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Digital Experiences in Mathematics Education

, Volume 3, Issue 2, pp 154–171 | Cite as

A Pedagogical Framework for Computational Thinking

  • Donna KotsopoulosEmail author
  • Lisa Floyd
  • Steven Khan
  • Immaculate Kizito Namukasa
  • Sowmya Somanath
  • Jessica Weber
  • Chris Yiu
Mathematics and Programming

Abstract

Our goal in this paper is to propose a Computational Thinking Pedagogical Framework (CTPF), developed from constructionism and social-constructivism theories. CTPF includes four pedagogical experiences: (1) unplugged, (2) tinkering, (3) making, and (4) remixing. Unplugged experiences focus on activities implemented without the use of computers. Tinkering experiences primarily involve activities that take things apart and engaging in changes and/or modifications to existing objects. Making experiences involve activities where constructing new objects is the primary focus. Remixing refers to those experiences that involve the appropriation of objects or components of objects for use in other objects or for other purposes. Objects can be digital, tangible, or even conceptual. These experiences reflect distinct yet overlapping CT experiences which are all proposed to be necessary in order for students to fully experience CT. In some cases, particularly for novices and depending on the concepts under exploration, a sequential approach to these experiences may be helpful.

Keywords

Computational thinking Experiences Mathematics Making Pedagogical Remixing Tinkering Unplugged 

Notes

Acknowledgements

This paper was based on the Namukasa et al. (2015) working group report from the Math + Coding Symposium, Western University, London, Canada. We would like to acknowledge the early contributions of Yasmin B. Kafai and Laura Morrison, and the feedback from George Gadanidis. This research was funded by a Social Sciences and Humanities Research Council grant to George Gadanidis, Donna Kotsopoulos, and Immaculate Kizito Namukasa.

