haakoak

• Skåsheim, Gunhild; Haara, Frode Olav & Kolderup, Håkon Andreas (2025). A review of measures aimed at low-performing students in mathematics—What to do? Frontiers in Education. 10. doi: 10.3389/feduc.2025.1705140. Fulltekst i vitenarkiv Vis sammendrag

  This review article investigates measures aimed at low-performing students in mathematics in general classroom settings in primary and middle school education, as described by 24 empirical studies published after The Organization for Economic Co-operation and Development (OECD)'s 2016 report on low performance in mathematics. The article identifies how low performance in mathematics is defined, what measures have been studied, and the implications both for teaching and for future research. The results show considerable variation in the way low performance is defined as well as a predominance of quantitative intervention studies. Four key areas in which measures have been taken were identified: teaching organization and structure, the use of tools and aids, students' own learning strategies, and in specific mathematical content. The review highlights that measures aimed at individual students often yield limited outcomes and suggests a need to shift toward more inclusive and collaboratively-oriented teaching practices. Further, it underscores the importance of teacher competence, classroom stability, and content-specific didactics for enhancing learning outcomes. Finally, the article argues for increased focus on qualitative studies relating to inclusive teaching practices that also include those students who struggle with mathematics.

• Kolderup, Håkon Andreas (2022). Remarks on classical number theoretic aspects of Milnor-Witt K-theory. Acta Arithmetica. ISSN 0065-1036. 202(4), s. 337–359. doi: 10.4064/aa210105-26-11. Fulltekst i vitenarkiv
• Elmanto, Elden & Kolderup, Håkon (2020). On modules over motivic ring spectra. Annals of K-theory. ISSN 2379-1683. 5(2), s. 327–355. doi: 10.2140/akt.2020.5.327. Fulltekst i vitenarkiv Vis sammendrag

  We provide an axiomatic framework that characterizes the stable ∞-categories that are module categories over a motivic spectrum. This is done by invoking Lurie’s ∞-categorical version of the Barr–Beck theorem. As an application, this gives an alternative approach to Röndigs and Østvær’s theorem relating Voevodsky’s motives with modules over motivic cohomology and to Garkusha’s extension of Röndigs and Østvær’s result to general correspondence categories, including the category of Milnor–Witt correspondences in the sense of Calmès and Fasel. We also extend these comparison results to regular Noetherian schemes over a field (after inverting the residue characteristic), following the methods of Cisinski and Déglise.

• Druzhinin, Andrei & Kolderup, Håkon Andreas (2020). Cohomological correspondence categories. Algebraic and Geometric Topology. ISSN 1472-2747. 20(3), s. 1487–1541. doi: 10.2140/agt.2020.20.1487. Fulltekst i vitenarkiv Vis sammendrag

  We prove that homotopy invariance and cancellation properties are satisfied by any category of correspondences that is defined, via Calmès and Fasel’s construction, by an underlying cohomology theory. In particular, this includes any category of correspondences arising from the cohomology theory defined by an MSL–algebra.

• Kolderup, Håkon Andreas (2019). Homotopy invariance of Nisnevich sheaves with Milnor-Witt transfers. Documenta Mathematica. ISSN 1431-0635. 24, s. 2339–2379. doi: 10.25537/dm.2019v24.2339-2379. Fulltekst i vitenarkiv Vis sammendrag

  The category of finite Milnor-Witt correspondences, introduced by Calmès and Fasel, provides a new type of correspondences closer to the motivic homotopy theoretic framework than Suslin-Voevodsky's finite correspondences. A fundamental result in the theory of ordinary correspondences concerns homotopy invariance of sheaves with transfers, and in the present paper we address this question in the setting of Milnor-Witt correspondences. Employing techniques due to Druzhinin, Fasel-Østvær and Garkusha-Panin, we show that homotopy invariance of presheaves with Milnor-Witt transfers is preserved under Nisnevich sheafification.

Se alle arbeider i NVA

• Kolderup, Håkon Andreas & Medbø, Jon Ingulf (2025). Bevis og argumentasjon i matematikk. Fulltekst i vitenarkiv
• Kolderup, Håkon Andreas & Medbø, Jon Ingulf (2025). Modellering. Fulltekst i vitenarkiv
• Kolderup, Håkon Andreas (2022). Homotopy invariance and Gersten complexes over fields and other base schemes. Fulltekst i vitenarkiv
• Kolderup, Håkon Andreas (2021). The strict homotopy invariance theorem over fields and other base schemes. Fulltekst i vitenarkiv
• Kolderup, Håkon Andreas (2021). Voevodsky’s derived category of motives and the strict homotopy invariance theorem. Fulltekst i vitenarkiv
• Kolderup, Håkon Andreas (2018). Cohomological correspondence categories. Fulltekst i vitenarkiv
• Kolderup, Håkon Andreas (2018). Cohomological correspondences and motivic Eilenberg-Mac Lane spectra. Fulltekst i vitenarkiv

Se alle arbeider i NVA