Abstract
This chapter deals with the recently re-emerged concept of computational thinking (CT) and its reception in mathematics education research and mathematics curriculum policy. We provide an overview of CT’s claimed potentials for mathematics teaching and learning and outline the most widely used definitions of CT in mathematics education research. Based on three illustrative cases from Denmark, Sweden, and England, we develop three typologies of ways in which CT and mathematics are related to each other in curricular resources. We also describe the opportunities and challenges these typologies are associated with for teachers in relation to connecting CT and mathematics in the mathematics education classrooms. We conclude the paper by discussing the relation between tendencies in how CT is enacted in mathematics curriculum policy and how it is studied in the mathematics education research community. Moreover, we reflect on the implications of this relation for the opportunities of informing CT in mathematics education through state-of-the-art research.
This is a preview of subscription content, log in via an institution to check access.
Notes
- 1.
- 2.
- 3.
- 4.
Papert (1980) defined Microworlds as a “subset of reality or a constructed reality whose structure matches that of a given cognitive mechanism so as to provide an environment where the latter can operate effectively. The concept leads to the project of inventing microworlds so structured as to allow a human learner to exercise particular powerful ideas or intellectual skills” (p. 204).
- 5.
For further information regarding the National Curriculum for Computing in England, please visit The Department for Education webpage: https://www.gov.uk/government/publications/national-curriculum-in-england-computing-programmes-of-study/national-curriculum-in-england-computing-programmes-of-study
- 6.
- 7.
- 8.
References
Barcelos TS, Munoz R, Villarroel R, Merino E, Silveira IF (2018) Mathematics learning through computational thinking activities: a systematic literature review. J Univ Comput Sci 24(7):815–845
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. 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. Digit Exp Math Educ 3(2):115–138. https://doi.org/10.1007/s40751-017-0028-x
Benton L, Kalas I, Saunders P, Hoyles C, Noss R (2018a) Beyond jam sandwiches and cups of tea: an exploration of primary pupils’ algorithm-evaluation strategies. J Comput Assist Learn 34(5):590–601. https://doi.org/10.1111/jcal.12266
Benton L, Saunders P, Kalas I, Hoyles C, Noss R (2018b) Designing for learning mathematics through programming: a case study of pupils engaging with place value. Int J Child-Comput Interact 16:68–76. https://doi.org/10.1016/j.ijcci.2017.12.004
Bers MU (2017) The Seymour test. Int J Child–Comput Interact 14(C):10–14
Berthelsen UD, Nielsen CF (2021) Democracy and computation: a normative perspective on the magic of the new millennium. In: Aman Y, Berthelsen UD (eds) Computational thinking in education: a pedagogical perspective. Routledge, pp 57–72
Bienkowski M, Snow E, Rutstein D, Grover S (2015) Assessment design patterns for computational thinking practices in secondary computer science: a first look. http://pact.sri.com/resources.html
Bocconi S, Chioccariello A, Kampylis P, Dagiené V, Wastiau P, Engelhardt K, Earp J, Horvath MA, Jasutė E, Malagoli C, Masiulionytė-Dagienė V, Stupurienė G (2022) Reviewing computational thinking in compulsory education. In: Inamorato dos Santos A, Cachia R, Giannoutsou N, Punie Y (eds) Reviewing computational thinking in compulsory education: state of play and practices from computing education. Publications Office of the European Union. https://doi.org/10.2760/126955
Børne- & Undervisningsministeriet (2018a) Handlingsplan for teknologi i undervisningen. [Action plan for technology in teaching]. https://www.uvm.dk/publikationer/folkeskolen/2018-handlingsplan-for-teknologi-i-undervisningen
