Publikasjoner om skolematematikk

2022

Lekaus, S. & Lossius, M. E. H. (2022). Språksensitiv matematikkundervisning [Language sensitive mathematics teaching]. Tangenten - Tidsskrift for matematikkundervisning, 33(3), 10–16. https://tangenten.no/tidligere-nummer/2022-2-2/

Steffensen, L., Hauge, K. H. & Nakling, J. G. (2022). Students’ discussions of cultural, social, economic, and political aspects of the COVID-19 pandemic. I J. Hodgen, et al. (Red.), Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12). Feb 2022, Bozen-Bolzano, Italy. University of Bozen-Bolzano and ERME. https://hal.archives-ouvertes.fr/hal-03747833

Abstrakt

Worldwide, students have experienced the impacts of the COVID-19 pandemic. This paper investigates students' reflective discussion of the consequences of measures taken during the pandemic in Norway. Socio-critical mathematics perspectives are used as a theoretical framework when analysing 13-14-year-old students' discussions of the pandemic. The students read, discuss, and present findings from media articles provided by their teacher. We found that the students identify and use mathematics-based argumentation when reflecting on cultural, social, economic, and political aspects from their own real world. They ask questions, investigate, listen to peers' argumentation, show awareness of, and discuss challenging issues such as mental health, increased violence during home-schooling, unemployment, loss of income, and rising inequality in society. We suggest that mathematics education can promote students' reflective discussion of wicked problems.

2021

Fosse, T. & Meaney, T. (2021). Milieus of learning in a Norwegian textbook. In Pre-ceedings of The Ninth Nordic Conference on Mathematics Education, NORMA 20. In G. A. Nortvedt, et al., (Eds.), Bringing Nordic mathematics education into the future: Preceedings of The Ninth Nordic Conference on Mathematics Education, NORMA 20, Oslo, 2021 (pp. 81-88). NCM & SMDF.

Abstrakt

This paper examines the methodological issues involved in investigating mathematical and relational competencies relevant to teaching mathematics. In the study, 14 mathematics teachers were asked to reflect on the teaching and learning of mathematics based on a mathematics lesson shown in a video sequence. These reflections were documented in three different ways: some teachers were interviewed individually, some were interviewed in focus groups and some wrote individual reflections on paper. The empirical materials from these three different types of documentation were analysed using the same framework. The results of the study indicate that mathematical and relational competencies came to light mainly in the individual and the focus group interviews. However, this may be due to the analytical framework used, and another framework may be better suited to analysing individual writings.

Hauge, I. O., Lie, J., Abtahi, Y., & Nilsen, A. G. (2021). Programming in the classroom as a tool for developing critical democratic competence in mathematics. In G. A. Nortvedt, et al., (Eds.), Bringing Nordic mathematics education into the future: Preceedings of The Ninth Nordic Conference on Mathematics Education, NORMA 20, Oslo, 2021 (pp. 113-120). NCM & SMDF.

Abstrakt

Herheim, R., & Johnsen-Høines, M. (2021). Students’ productive struggle when programming in mathematics. In G. A. Nortvedt et al. (Eds.), Bringing Nordic mathematics education into the future. Papers from NORMA 20. Proceedings of the Ninth Nordic Conference on Mathematics Education (pp. 121-128). Oslo/Göteborg: SMDF.

Abstrakt

The paper concerns two seventh grade students who share a computer and program a pentagon. The task proves to be challenging and the students face several kinds of struggles. However, the students are persistent, apply communication qualities, and make continuous refinements in ways that create an interesting interweaving of mathematics and programming

Lekaus, S., & Lossius, M. H. (2021). Facilitating argumentation in primary school. In G. A. Nortvedt, N. F. Buchholtz, J. Fauskanger, F. Hreinsdóttir, M. Hähkiöniemi, B. E. Jessen, J. Kurvits, Y. Liljekvist, M. Misfeldt, M. Naalsund, H. K. Nilsen, G. Pálsdóttir, P. Portaankorva-Koivisto, J. Radišić, & A. Wernberg (Eds.), Bringing Nordic mathematics education into the future: Preceedings of Norma 20 The ninth Nordic Conference on Mathematics Education Oslo, 2021 (pp. 177–184). SMDF Svensk Förening för MatematikDidaktisk Forskning Swedish Society for Research in Mathematics Education.

Abstrakt

In this article, we show some results from an ongoing project in which written dialogues are used as a tool to facilitate exploratory talk and argumentation in mathematics in primary school. Our data material was collected in a 7th grade classroom in Norway. The students were asked to individually write an imaginary dialogue between two fictive students applying ground rules for exploratory talk. Afterwards, the students had a discussion in groups of 3-4 participants about the same problem. Our findings indicate that the use of imaginary dialogues might be a valuable tool that makes students explore the characteristics of exploratory talk and facilitate argumentation in mathematics.

