Hans Erik Borgersen

• Wathne, Unni; Reinhardtsen, Jorunn; Borgersen, Hans Erik & Cestari, Maria Luiza (2019). Designed examples as mediating tools: Introductory algebra in two Norwegian grade 8 classrooms. In Kilhamn, Cecilia & Säljö, Roger (Ed.), Encountering algebra. A comparative study of classrooms in Finland, Norway, Sweden, and the USA. Springer Nature. ISSN 9783030175764. p. 71–109. doi: 10.1007/978-3-030-17577-1_5. Full text in Research Archive
• Bjurland, Raymond; Cestari, Maria Luiza & Borgersen, Hans Erik (2012). Professional mathematics teacher identity: analysis of reflective narratives from discourses and activities. Journal of Mathematics Teacher Education. ISSN 1386-4416. 15, p. 405–424. doi: 10.1007/s10857-012-9216-1. Full text in Research Archive
• Bjuland, Raymond; Cestari, Maria Luiza & Borgersen, Hans Erik (2010). A teacher's use of gesture and discourse as communicative strategies in concluding a mathematical task. In Durand-Guerrier, Viviane; Soury-Lavergne, Sophie & Arzarello, Ferdinando (Ed.), Proceedings of CERME 6. Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education. January 28th - February 1st 2009, Lyon (France). Institut National de Recherche Pedagogique. ISSN 9782734211907. p. 884–893. Full text in Research Archive Show summary

  An experienced teacher has been observed in dialogue with her sixth-grade pupils when summing up their solutions to a mathematical task. The pupils have worked in small groups on this task, which is related to a transposition of data (age and height) from a figure to a Cartesian diagram and to a written text. The teacher's discourse has been analysed, using the dialogical approach to communication and cognition. Analyses of gestures are based on McNeill's classification expanded by Edwards, using the concept of embodied cognition and complemented by the work of Goodwin, taking into account the contribution of the environment to the organisation of the gesture. Some communicative strategies used by the teacher have been identified, for example, questioning (who, how, why, asking for other suggestions). Pointing gestures are used, but they are not prominent. Our findings suggest that gestures are more used and connected to the teacher's explanations than to other procedures.

• Borgersen, Hans Erik; Cestari, Maria Luiza & Bjuland, Raymond (2010). An Overview of the Development of Research on Collaborative Problem Solving in Mathematics at the University of Agder. In Sriraman, Bharath; Bergsten, Christer; Goodchild, Simon; Pálsdóttir, Gudbjörg; Søndergaard, Bettina Dahl & Haapasalo, Lenni (Ed.), The First Sourcebook on Nordic Research in Mathematics Education Norway, Sweden, Iceland, Denmark and contributions from Finland. Information Age Publishing. ISSN 9781617350993. p. 139–153. Full text in Research Archive Show summary

  Published 2010 The First Sourcebook on Nordic Research in Mathematics Education: Norway, Sweden, Iceland, Denmark and contributions from Finland provides the first comprehensive and unified treatment of historical and contemporary research trends in mathematics education in the Nordic world. The book is organized in sections co-ordinated by active researchers in mathematics education in Norway, Sweden, Iceland, Denmark, and Finland. The purpose of this sourcebook is to synthesize and survey the established body of research in these countries with findings that have influenced ongoing research agendas, informed practice, framed curricula and policy. The sections for each country also include historical articles in addition to exemplary examples of recently conducted research oriented towards the future. The book will serve as a standard reference for mathematics education researchers, policy makers, practitioners and students both in and outside the Nordic countries.

• Bjuland, Raymond; Cestari, Maria Luiza & Borgersen, Hans Erik (2009). The constitution of mathematics teacher identity, Nordic research in mathematics education. Proceedings from Norma08 in Copenhagen, April 21-April 25, 2008. Brill | Sense. ISSN 9789087907822. p. 109–116. Full text in Research Archive
• Bjuland, Raymond; Cestari, Maria Luiza & Borgersen, Hans Erik (2009). The constitution of mathematics teacher identity. In Winsløw, Carl (Eds.), Nordic Research in Mathematics Education. Brill | Sense. ISSN 9789087907815. p. 109–116. Full text in Research Archive
• Bjuland, Raymond; Cestari, Maria Luiza & Borgersen, Hans Erik (2008). The Interplay Between Gesture and Discourse as Mediating Devices in Collaborative Mathematical Reasoning : A Multimodal Approach. Mathematical Thinking and Learning. ISSN 1098-6065. 10(3), p. 271–292. Full text in Research Archive Show summary

