Skip to main content
Log in

Programming and Computational Thinking in Mathematics Education

An Integration Towards AI Awareness

  • Discussion
  • Published:
KI - Künstliche Intelligenz Aims and scope Submit manuscript

Abstract

Artificial intelligence (AI) has become a part of everyday interactions with pervasive digital systems. This development increasingly calls for citizens to have a basic understanding of programming and computational thinking (PCT). Accordingly, countries worldwide are implementing several approaches to integrate critical elements of PCT into K-9 education. However, these efforts are confronted by difficulties that the PCT concepts are for students to grasp from purely theoretical perspectives. Recent literature indicates that the playful nature is particularly important when novices from both both early and higher education are to learn AI. These playful activities are characterised by setting a scene where PCT concepts such as algorithms, data processing, and simulations are meant to draw on to understand better how AI is integrated into our everyday digital life. This discussion paper analyses playful PCT resources developed around the game rock-paper-scissors developed in the UK and Denmark. Resources from these countries are interesting starting points since both have been or are in the process of integrating PCT as part of the K-9 curriculum. The central discussion raised by the paper, is the nature of the integration between mathematics and PCT in these tasks. These resources provide opportunities for discussion of how we may better integrate PCT and mathematics from the perspective of both subjects to build a solid foundation for a critical understanding of AI interactions in future generations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. 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, Thung Khru, Thailand. https://discovery.ucl.ac.uk/id/eprint/1475523/

  2. 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

    Article  Google Scholar 

  3. Benton L, Kalas I, Saunders P, Hoyles C, Noss R (2018) Beyond jam sandwiches and cups of tea: an exploration of primary pupils’ algorithm-evaluation strategies. J Comput Assist Learn 34(5):590–601

    Article  Google Scholar 

  4. Bocconi S, Chioccariello A, Dettori G, Ferrari A, Engelhardt K, Kampylis P, Punie Y (2016) Developing computational thinking in compulsory education—implications for policy and practice. Tech. Rep. EUR 28295 EN, Joint Research Centre (JRC). https://doi.org/10.2791/792158

  5. Bocconi S, Chioccariello A, Ear J (2018) The Nordic approach to introducing computational thinking and programming in compulsory education. Report prepared for the Nordic@BETT2018 Steering Grouphttps://doi.org/10.17471/54007

  6. Borovcnik M, Kapadia R (2014) A historical and philosophical perspective on probability. In: Chernoff EJ, Sriraman B (eds) Probabilistic thinking: presenting plural perspectives. Springer, Dordrecht, pp 7–34. https://doi.org/10.1007/978-94-007-7155-0_2

  7. Bråting K, Kilhamn C (2021) The integration of programming in Swedish school mathematics: investigating elementary mathematics textbooks. Scand J Educ Res pp. 1–16 . https://doi.org/10.1080/00313831.2021.1897879(Advance online publication)

  8. Buchberger B (1990) Should students learn integration rules? ACM SIGSAM Bull 24(1):10–17. https://doi.org/10.1145/382276.1095228

    Article  Google Scholar 

  9. Cedillo T, Kieran C (2003) Initiating students into algebra with symbol-manipulating calculators. Computer algebra systems in secondary school mathematics education pp. 219–239

  10. Clements DH, Sarama J (1997) Research on logo: a decade of progress. Comput Sch 14(1–2):9–46

    Article  Google Scholar 

  11. Druga S, Williams R, Park HW, Breazeal C (2018) How smart are the smart toys? Children and parents’ agent interaction and intelligence attribution. In: Proceedings of the 17th ACM Conference on Interaction Design and Children, pp 231–240

  12. Elicer R (2020) On the teaching and learning of probability and statistics in the perspective of Critical Mathematics Education. PhD thesis, Roskilde University, Roskilde, Denmark. http://thiele.ruc.dk/imfufatekster/pdf/513.pdf

  13. Elicer R, Tamborg AL (2022) Nature of the relations between programming and computational thinking and mathematics in Danish teaching resources. In: Jankvist UT, Clark-Wilson A, Weigand HG, Elicer R, Thomsen M (eds) Making and strengthening “Connections and Connectivity” for teaching mathematics with technology: proceedings of the 15th international conference on technology in mathematics teaching – ICTMT 15

  14. Geraniou E, Jankvist UT (2019) Towards a definition of mathematical digital competency. Educ Stud Math 102(1):29–45. https://doi.org/10.1007/s10649-019-09893-8

    Article  Google Scholar 

  15. Guzdial M, Kay A, Norris C, Soloway E (2019) Computational thinking should just be good thinking. Commun ACM 62(11):28–30. https://doi.org/10.1145/3363181

    Article  Google Scholar 

  16. Hoyles C (2018) Transforming the mathematical practices of learners and teachers through digital technology. Res Math Educ 20(3):209–228. https://doi.org/10.1080/14794802.2018.1484799