Keywords: exploratory talk, argumentation, imaginary dialogues.

Sjöblom, M., & Meaney, T. (2021). “I am part of the group, the others listen to me”: Theorising productive listening in mathematical group work. Educational Studies in Mathematics, 107(3), 565-581. 10.1007/s10649-021-10051-2

Abstrakt

Although group work is considered beneficial for problem solving, the listening that is needed for jointly solving mathematical problems is under-researched. In this article, the usefulness of two communication frameworks for understanding students’ listening is examined, using data from an educational design research study in an upper secondary mathematics classroom in Sweden. From the analysis, it was apparent that these frameworks did not provide sufficient information about the complexity of listening in this context. Consequently, a new framework, “productive listening,” is described which focuses on observable features connected to students’ ability to show willingness to listen and to request listening from others. This framework included the purpose for listening, connected to problem-solving stages, and social aspects to do with respecting the speaker’s contribution as being valuable and feeling that one’s own contribution would be listened to. These two aspects are linked to socio-mathematical norms about expecting to listen to others’ mathematical thinking and to ask clarifying questions about this thinking. By using this framework on the data from the earlier study, it was possible to better understand the complexity of listening in group work about mathematical problem solving.

Steffensen, L., Hauge, K. H., & Herheim, R. (2021). Ethical thinking and programming. In D. Kollosche (Ed.), Exploring new ways to connect: Proceedings of the Eleventh International Mathematics Education and Society
Conference (Vol. 3, pp. 957–966). Tredition. https://doi.org/10.5281/zenodo.5416599

Abstrakt

There is an increasing prevalence of programming in mathematics education. In this paper, we focus on ethical aspects of programming by first presenting a literature review. Three interrelated topics are identified in the review: reasons to include ethics in programming, code literacy, and facilitating ethical thinking. These three topics are then used to reflect on ethical thinking and programming in three tasks developed by a lower secondary school teacher. We argue that the context of programming tasks such as climate change, sustainability, and decision-making of self-driving cars, can facilitate students’ ethical thinking alongside their learning of how to program.

2020

Anderson, E. (2020). Argumentasjon i regnefortellinger. Tangenten- tidskrift for matematikkundervisgning. 31(1), 36-40.

Fosse, T. & Meaney, T. (2020). Using problem posing to bring real-life into the mathematics classroom: Can it be too real? For the Learning of Mathematics, 40(3), 40-44.

Abstrakt

Problem posing has been mooted as a way of making mathematics education meaningful and motivating for students. In Norway, there is a tradition of children posing and solving their own number problems, with an expectation that children would draw on contexts that are relevant for them. Yet those contexts can sometimes be challenging for teachers because they raise socially-taboo or socially-unacceptable topics, as problem posing allows students to include a range of affective responses to their everyday contexts. In this article, several examples from 7 to 8 year-old children’s problem posing are used to discuss the importance of educators finding respectful ways to respond that open up rather than close down conversations. Without educators reflecting on their professional power and expectations from the hidden curriculum, children’s possibilities for learning from engaging in problem posing may be limited as children are channelled into using less-challenging, textbook-like examples.

Herheim, R. & Johnsen-Høines, M. (2020). A culture perspective on students’ programming in mathematics. Journal of Mathematics and Culture, 14(2), 91-110.

Abstrakt

Digital technology has become a key part of the development of society and influences people’s ways of being, thinking, and communicating. Young people’s digital cultures are continuously developing, and this article investigates how two students’ productive struggle when programming in mathematics can be analyzed and understood from a cultural perspective. The data consists of two seventh-grade students who share a computer and program a pentagon. The task proves to be challenging and the students face several kinds of struggles. However, the students are persistent, apply communication qualities, and make continuous refinements in ways that create an interesting interweaving of mathematics and programming. The students’ communication qualities are used to describe characteristics of a productive struggle in the mathematics classroom and how such a culture can be supported.

Meaney, T. & Shockey, T. (2020). The influence of digital technologies on the relationship between mathematics and culture. Journal of Mathematics and Culture, 14(2), 132-151.

Abstrakt

Digital technologies are now an accepted part of many people’s everyday life, but there is little research which considers how they affect culture(s), especially non-Western culture(s), and mathematics when integrated into mathematics education. Rather digital technologies tend to
be considered benign additions to a teacher’s repertoire of teaching resources. In this overview of the articles in this special issue, the supposedly benign benefits of technology are problematised by considering how digital technologies replace, amplify or transform aspects of mathematics and/or culture, which may then reduce or dampened the visibility of other aspects. The findings show that in this small data set research focuses on digital technologies either replacing physical cultural artefacts with digital ones or transforming cultural understandings in new ways. Similarly, this study shows that research focuses on how digital technologies either replace existing ways of presenting mathematics or transform the mathematics being presented. The implications for mathematics education research is that what is valued in particular is the transformative aspect of digital technologies.