References

  1. Arduino (2016). Arduino. Retrieved August 14, 2016, from https://www.arduino.cc/.
  2. 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.CrossRefGoogle Scholar
  3. Berry, M. (2013). Computing in the national curriculum. A guide for primary teachers. Bedford: Computing at School.Google Scholar
  4. Bers, M. U., & Horn, M. S. (2010). Tangible programming in early childhood. In R. Berson & M. J. Berson (Eds.), High tech tots: Childhood in a digital world (pp. 49–69). Charlotte: IAP.Google Scholar
  5. Bowler, L. (2014). Creativity through "maker" experiences and design thinking in the education of librarians. Knowledge Quest, 42(5), 58–61.Google Scholar
  6. Brennan, K., & Resnick, M. (2012). New frameworks for studying and assessing the development of computational thinking. Paper presented at the American Educational Research Association. Canada: British Columbia.Google Scholar
  7. British Columbia Government. (2016). $6 million to help connect students with coding, new curriculum and computers. Retrieved August 11, 2016, from https://news.gov.bc.ca/releases/2016PREM0065-000994.
  8. Statistics Canada. (2013). Canadian internet use survey, 2012. Retrieved June 29, 2015, from http://www.statcan.gc.ca/daily-quotidien/131126/dq131126d-eng.htm.
  9. Colton, J. S. (2016). Revisiting digital sampling rhetorics with an ethics of care. Computers and Composition, 40, 19–31.CrossRefGoogle Scholar
  10. Corral, J. M. R., Balcells, A. C., Estévez, A. M., Moreno, G. J., & Ramos, M. J. F. (2014). A game-based approach to the teaching of object-oriented programming languages. Computers & Education, 73(83–92).Google Scholar
  11. Curzon, P. (2013). cs4fn and computational thinking unplugged. WiPSE ‘13 Proceedings of the 8th Workshop in Primary and Secondary Computing Education, 47–50.Google Scholar
  12. Curzon, P., McOwan, P., Plant, N., & Meagher, L. (2014). Introducing teachers to computational thinking using unplugged storytelling. WiPSCE’14 Proceedings of the 9th Workshop in Primary and Secondary Computing Education, 89–92.Google Scholar
  13. Dasgupta, S., Hale, W., Monroy-Hernandez, A., & Hill, B. M. (2016). Remixing as a pathway to computational thinking. Paper presented at the Proceedings of the 19th ACM Conference on Computer-Supported Cooperative Work & Social Computing.Google Scholar
  14. Davis, B. (2014). Toward a more power-full school mathematics. For the Learning of Mathematics, 34(1), 12–17.Google Scholar
  15. Dougherty, D. (2012). The maker movement. Innovations, 7(3), 11–14.CrossRefGoogle Scholar
  16. Farr, W., Yuill, N., & Raffle, H. (2010). Social benefits of a tangible user interface for children with autistic spectrum conditions. Autism, 14(3), 237–252.CrossRefGoogle Scholar
  17. Freiberger, M. (2016). Primes without 7 [Electronic Version]. +plus magazine. Retrieved August 11, 2016, from https://plus.maths.org/content/missing-7s.
  18. Gadanidis, G. (2015). Coding as a Trojan horse for mathematics education reform. Journal of Computers in Mathematics and Science Teaching, 34(2), 155–173.Google Scholar
  19. Gadanidis, G., Hughes, J. M., Minniti, L., & White, B. J. G. (2016). Computational thinking, grade 1 students and the binomial theorem [electronic version]. Digital Experiences in Mathematics Education. doi: 10.1007/s40751-016-0019-3.Google Scholar
  20. Govender, I., & Grayson, D. J. (2008). Pre-service and in-service teachers' experiences of learning to program in an object-oriented language. Computers & Education, 51(2), 874–885.CrossRefGoogle Scholar
  21. Government of England. (2013). National curriculum in England: Computing programmes of study. Retrieved June 29, 2015, from https://www.gov.uk/government/publications/national-curriculum-in-england-computing-programmes-of-study.
  22. Horn, M. S., Crouser, R. J., & Bers, M. U. (2012). Tangible interaction and learning: The case for a hybrid approach. Personal and Ubiquitous Computing, 16(4), 379–389.CrossRefGoogle Scholar
  23. Hoyles, C., & Noss, R. (2015). Revisiting programming to enhance mathematics learning, Math + Coding Symposium. Western University: Western University. London.Google Scholar
  24. Hughes, J., Gadanidis, G., & Yiu, C. (2016). Digital making in elementary mathematics education [electronic version]. Digital Experiences in Mathematics Education. doi: 10.1007/s40751-016-0020-x.Google Scholar
  25. Kafai, Y. B. (2015). Connected code: A new agenda for K-12 programming in classrooms, clubs, and communities. Paper presented at the Math + Coding Symposium: Western University, London.Google Scholar
