Nils Kristian Hansen

• Hansen, Nils Kristian & Hadjerrouit, Said (2023). Mathematical Problem-Solving by Means of Computational Thinking and Programming: A Use-Modify-Create Approach. In Sampson, D. G.; Ifenthaler, D. & Isaias, P. (Ed.), 20th International Conference on Cognition and Exploratory Learning in the Digital Age (CELDA 2023). IADIS Press. ISSN 978-989-8704-52-8. p. 179–186.
• Hansen, Nils Kristian & Hadjerrouit, Said (2023). Analyzing Students’ Computational Thinking and Programming Skills for Mathematical Problem Solving. In Ifenthaler, Dirk; Sampson, Demetrios G. & Isaías, Pedro (Ed.), Open and Inclusive Educational Practice in the Digital World. Springer Nature. ISSN 978-3-031-18512-0. p. 155–173. doi: https:/doi.org/10.1007/978-3-031-18512-0_10. Show summary

  The purpose of this chapter is to analyze students’ computational thinking and programming skills for mathematical problem-solving in a programming course at the undergraduate level. The chapter critically reviews the research literature in the field and proposes a model that connects mathematical thinking to computational thinking and programming. The model is then used as a theoretical basis to collect and analyze data from three groups of three students solving a mathematical task. The results reveal that the participating students faced several challenges: The lack of mathematical thinking, insufficient experience with computational thinking, and, more importantly, lack of deeper connection between computational and mathematical thinking, severely impeded their work. Conclusions, limitations, practical implications, and future research work are drawn from the results to explore mathematical problem solving through computational thinking and programming in a larger group of students. Studies involving a larger number of participants would be relevant to compare with findings of the present study to achieve more reliability and validity.

• Hadjerrouit, Said & Hansen, Nils Kristian (2022). Undergraduate Mathematics Students Engaging in Problem-Solving Through Computational Thinking and Programming: A Case Study. In Ifenthaler, Dirk; Sampson, Demetrios G. & Isaías, Pedro (Ed.), Orchestration of Learning Environments in the Digital World. Springer Nature. ISSN 978-3-030-90943-7. p. 197–214. doi: https:/doi.org/10.1007/978-3-030-90944-4_11. Show summary

  This paper aims at exploring students’ engagement in mathematical problem-solving through computational thinking (CT) and the programming language MATLAB. The work is a single case study conducted in the context of a first-year undergraduate course on programming with applications in mathematics. It uses a three-step approach based on theoretically derived insights from the research literature to address mathematical problem-solving by means of mathematical thinking, CT, and programming. The main method used is a semi-structured interview with two undergraduate students trying to solve a mathematical task related to Pythagoras’ theorem while responding to questions about the problem-solving process. The interviews were analyzed according to an inductive strategy based on the interplay between the three-step approach and the interview data. The results describe two students’ opposite experiences. While one was able to handle and solve the task using CT and MATLAB very easily, the other struggled to get acquainted with the task, CT, and the programming activity with MATLAB. Conclusions are drawn from the results to promote mathematical problem-solving through CT and programming in mathematics courses at the undergraduate level. Future work will address some of the research gaps found in the literature, in particular the links between mathematical thinking, CT, and programming to highlight their communalities and potential differences and deepen the knowledge about their connections.

• Hansen, Nils Kristian & Hadjerrouit, Said (2021). Exploring Students’ Computational Thinking for Mathematical Problem-Solving: A Case Study . In Sampson, Demetrios G.; Ifenthaler, Dirk & Isaías, Pedro (Ed.), Proceedings of the 18th International Conference on Cognition and Exploratory Learning in Digital Age (CELDA2021). IADIS Press. ISSN 978-989-8704-33-7. p. 251–260. Show summary

  The purpose of this paper is to investigate students’ engagement in computational thinking (CT) and programming with MATLAB when solving a mathematical task in a programming course at the undergraduate level. The data collection method is participant observation of three groups of three students presented with a mathematical task to solve. The study uses a deductive-inductive analysis strategy based on the interplay between the theoretical framework and the empirical data. The results reveal that engaging students in CT for mathematical problem-solving is challenging for many reasons: Lack of mathematical thinking (MT), insufficient experience with CT, and more importantly lack of deeper connection between CT and MT. Conclusions are drawn from the results to promote mathematical problem-solving by means of CT and MT at the undergraduate level.

