From policy to resources: programming, computational thinking and mathematics in the Danish curriculum
Abstract
This article investigates the relations between mathematics and programming and computational thinking (PCT). In scholarly knowledge, PCT is juxtaposed as an aid to mathematical problem solving, but also integrated as a collection of practices common to both domains. This knowledge is being turned into curriculum and teaching resources developed for Danish compulsory schools (students aged 6–15), in the context of a pilot project to embed a new technology comprehension subject into mathematics. In the curriculum, PCT is being juxtaposed to mathematics. The teaching resources are predominantly integrated, but lacking connections to mathematical problem solving and modelling. These misalignments are both missed opportunities and a leeway for a cautious integration in teaching practice.
References
Benton, L., Hoyles, C., Kalas, I. & Noss, R. (2016). Building mathematical knowledge with programming: insights from the ScratchMaths project. In Constructionism 2016: conference proceedings (pp. 26-33). Suksapattana Foundation. https://discovery.ucl.ac.uk/id/eprint/1475523
Benton, L., Hoyles, C., Kalas, I. & Noss, R. (2017). Bridging primary programming and mathematics: some findings of design research in England. Digital Experiences in Mathematics Education, 3 (2), 115-138. https://doi.org/10.1007/s40751-017-0028-x
Bocconi, S., Chioccariello, A. & Earp, J. (2018). The Nordic approach to introducing computational thinking and programming in compulsory education. Report prepared for the Nordic@BETT2018 Steering Group. doi: 10.17471/54007
Bocconi, S., Chioccariello, A., Kampylis, P., Wastiau, P., Engelhardt, K. et al. (2022). Reviewing computational thinking in compulsory education: state of play and practices from computing education. Publications Office of the European Union. doi: 10.2760/126955
Bosch, M. & Gascón, J. (2006). Twenty-five years of the didactic transposition. ICMI Bulletin, 58, 51-65.
Boylan, M., Demack, S., Wolstenholme, C., Reidy, J. & Reaney, S. (2018). ScratchMaths: evaluation report and executive summary. Education Endownment Foundation.
Bråting, K. & Kilhamn, C. (2021). Exploring the intersection of algebraic and computational thinking. Mathematical Thinking and Learning, 23 (2), 170-185. https://doi.org/10.1080/10986065.2020.1779012
Bråting, K. & Kilhamn, C. (2022). The integration of programming in Swedish school mathematics: investigating elementary mathematics textbooks. Scandinavian Journal of Educational Research, 66 (4), 594-609. https://doi.org/10.1080/00313831.2021.1897879
Brennan, K. & Resnick, M. (2012). New frameworks for studying and assessing the development of computational thinking. In Proceedings of AERA 2012 (pp. 1-25). American Educational Research Association.
Burger, W. F. & Shaughnessy, J. M. (1986). Characterizing the van Hiele levels of development in geometry. Journal for Research in Mathematics Education, 17 (1), 31-48. https://doi.org/10.2307/749317
BUVM (2018). Handlingsplan for teknologi i undervisningen [Action plan for technology in teaching]. Børne- og Undervisningsministeriet. https://www.uvm.dk/publikationer/folkeskolen/2018-handlingsplan-for-teknologi-i-undervisningen
BUVM (2019). Fælles mål for teknologiforståelse [Common goals for technology comprehension]. Børne- og Undervisningsministeriet. https://emu.dk/sites/default/files/2019-02/GSK.%20F%C3%A6lles%20M%C3%A5l.%20Tilg%C3%A6ngelig.%20Teknologiforst%C3%A5else.pdf
BUVM (2021a). Didaktiske prototyper - format og vejledning [Didactical prototypes - format and guidelines]. Børne- og Undervisningsministeriet. https://tekforsøget.dk/wp-content/uploads/2021/06/Format-og-vejledning-til-didaktiske-prototyper-maj-2021.pdf
BUVM (2021b). Forsøg med teknologiforståelse i folkeskolens obligatoriske undervisning: slutevaluering [Experiment with technology comprehension in compulsory education: final evaluation]. Børne- og Undervisningsministeriet. https://www.uvm.dk/-/media/filer/uvm/aktuelt/pdf21/okt/211004-slutevaluering-teknologoforstaaelse.pdf
