Hans Kristian Nilsen

• Nilsen, Hans Kristian & Knutsen, Kristoffer Heggelund (2023). First-Year Engineering Students’ Interpretations of Differentials and Definite Integrals. International Journal of Research in Undergraduate Mathematics Education. ISSN 2198-9745. 9(1), p. 173–200. doi: 10.1007/s40753-022-00208-6. Show summary

  In this paper we focus on Norwegian first-year engineering students’ interpretations of differentials and definite integrals. Through interviews with 15 engineering students, we investigated how the students interpreted the different symbols involved in the Fundamental Theorem of Calculus (FTC), as displayed in the textbook used in their calculus course. Through the students’ reflections, we aimed to gain insight into the students’ interpretations of differentials, infinitesimals, and limits, and how these concepts were used to interpret the definite integral. Despite a rather rigorous limit-based approach to definite integrals, provided in teaching and in the students’ textbook, we observed that most students offered conceptual interpretations closer linked with an infinitesimal approach, in terms of integrals being regarded as sums of narrow bars, in line with Leibniz.

• Fauskanger, Janne; Naalsund, Margrethe; Nilsen, Hans Kristian; Nortvedt, Guri A.; Pálsdóttir, Guðbjörg & Portaankorva-Koivisto, Päivi [Show all 9 contributors for this article] (2022). Bringing Nordic mathematics education into the future : a review of the papers presented at the NORMA20 conference. In Nortvedt, Guri A.; Buchholtz, Nils; Fauskanger, Janne; Hähkiöniemi, Markus; Jessen, Britta Eyrich; Nilsen, Hans Kristian; Naalsund, Margrethe; Pálsdóttir, Guðbjörg; Portaankorva-Koivisto, Päivi; Radišić, Jelena; Sigurjónsson, Jóhann Örn; Viirman, Olov Lui & Wernberg, Anna (Ed.), Bringing Nordic mathematics education into the future. Proceedings of Norma 20, The ninth Nordic Conference on Mathematics Education . Svensk förening för MatematikDidaktisk Forskning - SMDF. ISSN 978-91-984024-6-9. p. 281–294. Full text in Research Archive
• Goodchild, Simon; Bjørkestøl, Kirsten; Borge, Inger Christin; Nilsen, Hans Kristian & Tonheim, Odd Helge Mjellem (2021). Educating to inspire active learning approaches in mathematics in Norwegian universities. Nordic Journal of STEM Education. ISSN 2535-4574. 5(1). doi: 10.5324/njsteme.v5i1.3972. Full text in Research Archive
• Zakariya, Yusuf F.; Nilsen, Hans Kristian; Bjørkestøl, Kirsten & Goodchild, Simon (2021). Analysis of relationships between prior knowledge, approaches to learning, and mathematics performance among engineering students. International Journal of Mathematical Education in Science and Technology. ISSN 0020-739X. doi: 10.1080/0020739X.2021.1984596.
• Zakariya, Yusuf F.; Nilsen, Hans Kristian; Bjørkestøl, Kirsten & Goodchild, Simon (2020). Singular and combined effects of learning approaches, self-efficacy and prior knowledge on university students’ performance in mathematics. Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education (RUME). ISSN 2474-9346. p. 1003–1009.
• Nilsen, Hans Kristian (2020). First-year university students making sense of symbols in integration. International Network for Didactic Research in University Mathematics : INDRUM. ISSN 2496-1027. p. 248–257.
• Zakariya, Yusuf F.; Nilsen, Hans Kristian; Bjørkestøl, Kirsten & Goodchild, Simon (2020). Impact of attitude on approaches to learning mathematics: a structural equation modelling approach. In Hausberger, T.; Bosch, M. & Chelloughi, F. (Ed.), Proceedings of the Third Conference of the International Network for Didactic Research in University Mathematics. University of Carthage and INDRUM. ISSN 2496-1027. p. 268–277.
• Zakariya, Yusuf F.; Nilsen, Hans Kristian; Goodchild, Simon & Bjørkestøl, Kirsten (2020). Assessing first-year engineering students’ pre-university mathematics knowledge: Preliminary validity results based on an item response theory model. Journal of Technology and Science Education (JOTSE). ISSN 2014-5349. 10(2), p. 259–270. doi: 10.3926/jotse.1017. Full text in Research Archive