2019

Fosse, T. (2019). Regnefortellinger. Tangenten – tidsskrift for matematikkundervisning, 30(3), 14–18. Available from http://www.caspar.no/tangenten/2019/.

Abstrakt

Engasjerte matematikkelever fra skolestart er vel noe alle matematikklærere ønsker seg. Sammen med fire masterstudenter har jeg sett nærmere på regnefortellinger og argumentasjon på 2. og 3. trinn. Dette er del av et større forskningsprosjekt som blant annet har fokus på argumentasjon i matematikk. Denne teksten ser på muligheter som kan ligge i bruk av regnefortellinger i matematikkundervisningen og vil her trekke fram to eksempler fra elever på 2. trinn.

Herheim, R. (2019). Programmering og algoritmisk tenking. Tangenten - Tidsskrift for matematikkundervisning, 30(4), s. 1-1.

Lekaus, S. (2019). On teachers’ experiences with argumentation and proving activities in lower secondary mathematics classrooms. In Proceedings of the 11th Congress of Research in Mathematics Education. Utrecht: Freudenthal Institute, of Utrecht University.

Abstrakt

This article presents an analysis of reports about developmental work written by 23 lower-secondary school teachers from Norway who planned, implemented and reflected upon a lesson involving elements of exploration, argumentation, and proving. An analysis of the tasks that the teachers designed for their students and the scaffolding that was provided during the classroom implementation, revealed that there was little variation in the choice of task and that opportunities for investigation were reduced by providing subtasks and hints. The teachers also experienced that time constraints and large classes provided challenges when leaving traditional teaching practice.

Rangnes, T. E. & Herheim, R. (2019). Lærers tilrettelegging for argument og agens. I K. M. R. Breivega & T. E. Rangnes (Red.), Demokratisk danning i skolen: Tverrfaglige empiriske studier (s. 168–186). Universitetsforlaget. https://doi.org/10.18261/9788215031637-2019-09

Abstrakt

Dette kapittelet handler om tilrettelegging for elevers argumenter og agens som del av demokratisk opplæring i matematikkundervisning. Agens handler om å påvirke, og delt agens studeres ut fra elevers og lærers initiativer til samtale og hvordan det får virkning for fortsettelsen. Søkelyset rettes mot lærerens grep for at elever skal kunne og ville ta agens, mot å identifisere åpninger som skapes for å ta agens, og hvordan lærer møter elevens evne til å ta agens. Vi undersøker hvordan argumenter utvikles ut fra lærers og elevers initiativ gjennom Toulmins argumentstruktur. Empirien er hentet fra et prosjekt der læreren la til rette for elevers arbeid med problemstillinger knyttet til trafikksikkerhet på elevenes skolevei. Vi ser på lærerens ytringer og grep i en plenumsdiskusjon der elevpresentasjoner blir diskutert. Det blir identifisert hvordan demokratisk opplæring i matematikk kan knyttes til lokalt engasjement, deltakelse i å utvikle argumenter og ved å erfare matematikk som del av det levde liv.

Ulland, G., Røskeland, M. & Herheim, R. (2018). Språk teller: Om hvordan elever løser, tenker rundt og skriver om et regnestykke. Nordic Journal of Literacy Research, 4(1), 121–141. https://doi.org/10.23865/njlr.v4.1256

Abstrakt

I denne artikkelen undersøker vi potensielle sammenhenger mellom skriving og forståelse i matematikkfaget. Materialet består av 28 elevtekster der elever fra 7. og 10. trinn løser en regneoppgave og skriver om hvordan de tenker og går frem for å løse den. Ved å analysere elevtekster har vi søkt innsikt i hva elever vektlegger når de individuelt løser en oppgave skriftlig. Artikkelen har utspring i erfaringer fra satsingen på Ungdomstrinn i utvikling, særlig med kunnskapsområdet skriving som grunnleggende ferdighet. Der viste det seg at et fåtall av matematikklærerne ser på seg selv som skrivelærere, noe som også støttes i forskningslitteraturen. Analysene av elevtekstene viser hvordan elever posisjonerer seg som skrivere i matematikk gjennom språk, forklaringsmåte og utregning, og hvordan de anvender ulike representasjoner. Avslutningsvis diskuteres forholdet mellom å forklare og å tenke i elevtekstene. Vi finner at en kombinasjon av utregning og forklarende tekst gir mer informasjon om elevens matematikkforståelse og holdning til faget enn utregningen med tall alene. Skrivingen kan dessuten utvikle fagspråk og bidra til læring i matematikk. Vi finner også at selve oppgavedesignet gir føringer for hvordan elevene løser oppgaven. I tillegg kan elevenes skriving gi læreren et bedre utgangspunkt for å veilede elevene i matematikk.