Computational thinking as a tool in primary and secondary mathematical problem solving: a literature review

Authors

  • Kim André Stavenæs Refvik
  • Annette Hessen Bjerke

Abstract

In this systematic literature review, we investigate the connections between computational thinking and problem solving in the context of primary and secondary mathematics education. We do this by exploring how and at which steps in the mathematics problem-solving process seven peer reviewed studies report on the inclusion of computational thinking concepts, practices and perspectives. Overall, the studies show that it is possible and at times beneficial to include computational thinking in mathematics problem solving. However, more research is needed to see whether simply including computational thinking and its programming tools enhances students’ problem-solving skills in mathematics.

References

Barr, V. & Stephenson, C. (2011). Bringing computational thinking to K-12: What is involved and what is the role of the computer science education community? ACM Inroads, 2 (1), 48-54. https://doi.org/10.1145/1929887.1929905

Bocconi, S., Chioccariello, A., Dettori, G., Ferrari, A. & Engelhardt, K. (2016). Developing computational thinking in compulsory education. European Commission. https://publications.jrc.ec.europa.eu/repository/bitstream/ JRC104188/jrc104188_computhinkreport.pdf

Bocconi, S., Chioccariello, A. & Earp, J. (2018). The Nordic approach to introducing computational thinking and programming in compulsory education. Nordic@BETT2018 Steering Group. doi: 10.17471/54007

Brennan, K. & Resnick, M. (2012). New frameworks for studying and assessing the development of computational thinking. Paper presented at AERA2012, Vancouver, Canada. https://web.media.mit.edu/~kbrennan/files/Brennan_Resnick_AERA2012_CT.pdf

Burkhardt, H. & Bell, A. (2007). Problem solving in the United Kingdom. ZDM, 39 (5), 395-403. https://doi.org/10.1007/s11858-007-0041-4

Cai, J., Wang, N., Moyer, J. C., Wang, C. & Nie, B. (2011). Longitudinal investigation of the curricular effect: an analysis of student learning outcomes from the LieCal Project in the United States. International Journal of Educational Research, 50 (2), 117-136. https://doi.org/10.1016/j.ijer.2011.06.006

Calder, N. (2018). Using Scratch to facilitate mathematical thinking. Waikato Journal of Education, 23 (2), 43-58. https://doi.org/10.15663/wje.v23i2.654

Carreira, S. & Jacinto, H. (2019). A model of mathematical problem solving with technology: the case of Marco solving-and-expressing two geometry problems. In P. Liljedahl & M. Santos-Trigo (Eds.), Mathematical problem solving: current themes, trends, and research (pp. 41-62). Springer Nature. https://doi.org/10.1007/978-3-030-10472-6_3

Cui, Z. & Ng, O.-L. (2021). The interplay between mathematical and computational thinking in primary school students' mathematical problem- solving within a programming environment. Journal of Educational Computing Research, 59 (5), 988-1012. https://doi.org/10.1177/0735633120979930

Directorate of Education. (2020). Nye læreplaner - grunnskolen. https://www.udir.no/laring-og-trivsel/lareplanverket/Nye-lareplaner-i-grunnskolen-og-gjennomgaende-fag-vgo/

English, L. D. & Gainsburg, J. (2015). Problem solving in a 21st-century mathematics curriculum. In L. D. English & D. Kirshner (Eds.), Handbook of international research in mathematics education (3rd ed., pp. 313-335). Routledge. https://doi.org/10.4324/9780203448946-20

Geraniou, E. & Jankvist, U. T. (2019). Towards a definition of "mathematical digital competency". Educational Studies in Mathematics, 102 (1), 29-45. https://doi.org/10.1007/s10649-019-09893-8

Green, W. H. & Gilhooly, K. (2005). Problem solving. In N. Braisby & A. Gellatly (Eds.), Cognitive psychology (2nd ed., pp. 301-333). Oxford University Press. https://doi.org/10.4324/9780203978733-13

Grover, S. & Pea, R. (2013). Computational thinking in K-12: a review of the state of the field. Educational Researcher, 42 (1), 38-43. https://doi.org/10.3102/0013189X12463051

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. Suurtamm (Eds.), International perspectives on mathematics curriculum (pp. 41-70). International Age. https://hal.archives-ouvertes.fr/hal-01599059

