Abstract
Programming is an interdisciplinary practice with applications in both mathematics and computer science. Mathematics concerns rigor, abstraction, and generalization. Computer science predominantly concerns efficiency, concreteness, and physicality. This makes programming a medium for problem solving that mediates between mathematics and computer science in intriguing ways. Behind programming practices is computational thinking (CT), a mode of thinking involved in formulating and solving problems so that the solutions could be represented and carried out by computing means. In this paper, CT is seen as a boundary object connecting mathematics and computer science in a school problem-solving context. In particular, we examine and analyse middle school students’ work upon engaging in mathematical problem solving-in a programming environment, taking CT as a boundary object embedded in the block-based programming environment, Scratch. The analysis is guided by observing boundary crossing features of CT in the students’ artefacts produced in Scratch while solving mathematical problems related to symmetry and arithmetic sequence. The findings of this study open up new dimensions to explore CT as a boundary object in integrated STEM pedagogy.
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References
Aho, A. V. (2012). Computation and computational thinking. The Computer Journal, 55(7), 832–835. https://doi.org/10.1093/comjnl/bxs074.
Baldwin, D., Walker, H. M., & Henderson, P. B. (2013). The roles of mathematics in computer science. ACM Inroads, 4(4), 74–80. https://doi.org/10.1145/2537753.2537777
Benton, L., Hoyles, C., Kalas, I., & Noss, R. (2017). Bridging primary programming and mathematics: some findings of design research in England. Digital Experience in Math Education, 3, 115–138. https://doi.org/10.1007/s40751-017-0028-x
Brennan, K., & Resnick, M. (2012). New frameworks for studying and assessing the development of computational thinking. In Proceedings of the 2012 Annual Meeting of the American Educational Research Association (Vol. 1, pp. 1–25). AERA. http://scratched.gse.harvard.edu/ct/files/AERA2012.pdf.
Cetin, I., & Dubinsky, E. (2017). Reflective abstraction in computational thinking. The Journal of Mathematical Behavior, 47, 70–80. https://doi.org/10.1016/j.jmathb.2017.06.004.
Cui, Z., & Ng, O. (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.
Dickes, A. C., Farris, A. V., & Sengupta, P. (2020). Sociomathematical norms for integrating coding and modeling with elementary science: A dialogical approach. Journal of Science Education and Technology, 29(1), 35–52. https://doi.org/10.1007/s10956-019-09795-7.
diSessa, A. (2001). Changing minds: computers, learning, and literacy. MIT Press.
diSessa, A. A., & Cobb, P. (2004). Ontological innovation and the role of theory in design experiments. The journal of the learning sciences, 13(1), 77–103. https://doi.org/10.1207/s15327809jls1301_4.
Duval, R. (1998). Geometry from a cognitive point of view. In C. Mammana & yV. Villani (Eds.), Perspectives on the teaching of geometry for the 21st century (pp. 37–51). Kluwer Academic Publishers.
Ehsan, H., Rehmat, A. P., & Cardella, M. E. (2021). Computational thinking embedded in engineering design: capturing computational thinking of children in an informal engineering design activity. International Journal of Technology and Design Education, 31(3), 441–464. https://doi.org/10.1007/s10798-020-09562-5
English, L. D. (2016). STEM education K-12: perspectives on integration. International Journal of STEM education, 3(1), 1–8. https://doi.org/10.1186/s40594-016-0036-1
Gadanidis, G., Clements, E., & Yiu, C. (2018). Group theory, computational thinking, and young mathematicians. Mathematical Thinking and Learning, 20(1), 32–53.
Hoppe, H. U., & Werneburg, S. (2019). Computational thinking—more than a variant of scientific inquiry! In S. C. Kong & H. Abelson (Eds.), Computational thinking education (pp. 13–30). Springer.
Juardak, M. (2016). Learning and teaching real world problem solving in school mathematics: a multiple perspective framework for crossing the boundary. Springer International Publishing.
