Kristoffer Heggelund Omarhaug

• 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.

• Opheim, Linda Gurvin; Knutsen, Kristoffer Heggelund & Brodahl, Cornelia (2023). Pre-Service Teachers’ Self-efficacy as Future Mathematics Teachers in a Second Language Classroom. Journal of the International Society for Teacher Education. ISSN 1029-5968. 27(2). doi: 10.26522/jiste.v27i2.4427. Full text in Research Archive Show summary

  This study contributes to the field of research on teacher self-efficacy by investigating a group of multilingual pre-service teachers' perceptions of self-efficacy in Norwegian mathematics classrooms. In recent years, several quantitative studies exploring teacher self-efficacy have been conducted, but according to Xenofontos and Andrews (2020) there are few qualitative studies addressing conceptualizations of self-efficacy across various contexts. Furthem1ore, the cultural and language dimensions related to self-efficacy are usually not addressed. Pertaining to this group of multilingual pre-service teachers, all enrolled in the multilingual teacher preparation program at the University of Agder, we found that it was not sufficient for them to focus solely on acquiring mathematical knowledge or developing their mathematics teaching skills. They also needed to navigate a different classroom culture and a language that is not their first language. As a result, this study contributes crucial insights to complement the theory of teacher self-efficacy. Keywords: Mathematics education, pre-service teachers, multilingual, self-efficacy, culture

• 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.

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• Breive, Svanhild & Knutsen, Kristoffer Heggelund (2026). Hva kjennertegner god begynneropplæring i matematikk? Del 2. Full text in Research Archive
• Breive, Svanhild & Knutsen, Kristoffer Heggelund (2026). Hva kjennetegner god begynneropplæring i matematikk? Del 1. Full text in Research Archive
• Opheim, Linda Gurvin; Knutsen, Kristoffer Heggelund & Brodahl, Cornelia (2023). Multilingual Teacher Students’ Self-efficacy as Future Mathematics Teachers in a Second Language Classroom. Full text in Research Archive Show summary

  The multilingual teacher program at the University of Agder is unique in a national perspective. It is the only Norwegian teacher education program tailored to students of a different mother tongue and a rich variety of cultural backgrounds. To get to know the 24 students, and to better understand their perspectives on learning and teaching mathematics, they were given a reflective questionnaire. Their responses to open-ended questions revealed aspects related to their self-efficacy as future mathematics teachers in Norwegian classrooms. In recent years, several quantitative studies exploring teacher self-efficacy have been conducted, but according to Xenofontos and Andrews (2020) there are few qualitative studies addressing conceptualization of self-efficacy in various contexts. Furthermore, the cultural and language dimensions related to self-efficacy is usually not addressed. This study contributes to the field of research by investigating multilingual teacher students’ perceptions of self-efficacy in the Norwegian mathematics classroom. For this group of teacher students, it is not sufficient to learn mathematics or how to teach mathematics. They also need to adapt to a different classroom culture and a language that is not their first language. Hence, this study adds essential dimensions to complement the theory of teacher self-efficacy.

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