Haddaway, N. R., Collins, A. M., Coughlin, D. & Kirk, S. (2015). The role of Google scholar in evidence reviews and its applicability to grey literature searching. PLoS ONE, 10 (9). https://doi.org/10.1371/journal.pone.0138237

Hambrusch, S., Hoffmann, C., Korb, J. T., Haugan, M. & Hosking, A. L. (2009). A multidisciplinary approach towards computational thinking for science majors. ACM SIGCSE Bulletin, 41 (1), 183-187. https://doi.org/10.1145/1539024.1508931

Heintz, F., Mannila, L., Nordén, L.-Å., Parnes, P. & Regnell, B. (2017). Introducing programming and digital competence in Swedish K-9 education. In V. Dagiené & 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

Hemmi, K., Krzywacki, H. & Partanen, A.-M. (2017). Mathematics curriculum: the case of Finland. In D. R. Thompson, M. A. Huntley & C. Suurtamm (Eds.), International perspectives on mathematics curriculum (pp. 71-102). Information Age.

Hsu, T.-C., Chang, S.-C. & Hung, Y.-T. (2018). How to learn and how to teach computational thinking: suggestions based on a review of the literature. Computers & Education, 126, 296-310. https://doi.org/10.1016/j.compedu.2018.07.004

Ioannidou, A., Bennett, V., Repenning, A., Koh, K. H. & Basawapatna, A. (2011). Computational thinking patterns. Paper presented at AERA 2011, New Orleans, United States. https://files.eric.ed.gov/fulltext/ED520742.pdf

Israel, M., Pearson, J. N., Tapia, T., Wherfel, Q. M. & Reese, G. (2015). Supporting all learners in school-wide computational thinking: A cross-case qualitative analysis. Computers & Education, 82, 263-279. https://doi.org/10.1016/j.compedu.2014.11.022

Jäder, J., Lithner, J. & Sidenvall, J. (2020). Mathematical problem solving in textbooks from twelve countries. International Journal of Mathematical Education in Science and Technology, 51 (7), 1120-1136. https://doi.org/10.1080/0020739X.2019.1656826

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

Kaufmann, O. T. & Stenseth, B. (2021). Programming in mathematics education. International Journal of Mathematical Education in Science and Technology, 52 (7), 1029-1048. https://doi.org/10.1080/0020739X.2020.1736349

Kurland, D. M. & Pea, R. D. (1985). Children's mental models of recursive Logo programs. Journal of Educational Computing Research, 1 (2), 235-243. https://doi.org/10.2190/JV9Y-5PD0-MX22-9J4Y

Kurland, D. M., Pea, R. D., Clement, C. & Mawby, R. (1986). A study of the development of programming ability and thinking skills in high school students. Journal of Educational Computing Research, 2 (4), 429-458. https://doi.org/10.2190/BKML-B1QV-KDN4-8ULH

Lester, F. K. & Cai, J. (2016). Can mathematical problem solving be taught? Preliminary answers from 30 years of research. In P. Felmer, E. Pehkonen & J. Kilpatrick (Eds.), Posing and solving mathematical problems: advances and new perspectives (pp. 117-135). Springer. https://doi.org/10.1007/978-3-319-28023-3_8

Liljedahl, P. & Cai, J. (2021). Empirical research on problem solving and problem posing: a look at the state of the art. ZDM, 53 (4), 723-735. https://doi.org/10.1007/s11858-021-01291-w

Lye, S. Y. & Koh, J. H. L. (2014). Review on teaching and learning of computational thinking through programming: What is next for K-12? Computers in Human Behavior, 41, 51-61. https://doi.org/10.1016/j.chb.2014.09.012

Martin, A. & Grudziecki, J. (2006). DigEuLit: concepts and tools for digital literacy development. Innovation in Teaching and Learning in Information and Computer Sciences, 5 (4), 249-267. https://doi.org/10.11120/ital.2006.05040249

Ng, O.-L. & Cui, Z. (2021). Examining primary students' mathematical problem-solving in a programming context: towards computationally enhanced mathematics education. ZDM, 53(4), 847-860. https://doi.org/10.1007/s11858-020-01200-7

Niss, M. & Højgaard, T. (2002). Kompetencer og matematiklæring: ideer og inspiration til udvikling af matematikundervisning i Danmark. Undervisningsministeriets forlag. http://static.uvm.dk/publikationer/2002/kom/hel.pdf

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. (2022a). Computational thinking in the primary mathematics classroom: a systematic review. Digital Experiences in Mathematics Education, 8, 27-49. https://doi.org/10.1007/s40751-022-00102-5

Nordby, S. K., Bjerke, A. H. & Mifsud, L. (2022b). Primary mathematics teachers' understanding of computational thinking. KI - Künstliche Intelligenz, 36, 35-46. https://doi.org/10.1007/s13218-021-00750-6

Noss, R. & Hoyles, C. (1996). Windows on mathematical meanings: learning cultures and computers (vol. 17). Springer. https://doi.org/10.1007/978-94-009-1696-8

Papert, S. (1980). Mindstorms. Harvester Press.