Caeli, E. N. & Yadav, A. (2020). Unplugged approaches to computational thinking: a historical perspective. TechTrends, 64, 29-36. https://doi.org/10.1007/s11528-019-00410-5
Chevallard, Y. & Sensevy, G. (2014). Anthropological approaches in mathematics education, French perspectives. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 38-43). Springer. https://doi.org/10.1007/978-94-007-4978-8_9
Department of Education (2014). National curriculum and assessment from September 2014: information for schools. Assets Publishing Service. https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/1152583/WITHDRAWN_-_NC_assessment_quals_factsheet_Sept_update.pdf
Ejsing-Duun, S., Misfeldt, M. & Andersen, D. G. (2021). Computational thinking karakteriseret som et sæt af kompetencer [Computational thinking characterised as a set of competencies]. Learning Tech - Tidsskrift for læremidler, didaktik og teknologi, 10, 405-429. https://doi.org/10.7146/lt.v6i10.125258
Elicer, R. & Tamborg, A. L. (2022). Nature of the relations between programming and computational thinking and mathematics in Danish teaching resources. In U. T. Jankvist, R. Elicer, A. Clark-Wilson, H.-G. Weigand & M. Thomsen (Eds.), Proceedings of ICTMT 15 (pp. 45-52). Aarhus University.
Gadanidis, G., Cendros, R., Floyd, L. & Namukasa, I. (2017). Computational thinking in mathematics teacher education. Contemporary Issues in Technology and Teacher Education, 17 (4), 458-477.
Gueudet, G., Bueno-Ravel, L., Modeste, S. & Trouche, L. (2017) Curriculum in France. A national frame in transition. In D. R. Thompson, M. A. Huntley & C. Suurtmamm (Eds.), International perspectives on mathematics curriculum (pp. 41-69). Information Age.
Hansen, B. & Winsløw, C. (2010). Research and study course diagrams as an analytic tool: the case of bi-disciplinary projects combining mathematics and history. In M. Bosch, M., J. Gascón, A. Ruiz Olarría, M. Artaud, A. Bronner et al. (Eds.), Un panorama de la TAD (pp. 685-694). Centre de Recerca Matemàtica.
Heintz, F., Mannila, L., Nordén, L. Å., Parnes, P. & Regnell, B. (2017). Introducing programming and digital competence in Swedish K-9 education. In V. Dagienė & A. Hellas (Eds.), Informatics in schools: focus on learning programming (pp. 117-128). Springer. https://doi.org/10.1007/978-3-319-71483-7_10
Helenius, O. & Misfeldt, M. (2021). Programmeringens väg in i skolan - en jämförelse mellan Danmark och Sverige [Programming's way into school - a comparison between Denmark and Sweden]. In K. Bråting, C. Kilhamn & L. Rolandsson (Eds.), Programmering i skolmatematiken: möjligheter och utmaningar (pp. 39-56). Studentlitteratur.
Jahnke, A. (Ed.) (2020). Programmering i skolan. Var, när, hur och varför? Slutrapport från FoU-programmet Programmering i ämnesundervisningen [Programming in school. Where, when, how and why? Final report from the FoU program Programming in subject teaching]. Ifous.
Jessen, B. E. & Kjeldsen, T. H. (2021). Mathematical modelling in scientific contexts and in Danish upper secondary education: Are there any relations? Quadrante, 30 (2), 37-57. doi: 10.48489/quadrante.23658
Kallia, M., Borkulo, S. P. van, Drijvers, P., Barendsen, E. & Tolboom, J. (2021). Characterising computational thinking in mathematics education: a literature-informed Delphi study. Research in Mathematics Education, 23 (2), 159-187. https://doi.org/10.1080/14794802.2020.1852104
Li, Y., Schoenfeld, A. H., diSessa, A. A., Graesser, A. C., Benson, L. C. et al. (2020). Computational thinking is more about thinking than computing. Journal for STEM Education Research, 3 (1), 1-18. https://doi.org/10.1007/s41979-020-00030-2
Misfeldt, M., Szabo, A. & Helenius, O. (2019). Surveying teachers' conception of programming as a mathematics topic following the implementation of a new mathematics curriculum. In U. T. Jankvist, M. Van den Heuvel-Panhuizen & M. Veldhuis (Eds.), Proceedings of CERME11 (pp. 2713-2720). Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.