• Hadjerrouit, Said & Hansen, Nils Kristian (2020). Challenges encountered in mathematical problem-solving through computational thinking and programming activities. In Donevska-Todorova, Ana; Faggiano, Eleonora; Trgalova, Jana; Lavicza, Zsolt; Weinhandl, Robert; Clark-Wilson, Alison & Weigand, Hans-Georg (Ed.), Proceedings of the Tenth ERME Topic Conference (ETC 10) on Mathematics Education in the Digital Age (MEDA), 16-18 September 2020 in Linz, Austria. European Society for Research in Mathematics Education. ISSN 978-3-9504630-5-7. p. 369–376.
• Hadjerrouit, Said & Hansen, Nils Kristian (2020). Students Engaging in Mathematical Problem-Solving through Computational Thinking and Programming Activities: A Synthesis of thwo Opposite Experiences. In Sampson, Demetrios G.; Ifenthaler, Dirk & Isaías, Pedro (Ed.), Proceedings of the 17th International Conference on Cognition and Exploratory Learning in the Digital Age (CELDA 2020). IADIS Press. ISSN 978-989-8704-22-1. p. 91–98. Show summary

  This paper aims at exploring students’ experiences when engaging in mathematical problem-solving through computational thinking and programming by a combination of theoretically derived insights and task-based activities. The main method used is a semi-structured interview with two undergraduate students who were presented with a mathematical task to solve while responding to questions about the mathematical solving process. The results reveal two students’ opposite experiences. While one struggled to get acquainted with the task and the associated programming activity, the other was able to handle and solve the task using computational thinking (CT) and programming skills very easily. Conclusions are drawn from the students’ experiences to promote mathematical problem-solving through computational thinking and programming in mathematics education at the undergraduate level.

• Brodahl, Cornelia & Hansen, Nils Kristian (2014). Education students’ use of collaborative writing tools in collectively reflective essay papers. Journal of Information Technology Education: Research (JITE: Research). ISSN 1547-9714. 13(1), p. 91–120. doi: 10.28945/1960. Show summary

  Google Docs and EtherPad are Web 2.0 tools providing opportunity for multiple users to work online on the same document consecutively or simultaneously. Over the last few years a number of research papers on the use of these collaborative tools in a teaching and learning environment have been published. This work builds on that of Brodahl, Hadjerrouit, and Hansen (2011) expanding its case study. The theoretical framework is the same as the one underlying Brodahl et al. (2011), drawing on two learning theories, the social-constructivist learning theory and the community of practice, and their relationships to collaborative tools. The literature review is extended to cover the recent research work in the field, related to Web 2.0 technologies in higher education. The case study of Brodahl et al. (2011) involved 201 education students who had just begun their four-year initial teacher education. However, 24 students are omitted in the current work, and the result tables from Brodahl et al. (2011) accordantly updated. Dis-regarding particular groups of students was due to their specific local dispersion, as they conducted their entire assignment and collectively reflective essay paper at the same physical location and, with respect to this, reported the use of collaborative tools as superfluous and unwanted in their setting. Partly based on the same survey, this work presents a case study investigating education students’ perceptions of collaborative writing reflective essay papers. However, where Brodahl et al. (2011) presented a solely quantitative study derived from closed-ended questions, this work incorporates the survey’s open-ended questions in a qualitative analysis. The analysis also draws on the students’ written reflections on their experiences. The qualitative analysis supports the conclusion of Brodahl et al. (2011) that technical problems were a major issue, mostly related to EtherPad. All but one complaint about tech-nical difficulties stemmed from EtherPad users during a limited period of time. Other major negative feedback concerned group size; several groups pointed out difficulties with organizing the work, problems of keeping track when editing simultaneously, and failure to produce a unified document. Positive issues frequently mentioned are the ability to work asynchronously and from different places. Furthermore, a majority of the reports on commenting on and editing each other’s work were positive, mentioning that it is an advantage to be able to correct spelling errors and bad formulations, that it is educational, that one may contribute with ideas that the others do not have, and that it improves the final text. Larger issues on the negative side were fear of insulting or misunderstanding, and difficulties because of various work modes. Also qualitative results indicate that females are more concerned with group size than males, but less preoccupied with technical difficulties. Furthermore, younger students appear more concerned about the importance of preparation and planning than older ones. The major conclusions are that EtherPad and Google Docs facilitate new ways of ap-proaching communication, for different collaborative writing work modes as well as in different settings. However, the setting in which the tool is used exerts an influence on the way students perceive its usefulness. Recommendations derived from students’ perception of factors of success for using the collaborative writing tool include the following: group size should preferably not exceed three persons; the students ought to be prepared for technical difficulties and have a contingency plan; and they should have time in advance to discuss their work mode and agree on rules for commenting on and editing each other’s work.