• Zakariya, Yusuf F.; Nilsen, Hans Kristian; Goodchild, Simon & Bjørkestøl, Kirsten (2020). Self-efficacy and approaches to learning mathematics among engineering students: empirical evidence for potential causal relations. International Journal of Mathematical Education in Science and Technology. ISSN 0020-739X. p. 1–16. doi: 10.1080/0020739X.2020.1783006. Full text in Research Archive
• Zakariya, Yusuf F.; Bjørkestøl, Kirsten & Nilsen, Hans Kristian (2020). Teacher job satisfaction across 38 countries and economies: An alignment optimization approach to a cross-cultural mean comparison. International Journal of Educational Research. ISSN 0883-0355. 101. doi: 10.1016/j.ijer.2020.101573. Full text in Research Archive
• Nilsen, Hans Kristian (2019). First-year university students' interpretation of praxeology when solving an integration task. In Graven, Mellony; Venkat, Hamsa; Essien, Anthony A. & Vale, Pamela (Ed.), Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education. Proceedings of the International Groups for the Psychology of Mathematics Education. ISSN 978-0-6398215-4-2. p. 129–137.
• Zakariya, Yusuf F.; Bjørkestøl, Kirsten; Nilsen, Hans Kristian; Goodchild, Simon & Lorås, Madeleine (2019). University students’ learning approaches: An adaptation of the revised two-factor study process questionnaire to Norwegian. Studies in Educational Evaluation. ISSN 0191-491X. 64. doi: 10.1016/j.stueduc.2019.100816. Full text in Research Archive
• Zakariya, Yusuf; Goodchild, Simon; Bjørkestøl, Kirsten & Nilsen, Hans Kristian (2019). Calculus Self-Efficacy Inventory: Its Development and Relationship with Approaches to Learning. Education Sciences. ISSN 2227-7102. 9(3), p. 1–14. doi: 10.3390/educsci9030170. Full text in Research Archive
• Nilsen, Hans Kristian & Vegusdal, Anne (2017). Mathematics at the enterprise: Industry, university and school working together to facilitate learning. In Dooley, Thérèse & Gueudet, Ghislaine (Ed.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME 10). European Society for Research in Mathematics Education. ISSN 978-1-873769-73-7. p. 1537–1544.
• Nilsen, Hans Kristian (2015). The introduction of functions at lower secondary and upper secondary school, Proceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education, Volume 2. The International Group for the Psychology of Mathematics Education. ISSN 978-1-86295-829-6. p. 281–289.
• Nilsen, Hans Kristian (2012). Transition from lower secondary to upper secondary mathematics in Norway: gradients of linear functions. In Gunnarsdottir, Gudny Helga; Hreinsdottir, Freyja; Pálsdóttir, Guðbjörg; Hannula, Markku; Hannula-Sormunen, Minna; Jablonka, Eva; Jankvist, Uffe Thomas; Ryve, Andreas; Valero, Paola & Wæge, Kjersti (Ed.), Proceedings of NORMA 11 The Sixth Nordic Conference on Mathematics Education. University of Iceland Press. ISSN 978-9979-54-965-9. p. 435–444.

View all works in Cristin

• Nortvedt, Guri A.; Buchholtz, Nils; Fauskanger, Janne; Hähkiöniemi, Markus; Jessen, Britta Eyrich & Nilsen, Hans Kristian [Show all 13 contributors for this article] (2022). Bringing Nordic mathematics education into the future. Proceedings of Norma 20, The ninth Nordic Conference on Mathematics Education . Svensk förening för MatematikDidaktisk Forskning - SMDF. ISBN 978-91-984024-6-9. 302 p. Full text in Research Archive
• Nortvedt, Guri A.; Buchholtz, Nils; Fauskanger, Janne; Hreinsdottir, Freyja; Hähkioniemi, Marcus & Jessen, Britta Eyrich [Show all 15 contributors for this article] (2021). Bringing Nordic mathematics education into the future : Preceedings of Norma 20 : The ninth Nordic conference on mathematics education Oslo, 2021. SMDF, Swedish Society for Research in Mathematics Education. ISBN 9789198402438. 296 p. Full text in Research Archive