  This article aims to identify the mathematical reasoning strategies expressed through gestures and speech used by two groups of sixth-grade pupils when solving a task related to the transition between two semiotic representations: figure and Cartesian diagram. The article also identifies the difficulties the pupils meet in the solution process. The analyses of the group dialogues focus particularly on the gesture dimension of deixis. The pupils in both groups have used the following deictic gestures: pointing, held-point, linear point-slide, and circular point-slide in their solution process, while repeated pointing has been identified only in one of the groups. These pointing gestures are related to the reasoning strategies: comparison of persons in the figure, coordination of two dimensions in the diagram, recapitulation and going to an extreme location. The pupils use the modalities of speech, gesture, and writing in order to solve the mathematical task. Their pointing gestures related to their use of reasoning strategies play a multifaceted role in developing collaborative mathematical reasoning in the two small groups.

• Bjuland, Raymond; Cestari, Maria Luiza & Borgersen, Hans Erik (2008). A teacher's use of gesture and discourse as communicative strategies in the presentation of mathematical task, Proceedings of the 32th Conference of the International Group for the Psychology of Mathematics Education (PME 32). p. 185–192. Full text in Research Archive
• Bjuland, Raymond; Cestari, Maria Luiza & Borgersen, Hans Erik (2007). Pupils' mathematical reasoning expressed through gesture and discourse: A case study from a sixth-grade lesson, European Research in Mathematics Education : Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education. European Society for Research in Mathematics Education. p. 1129–1139. Full text in Research Archive Show summary

  This paper reports research that focuses on pupils¿ reasoning expressed through gesture and discourse while working on a mathematical task in a school lesson. Our aim is to illustrate how two groups of pupils make the transition between two systems of representation, figure and Cartesian diagram. Through detailed analyses of two group dialogues, we reveal that the gesture strategies pointing and sliding are prominent in both groups. These are also related to the discourse strategies comparison, coordination and going to an extreme location. Our study supports the claim that gesture and speech develop simultaneously in the pupils' mathematical reasoning. The gestures stimulate joint attention and reinforce the verbal discussion among the pupils. They also function as connectors between the two systems of semiotic representation and as memory markers.

• Borgersen, Hans Erik & Bjuland, Raymond (2007). Verksted for problemløsning i matematikk: Mening, bevis og generalisering, Læringsfellesskap i matematikk. Caspar Forlag. Full text in Research Archive
• Bjuland, Raymond; Cestari, Maria Luiza & Borgersen, Hans Erik (2007). En lærers bruk av problemløsningsverksted: Fra LCM til klasserommet, Læringsfellesskap i matematikk. Caspar Forlag. Full text in Research Archive
• Borgersen, Hans Erik (2004). Open ended problem solving in geometry revisited. NOMAD – Nordisk matematikkdidaktikk. ISSN 1104-2176. 9(3), p. 35–66. Full text in Research Archive Show summary

  Denne artikkelen er en videreføring av Borgersens (1994) undersøkelse av et problemløsningsprosjekt, basert på samarbeid i smågrupper og organisert som del av et geometrikurs på universitet/høgskolenivå. Artikkelen fokuserer på effekten av en gradvis endring av prosjektet. Den undersøker prosjektene fra 1994 til 1996 (Borgersen 1995, 1997, 1999), idet geometrikurset endret seg fra å være et middels stort kurs med omlag tretti studenter fra samme studieprogram til å bli et stort kurs med nær ett hundre studenter fra tre ulike studieprogram. This article is a successor to Borgersen?s (1994) study of a project on cooperative problem solving in small groups, organized as part of a geometry course at the college level. It focuses on the effects of a gradual change of the project. This report studies the transition of the project from 1994 to 1996 (Borgersen 1995, 1997, 1999) as the course changed from being a medium size course for about thirty students from the same study program to become a large course for nearly onehundred students from three different study programs.

• Skau, Ivar & Borgersen, Hans Erik (1998). Tettere inn på Pascals setning. Normat. ISSN 0801-3500. p. 26–32. Full text in Research Archive Show summary

  Blaise Pascal (1623-1662) publiserte i 1640, bare 16 år gammel, en kort avhandling omkjeglesnitt [9] der han gir Desargues æren for å ha gjort ham kjent med de projektive metoder. Dette arbeidet inneholder setningen som han selv kalte Hexagramma Mysticum, av ettertiden kjent som Pascals setning: Hvis en sekskant er innskrevet i et kjeglesnitt, så skjærer motstående sider hverandre i tre punkter som ligger på linje.

