orleans, USA.

Rangkuti, M. A., Karam, R. (2023). Students epistemological beliefs in understanding the 1-D wave equation. GIREP-EPEC 2023 Conference – Košice, Slovakia, July 3-7. https://indico.cern.ch/event/1162406/attachments/2724005/4738517/2023GIREP-BookExtendedAbstracts.pdf

Rangkuti, M. A., Karam, R. (2022). How students understand the one-dimensional wave equation. GIREP 2022 Conference – Ljubljana, Slovenia, July 4-8. https://indico.cern.ch/event/1092708/book-of-abstracts.pdf

Oktarisa, Y., Karam, R. (2019) From central force to Kepler’s area law. GIREP/MPTL 2019 Conference – Budapest, Hungary, July 7-12.

Veddel, S., Hansen, S. & Karam, R. (2019) Why is centripetal acceleration v²/r? Students’ struggles and preferences after seeing different derivations. GIREP/MPTL 2019 Conference – Budapest, Hungary, July 7-12.

Karam, R. (2019) Schrödinger’s struggles with a complex wave function. GIREP/MPTL 2019 Conference – Budapest, Hungary, July 7-12.

Karam, R. (2019) Schrödinger’s struggles with a complex wave function. History for Physics: Quantum Foundations. Vienna, Austria,September 23–24. Available on YouTube, most viewed presentation.

Karam, R. (2017) Designing a history of physics course at the University of Copenhagen. 25th International Congress of History of Science, and Technology (ICHST), Rio de Janeiro, Brazil, July 23-29.

Kneubil, F., Karam, R. (2015). Looking through the keyhole: Physics equations as bridges between the macro and micro worlds. Oral communication. 13th IHPST Conference – Rio de Janeiro, July 22-25, 2015.

Karam, R., Wolfsberg, A. (2015). Knwoledge transfer from fluid dynamics to electromagnetism. Oral communication. 13th IHPST Conference – Rio de Janeiro, July 22-25, 2015.

Karam, R., & Mäntylä, T. (2015). The influence of mathematical representations on students’ conceptualizations of the electrostatic field. In F. Claudio, & R. M. Sperandeo Mineo (Eds.): Teaching/Learning Physics: Integrating Research into Practice: Proceedings of the GIREP-MPTL 2014 International Conference. Palermo: Dipartimento di Fisica e Chimica, Università degli Studi di Palermo (819-826).Available in Research Gate.

Karam, R. (2014). Analogies and metaphors in teaching Maxwell’s equations: Analyzing the didactic discourse of a distinguished physics professor. Oral communication. 9th International Conference on Conceptual Change – Bologna, August 26-29, 2014.

Karam, R., Uhden, O., Höttecke, D. (2014). Mathematik im Physikunterricht – Ein Entwicklungsprojekt Annual conference of the German Society of Didactics of Physics and Chemistry (GDCP 2014), Bremen, September 15-18, 2014.

Karam, R., Krey, O. (2014). Was zu beweisen war: Formelverständnis in der Physik-Lehramtsausbildung. nnual conference of the German Physical Society (DPG 2014) – Frankfurt, March 17-20, 2014.

Karam, R. (2013). Formale Analogien in der Physik-Lehramtsausbildung. In: S. Bernholt (Hrsg.), Inquiry-based Learning – Forschendes Lernen. Gesellschaft für Didaktik der Chemie und Physik, Jahrestagung in Hannover 2012 (S. 506 – 508). Kiel: IPN.

Karam, R., Quale, A., Rowlands, S., Mäntylä, T. (2013). Mathematical models and the physical world: HPS aspects and educational issues. International Symposium organized at the IHPST 2013 Conference. Pittsburgh, June 19-22, 2013.

Karam, R., Mäntylä, T. (2013). Mathematical reasoning and knowledge organization: Comparing students’ conceptualizations of the electrostatic field. ICPE-EPEC 2013 Conference – Prag, August 5-9, 2013.

Karam, R. (2013). Understanding physics equations and PCK: The case of centripetal acceleration. ICPE-EPEC 2013 Conference – Prag, August 5-9, 2013.

Karam, R., Pospiech, G., Höttecke, D. (2013). Formelverständnis in der Physik-Lehramtsausbildung am Beispiel der Radialbeschleunigung. Annual conference of the German Physical Society (DPG 2013) – Jena, February 25-28, 2013.

Karam, R. (2012). The manifold character of physics’ mathematical nature: Analyzing didactical approaches. Oral communication. NORD-HPS&ST 2 – Helsinki, October 24-26, 2012.