  26. Kafai, Y. B., & Burke, Q. (2013). Computer programming goes back to school. Phi Delta Kappan, 95(1), 61.CrossRefGoogle Scholar
  27. Kazakoff, E. R., Sullivan, A., & Bers, M. U. (2013). The effect of a classroom-based intensive robotics and programming workshop on sequencing ability in early childhood. Early Childhood Education Journal, 41(4), 245–255.CrossRefGoogle Scholar
  28. Kwon, D.-Y., Kim, H.-S., Shim, J.-K., & Lee, W.-G. (2012). Algorithmic bricks: A tangible robot programming tool for elementary school students. IEEE Transactions on Education 55, 4(11), 474–479.CrossRefGoogle Scholar
  29. Lamagna, E. (2015). Algorithmic thinking unplugged. Journal of Computing Sciences in Colleges, 30(6), 45–52.Google Scholar
  30. Lambert, L., & Guiffre, H. (2009). Computer science outreach in an elementary school. Journal of Computing Sciences in Colleges, 24(3), 118–124.Google Scholar
  31. LeMay, S., Costantino, T., O’Connor, S., & ContePitcher, E. (2014). Screen time for children. IDC’14 Proceedings of the 2014 conference on Interaction design and children, 217–220.Google Scholar
  32. Lifelong Kindergarten Group at the MIT Media Lab. (2016). Scratch. Retrieved August 11, 2016, from https://scratch.mit.edu/.
  33. Liu, C., Liu, K., Wang, P., Chen, G., & Su, M. (2012). Applying tangible story avatars to enhance children's collaborative storytelling. British Journal of Educational Technology, 43(1), 39–51.CrossRefGoogle Scholar
  34. Lovell, E., & Buechley, L. (2011). LilyPond: An online community for sharing e-textile projects. New York: Paper presented at the Proceedings of the 8th ACM conference on Creativity and Cognition.CrossRefGoogle Scholar
  35. 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.CrossRefGoogle Scholar
  36. Matos, J. (1990). The historical development of the concept of angle. The Mathematics Educator, 1(1), 4–11.Google Scholar
  37. Matos, J. (1991). The historical development of the concept of angle (2). The Mathematics Educator, 2(1), 18–24.Google Scholar
  38. Namukasa, I. K., Kotsopoulos, D., Floyd, L., Weber, J., Kafai, Y. B., Khan, S., et al. (2015). From computational thinking to computational participation: Towards achieving excellence through coding in elementary schools. In G. Gadanidis (Ed.), Math + coding symposium. London: Western University.Google Scholar
  39. Nishida, T., Kanemune, S., Idosaka, Y., Namiki, M., Bell, T., & Kuno, Y. (2009). A CS unplugged design pattern. SIGCSE, 41(1), 231–235.CrossRefGoogle Scholar
  40. O'Sullivan, D., & Igoe, T. (2004). Physical computing: Sensing and controlling the physical world with computers. Boston: Thomson.Google Scholar
  41. Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. New York: Basic Books.Google Scholar
  42. Papert, S. (1987). Constructionism: A new opportunity for elementary science education. Retrieved August 1, 2016, 2016, from http://nsf.gov/awardsearch/showAward?AWD_ID=8751190.
  43. Papert, S., & Harel, I. (1991). Constructionism: Ablex publishing corporation.Google Scholar
  44. Parker, T. (2012). ALICE in the real world. Mathematics Teaching in the Middle School, 17(7), 410.CrossRefGoogle Scholar
  45. Pierce, M. (2013). Coding for middle schoolers: Next-generation programming languages for children are taking up where Logo left off and teaching young students how to code to learn. T H E Journal [Technological Horizons In Education], 40(5), 20+.Google Scholar
  46. Province of Nova Scotia. (2015). Minister announces coding as a priority during education day. Retrieved August 11, 2016, from http://novascotia.ca/news/release/?id=20151021002.
  47. Przybylla, M., & Romeike, R. (2014). Physical computing and its scope - towards a constructionist computer science curriculum with physical computing. Informatics in Education, 13(2), 225–240.CrossRefGoogle Scholar
  48. Resnick, M., Myers, B., Nakakoji, K., Shneiderman, B., Pausch, R., Selker, T., et al. (2005). Design principles for tools to support creative thinking. Washington DC: National Science Foundation workshop on Creativity Support Tools.Google Scholar
  49. Resnick, M., Maloney, J., Monroy-Hernandez, A., Rusk, N., Eastmond, E., Brennan, K., et al. (2009). Scratch: Programming for all. Communications of the ACM, 52(11), 60–67.CrossRefGoogle Scholar
  50. Scarlatos, L. L. (2006). Tangible math. Interactive Technology and Smart Education, 3(4), 293–309.CrossRefGoogle Scholar