• Borgersen, Hans Erik (1994). Open ended problem solving in geometry. ?. 2(2), p. 6–35. Full text in Research Archive

View all works in NVA

• Bjuland, Raymond; Cestari, Maria Luiza & Borgersen, Hans Erik (2009). A teachers? use of gesture and discourse as communicative strategies in concluding a mathematical task. Full text in Research Archive
• Cestari, Maria Luiza; Bjuland, Raymond & Borgersen, Hans Erik (2007). Identity in education. The constitution of mathematics teacher identity from a socio cultural perspective. Full text in Research Archive
• Bjuland, Raymond; Borgersen, Hans Erik; Damsgaard, Kjetil & Mjølund, Tor Arne (2007). Styrt utforsking og samarbeidslæring i videregående skole. Full text in Research Archive
• Bjuland, Raymond; Cestari, Maria Luiza & Borgersen, Hans Erik (2007). Pupil's mathematical reasoning expressed through gesture and discourse: A case study from a sixth-grade lesson. Full text in Research Archive
• Fuglestad, Anne Berit; Borgersen, Hans Erik; Daland, Espen; Goodchild, Simon & Jaworski, Barbara (2007). KUL matematikk - glimt fra en konferanse. Tangenten - Tidsskrift for matematikkundervisning. ISSN 0802-8192. 16(3), p. 28–33. Full text in Research Archive Show summary

  Artikkelen presenterer et utvalg av foredrag og verksteder på en konferanse om læring og undervisning i matematikk. Konferansen var knyttet til forskningsprosjektene "Læringsfellesskap i matematikk "og "IKT og læring i matematikk" ved Høgskolen i Agder, og ble holdt i september 2006. Artikkelen viser spesielt hvordan en spørrene, undersøkende og utforskende tilnærming til undervisning har betydning for matematikkundervisningen.

• Borgersen, Hans Erik (2006). Problemløsning i matematikk: Mening, Bevis, Generalisering. Full text in Research Archive
• Bjuland, Raymond; Cestari, Maria Luiza & Borgersen, Hans Erik (2006). En lærers bruk av problemløsningsverksted: Fra LCM til klasserommet. Full text in Research Archive
• Borgersen, Hans Erik (2000). Large classes of college students cooperating in small groups: Open ended problem solving in geometry. Universitetet i Agder. ISSN 9788271174286. Full text in Research Archive
• Borgersen, Hans Erik (1999). Open ended problem solving in geometry 1996. A large class of students cooperating in small groups. Universitetet i Agder. ISSN 9788271174026. Full text in Research Archive Show summary

  This is a report on cooperative problem solving in small groups; part of a geometry course at Agder College, in 1996. The report is a successor to [1],[2],[4] and [5] on courses given from 1986 to 1995. -The main conclusions of these earlier repo rts are supported. -The project had 80 students in 18 groups and was managed by one teacher. -As reported in [5], the positive effect of the students' presenta- tions of their s olutions in class, documented in [2] and [4], has been reduced. There has been no discussion of the group work in plenary session. -There has been a considerable progress in proof writing, s ome pro- gress on generalization, and a decline in process writing, compared to what was reported in [5]. -The students experienced the importance of all being actively in- volved and willing to help each other. The students experienced dis- cussions and reflections that contributed to a deeper understanding through their cooperation in small groups. -There were strong emotions connected to the process of solving open ended problems in geometry. -The groups have controlled their problem solving process, also the affective side of it, very well. -The groups' evaluations were remarkably similar to those reported in [5]. -A majority of groups had students from different study programs, and a clear majority of groups were of mixed gender. -Less than half the g roups typed their reports, and about half of these groups used a computer program (Cabri) to draw their figures. -It was suggested that more ordinary group hours or lecture hours were allocated to the project.

• Borgersen, Hans Erik (1997). Open ended problem solving in geometry 1995. One hundred students cooperating in small groups. Universitetet i Agder. ISSN 9788271173425. Full text in Research Archive
• Borgersen, Hans Erik (1995). Open ended problem solving in geometry 1994. Universitetet i Agder. ISSN 9788271173005. Full text in Research Archive

View all works in NVA