Resumé
Faglig sammenhæng og progression spiller en central rolle for elevers læring af matematik. Sammenhæng og progression er imidlertid vanskelige at beskrive på måder, der kan støtte en realisering af dem i matematikundervisningen. Børne- og Undervisningsministeriet har bedt Nationalt Center for Udvikling af Matematikundervisning om at udvikle sådanne beskrivelser som grundlag for en fælles indsats for tal og algebra i grundskolen og på ungdomsuddannelserne. Baggrunden er de udfordringer med tal og algebra, som mange elever oplever. I artiklen diskuterer vi, hvordan læringsspor, der er et relativt nyt forskningsfelt, kan bidrage til det, og vi udfolder og eksemplificerer vores tilgang, kaldet fælles matematiske praksisser.
Referencer
Bundsgaard, J. & Hansen, T.I. (2018). Blik på undervisning. I J. Bundsgaard, M. Georgsen, S.T. Graf, T.I. Hansen & C.K. Skott (red.), Skoleudvikling med IT (s. 106-142). Aarhus Universitetsforlag.
Børne- og Undervisningsministeriet. (2015). Fælles mål for faget matematik. https://emu.dk/grundskole/matematik/faghaefte-faelles-maal-laeseplan-og-vejledning
Clements, D.H. & Sarama, J. (2021). Learning and teaching early math: The learning trajectory approach (3. udg.). Routledge.
Cobb, P. (1999). Individual and collective mathematical development: The case of statistical data analysis. Mathematical Thinking and Learning, 1(1), 5-43. https://doi.org/10.1207/s15327833mtl0101_1
Cobb, P. & Gravemeijer, K. (2008). Experimenting to support and understand learning processes. I A.E. Kelly, R.A. Lesh & J.Y. Baek (red.), Handbook of design research methods in education: Innovations in science, technology, engineering, and mathematics learning and teaching (s. 68-95). Routledge.
Cobb, P., Stephan, M., McClain, K. & Gravemeijer, K. (2001). Participating in classroom mathematical practices. Journal of the Learning Sciences, 10(1-2), 113-163. https://doi.org/10.1007/978-90-481-9729-3_9
Cobb, P. & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31(3-4), 175-190. https://doi.org/10.1080/00461520.1996.9653265
Confrey, J., Maloney, A.P. & Corley, A.K. (2014). Learning trajectories: A framework for connecting standards with curriculum. ZDM – International Journal on Mathematics Education, 46(5), 719-733. https://doi.org/10.1007/s11858-014-0598-7
Confrey, J., Maloney, A.P. & Nguyen, K. (2014). Learning trajectories in mathematics. I A.P. Maloney, J. Confrey & K. Nguyen (red.), Learning trajectories in mathematics (s. xi-xxii). Information Age Publishing.
Gissel, S.T., Hjelmborg, M., Kristensen, B.T. & Moeskær Larsen, D. (2019). Kompetencedækning i analoge matematiksystemer til mellemtrinnet. MONA, 2019(3), 7-27. https://tidsskrift.dk/mona/article/view/115580/163893
Gravemeijer, K. (2020). Emergent modeling: An RME design heuristic elaborated in a series of examples. Education Designer, 4(13), 1-31. https://www.researchgate.net/profile/Koeno-Gravemeijer/publication/344057779_Emergent_Modeling_an_RME_Design_Heuristic_Elaborated_in_a_Series_of_Examples/links/5f4feea892851c250b8b2b75/Emergent-Modelingan-RME-Design-Heuristic-Elaborated-in-a-Series-of-Examples.pdf
Gravemeijer, K., Cobb, P., Bowers, J. & Whitenack, J.W. (2000). Symbolizing, modeling, and instructional design. I P. Cobb, E. Yackel & K. McClain (red.), Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design (s. 225-273). Lawrence Erlbaum Associates.
Huang, X., Huang, R., & Skott, C. K. (2023). Research-informed instruction through lesson study: A case of boundary crossing. International Journal of Science and Mathematics Education. Published online.
Kjeldsen, C.C., Kristensen, R.M. & Christensen, A.A. (2019). Matematik og natur/teknologi i 4. klasse. Resultater af TIMSS-undersøgelsen 2019. Aarhus Universitetsforlag.
Kaas, T. (2019). Tilgange til tidlig algebra. Nordic Studies of Mathematics Education, 24(3-4), 15-41. https://ncm.gu.se/wp-content/uploads/2021/10/24_34_015042_kaas.pdf
Kaas, T. (2022). Tidlig algebra i grundskolens matematikundervisning. Ph.d.-afhandling. DPU, Aarhus Universitet.
Lobato, J. & Walters, D. (2017). A taxonomy of approaches to learning trajectories and progressions.
I J. Cai (red.), The compendium for research in mathematics education (s. 74-101). National Council of Teachers of Mathematics.
Ma, L. (2010). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Routledge.
NCTM. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
Potari, D., Psycharis, G., Sakonidis, C. & Zachariades, T. (2019). Collaborative design of a reformoriented mathematics curriculum: Contradictions and boundaries across teaching, research, and policy. Educational Studies in Mathematics, 102(3), 417-434. https://doi.org/10.1007/s10649-018-9834-3
Radford, L (2022). Introducing equations in early algebra. ZDM – International Journal on Mathematics Education, 54, 1151-1167. https://doi.org/10.1007/s11858-022-01422-x
Simon, M.A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114-145. https://doi.org/10.2307/749205
Skott, C.K., Christensen, B.K., Zacho, L., Thompsen, M., Teglskov, R., Øhrstrøm, A., Rønne, M., Riisgaard, T.B., Tange, B., Granerud, L.S., Hørup, L.A., Winsløw, C., Sunde, P.B. & Brockhoff, P. (2022). Fælles udvikling af matematik: Om udfordringer og mulige løsninger i forhold til matematik i grundskolen, på de gymnasiale uddannelser og på erhvervsuddannelserne. Børne- ogUndervisningsministeriet.
Skott, J. (2008). Introduktion til Paul Cobbs matematikdidaktiske arbejde. MONA, 2008(4), 42-58. https://tidsskrift.dk/mona/article/view/36629/37927
Skott, J., Skott, C.K., Jess, K. & Hansen, H.C. (2018). Matematik for lærerstuderende. Delta 2.0 – fagdidaktik 1.-10. klasse. Samfundslitteratur.
Stigler, J.W. & Hiebert, J. (2009). Closing the teaching gap. Phi Delta Kappan, 91(3), 32-37. https://doi.org/10.1177/003172170909100307
Sztajn, P., Confrey, J., Wilson, P.H. & Edgington, C. (2012). Learning trajectory based instruction: Toward a theory of teaching. Educational Researcher, 41(5), 147-156. https://doi.org/10.3102/0013189X12442801
Verschaffel, L., Greer, B. & De Corte, E. (2007). Whole number concepts and operations. I F.K. Lester (red.), Second handbook of research on mathematics teaching and learning (s. 557-628). National Council of Teachers of Mathematics.
Wilson, P.H. (2014). Learning trajectories and professional development. I A.P. Maloney, J. Confrey & K.H. Nguyen (red.), Learning over time: Learning trajectories in mathematics education (s. 227-242). Information Age Publishing.