• Hansen, Nils Kristian & Mitchell, James Robert (2013). An interdisciplinary school project using a Nintendo Wii controller for measuring car speed. Physics Education. ISSN 0031-9120. 48(2), p. 184–189. doi: 10.1088/0031-9120/48/2/184. Full text in Research Archive
• Brodahl, Cornelia; Hadjerrouit, Said & Hansen, Nils Kristian (2011). Collaborative Writing with Web 2.0 Technologies: Education Students’ Perceptions. Journal of Information Technology Education: Research (JITE: Research). ISSN 1547-9714. 10, p. IIP73–IIP103. doi: 10.28945/1384.

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• Hansen, Nils Kristian (2024). Programmering i statistikk og sannsynlighet.
• Hansen, Nils Kristian (2023). Å introdusere programmering i matematikk-videreutdanning 5-10.
• Hansen, Nils Kristian (2022). Tilrettelegging for høytpresterende elever. Fædrelandsvennen. ISSN 0805-3790.
• Hansen, Nils Kristian (2018). Programmering med Scratch. Show summary

  Foredraget ga en innføring i programmering ved hjelp av det blokkbaserte programmeringsspråket Scratch, som er godt egnet for barn. Hands-on deltakerøvelser var en viktig del av opplegget.

• Opheim, Linda Gurvin; Brodahl, Cornelia & Hansen, Nils Kristian (2017). Nettstudier i Canvas. Show summary

  Canvas har vært brukt i ulike anledninger for nettstudier i matematikk, bl.a. MOOC på Bibsys sin server, og EVU kursene på inst. for matematiske fag har vært blant pilotene som har brukt Canvas på UiA. Vi utdypet hvorfor rene nettbaserte emner setter høye krav til funksjonalitet i Canvas. Vi ønsket i utgangspunkt å bruke designet til IKT-senteret for UiA sin MOOC på Canvas, og la fram hvorfor vi har gått bort fra det. Vi presenterte også de ulike hjemmesidene for nettstudiene og organisering av modulene. Presentasjonen ble streamet. Omtale: https://beta.uia.no/?p=2220

• Hansen, Nils Kristian (2014). Succeed with Mathematical Games. Show summary

  The presentation deals with the use of video games in teaching mathematics. It sets out with an example where a juvenile street seller uses a strange method to calculate how much to charge for 10 coconuts, instead of using the simple multiplication method he learned in school. The point is that he didn't know how to employ his school math, and created his own to be able to cope with a real life situation. The objective is to motivate for the idea of creating an interactive, virtual world in a video game, presenting players with mathematical challenges they have to overcome to advance in the game. The presentation continues with a quick review of the history of video games. It then discusses the difficulty of incorporating symbol manipulation and stringent mathematical arguments into a game, and suggests that one should not aim for advanced mathematics, but "everyday maths" that may be incorporated seamlessly. Then a coarse classification of mathematical topics is given, followed by a brief review of the history of mathematics teaching leading up to the NRC report introducing the five skills of mathematical proficiency. Some ideas on how these skills can be exercised in a video game are then discussed. The presentation concludes by emphasizing that mathematical video games are not a replacement for, but a supplement to classroom education.

• Brodahl, Cornelia & Hansen, Nils Kristian (2014). Education students' use of collaborative writing tools in collectively reflective essay papers. Show summary

  A case study investigating education students’ perceptions of collaborative writing reflective essay papers, by means of a survey questionnaire and students’ written reflections on their experiences. Variables potentially being critical such as gender, age, digital competence and interest in digital tools are examined quantitatively. Further, based on qualitative data collected, the work explores what factors or practices students perceive to be important to make collaborative writing easy and effective, and motivate for future use of the tools in group work.

• Brodahl, Cornelia; Hansen, Nils Kristian & Hadjerrouit, Said (2011). Collaborative Writing with Web 2.0 Technologies: Education Students’ Perceptions.

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