View all works in Cristin

• Borge, Inger Christin; Bjørkestøl, Kirsten; Goodchild, Simon; Nilsen, Hans Kristian & Tonheim, Odd Helge Mjellem (2022). Aktive læringsformer i matematikk - Nasjonal kartlegging av matematikkundervisning i universitets- og høgskolesektoren desember 2019 – januar 2020.
• Borge, Inger Christin; Bjørkestøl, Kirsten; Goodchild, Simon; Nilsen, Hans Kristian & Tonheim, Odd Helge Mjellem (2022). Educating to inspire active learning approaches in mathematics in Norwegian universities - Teaching approaches used in Norwegian higher education mathematics courses .
• Nilsen, Hans Kristian (2020). First-year university students making sense of symbols in integration.
• Goodchild, Simon; Bjørkestøl, Kirsten; Nilsen, Hans Kristian; Borge, Inger Christin & Tonheim, Odd Helge Mjellem (2020). Active learning - Undersøkelse ved MatRIC i samarbeid med NMR.
• Nilsen, Hans Kristian (2019). First-year engineering students’ reflections on the Fundamental Theorem of Calculus.
• Nilsen, Hans Kristian (2019). First-year engineering students’ reflections on integration and the Fundamental Theorem of Calculus.
• Nilsen, Hans Kristian & Gjesteland, Thomas (2019). How do we get active students? Students enjoying transformed and improved learning experiences of mathematics in higher education.
• Bjørkestøl, Kirsten; Borge, Inger Christin; Goodchild, Simon; Nilsen, Hans Kristian & Tonheim, Odd Helge Mjellem (2019). Student-active learning in mathematics: Operationalisation of 'constructive alignment'. Nordic Journal of STEM Education. ISSN 2535-4574. 3, p. 220–224.
• Borge, Inger Christin; Bjørkestøl, Kirsten; Goodchild, Simon; Nilsen, Hans Kristian & Tonheim, Odd Helge Mjellem (2019). Student-active learning in mathematics: Operationalisation of ‘constructive alignment’. Show summary

  This presentation/paper describes the beginning of a developmental process leading to the creation of a survey instrument to explore the use of active learning approaches in higher education mathematics. The paper begins by arguing a relation between active learning and the conference theme “constructive alignment”. The first stages of the developmental process are based on a “Delphi-study” research design in which the meanings of “active learning” and teaching/approaches that may promote active learning are elicited from a selected group of students, mathematics instructors, mathematicians and mathematics education researchers. The Delphi-study is described and the analysis of outcomes from the first stage of the study are reported in this paper. The conference presentation will also include details from the second stage of the study that is planned at the time of writing. A working definition of “active learning” is established from the study, together with a number of teaching/learning approaches that might promote active learning in mathematics. The paper concludes with reflections on how the outcomes of the study will influence the design and content of the survey instrument. It is hoped the discussion at the conference will also inform the further development of the instrument.

• Nilsen, Hans Kristian; Vegusdal, Anne & Dean, Evert (2016). Mathematics at the Enterprise, University and School (MathEUS).
• Vegusdal, Anne & Nilsen, Hans Kristian (2016). Lærerstudenter med Lektor2 på pensum. Naturfag. ISSN 1504-4564. p. 44–45.
• Nilsen, Hans Kristian (2016). Seriøst, Schaanning? Morgenbladet. ISSN 0805-3847.
• Nilsen, Hans Kristian & Vegusdal, Anne (2015). MathEUS – Matematikk med mening. Et FoU-samarbeid mellom skole, universitet og arbeidsliv.
• Nilsen, Hans Kristian (2015). The introduction of functions at lower secondary and upper secondary school.
• Bjørkestøl, Kirsten; Borge, Inger Christin; Goodchild, Simon; Nilsen, Hans Kristian & Tonheim, Odd Helge Mjellem (2020). Nasjonal kartlegging av matematikkundervisning i universitets- og høgskolesektoren desember 2019 – januar 2020 - Foreløpig rapport: September 2020. Norsk matematikkråd og MatRIC.
• Nilsen, Hans Kristian (2019). First-year engineering students’ reflections on the Fundamental Theorem of Calculus. Conference proceedings: https://matric-calculus.sciencesconf.org/.

View all works in Cristin