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Using Grey-based Mathematical Equations of Decision-making as Teaching Scaffolds: from an Unplugged Computational Thinking Activity to Computer Programming

Meng-Leong How, Chee-Kit Looi


Computational Thinking (CT) is pervasive in our daily lives and is useful for problem-solving. Decision-making is a crucial part of problem-solving. In the extant literature, problem-solving strategies in educational settings are often conveniently attributed to intuition; however, it is well documented that computer programmers might even have difficulty describing about their intuitive insights during problem-solving using natural language (such as English), and subsequently convert what has been described using words into software code. Hence, a more analytical approach using mathematical equations and descriptions of CT is offered in this paper as a potential form of rudimentary scaffolding, which might be useful to facilitators and learners of CT-related activities. In the present paper, the decision-making processes during an unplugged CT activity are delineated via Grey-based mathematical equations, which is useful for informing educators who may wish to explain to their learners about the various aspects of CT which are involved in the unplugged activity and simultaneously use these mathematical equations as scaffolds between the unplugged activity and computer code programming. This theoretical manuscript may serve as a base for learners, should the facilitator ask them to embark on a software programming activity that is closely associated to the unplugged CT activity.


grey-based mathematical equations; decision making; computational thinking; scaffolding for teaching; computer software programming; unplugged computational thinking activity


Barr, D., Harrison, J., & Conery, L. (2011). Computational Thinking: A Digital Age Skill for Everyone. Learning and Leading with Technology, 38(6), 20–23.

Bell, T., Alexander, J., Freeman, I., & Grimley, M. (2009). Computer Science Unplugged: School Students Doing Real Computing Without Computers. Journal of Applied Computing and Information Technology, 13(1), 20–29.

Boticki, I., Barisic, A., Martin, S., & Drljevic, N. (2013). Teaching and learning computer science sorting algorithms with mobile devices: A case study. Computer Applications in Engineering Education, 21, 41–50.

Brown, J. P. (2015). Visualisation Tactics for Solving Real World Tasks. (G. A. Stillman, W. Blum, & M. S. Biembengut, Eds.), Mathematical Modelling in Education Research and Practice: Cultural, Social and Cognitive Influences.

Brownlee, J. (2016). Making Predictions with Sequences. Retrieved February 6, 2018, from

Bundy, A. (2007). Computational Thinking is Pervasive. Journal of Scientific and Practical Computing, 1(2), 67–69.

Busemeyer, J. R., & Johnson, J. G. (2004). Computational models of decision making. In Blackwell handbook of judgment and decision making (pp. 133–154).

Cetin, I., & Dubinsky, E. (2017). Reflective abstraction in computational thinking. Journal of Mathematical Behavior, 47(November 2016), 70–80.

Chung, T. J. (2010). Computational fluid dynamics. Cambridge university press.

Cortina, T. J. (2015). Broadening Participation: Reaching a broader population of students through “unplugged†activities. Communications of the ACM, 58(3), 25–27.

Curzon, P., McOwan, P. W. P., Plant, N., & Meagher, L. R. (2014). Introducing teachers to computational thinking using unplugged storytelling. Proceedings of the 9th Workshop in Primary and Secondary Computing Education, 89–92.

D’Ambrosio, U. (2015). Mathematical Modelling as a Strategy for Building-Up Systems of Knowledge in Different Cultural Environments. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical Modelling in Education Research and Practice: Cultural, Social and Cognitive Influences (pp. 35–44).

Deng, J. (1989). Introduction to Grey System Theory. The Journal of Grey System, 1, 1–24.

du Boulay, B., O’Shea, T., & Monk, J. (1981). The black box inside the glass box: presenting computing concepts to novices. International Journal of Man-Machine Studies, 14, 237–249.

Feaster, Y., Segars, L., Wahba, S., & Hallstrom, J. (2011). Teaching CS unplugged in the high school (with limited success). ITiCSE, 248–252.

Gouws, L. A., Bradshaw, K., & Wentworth, P. (2013). Computational thinking in educational activities. Proceedings of the 18th ACM Conference on Innovation and Technology in Computer Science Education - ITiCSE ’13, 10.

Griffin, J. M. (2016). Learning by Taking Apart: Deconstructing Code by Reading, Tracing, and Debugging. Proceedings of the 17th Annual Conference on Information Technology Education (SIGITE ’16), 148–153.

Grover, S. (2015). “Systems of Assessments†for Deeper Learning of Computational Thinking in K-12. Annual Meeting of the American Educational Research Association, (650).

Grover, S., Pea, R., & Cooper, S. (2015). Designing for deeper learning in a blended computer science course for middle school students. Computer Science Education, 25(2), 199–237.

Hu, C. (2011). Computational thinking. Proceedings of the 16th Annual Joint Conference on Innovation and Technology in Computer Science Education, ITiCSE ’11, 223–227.

Humphreys, P. (2004). Extending ourselves: Computational science, empiricism, and scientific method. Oxford University Press.

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 and Education, 82, 263–279.