Misfeldt, M., Jankvist, U. T., Geraniou, E. & Bråting, K. (2020). Relations between mathematics and programming in school: Juxtaposing three different cases. In A. Donevska-Todorova, E. Faggiano, J. Trgalova, Z. Lavicza, R. Weinhandl et al. (Eds.), Proceedings of the 10th ERME topic conference MEDA 2020 (pp. 255-262). Johannes Kepler University. https://hal.archives-ouvertes.fr/hal-02932218/document#page=268
Modeste S. (2016). Impact of informatics on mathematics and its teaching. On the importance of epistemological analysis to feed didactical research. In F. Gadducci & M. Tavosanis (Eds.), History and philosophy of computing (pp. 243-255). Springer. https://doi.org/10.1007/978-3-319-47286-7_17
Modeste, S. (2018). Relations between mathematics and computer science in the French secondary school: a developing curriculum. In Y. Shimizu & R. Vithal (Eds.), ICMI Study 24, School mathematics curriculum reforms: challenges, changes and opportunities (pp. 277-284). ICMI and University of Tsukuba.
Modeste, S. & Rafalska, M. (2017). Algorithmics in secondary school: a comparative study between Ukraine and France. In T. Dooley & G. Gueudet (Eds.), Proceedings of CERME10 (pp. 1634-1641). DCU Institute of Education & ERME. https://hal.archives-ouvertes.fr/hal-01938178
Niss, M. & Højgaard, T. (2019). Mathematical competencies revisited. Educational Studies in Mathematics, 102 (1), 9-28. https://doi.org/10.1007/s10649-019-09903-9
Nordby, S. K., Bjerke, A. H. & Mifsud, L. (2022) Primary mathematics teachers' understanding of computational thinking. KI - Künstliche Intelligens, 35 (1), 35-46. https://doi.org/10.1007/s13218-021-00750-6
Papert, S. (1980). Mindstorms: children, computers, and powerful ideas. Basic Books.
Pérez, A. (2018). A framework for computational thinking dispositions in mathematics education. Journal for Research in Mathematics Education, 49 (4), 424-461. https://doi.org/10.5951/jresematheduc.49.4.0424
Selby, C. & Woollard, J. (2013). Computational thinking: the developing definition. University of Southampton. https://eprints.soton.ac.uk/356481/
Smith, R. C., Bossen, C., Dindler, C. & Sejer Iversen, O. (2020). When participatory design becomes policy: technology comprehension in Danish education. In C. Del Gaudio, L. Parra-Agudelo, R. Clarke, J. Saad-Sulonen, A. Botero et al. (Eds.), Proceedings of the 16th Participatory Design Conference 2020 (pp. 148-158). ACM. https://doi.org/10.1145/3385010.3385011
Swedish National Agency of Education (2018). Curriculum for the compulsory school, preschool class and school-age educare 2011. Skolverket.
Tamborg, A. L. (2022). A solution to what? Aims and means of implementing informatics-related subjects in Sweden, Denmark, and England. Acta Didactica Norden, 16 (4), article 2. https://doi.org/10.5617/adno.9184
Tamborg, A. L., Elicer, R., Misfeldt, M. & Jankvist, U. T. (2022). Computational thinking in Denmark from an anthropological theory of the didactic perspective. In C. Fernández, S. Llinares, Á. Gutiérrez & N. Planas (Eds.), Proceedings of PME 45 (Vol. 4, pp. 91-98). PME.
Vernon, W. (2009). The Delphi technique: a review. International Journal of Therapy and Rehabilitation, 16 (2), 69-76. https://doi.org/10.12968/ijtr.2009.16.2.38892
Weintrop, D., Beheshti, E., Horn, M., Orton, K., Jona, K. et al. (2016). Defining computational thinking for mathematics and science classrooms. Journal of Science Education and Technology, 25 (1), 127-147. https://doi.org/10.1007/s10956-015-9581-5
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.