Helmer Aslaksen

• Aslaksen, Helmer & Kirfel, Johann Christoph (2026). In the Realm of Cubics. Mathematics Magazine. ISSN 0025-570X. doi: 10.1080/0025570X.2026.2627857. Full text in Research Archive Show summary

  We study various properties of cubic polynomials with extrema. We consider extrema, points of inflection, tangents and their slopes, intersection points and areas and state various properties that hold for all such cubics. We first formulate these results without proof, and then show that instead of proving them algebraically, we can give a unified proof using transformation geometry.

• Aslaksen, Helmer & Kirfel, Johann Christoph (2024). Utforskende oppgaver med tredjegradskurver. Tangenten - Tidsskrift for matematikkundervisning. ISSN 0802-8192. 35(1), p. 28–33. Full text in Research Archive
• Aslaksen, Helmer & Kirfel, Johann Christoph (2024). LINEAR SUPPORT FOR THE PRIME NUMBER SEQUENCE AND THE FIRST AND SECOND HARDY-LITTLEWOOD CONJECTURES. Mathematica Scandinavica. ISSN 0025-5521. 130(2), p. 198–220. doi: 10.7146/MATH.SCAND.A-143425. Full text in Research Archive
• Allmendinger, Henrike; Aslaksen, Helmer & Buchholtz, Nils (2024). Mathematical orientation as part of teaching competence. International Network for Didactic Research in University Mathematics : INDRUM. p. 549–558. Full text in Research Archive
• Aslaksen, Helmer & Kirfel, Johann Christoph (2023). Utforskende oppgaver med parabler. Tangenten - Tidsskrift for matematikkundervisning. ISSN 0802-8192. 34(4), p. 37–42. Full text in Research Archive
• Allmendinger, Henrike; Aslaksen, Helmer & Buchholtz, Nils (2023). Strengthening mathematical orientation: how university mathematics courses can gain relevance for pre-service teachers. ZDM: Mathematics Education. ISSN 1863-9690. doi: 10.1007/s11858-023-01492-5. Full text in Research Archive Show summary

  Abstract The aim of the article is to discuss how university mathematics courses can become more relevant for pre-service teachers (PSTs). We therefore introduce a concept we call mathematical orientation and develop an analytical framework based on Felix Klein’s pervasive approach to elementary mathematics from a higher standpoint and the work of the practical philosopher Stegmaier on orientation. This framework is used to analyze the mathematical orientation of PSTs on two mathematics courses in Norway and Switzerland. In a qualitative empirical approach, we analyzed 85 reflections written by PSTs on the topic of decimal expansions and reconstructed aspects of their individual mathematical orientation. Our results show that mathematical orientation varies across PSTs to a certain extent. In particular, different points of reference, perspectives, standpoints, and types of links between the mathematical content and teaching situations could be identified. We therefore propose that mathematical orientation can be considered a key variable in addressing the mathematical needs of PSTs in university courses.

• Aslaksen, Helmer & Kirfel, Johann Christoph (2022). Integration by Riemann Triangles. Mathematics Magazine. ISSN 0025-570X. 97(1), p. 4–22. doi: 10.1080/0025570X.2023.2285389. Full text in Research Archive Show summary

  In this article we present a method of integration inspired by an example from Proofs Without Words II by Nelsen. Riemann rectangles under a curve are transformed into triangles. The limit of the collection of triangles gives us a new shape. The area under the original curve and the area of the new shape are the same. In this way, interesting connections between areas under different curves are established and integration formulae are obtained. Only elementary concepts like similarity and Riemann rectangles are used. A variety of examples is worked out to show the strength of the method. The method may be used for first year calculus students to deepen their understanding of the Riemann integral.

• Allmendinger, Henrike; Aslaksen, Helmer & Buchholtz, Nils (2021). Das stochastische Quiz „Borel“. Mathematik lehren : Die Zeitschrift für den Unterricht in allen Schulstufen. ISSN 0175-2235. Full text in Research Archive
• Kirfel, Christoph & Aslaksen, Helmer (2018). Ein alternativer Zugang zur Ableitung: Betrachtungen zu Volumen, Flächeninhalt und Umfang. Der Mathematikunterricht. ISSN 0025-5807. 64(3), p. 23–32. Full text in Research Archive
• Kirfel, Christoph & Aslaksen, Helmer (2018). Areal, volum og derivasjon. Tangenten - Tidsskrift for matematikkundervisning. ISSN 0802-8192. 29(3), p. 34–38. Full text in Research Archive
• Kirfel, Christoph & Aslaksen, Helmer (2018). Areal, omkrets og derivasjon. Tangenten - Tidsskrift for matematikkundervisning. ISSN 0802-8192. 29(2), p. 37–41. Full text in Research Archive
• Aslaksen, Helmer & Beltrami, Olivier (2017). Why Did Deepavali Move By A Month In Singapore In 2009? Computing Deepavali (Nakara Chaturdashi) And Diwali (Laksmi Puja) Around The World. In Nha, Il-Seong; Orchiston, Wayne & Stephenson, F. Richard (Ed.), The History of World Calendars and Calendar-making, from the Proceedings of the International Conference in Commemoration of the 600th Anniversary of the Birth of Kim Dam. Yonsei University Press. ISSN 9788968501883. p. 91–98. Full text in Research Archive
• Hansen, Kajsa Yang; Aslaksen, Helmer; Borge, Inger Christin & Grønmo, Liv Sissel (2013). Hjemmebakgrunn og prestasjoner. In Grønmo, Liv Sissel & Onstad, Torgeir (Ed.), Opptur og nedtur. Analyser av TIMSS-data for Norge og Sverige. Akademika forlag. ISSN 9788232103324. p. 139–162. Full text in Research Archive
• Aslaksen, Helmer (2012). Mathematics, Astronomy and Culture: Helping Students See Connections. In Kaur, Berinderjeet & Toh, Tin Lam (Ed.), Reasoning , Communication and Connections in Mathematics. Yearbook 2012, Association of Mathematics Educators. World Scientific. ISSN 9789814405416. p. 309–317. doi: 10.1142/9789814405430_0015. Full text in Research Archive
• Aslaksen, Helmer (2011). Heavenly Mathematics: Observing the Sun and the Moon from Different Parts of the World. In Shubin, Tatiana; Hayes, David F. & Alexanderson, Gerald L (Ed.), Expeditions in Mathematics. The Mathematical Association of America. ISSN 9780883855713. p. 233–248. Full text in Research Archive