Børne- & Undervisningsministeriet (2018b) Kontraktbilag 1: Kravspecifikation. Forsøg med teknologiforståelse i folkeskolens obligatoriske undervisning. [Contract appendice 1: Requirement Specification. Experiment with technology comprehension in the compulsory school’s mandatory teaching]. DocPlayer. http://docplayer.dk/149137888-Kontraktbilag-1-kravspecifikation-forsoeg-med-teknologiforstaaelse-i-folkeskolens-obligatoriske-undervisning.html
Børne- & Undervisningsministeriet (2020) Miedtvejsevaluering: Forsøg med teknologiforståelse i folkeskolens obligatoriske undervisning. [Mid-way evaluation: Experiment with technology comprehension in the compulsory school’s mandatory teaching]. Emu. https://emu.dk/sites/default/files/2020-06/Midtvejsevaluering%20-%20Fors%C3%B8g%20med%20teknologiforst%C3%A5else.pdf
Børne- & Undervisningsministeriet (2021) Folkeskolens Formål [The purpose of Danish compulsory schools]. Børne- & Undervisningsministeriet. https://www.uvm.dk/folkeskolen/folkeskolens-maal-love-og-regler/om-folkeskolen-og-folkeskolens-formaal/folkeskolens-formaal
Bråting K, Kilhamn C (2021) The integration of programming in Swedish school mathematics: investigating elementary mathematics textbooks. Scand J Educ Res 1–16. https://doi.org/10.1080/00313831.2021.1897879
Breidenbach D, Dubinsky E, Hawks J, Nichols D (1992) Development of the process conception of function. Educ Stud Math 23(3):247–285. https://doi.org/10.1007/BF02309532
Brennan K, Resnick M (2012, April) New frameworks for studying and assessing the development of computational thinking. In: Proceedings of the 2012 annual meeting of the American educational research association, Vancouver, vol 1, p 25
Chevallard Y, Sensevy G (2014) Anthropological approaches in mathematics education: French perspectives. In: Lerman S (ed) Encyclopedia of mathematics education. Springer, pp 38–43. https://doi.org/10.1007/978-94-007-4978-8_9
Clements DH, Battista MT (1992) Geometry and spatial reasoning. In: Grouws DA (ed) Handbook of research on mathematics teaching and learning: a project of the National Council of teachers of mathematics. Macmillan Publishing Co, Inc., New York, pp 420–464
Clements DH, Sarama J (1997) Research on Logo: a decade of progress. Comput Sch 14(1–2):9–46. https://doi.org/10.1300/J025v14n01_02
Council of Professors and Heads of Computing (2008) The decline in computing graduates: A threat to the knowledge economy and global competitiveness. https://cphcuk.files.wordpress.com/2014/01/cphc-computinggraduates-june08.pdf
Council of Professors and Heads of Computing. (2009) A response to the interim “Digital Britain Report” from the Council of Professors and Heads of Computing UK. https://cphcuk.files.wordpress.com/2014/01/cphc-db-response.pdf
Department for Education (2013) National Curriculum in England: Computing programmes of study. https://www.gov.uk/government/publications/national-curriculum-in-england-computing-programmes-of-study/national-curriculum-in-england-computing-programmes-of-study
Department for 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/358070/NC_assessment_quals_factsheet_Sept_update.pdf
Department of Education and Employment (1999) Information and communication technology: The national curriculum for England. Teachers TV. http://archive.teachfind.com/qcda/curriculum.qcda.gov.uk/uploads/ICT%201999%20programme%20of%20study_tcm8-12058.pdf
Digitaliseringskommissionen (2015) Gör Sverige i framtiden – Digtial kompetans. Regeringen. [Make Sweden in the future – digital competence]. https://www.regeringen.se/rattsliga-dokument/statens-offentliga-utredningar/2015/03/sou-201528/
DiSessa AA, Cobb P (2004) Ontological innovation and the role of theory in design experiments. J Learn Sci 13(1):77–103. https://doi.org/10.1207/s15327809jls1301_4