    Article  Google Scholar 

  17. Jankvist UT, Geraniou E (2021) Whiteboxingthe Content of a formal mathematical text in a dynamic geometry environment. Dig Exp Math Educ 7(2):222–246. https://doi.org/10.1007/s40751-021-00088-6

    Article  Google Scholar 

  18. Kilhamn C, Rolandsson L, Bråting K (2021) Programmering i svensk skolmatematik. LUMAT Int J Math Sci Technol Educ. https://doi.org/10.31129/lumat.9.2.1457

  19. Manheim K, Kaplan L (2019) Artificial intelligence: risks to privacy and democracy. Yale JL Tech 21:106

    Google Scholar 

  20. Misfeldt M, Jankvist UT, Geraniou E, Bråting K (2020) Relations between mathematics and programming in school: Juxtaposing three different cases. In: Donevska-Todorova R, Faggiano A, Trgalova E, Lavicza J Weinhandl Z, Clark-Wilson A, Weigand HG (eds) Proceedings of the Tenth ERME Topic Conference (ETC 10) on Mathematics Education in the Digital Age (MEDA). Johannes Kepler University, Linz, Austria, pp 255–262. https://hal.archives-ouvertes.fr/hal-02932218/document#page=268

  21. Moore DS (2010) The basic practice of statistics, 5th edn. Freeman, New York

    Google Scholar 

  22. Niss M, Højgaard T (2019) Mathematical competencies revisited. Educ Stud Math 102(1):9–28. https://doi.org/10.1007/s10649-019-09903-9

    Article  Google Scholar 

  23. Nobre S (1989) The ethnomathematics of the most popular lottery in Brazil: The “Animal Lottery”. In: Keitel P, Damerow C, Bishop A, Gerdes P (eds) Mathematics, education, and society. UNESCO, Paris, France, pp 175–177

  24. Noss R (1986) Constructing a conceptual framework for elementary algebra through logo programming. Educ Stud Math 17(4):335–357

    Article  Google Scholar 

  25. Noss R (1987) Children’s learning of geometrical concepts through logo. J Res Math Educ 18(5):343–362

    Article  Google Scholar 

  26. 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

    Article  Google Scholar 

  27. Papert S (1980) Mindstorms: children, computers, and powerful ideas. Basic books

  28. Papert S (1996) An exploration in the space of mathematics educations. Int J Comput Math Learn. https://doi.org/10.1007/BF00191473

    Article  Google Scholar 

  29. 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

    Article  Google Scholar 

  30. Shamir G, Levin I (2020) Transformations of computational thinking practices in elementary school on the base of artificial intelligence technologies. In: Proceedings of EDULEARN20 Conference, vol. 6, p 7

  31. Shute VJ, Sun C, Asbell-Clarke J (2017) Demystifying computational thinking. Educ Res Rev 22:142–158. https://doi.org/10.1016/j.edurev.2017.09.003

    Article  Google Scholar 

  32. Smith RC, Bossen C, Dindler C (2020) When participatory design becomes policy: technology comprehension in Danish education. In: Proceedings of the 16th Participatory Design Conference 2020—Participation(s) Otherwise—Volume 1. ACM, New York, NY, USA, pp 48–158. https://doi.org/10.1145/3385010.3385011

  33. Solorio T, Shafaei M, Smailis C, Augenstein Isabelle Mitchell M, Stapf I, Kakadiaris I (2021) White paper—creating a repository of objectionable online content: addressing undesirable biases and ethical considerations. https://openreview.net/pdf?id=i3kSsvYOO18

  34. Watson J, Callingham R (2003) Statistical literacy: a complex hierarchical construct. Stat Educ Res J 2(2):3–46

    Article  Google Scholar 

  35. 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

    Article  Google Scholar 

  36. Williams R, Park HW, Oh L, Breazeal C (2019) Popbots: designing an artificial intelligence curriculum for early childhood education. In: Proceedings of the AAAI Conference on Artificial Intelligence 33:9729–9736

  37. Wing JM (2006) Computational thinking. Commun ACM 49(3):33–35. https://doi.org/10.1145/1118178.1118215

    Article  Google Scholar 

  38. Wing JM (2019) A conversation about computational thinking. https://www.education.nsw.gov.au/content/dam/main-education/teaching-and-learning/education-for-a-changing-world/media/documents/Computational-Conversation_1_A.pdf

Download references

Acknowledgements

The research is funded by Novo Nordisk Foundation Grant NNF19OC0058651.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Daniel Spikol.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

The first two authors of this article are funded by the NOVO Foundation Grant 0058651.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tamborg, A.L., Elicer, R. & Spikol, D. Programming and Computational Thinking in Mathematics Education. Künstl Intell 36, 73–81 (2022). https://doi.org/10.1007/s13218-021-00753-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13218-021-00753-3

Keywords

Navigation