Hans Kristian Nilsen

• Omarhaug, Kristoffer Heggelund & Nilsen, Hans Kristian (2026). The Didactical Transposition and Praxeology related to the study of Integration at the Secondary and Tertiary levels in Norway. Annales de Didactique et de Sciences Cognitives. ISSN 0987-7576. Thématique 4, p. 159–186. doi: 10.4000/15rjc. Full text in Research Archive Show summary

  This paper builds on two studies conducted in Norway, respectively with students in their last year at upper secondary school and engineering students in their first year at university. From the perspective of the Anthropological Theory of the Didactic (ATD), we discuss the didactical transposition concerning the topic of integration relevant for both institutions. The curricula do not favour any one specific approach to integration, and Riemann-sums dominate the textbook used in the university, while an infinitesimal-based approach was offered at upper secondary. The praxeology at upper secondary school seems to lead students exclusively towards anti-derivative and area-interpretations of the integral, while the university students show more varied infinitesimal-based interpretations. We argue a need for revising how integrals are presented and worked with, at both levels of schooling.

• 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. Full text in Research Archive 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 9789198402469. p. 281–294. Full text in Research Archive Show summary

  The NORMA conferences held triennially gather academics from the Nordic area and beyond. The conferences offer a window into the key topics and outcomes of Nordic mathematics education research. This paper presents an analysis of the 73 regular papers presented at the NORMA20 conference held in Oslo in June 2021 and published in the conference pre- and proceedings. The analysis yields research questions, methods, and key findings for the educational levels spanning kindergarten through to higher education. The majority of the papers present research from primary school-level and pre- and in-service teacher education. Across the educational levels, teaching methods and classroom discourse emerged as the most frequent topics, dominated by empirical studies that applied qualitative methods.

• 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. 54(6). doi: 10.1080/0020739X.2021.1984596. Full text in Research Archive Show summary

  Approaches to learning have been identified as crucial factors that influence students’ mathematics performance. However, there have been mixed findings on which of the different approaches improve performance in undergraduate mathematics. Thus, this study aimed to unravel the specific effects of prior mathematics knowledge and approaches to learning on performance in mathematics among first-year engineering students. The design is cross-sectional, and the data are analysed with some structural equation modelling techniques. The findings show a positive effect of prior mathematics knowledge on performance. The effect of surface approaches to learning on performance is significant, negative, and surface approaches to learning mediate the effect of prior mathematics knowledge on performance. There are no substantial relations between prior mathematics knowledge, deep approaches to learning, and performance. Students who adopt surface approaches performed poorly but we found no evidence to claim that students who adopt deep approaches perform better in the course. By implication, our findings underscore the importance of discouraging engineering students from capitalizing on surface approaches to learning mathematics.

• 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. 5(1). doi: 10.5324/njsteme.v5i1.3972. Full text in Research Archive Show summary

  This is a report of an analysis of some of the data generated by a national survey of teaching approaches used in higher education mathematics courses. The overall purpose of the survey was to explore how widespread is the use of teaching approaches that might promote students’ active learning of mathematics. The paper includes a brief presentation of the authors meaning of the expression “teaching actions that have the potential to promote active learning”. The analysis focuses on the responses of 95 lecturers working in 13 Norwegian HE institutions. The goal is to expose underlying patterns in lecturers’ responses to questions about the teaching actions they may incorporate in their practice. The analysis incorporates descriptive statistics (e.g., mean scores) and exploratory factor analysis to expose underlying reasons for patterns of lecturers’ responses. Qualitative, interpretative approaches are used, both in the design of the survey instrument and in making sense of the outcome from the statistical analysis.

• 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. p. 268–277. 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.; 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). p. 1003–1009. Full text in Research Archive
• 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.; 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 (2020). First-year university students making sense of symbols in integration. International Network for Didactic Research in University Mathematics : INDRUM. p. 248–257. 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 9780639821542. p. 129–137. 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. 9(3), p. 1–14. doi: 10.3390/educsci9030170. Full text in Research Archive
• 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 Show summary

  This paper reports a Norwegian validation study of a widely used instrument to measure students’ approaches to learning, namely, Bigg’s revised two-factor study process questionnaire (R-SPQ-2F). Its cultural sensitivity and psychometry evaluations have provoked rigorous discussion among educators in different languages. A survey design was adopted involving 253 undergraduate engineering students across two universities. Confirmatory factor analyses were used to test six models hypothesized to reflect the factor structures of R-SPQ-2F and unidimensionality of its subscales. The results showed appropriate fits of a two-factor first-order model with 10 items measuring deep approach and 9 items measuring surface approach subscales. The reliability was found to be high with coefficients of .81, .72 and .63 on deep subscale, surface subscale and the whole instrument respectively. Findings may be interpreted as evidence of cultural sensitivity of the instrument and more validation studies were recommended.

• 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 9781873769737. p. 1537–1544. Full text in Research Archive
• 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 9781862958296. p. 281–289. Full text in Research Archive
• 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 9789979549659. p. 435–444. Full text in Research Archive

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• 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 9789198402469. 302 p. Full text in Research Archive Show summary

  The story about the NORMA20 conference is the story about a conference that had to be postponed, as a pandemic prevented us from coming together to present and discuss our research. When we made the decision to postpone just after Easter in 2020, we were all sad and disappointed that all the efforts made by authors, reviewers, LOC and IPC members might be for nothing. However, during 2020, digital solutions for cooperation emerged so we could host NORMA20 as an online conference in June 2021.<p> <p>Delaying the conference had both positive and negative consequences. On the positive side, postponing allowed us to make a call for contributions in both 2019 and 2020, substantially increasing the number of submissions. Not only was the number of submissions large but the number of accepted submissions also increased. During the conference, 72 regular papers, 30 short communications, nine poster presentations, four keynotes, and one working group were presented. This made the NORMA20 conference the largest NORMA conference to date.