Du Boulay B (1986) Part 11: Logo confessions. In: Lawler R, du Boulay B, Hughes M, Macleod TL (eds) Cognitions and computers. Studies in learning. Ellis Horwood Limited, Great Britain, pp 81–178
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 the 15th international conference on technology in mathematics teaching (ICTMT 15) (pp. 45–52). Aarhus University, Copenhagen
Elicer R, Tamborg AL (2023) From policy to resources: programming, computational thinking and mathematics in the Danish curriculum [Manuscript submitted for publication]. Department of Science Education, University of Copenhagen
Fowler B, Vegas E (2021) How England implemented its computer science education program. Center for Universal Education at Brookings, Washington DC, USA. https://www.brookings.edu/wp-content/uploads/2021/01/How-England-implemented-its-computer-science-education-program.pdf
Gadanidis G (2017) Five affordances of computational thinking to support elementary mathematics education. J Comput Math Sci Teach 36(2):143–151
Gadanidis G, Hughes J, Minniti L, White B (2017a) Computational thinking, grade 1 students and the binomial theorem. Digit Exp Math Educ 3(2):77–96. https://doi.org/10.1007/s40751-016-0019-3
Gadanidis G, Cendros R, Floyd L, Namukasa I (2017b) Computational thinking in mathematics teacher education. Contemp Issues Technol Teach Educ 17(4):458–477
Grover S (2022) ‘CTIntegration’: a conceptual framework guiding design and analysis of integration of computing and computational thinking into school subjects. EdAr**v. https://doi.org/10.35542/osf.io/eg8n5
Grover S, Pea R (2018) Computational thinking: a competency whose time has come. In: Sentance S, Barendsen E, Schulte C (eds) Computer science education: perspectives on teaching and learning in school. Bloomsbury Academic, London, pp 19–38. https://doi.org/10.5040/9781350057142.ch-003
Grover S, Biswas G, Dickes A, Farris A, Sengupta P, Covitt B, Gunckel K, Berkowitz A, Moore J, Irgens GA, Horn M, Wilensky U, Metcalf S, Jeon S, Dede C, Puttick G, Bernstein D, Wendell K, Danahy E, Cassidy M, Shaw F, Damelin D, Roderick S, Stephens AL, Shin N, Lee I, Anderson E, Dominguez X, Vahey P, Yadav A, Rich K, Schwarz C, Larimore R, Blikstein P (2020) Integrating STEM and computing in PK-12: operationalizing computational thinking for STEM learning and assessment. In: Gresalfi M, Horn IS (eds) The Interdisciplinarity of the learning sciences, 14th international conference of the learning sciences (ICLS) 2020, vol 3. International Society of the Learning Sciences, Nashville, pp 1479–1486
Hazzan O, Ragonis N, Lapidot T, Rosenberg-Kima R (2020) Computational European Commission/EACEA/Eurydice. (2019). Digital Education at School in Europe. Publications Office of the European Union, Luxembourg. https://doi.org/10.2797/66552
Heintz F, Mannila L, Nordén LÅ, Parnes P, Regnell B (2017) Introducing programming and digital competence in Swedish K-9 education. In: Dagienė V, Hellas A (eds) Informatics in schools: focus on learning programming: 10th international conference on informatics in schools: situation, evolution, and perspectives, ISSEP 2017, Helsinki, November 13–15, 2017, proceedings, vol 10696. Springer, Finland, pp 117–128
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: Bråting K, Kilhamn C, Rolandsson L (eds) Programmering i skolmatematiken: Möjligheter och utmaningar. Studentlitteratur, Lund, Sweden, pp 39–56
Hoyles C, Lagrange J-B (2010) Introduction. In: Hoyles C, Lagrange J-B (eds) Mathematics education and technology: rethinking the terrain. Springer, New York, USA, pp 250–284
Jensen JH, Jankvist UT (2018) Disciplinary competence descriptions for external use. Nord Stud Math Educ 23(2):3–24
Kallia M, van Borkulo SP, Drijvers P, Barendsen E, Tolboom J (2021) Characterising computational thinking in mathematics education: a literature-informed Delphi study. Res Math Educ 23(2):159–187. https://doi.org/10.1080/14794802.2020.1852104
