Reasoning and proving in primary education

According to the new curriculum standard in Norway, reasoning and argumentation should be integrated part of all mathematics teaching in primary school. More knowledge on primary school students work on the topic is needed, and important for implementation of the new curriculum. The projects overall objective is to develop innovative knowledge on students? learning, teachers? practices and pre-service teachers? learning-to-teach within work on reasoning and proving, in order to design teaching resources for primary education that can support such work. We have four secondary objectives: A. We will study the state of the art by documenting current instructional practices and students? opportunities for learning reasoning and proving in primary school. B. We will develop theory-driven and empirically tested resources that effectively can support teaching and learning reasoning and proving in primary school. C. We will investigate how resources developed in B can contribute to transform practice in primary school and use the new knowledge to further develop the resources and make them more amenable for use. D. Building on knowledge developed in A and B, we will study approaches in teacher education that can support pre-service teachers? learning-to-teach reasoning and proving. The project is a collaboration between researchers from NTNU and Trondheim municipality. Teachers from two primary schools are involved in the project. We have developer online resources for teachers and for teacher educators: https://www.ntnu.no/web/ilu/aril-argumentasjon-rollespill-laererutdanning https://www.ntnu.no/ilu/laeringsressurser/matematisk-argumentasjon-grunnskolen Publications so far in the project: - Aune, T. E., Enge, O., Hindkjær, C. L., Iversen, S., Reitan, L. E. & Valenta, A. (2022). Hvorfor blir det slik? Tangenten – tidsskrift for matematikkundervisning 2022(3) - Arnesen, K. & Rø, K. (2022). The complexity of supporting reasoning in a mathematics classroom of shared authority. Mathematical thinking and learning. DOI: 10.1080/10986065.2022.2059628 - Arnesen, K. & Dahl, H. (2022). “Why have you written six times five?” Teachers’ use of why in Norwegian mathematics classrooms. Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education. - Arnesen, K. K. (2022) Generiske eksempler som argumentasjon. Tangenten - Tidsskrift for matematikkundervisning. vol. 33 (1). http://www.tangenten.no/wp-content/uploads/2022/01/tangenten-1-2022-krogh_arnesen.pdf - Arnesen, K. K. & Valenta, A. (2023). Lesson plays as an approach to learning to teach proving. International journal of mathematics education in science and technology. - Burheim, O. T., Dahl, H., Hansen, E. S., Langfeldt, M. B., Lægran, M., & Skarderud, A. (2023). Kom i gang med argumentasjon! Tangenten - Tidsskrift for matematikkundervisning, 33(4), 24–28. - Enge, O. & Valenta, A. (2022). Matematisk resonnering, argumentasjon og bevis på barnetrinnet. I T. S. Gustavsen, R. A. Rinvold, K. R. C. Hinna & T. Sundtjønn (Red.), QED 1-7. Matematikk for grunnskolelærerutdanning, Bind 1. (2.utgave, s. 507-544). Cappelen Damm Akademisk - Enge, O. & Valenta, A. (2022). Helhetlig matematikkundervisning. I T. S. Gustavsen, R. A. Rinvold, K. R. C. Hinna & T. Sundtjønn (Red.), QED 1-7. Matematikk for grunnskolelærerutdanning, Bind 1. (2.utgave, s. 619-657). Cappelen Damm Akademisk - Iversen, S. (2022). Seventh-grade students’ perceptions of qualities in a mathematical argument. Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education. - Rø, K. & Arnesen, K. K. (2020). The opaque nature of generic examples: The structure of student teachers' arguments in multiplicative reasoning. The Journal of Mathematical Behavior 58, doi: https://doi.org/10.1016/j.jmathb.2019.100755 - Skott, E. L. B. & Valenta, A. (i trykk). Kommunikasjonsmønster under arbeid med matematiske resonnering. Nordisk tidsskrift for utdanning og praksis. - Valenta, A. & Enge, O. (2020). Bevisrelaterte kompetanser i læreplan LK20 for matematikk i grunnskolen. Acta Didactica Norden (ADNO). vol. 14 (3). https://journals.uio.no/adnorden/article/view/8195/7274 - Valenta, A. & Enge, O. (2022). Teaching practices promoting meta-level learning in work on exploration-requiring proving tasks. Journal of Mathematical Behavior 67 https://doi.org/10.1016/j.jmathb.2022.100997 - Ødegaard, R. P. & Langfeldt, M. B. (2022). Developing an identity as a mathematics teacher through group work. Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education. Book: Burheim, Oda Tingstad; Dahl, Heidi; Enge, Ole; Rø, Kirsti. (2023) Alltid, aldri eller noen ganger? Om matematisk argumentasjon i grunnskolen. Caspar Forlag Caspar Forlag

This project seeks to strengthen the knowledge base for teachers’ professional practice and teacher education through a solid collaboration between a university-based research group, the field of practice and international researchers. The project’s objective is to investigate and support students’ learning and teachers’ practices in primary school, and pre-service teachers’ learning in teacher education, within reasoning and proving in mathematics. A new mathematics curriculum is being devised in Norway and is scheduled to be implemented by 2020. The curriculum will be organised around some core aspects in mathematics, one of which is reasoning and justification. The definition of this core aspect in the curriculum corresponds with our use of the notion of reasoning and proving (RP) to denote activities involved in the process of identifying patterns, making conjectures about relations between mathematical objects involved, and providing arguments for validity of the conjectures. The new curriculum will employ a stronger emphasis on RP than the previous one (from 2006), as RP is set to get a prominent place in the mathematics curriculum. Our focus on the proposed project concerns primary-school mathematics, as the need for more knowledge about students’ learning and teachers’ practices within RP work in primary-school mathematics is emphasised in several research reviews. This project addresses thematic priority Area A in the call––students’ learning processes––in addition to Area B––teachers’ practices––as students’ opportunities to learn are greatly determined by the teaching practices employed. Moreover, this project addresses opportunities in teacher education for developing pre-service teachers’ (PSTs) practices within RP in primary-school mathematics.