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• Grønmo, Liv Sissel; Onstad, Torgeir; Nilsen, Trude; Hole, Arne; Aslaksen, Helmer & Borge, Inger Christin (2012). Framgang, men langt fram. Norske elevers prestasjoner i matematikk og naturfag i TIMSS 2011. Akademisk Forlag. ISBN 9788232101870. 138 p. Full text in Research Archive

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• Brander, Tommi; Abtahi, Yasmine & Aslaksen, Helmer (2026). Secret Hitler: Reflecting on democracy and human rights, through probabilistic reasoning. Full text in Research Archive Show summary

  The Norwegian school curriculum includes an interdisciplinary component called “Democracy and citizenship”, and teachers in all subjects are looking for ways to relate this topic to their subjects. We explore the mathematical affordances of the board game Secret Hitler (Boxleiter et al., 2016), its relationship to human rights values (HRVs), and most importantly highlight how to meaningfully integrate the HRVs into mathematics classrooms. We understand games as cultural artefacts that carry embedded narratives, values, and ideologies; upholding or violating the principles of human rights (Abtahi et al., 2025). Secret Hitler is a social deduction game, where some players are secretly designated as fascists, while the others are liberals. The players participate in legislation and elections and thus reveal uncertain and limited information about their political allegiance. The game creates opportunities for players to debate who is most likely to be a fascist and justify their reasoning. It thus provides a meaningful context for teaching both mathematical concepts and human rights values. The mathematical topics in the game are argumentation and probabilistic reasoning. In response to its rich mathematical structure, players can apply Bayesian reasoning to analyze what implemented policies reveal about the political alignments of participants. Bayes’ theorem (Stone, 2013/2014), typically introduced in high school probability, can be incorporated into the lesson if students have a basic understanding of probability. Thus, the game serves as a mathematical model of political argumentation and decision-making. Democratic forms of government consistently perform better than other political systems in upholding human rights obligations and ensuring that these rights are realized in practice (Landman, 2018), thus connecting the political theme to HRV. Different forms of democracy include different levels of human rights integration. Landman (2018) looks at three forms of government: procedural, liberal, and social. Procedural definitions of democracy include the dimensions of contestation and participation. Liberal definitions preserve the notions found in procedural definitions but add more explicit references to the protection of certain human rights. Social definitions maintain the institutional and rights dimensions found in liberal models of democracy but expand the types of rights that ought to be protected, including social, economic and cultural rights. It should be noted that the name of the game is controversial, and many people feel that “turning fascism into a game” is not appropriate. While we understand and respect that view, we feel that the game treats the subject with respect (Edesa-Filios, 2025; Filios & Schröter, 2024), and that the point of the game is not that “fascism is fun", but that learning about complex issues such as democratic backsliding and political violence can be engaging and interactive when explored through the game, set in the historical context of 1930s Germany. We believe that the game helps build awareness about the danger of fascism, treats the subject matter with respect, and trains in political decision-making under uncertainty and incomplete information by treating these concepts mathematically. Bibliography Abtahi, Y., Brander, T., & Reinhard-Hansen, C. (2025). Mathematics and the (violation of) human dignity in board games. For the Learning of Mathematics, 45(3), 45–47. Boxleiter, M., Maranges, T., & Schubert, M. (2016). Secret Hitler. Goat, Wolf, & Cabbage. https://www.secrethitler.com/ Edesa-Filios, C. (2025). Secret Hitler: Political symbolism and metagaming in social deduction. In M. Heron, Demystifying Game Studies (1st edn, pp. 51–64). CRC Press. https://doi.org/10.1201/9781003530282-3 Filios, C.-E., & Schröter, P. (2024). Ways in which sensitive themes can be effectively handled within games: A study on Secret Hitler, the board game, and other similar games. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.4811880 Landman, T. (2018). Democracy and Human Rights: Concepts, Measures, and Relationships. Politics and Governance, 6(1), 48–59. https://doi.org/10.17645/pag.v6i1.1186 Stone, J. V. (2014). Bayes’ rule: A tutorial introduction to Bayesian analysis (First edition, third printing [with corrections]). Sebtel Press. (Original work published 2013)

• Aslaksen, Helmer (1988). SO(2) invariants of a set of 2x2 matrices. Universitetet i Oslo. Full text in Research Archive

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