Kieran C (1986) Logo and the notion of angle among fourth and sixth grade children. In: Hoyles C, Burton L (eds) Proceedings of the tenth annual meeting of the International Group for Psychology in Mathematics Education. City University, London, pp 99–104
Kieran C, Hillel J (1990) “It’s tough when you have to make triangles angles”: insights from a computer-based geometry environment. J Math Behav 9:99–127
Knuth DE (1985) Algorithmic thinking and mathematical thinking. Am Math Mon 92(3):170–181
Larke LR (2019) Agentic neglect: teachers as gatekeepers of England’s national computing curriculum. Br J Educ Technol 50:1137–1150. https://doi.org/10.1111/bjet.12744
Lodi M, Martini S (2021) Computational thinking, between Papert and Wing. Sci & Educ 30(4):883–908. https://doi.org/10.1007/s11191-021-00202-5
Malyn-Smith J, Lee IA, Martin F, Grover S, Evans MA, Pillai S (2018) Develo** a framework for computational thinking from a disciplinary perspective. In: Kong SC, Andone D, Biswas G, Crick T, Hoppe HU, Hsu TC, Huang RH, Li KY, Looi CK, Milrad M, Sheldon J, Shih JL, Sin KF, Tissenbaum M, Vahrenhold J (eds) Proceedings of the international conference on computational thinking education 2018. The Education University of Hong Kong, Hong Kong, pp 182–186
Microsoft (2007) Develo** the Future: A report on the challenges and opportunities facing the UK software development industry. https://download.microsoft.com/documents/UK/develo**thefuture/Develo**%20_The_Future_07.pdf
Misfeldt M, Ejsing-Duun S (2015) Learning mathematics through programming: an instrumental approach to potentials and pitfalls. In: Krainer K, Vondrová N (eds) Proceedings of the ninth congress of the European Society for Research in Mathematics Education. Charles University in Prague, Faculty of Education and ERME, Czech Republic, pp 2524–2530
Modeste S (2016) Impact of informatics on mathematics and its teaching. On the importance of epistemological analysis to feed didactical research. In: Gadducci F, Tavosanis M (eds) History and philosophy of computing, series: IFIP advances in information and communication technology, vol 487. Springer, Pisa, Italy, pp 243–255. 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 develo** curriculum. In: Shimizu Y, Vithal R (eds) ICMI Study 24, school mathematics curriculum reforms: challenges, changes and opportunities. International Commission on Mathematical Instruction and University of Tsukuba, Japan, pp 277–284
Niss M, Højgaard T (2019) Mathematical competencies revisited. Educ Stud Math 102(1):9–28. https://doi.org/10.1007/s10649-019-09903-9
Noss R (1986) Constructing a conceptual framework for elementary algebra through Logo programming. Educ Stud Math 17(4):335–357. https://doi.org/10.1007/BF00311324
Noss R (1987) How do children do mathematics with LOGO? J Comput Assist Learn 3(1):2–12. https://doi.org/10.1111/j.1365-2729.1987.tb00303.x
Noss R, Hoyles C (1996) Windows on mathematical meanings: learning cultures and computers. Kluwer, Dordrecht
Nouri J, Zhang L, Mannila L, Norén E (2020) Development of computational thinking, digital competence and 21st century skills when learning programming in K-9. Educ Inq 11(1):1–17. https://doi.org/10.1080/20004508.2019.1627844
Olive J, Lankenau CA, Scally SP (1986) Teaching and understanding geometric relationships through Logo: phase 11. Emory University, Atlanta, Georgia, USA
Olofsson AD, Lindberg JO, Young Pedersen A, Arstorp A-T, Dalsgaard C, Einum E, Caviglia F, Ilomäki L, Veermans M, Häkkinen P, Willermark S (2021) Digital competence across boundaries – beyond a common Nordic model of the digitalisation of K-12 schools? Educ Inq 12(4):317–328. https://doi.org/10.1080/20004508.2021.1976454
Papert S (1980) Mindstorms: children, computers, and powerful ideas. Basic Books, New York City, USA
Papert S (2000) What’s the big idea? Toward a pedagogy of idea power. IBM Syst J 39(3.4):720–729