Papert, S. (1996). An exploration in the space of mathematics educations. International Journal of Computers for Mathematical Learning, 1 (1), 95-123. https://doi.org/10.1007/BF00191473

Pei, C., Weintrop, D. & Wilensky, U. (2018). Cultivating computational thinking practices and mathematical habits of mind in Lattice land. Mathematical Thinking and Learning, 20 (1), 75-89. https://doi.org/10.1080/10986065.2018.1403543

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

Polya, G. (1954). How to solve it: a new aspect of mathematical method. Doubleday Anchor Books.

Psycharis, S. & Kallia, M. (2017). The effects of computer programming on high school students' reasoning skills and mathematical self-efficacy and problem solving. Instructional Science, 45 (5), 583-602. https://doi.org/10.1007/s11251-017-9421-5

Resnick, M., Maloney, J., Monroy-Hernández, A., Rusk, N., Eastmond, E.et al. (2009). Scratch: programming for all. Communications of the ACM, 52 (11), 60-67. https://doi.org/10.1145/1592761.1592779

Rodríguez-Martínez, J. A., González-Calero, J. A. & Sáez-López, J. M. (2019). Computational thinking and mathematics using Scratch: an experiment with sixth-grade students. Interactive Learning Environments, 28 (3), 316-327. https://doi.org/10.1080/10494820.2019.1612448

Santos-Trigo, M. (2019). Mathematical problem solving and the use of digital technologies. In P. Liljedahl & M. Santos-Trigo (Eds.), Mathematical problem solving: current themes, trends, and research (pp. 63-89). Springer. https://doi.org/10.1007/978-3-030-10472-6_4

Schoenfeld, A. H. (1985). Mathematical problem solving. Academic Press.

Selby, C. & Woollard, J. (2013). Computational thinking: the developing definition. University of Southampton. https://eprints.soton.ac.uk/356481/

Shute, V. J., Sun, C. & Asbell-Clarke, J. (2017). Demystifying computational thinking. Educational Research Review, 22, 142-158. https://doi.org/10.1016/j.edurev.2017.09.003

Sneider, C., Stephenson, C., Schafer, B. & Flick, L. (2014). Exploring the science framework and NGSS: computational thinking in the science classroom. Science Scope, 38 (3), 10-15. https://doi.org/10.2505/4/ss14_038_03_10

Voogt, J., Fisser, P., Good, J., Mishra, P. & Yadav, A. (2015). Computational thinking in compulsory education: towards an agenda for research and practice. Education and Information Technologies, 20 (4), 715-728. https://doi.org/10.1007/s10639-015-9412-6

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

Wing, J. (2006). Computational thinking. Communications of the ACM, 49 (3), 33-35. https://doi.org/10.1145/1118178.1118215

Wing, J. (2008). Computational thinking and thinking about computing, Philosophical Transactions of the Royal Society of London: a Mathematical, Physical and Engineering Sciences, 366, 3717-3725. https://doi.org/10.1098/rsta.2008.0118

Wing, J. (2011). Research notebook: computational thinking - What and why? Carnegie Mellon University. https://www.cs.cmu.edu/link/research-notebook-computational-thinking-what-and-why

Zhang, L. & Nouri, J. (2019). A systematic review of learning computational thinking through Scratch in K-9. Computers & Education, 141, 1-25. https://doi.org/10.1016/j.compedu.2019.103607

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Published

2024-11-19

How to Cite

Stavenæs Refvik, K. A., & Bjerke, A. H. (2024). Computational thinking as a tool in primary and secondary mathematical problem solving: a literature review. NOMAD Nordic Studies in Mathematics Education, 27(3), 5–27. Retrieved from https://tidsskrift.dk/NOMAD/article/view/149191

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