ProPrimEd: Reasoning and proving in primary education 2020–2024

Research – Department of Teacher Education

ProPrimEd: Reasoning and proving in primary education 2020–2024

The project is a collaboration between NTNU and Trondheim municipality, and it is partly funded by Norwegian Research Council, FINNUT-program. Teachers from two primary schools work together with the researchers in development of resources for use in primary education.

Reasoning and proving are central aspects of mathematics as a discipline, and many researchers have argued that these skills should form a central part of school mathematics at all grades and in all subject areas. For a long time, mathematical proof has been seen by many educators as rigorous and formal and thus in conflict with the idea of school mathematics as useful, creative and enjoyable. A growing body of knowledge in mathematics education shows that mathematical learning, knowing and proving cannot be separated and that a tight connection between exploring and proving has a positive impact on students’ learning in mathematics.

The project’s overall objective is to develop innovative knowledge on primary school 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 that work.

The project has four parts: Part A: Study of the state of the art by documenting primary mathematics teachers’ current instructional practices and students’ opportunities for learning reasoning and proving in primary school. Part B: Developing of resources that can support mathematics teachers’ practices and students’ opportunities for learning reasoning and proving in primary school. Part C: Investigation on how resources developed in B can contribute to discursive changes in primary-school classrooms. Based on that, further development of the. Part D: Building on knowledge developed in A, B and C, development of approaches in teacher education that can support pre-service teachers’ learning-to-teach reasoning and proving in primary school. Model
Overview of the project.

Teaching resources for teacher education developed within the project can be found here (only in Norwegian).

Teaching resources for primary school are still under development, will be completed during autumn 2023.
 

More about the project (PDF)

Publications so far in the project (April 2024)

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.

Arnesen, K., & Dahl, H. (i trykk). “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, Kristin Krogh. (2022) Generiske eksempler som argumentasjon. Tangenten - Tidsskrift for matematikkundervisning. vol. 33 (1).

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.

Langfeldt, M. B., Valenta, A., & Hansen, T. H.  (2023). Pre-service teachers’ use of the word explain when working on mathematical reasoning and proving. In P. Drijvers, C. Csapodi, H. Palmér, K. Gosztonyi, & E. Kónya (Eds.), Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13) (pp. 168–175). Alfréd Rényi Institute of Mathematics and ERME.

Klock, S. I. (2024). Arguments and group discussions: middle-school students’ initial work with mathematical arguments. International Journal of Mathematical Education in Science and Technology.

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.

Skott, E. L. B. & Valenta, A. (2022). Kommunikasjonsmønster under arbeid med matematiske resonnering. Nordisk tidsskrift for utdanning og praksis. 16(2), 61-82. 

Valenta, A. & Enge, O. (2020). Bevisrelaterte kompetanser i læreplan LK20 for matematikk i grunnskolen. Acta Didactica Norden (ADNO). vol. 14 (3).

Valenta, A. & Enge, O. (2022). Teaching practices promoting meta-level learning in work on exploration-requiring proving tasks. Journal of Mathematical Behavior 67.

Valenta, A., Rø, K., & Klock, S. I. (2024). A framework for reasoning in school mathematics: Analyzing the development of mathematical claims. Educational Studies in Mathematics.

Ødegaard, R. P. (2023). Moves for eliciting and promoting reasoning and proving. In P. Drijvers, C. Csapodi, H. Palmér, K. Gosztonyi, & E. Kónya (Eds.), Proceedings of the Thirteenth Congress of the European Society for Research in Mathematics Education (CERME13) (pp. 3451–3458). Alfréd Rényi Institute of Mathematics and ERME.

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.

Conference presentations

Arnesen, K.K. (2021). Hva gjør generiske eksempler vanskelige? Lærerstudenters skriftlige argumenter for en påstand i multiplikasjon. Presentasjon på Konferansen for matematikklærerutdannere KLæM 21, 20-22. september 2021

Arnesen, K., & Dahl, H. (2022) “Why have you written six times five?” Teachers’ use of why in Norwegian mathematics classrooms. Presentasjon på Twelfth Congress of the European Society for Research in Mathematics Education, 2-5. februar 2022

Burheim, Oda Tingstad; Dahl, Heidi; Langfeldt, Marit Buset. (2023) Arbeid med matematisk argumentasjon i grunnskolen. Matematikksenteret Novemberkonferansen , Trondheim 2023-11-22 - 2023-11-23

Enge, O. (2022). Proof related competences in the new Norwegian curriculum grades 1-10. Presentasjon på Den 16. Nordiske Læreruddannelseskonference – Innovation i Undervisning og Læring, Færøyene, 3-5. mai 2022

Enge, O., & Valenta, A. (2021). Bevisrelaterte kompetanser i læreplan LK20 for matematikk i grunnskolen. Presentasjon på Konferansen for matematikklærerutdannere KLæM 21, 20-22. september 2022

Iversen, S. (2022). Seventh-grade students’ perceptions of qualities in a mathematical argument. Presentasjon på Twelfth Congress of the European Society for Research in Mathematics Education, 2-5. februar 2022

Iversen, S., & Hindkjær, C. L. (2021). Argumentasjon og bevis på barnetrinnet. Verksted på Novemberkonferansen 2021, 30. november-1. desember 2021

Langfeldt, Marit Buset. (2023) Pre-service teachers’ use of the word explain when working on mathematical reasoning and proving. The 13th Congress of the European Society for Research in Mathematics Education (CERME13) , Budapest 2023-07-10 - 2023-07-14

Langfeldt, M. B., & Valenta, A. (2022). Decomposing the practice planning a mathematical discussion towards a given goal in Norwegian teacher education. Presentasjon på Den 16. Nordiske Læreruddannelseskonference – Innovation i Undervisning og Læring, Færøyene, 3-5. mai 2022

Klock, Sigrid Iversen. (2023) En intervensjonsbasert studie av argumentasjon og bevis på barnetrinnet. KLæM23 - Konferanse for lærerutdannere i matematikk 2023-09-18 - 2023-09-20

Ødegaard, Reidun Persdatter. (2023) Moves for eliciting and promoting students' reasoning and proving. Alfréd Rényi Institute of Mathematics The 13th Congress of the European Society for Research in Mathematics Education (CERME13) , Budapest 2023-07-10 - 2023-07-14

Ødegaard, Reidun Persdatter. (2023) Muligheter for å lære å fremme resonnering og bevis i matematiske samtaler gjennom rollespill i lærerutdanninga. NTNU - Institutt for lærerutdanning Konferanse for lærerutdannere i matematikk , Røros 2023-09-18 - 2023-09-20

Ødegaard, R. P., & Langfeldt, M. B. (2022). Developing an identity as a mathematics teacher through group work. Presentasjon på Twelfth Congress of the European Society for Research in Mathematics Education, 2-5. februar 2022.

Ødegaard, R. P. & Langfeldt, M. B. (2022). Brobygging mellom teori og praksis, resonnering og bevis. Presentasjon på KLæM 2022 i Kristiansand, 19-21. September 2022.

Arnesen, K. & Dahl, H. (2022). Hvorfor har du skrevet seks ganger fem? En kvalitativ studie av læreres bruk av hvorfor i matematikk. Poster på Lærekraft 100. Arrangement i forbindelse med 100 år med lærerutdanning i Trondheim, 3. oktober 2022.

Valenta, A. & Enge, O. (2022). Undervisningspraksiser som fremmer elevers læring innen arbeid med bevis i matematikk. Poster på Lærekraft 100. Arrangement i forbindelse med 100 år med lærerutdanning i Trondheim, 3. oktober 2022.