• 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 Show summary

  This volume presents Nordic mathematics education research, which will be presented at the Ninth Nordic Conference on Mathematics Education, NORMA 20, in Oslo, Norway, in June 2021. The theme of NORMA 20 regards what it takes or means to bring Nordic mathematics education into the future, highlighting that mathematics education is continuous and represents stability just as much as change.

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• Larson, Niclas & Nilsen, Hans Kristian (2025). Den mystiske og magiske integrasjonen (del 1). doi: https:/podcasts.apple.com/no/podcast/den-mystiske-og-magiske-integrasjonen-del-1/id1586322365?i=1000709362330. Full text in Research Archive Show summary

  Dette er den første episoden i en serie med totalt to episoder av Spøkelser etter avdøde størrelser, der Niclas Larson vil ha en semistrukturert samtale med kollega Hans Kristian Nilsen, førsteamanuensis på Institutt for matematiske fag ved Universitetet i Agder. Episodene handler om integrasjon og derivasjon med utgangspunkt i Hans Kristians fagdidaktiske forskning på temaet. I denne episoden blir det fokus på hva derivasjon og integrasjon handler om. Hans Kristian og Niclas drøfter også noen kjente vanskeligheter med disse begrepene. Del 2 vil bli publisert om to uker. Da fortsetter Niclas og Hans Kristian praten med mer fokus på resultater og erfaringer fra Hans Kristians undersøkelser blant ingeniør- og økonomistudenter. I tillegg har vi en cliffhanger til del 2, der det vil bli avslørt hva Hans Kristian er norsk mester i. To ganger på rad, dessuten.

• Larson, Niclas & Nilsen, Hans Kristian (2025). Den mystiske og magiske integrasjonen (del 2): Fagdidaktisk forskning på kryss og tvers. doi: https:/podcasts.apple.com/no/podcast/den-mystiske-og-magiske-integrasjonen-del-2-fagdidaktisk/id1586322365?i=1000711239866. Full text in Research Archive Show summary

  Sesongens niende episode av Spøkelser etter avdøde størrelser er den andre episoden om didaktiske spørsmål ved introduksjon av integrasjon i universitetsmatematikken. Igjen er det Niclas Larson og Hans Kristian Nilsen som har en semistrukturert samtale. Denne gangen er det enda større fokus på Hans Kristians fagdidaktiske forskning. For eksempel drøfter de hvordan man kan introdusere integrasjon vha. infinitesimaler. Et begrep som er minst like vanskelig å uttale som å skjønne betydningen av. Til slutt får vi vite hva Hans Kristian er norsk mester i og litt mer rundt den konkurransen.

• 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. Full text in Research Archive
• 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. Full text in Research Archive
• Goodchild, Simon; Bjørkestøl, Kirsten; Nilsen, Hans Kristian; Borge, Inger Christin & Tonheim, Odd Helge Mjellem (2020). Active learning - Undersøkelse ved MatRIC i samarbeid med NMR. Full text in Research Archive
• Nilsen, Hans Kristian (2020). First-year university students making sense of symbols in integration. Full text in Research Archive
• Borge, Inger Christin; Bjørkestøl, Kirsten; Goodchild, Simon; Nilsen, Hans Kristian & Tonheim, Odd Helge Mjellem (2019). Student-active learning in mathematics: Operationalisation of ‘constructive alignment’. Full text in Research Archive 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.

• 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. 3, p. 220–224. Full text in Research Archive
• Nilsen, Hans Kristian (2019). First-year engineering students’ reflections on integration and the Fundamental Theorem of Calculus. Full text in Research Archive
• Nilsen, Hans Kristian & Gjesteland, Thomas (2019). How do we get active students? Students enjoying transformed and improved learning experiences of mathematics in higher education. Full text in Research Archive
• Nilsen, Hans Kristian (2019). First-year engineering students’ reflections on the Fundamental Theorem of Calculus. Full text in Research Archive
• Vegusdal, Anne & Nilsen, Hans Kristian (2016). Lærerstudenter med Lektor2 på pensum. Naturfag. ISSN 1504-4564. p. 44–45. Full text in Research Archive
• Nilsen, Hans Kristian (2016). Seriøst, Schaanning? Full text in Research Archive
• Nilsen, Hans Kristian; Vegusdal, Anne & Dean, Evert (2016). Mathematics at the Enterprise, University and School (MathEUS). Full text in Research Archive
• Nilsen, Hans Kristian & Vegusdal, Anne (2015). MathEUS – Matematikk med mening. Et FoU-samarbeid mellom skole, universitet og arbeidsliv. Full text in Research Archive
• Nilsen, Hans Kristian (2015). The introduction of functions at lower secondary and upper secondary school. Full text in Research Archive
• 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. Full text in Research Archive
• Nilsen, Hans Kristian (2019). First-year engineering students’ reflections on the Fundamental Theorem of Calculus. Conference proceedings: https://matric-calculus.sciencesconf.org/. Full text in Research Archive

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