Pérez A (2018) A framework for computational thinking dispositions in mathematics education. J Res Math Educ 49(4):424–461. https://doi.org/10.5951/jresematheduc.49.4.0424
PISA O (2022) Mathematics framework (Draft). Retrieved from https://pisa2022-maths.oecd.org/files/PISA%202022%20Mathematics%20Framework%20Draft.pdf
Regeringen (2018) Teknologiforståelse skal være obligatorisk i folkeskolen. [Technology will be mandatory in compulsory schools]. https://www.regeringen.dk/nyheder/2018/teknologiforstaaelse-fag-i-folkeskolen/
Román-González M, Pérez-González J-C, Jiménez-Fernández C (2017) Which cognitive abilities underlie computational thinking? Criterion validity of the computational thinking test. Comput Hum Behav 72:678–691. https://doi.org/10.1016/j.chb.2016.08.047
Royal Society (2012) Shut down or restart? The way forward for computing in UK schools. https://royalsociety.org/-/media/education/computing-inschools/2012-01-12-computing-in-schools.pdf
Selwyn N (2008) From state-of-the-art to state-of-the-actual? Introduction to a special issue. Technol Pedagog Educ 17(2):83–87. https://doi.org/10.1080/14759390802098573
Swedish National Agency of Education (2018) Curriculum for the compulsory school, preschool class and school-age educare, Lgr18. Elanders Sverige AB. https://www.skolverket.se/download/18.6bfaca41169863e6a65d48d/1553968042333/pdf3975.pdf
Swedish National Agency of Education (2022) The curriculum for compulsory school, preschool class and school-age educare, Lgr22. Elanders Sverige AB. https://www.skolverket.se/getFile?file=9718
Tamborg AL, Elicer R, Misfeldt M, Jankvist UT (2022) Computational thinking in Denmark from an anthropological theory of the didactic perspective. In: Fernández C, Llinares S, Gutiérrez Á, Planas N (eds) Proceedings of the 45th conference of the International Group for the Psychology of Mathematics Education, vol 4. PME, Alicante, pp 91–98
Tikva C, Tambouris E (2021) Map** computational thinking through programming in K-12 education: a conceptual model based on a systematic literature review. Comput Educ 162. https://doi.org/10.1016/j.compedu.2020.104083
Vernon W (2009) The Delphi technique: a review. Int J Ther Rehabil 16(2):69–76
Voogt J, Fisser P, Good J, Mishra P, Yadav A (2015) Computational thinking in compulsory education: towards an agenda for research and practice. Educ Inf Technol 20(4):715–728. https://doi.org/10.1007/s10639-015-9412-6
Weintrop D, Beheshti E, Horn M, Orton K, Jona K, Trouille L, Wilensky U (2016) Defining computational thinking for mathematics and science classrooms. J Sci Educ Technol 25(1):127–147. https://doi.org/10.1007/s10956-015-9581-5
Williamson B, Bergviken Rensfeldt A, Player-Koro C, Selwyn N (2019) Education recoded: policy mobilities in the international ‘learning to code’ agenda. J Educ Policy 34(5):705–725. https://www.tandfonline.com/doi/full/10.1080/02680939.2018.1476735
Wing JM (2006) Computational thinking. Commun ACM 49(3):33–35. https://doi.org/10.1145/1118178.1118215
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2023 Springer Nature Switzerland AG
About this entry
Cite this entry
Tamborg, A.L., Elicer, R., Bråting, K., Geraniou, E., Jankvist, U.T., Misfeldt, M. (2023). The Politics of Computational Thinking and Programming in Mathematics Education: Comparing Curricula and Resources in England, Sweden, and Denmark. In: Pepin, B., Gueudet, G., Choppin, J. (eds) Handbook of Digital Resources in Mathematics Education. Springer International Handbooks of Education. Springer, Cham. https://doi.org/10.1007/978-3-030-95060-6_55-1
Download citation
DOI: https://doi.org/10.1007/978-3-030-95060-6_55-1
Received:
Accepted:
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-95060-6
Online ISBN: 978-3-030-95060-6
eBook Packages: Springer Reference EducationReference Module Humanities and Social SciencesReference Module Education