Kawakami, T., Saeki, A., & Matsuzaki, A. (2015). How Do Students Share and Refine Models Through Dual Modelling Teaching: The Case of Students Who Do Not Solve Independently. (G. A. Stillman, W. Blum, & M. S. Biembengut, Eds.), Mathematical Modelling in Education Research and Practice: Cultural, Social and Cognitive Influences.

Kordaki, M., Miatidis, M., & Kapsampelis, G. (2008). A computer environment for the learning of sorting algorithms: Design and pilot evaluation. Computers & Education, 51, 708–723.

Liu, S., & Lin, Y. (2010). Grey Systems: Theory and Applications. Berlin: Springer-Verlag.

Liu, S., Yang, Y., & Forrest, J. (2016). Grey Data Analysis. Singapore: Springer-Verlag.

Lu, J. J., & Fletcher, G. H. L. (2009). Thinking About Computational Thinking. In SIGCSE ’09 Proceedings of the 40th ACM technical symposium on Computer science education (pp. 260–264). Chattanooga, TN, USA.

McGill, T. J., & Volet, S. E. (1997). A Conceptual Framework for Analyzing Students’ Knowledge of Programming. Journal of Research on Computing in Education, 6504(December), 37–41.

Metcalfe, J., & Wiebe, D. (1987). Intuition in insight and noninsight problem solving. Memory & Cognition, 15(3), 238–246.

Monteiro, I. T., Salgado, L. C. de C., Mota, M. P., Sampaio, A. L., & de Souza, C. S. (2016). Signifying software engineering to computational thinking learners with AgentSheets and PoliFacets. Journal of Visual Languages and Computing, (February 2016), 1–21.

Ng, K. E. D., & Stillman, G. A. (2015). Exploring Interconnections Between Real-World and Application Tasks: Case Study from Singapore. (G. A. Stillman, W. Blum, & M. S. Biembengut, Eds.), Mathematical Modelling in Education Research and Practice: Cultural, Social and Cognitive Influences.

Oxford Living Dictionaries. (2017). Countermeasure. Retrieved December 4, 2017, from

Pretz, J. E. (2008). Intuition versus analysis: Strategy and experience in complex everyday problem solving. Memory & Cognition, 36(3), 554–566.

Reber, P., & Kotovsky, K. (1997). Implicit learning in problem solving: The role of working memory capacity. Journal of Experimental Psychology: General, 126(2), 178.

Rodriguez, B. R. (2015). Assessing Computational Thinking in Computer Science Unplugged Activities. Thesis- Colorado School of Mines in Partial Fulfillment of the Requirements for the Degree of Master of Science (Computer Science)., 1, 1–136.

Selby, C. (2013). Computational Thinking : The Developing Definition. ITiCSE Conference 2013, 5–8.

Selby, C. (2015). Relationships: Computational Thinking, Pedagogy of Programming, and Bloom’s Taxonomy. Proceedings of the Workshop in Primary and Secondary Computing Education, 80–87.

Somers, J. (2017). The Coming Software Apocalypse A small group of programmers wants to change how we code—before catastrophe strikes. Retrieved October 3, 2017, from

Stillman, G. A., Blum, W., & Biembengut, M. S. (Eds.). (2015). Mathematical Modelling in Education Research and Practice: Cultural, Social and Cognitive Influences.

Taub, R., Armoni, M., & Ben-Ari, M. (2012). CS Unplugged and Middle-School Students’ Views, Attitudes, and Intentions Regarding CS. ACM Transactions on Computing Education, 12(2), 1–29.

Taylor, D. W. (2013). Decision making and problem solving. In Handbook of organizations (pp. 48–86).

Thies, R., & Vahrenhold, J. (2013). On plugging “unplugged†into CS classes. Proceeding of the 44th ACM Technical Symposium on Computer Science Education - SIGCSE ’13, 365–370.

Thies, R., & Vahrenhold, J. B. (2012). Reflections on outreach programs in CS classes: Learning objectives for “unplugged†activities. SIGCSE12 Proceedings of the 43rd ACM Technical Symposium on Computer Science Education, 487–492.

Ugur, Ö. (2008). An introduction to computational finance. World Scientific Books.

Waterman, M. S. (1995). Introduction to computational biology: maps, sequences and genomes. CRC Press.

Weintrop, D., Beheshti, E., Horn, M., Orton, K., Jona, K., Trouille, L., & Wilensky, U. (2016). Defining Computational Thinking for Mathematics and Science Classrooms. Journal of Science Education and Technology, 25(1), 127–147.

Wing, J. (2008). Computational thinking and thinking about computing. Philosophical Transactions of the Royal Society of London: Mathematical, Physical and Engineering Sciences, (July), 3717–3725.

Wing, J. M. (2006). Computational Thinking. Communications of the ACM, 49(3), 33–35.

Wolfram Research Incorporated. (2017). Mathematica, Version 11.2, (2017). Champaign, IL.

Zagami, J. (2012). Seeing is understanding: The effect of visualisation in understanding programming concepts.

Zsambok, C. E. (2014). Naturalistic decision making. Chicago: Psychology Press.

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DOI: 10.21585/ijcses.v2i2.24


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