Karam, R. (2012). Comparing different teaching approaches about Maxwell’s displacement current. Poster presented at the NORD-HPS&ST 2 – Helsinki, October 24-26, 2012.

Karam, R. (2012). The manifold character of physics’ mathematical nature: Analyzing didactical approaches. Oral communication. First IHPST Asian Regional Conference – Seoul, October 18-20, 2012.

Karam, R., Pietrocola, M., Pospiech, G. (2012). Die Rolle der Mathematik in Physikvorlesungen: Eine Vergleichstudie. In: S. Bernholt (Org.) Konzepte fachdidaktischer Strukturierung für den Unterricht. Gesellschaft für Didaktik der Chemie und Physik. Jahrestagung Oldenburg 2011, Berlin: LIT Verlag, 221-223.

Karam, R., Pospiech, G., Pietrocola, M. (2011): Mathematik im Physikuntericht: Entwicklung struktureller Fähigkeiten. In: D. Höttecke (Org.) Naturwissenschaftliche Bildung als Beitrag zur Gestaltung partizipativer Demokratie. Gesellschaft für Didaktik der Chemie und Physik. Jahrestagung Potsdam 2010, Berlin: LIT Verlag, 173-175.

Karam, R., Pietrocola, M. (2010). Recognizing the Structural Role of Mathematics in Physical Thought. In M.F. Taşar & G. Çakmakci (Eds.). Contemporary science education research: international perspectives. Ankara: Pegem Akademi, v. 1, p. 65-76.

Pospiech, G., Karam, R. (2010). Mathematics in physics lessons: problems and perspectives. In D. Raine, C. Hurkett & L. Rogers (Eds.) Physics Community and Cooperation. Volume 2, pp. 66-96. Symposium organized at the GIREP-EPEC & PHEC 2009 International Conference, Leicester.

Karam, R., Forato, T.M.C., Pietrocola, M. (2010). Explanation versus Description: Philosophical Debate and Implications for Physics Teaching. In D. Raine, C. Hurkett & L. Rogers (Eds.) Physics Community and Cooperation. Volume 2, pp. 171-179.

Karam, R., Pietrocola, M. (2009). Discussão das relações entre Matemática e Física no ensino de Relatividade Restrita: um estudo de caso [Discussing the interrelations between mathematics and physics in relativity lessons: a case study]. In: Proceedings of the VII ENPEC, Florianópolis – SC.

Karam, R., Brockington, G., Beig, F. (2009) Aplicação da adição galileana à luz: algumas contradições. [Galilean transformations applied to light: some contradictions] In: Proceedings of the XVIII SNEF, Vitória, ES.

Karam, R., Brockington, G. (2009). Assessing physics’ teachers’ conceptions on the importance of symmetry. Poster presented at the ESERA Conference 2009 – Instanbul, August 31st – September 4th, 2009.

Karam, R. (2009) Distorção do papel da Matemática na Resolução de Problemas de Física [Distortion of the role of mathematics in physics problem solving]In: VIII Congreso Internacional sobre Investigación en Didáctica de las Ciencias, 2009 – Barcelona, September 2-5, 2009. Enseñanza de las Ciencias pp. 1763-1766.

Karam, R., Pietrocola, M. (2008). Formalização matemática x física moderna no ensino médio: é possível solucionar esse impasse? [Mathematical formalization vs. modern physics in high school: is it possible to solve this impasse?]. In: Proceedings of the XI EPEF, Curitiba – PR.

Karam, R. (2007) Matemática como estruturante e Física como motivação: uma análise de concepções sobre as relações entre Matemática e Física. [Mathematics as scaffolding and physics as motivation: broadening conceptions about the relations between mathematics and physics.] In: Proceedings of the VI ENPEC, Florianópolis – SC.

Karam, R., Liblik, A. M. P. (2006) Skilled calculus from Brazilian’s northeastern farming region. In: Third International Conference on Ethnomathematics – ICEM3, Auckland.

Moraes, G. H.; Karam, R. (2006) A Suposta Mudança Epistemológica de Albert Einstein. [Einstein’s supposed epistemological change] In: Proceedings of the X EPEF, Londrina – PR.

Karam, R., Souza Cruz, S. M. S. C., Coimbra, D. (2005) Ampliando o conceito de tempo através da inserção da teoria da relatividade restrita no ensino médio. [Broadening students’ conception of time by teaching the special theory of relativity in high school] In: Proceedings of the V ENPEC, Baurú, SP.