  51. Shodiev, H. (2013). Computational thinking and simulation in teaching science and mathematics. Toronto: Paper presented at the Association for Computer Studies Educators Conference.Google Scholar
  52. SITRA. (2014). Future will be built by those who know how to code. Retrieved June 29, 2015, from http://www.sitra.fi/en/artikkelit/well-being/future-will-be-built-those-who-know-how-code.
  53. Smith, C. P., & Neumann, M. D. (2014). Scratch it out! Enhancing geometrical understanding. Teaching Children Mathematics, 21(3), 185–188.CrossRefGoogle Scholar
  54. Sneider, C., Stephenson, C., Schafer, B., & Flick, L. (2014). Exploring the science framework and NGSS: Computational thinking in the science classroom. The Science Teacher, 38(3), 10–15.Google Scholar
  55. Sphero. (2016). Retrieved August 11, 2016, from http://www.sphero.com/about.
  56. Strawhacker, A., & Bers, M. U. (2015). "I want my robot to look for food": Comparing kindergartner's programming comprehension using tangible, graphic, and hybrid user interfaces. International Journal of Technology and Design Education, 25(3), 293–319.CrossRefGoogle Scholar
  57. Sullivan, A., Kazakoff, E. R., & Bers, M. U. (2013). The wheels on the bot go round and round: Robotics curriculum in pre-kindergarten. Journal of Information Technology Education: Innovations in Practice, 12, 203–219.Google Scholar
  58. Taub, T., Armoni, M., & Ben-Ari, M. (2012). CS unplugged and middle-wchool students’ views, attitudes, and intentions regarding CS. ACM Transactions on Computing Education (TOCE), 12(2), 8.Google Scholar
  59. The White House. (2016). Computer science for all. Retrieved August 11, 2016, from https://www.whitehouse.gov/blog/2016/01/30/computer-science-all
  60. Thies, R., & Vahrenhold, J. (2013). On plugging “unplugged” into CS classes. SIGCSE ‘13 Proceeding of the 44th ACM technical symposium on computer science education, 365–270.Google Scholar
  61. Vygotsky, L. S. (1978). Mind in society. Cambridge: Harvard University Press.Google Scholar
  62. Watters, A. (2011a). Scratch: Teaching the difference between creating and remixing [Electronic Version]. Retrieved July 7, 2015, from http://ww2.kqed.org/mindshift/2011/08/11/scratch-teaching-kids-about-programming-teaching-kids-about-remixing/.
  63. Watters, A. (2011b). Scratch: Teaching the difference between creating and remixing 2015, from http://ww2.kqed.org/mindshift/2011/08/11/scratch-teaching-kids-about-programming-teaching-kids-about-remixing/.
  64. Weintrop, D., Beheshti, E., Horn, M., Orton, K., Jona, K., Trouille, L., et al. (2016). Defining computational thinking for mathematics and science classrooms. Journal of Science Education and Technology, 25(1), 127–147.CrossRefGoogle Scholar
  65. Wilkerson-Jerde, M. (2014). Construction, categorization, and consensus: Student generated computational artifacts as a context for disciplinary reflection. Educational Technology Research and Development, 62(1), 99–121.CrossRefGoogle Scholar
  66. Wing, J. M. (2006). Computational thinking and thinking about computing. Communications of the ACM, 49, 33–35.CrossRefGoogle Scholar
  67. Wing, J. M. (2008). Computational thinking and thinking about computing. Philosophical Transactions of the Royal Society A, 366, 3717–3725.CrossRefGoogle Scholar
  68. Yadav, A., Zhou, N., Mayfield, C., Hambrusch, S., & Korb, J. T. (2011). Introducing computational thinking in education courses. SIGCSE, 11, 465–470.Google Scholar
  69. Yiu, C. (2016). Using an Arduino - coding a bicolour LED grid to create math patterns [electronic version] (p. 1). Math + Coding 'Zine: Exploring Math Through Code Retrieved August 16, 2016, from http://researchideas.ca/mc/article-1-title-recent-issue/arduino-math-patterns-on-an-led-matrix/.Google Scholar

Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  • Donna Kotsopoulos
    • 1
    Email author
  • Lisa Floyd
    • 2
  • Steven Khan
    • 3
  • Immaculate Kizito Namukasa
    • 4
  • Sowmya Somanath
    • 5
  • Jessica Weber
    • 6
  • Chris Yiu
    • 7
  1. 1.Faculty of Education and Faculty of Science (Department of Mathematics)Wilfrid Laurier UniversityONCanada
  2. 2.Faculty of EducationWestern University/Thames Valley District School BoardLondonCanada
  3. 3.Faculty of EducationBrock UniversitySt. CatharinesCanada
  4. 4.Faculty of EducationWestern UniversityLondonCanada
  5. 5.Department of Computer ScienceUniversity of CalgaryCalgaryCanada
  6. 6.Waterloo Catholic District School BoardWaterlooCanada
  7. 7.Department of Computer ScienceWestern UniversityLondonCanada

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