Jurado, E., Fonseca, D., Coderch, J., & Canaleta, X. (2020). Social STEAM learning at an early age with robotic platforms: a case study in four schools in Spain. Sensors (Basel, Switzerland), 20(13), 3698. https://doi.org/10.3390/s20133698
Kalelioglu, F., Gulbahar, Y., & Kukul, V. (2016). A framework for computational thinking based on a systematic research review. Baltic Journal of Modern Computing, 4(3), 583–596.
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.
Leung, A. (2020). Boundary crossing pedagogy in STEM education. International Journal of STEM Education, 7(1), 15. https://doi.org/10.1186/s40594-020-00212-9.
Leung, A. (2021). Realizing STEM Heuristic in a Mathematics Problem Solving Activity. In D. Anderson, M. Milner-Bolotin, R. Santos, & S. Petrina (Eds.), Proceedings of the 6th International STEM in Education Conference (STEM 2021). (pp. 242–248). University of British Columbia. https://doi.org/10.14288/1.0402129.
Ling, D. M. K., & Loh, S. C. (2021). Relationships between cognitive pattern recognition and specific mathematical domains in mathematics education. International Journal of Mathematical Education in Science and Technology https//. https://doi.org/10.1080/0020739X.2021.1949059.
Miller, J. (2019). STEM education in the primary years to support mathematical thinking: using coding to identify mathematical structures and patterns. ZDM Mathematics Education, 51(6), 915–927. https://doi.org/10.1007/s11858-019-01096-y
Muñoz, L., Villarreal, V., Morales, I., Gonzalez, J., & Nielsen, M. (2020). Developing an interactive environment through the teaching of mathematics with small robots. Sensors (Basel, Switzerland), 20(7), 1935. https://doi.org/10.3390/s20071935.
Ng, O., & Cui, Z. (2021). Examining primary students’ mathematical problem-solving in a programming context: Towards computationally enhanced mathematics education. ZDM Mathematics Education, 53(4), 847–860. https://doi.org/10.1007/s11858-020-01200-7
Ng, O., Liu, M., & Cui, Z. (2021). Students’ in-moment challenges and developing maker perspectives during problem-based digital making. Journal of Research on Technology in Education. https://doi.org/10.1080/15391523.2021.1967817
Noss, R., & Hoyles, C. (1992). Looking back and looking forward. In C. Hoyles & R. Noss (Eds.), Learning mathematics and logo (pp. 431–468). The MIT Press.
Pólya, G. (1945). How to Solve it?. Princeton, NJ: Princeton University Press.
Rodríguez-Martínez, J. A., González-Calero, J. A., & Sáez-López, J. M. (2020). 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
Sengupta, P., Kinnebrew, J. S., Basu, S., Biswas, G., & Clark, D. (2013). Integrating computational thinking with K-12 science education using agent-based computation: a theoretical framework. Education and Information Technologies, 18(2), 351–380. https://doi.org/10.1007/s10639-012-9240-x
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.
Sinclair, N., & Patterson, M. (2018). The dynamic geometrisation of computer programming. Mathematical Thinking and Learning, 20(1), 54–74. https://doi.org/10.1080/10986065.2018.1403541.
Star, S. L., & Griesemer, J. R. (1989). Institutional ecology, ‘translations’ and boundary objects: amateurs and professionals in Berkeley’s Museum of Vertebrate Zoology, 1907-39. Social Studies of Science, 19(3), 387–420. https://doi.org/10.1177/030631289019003001
Vasquez, J., Sneider, C., & Comer, M. (2013). STEM lesson essentials, grades 3–8: Integrating science, technology, engineering, and mathematics. Heinemann.
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. 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. (2011). Research notebook: computational thinking—what and why. The Link Magazine, 6, 20–23.
Wolfram, C. (2010). Teaching kids real math with computers [TED Talk]. https://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers
Ye, H., Liang, B., Ng, O., & Chai, C. S. (2023). Integration of computational thinking in K-12 mathematics education: a systematic review on CT-based mathematics instruction and student learning. International Journal of STEM Education, 10(1), 1–26. https://doi.org/10.1186/s40594-023-00396-w
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This work was supported by the Research Grants Council, General Research Fund (Reference No. 14603720).
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Ng, OL., Leung, A. & Ye, H. Exploring computational thinking as a boundary object between mathematics and computer programming for STEM teaching and learning. ZDM Mathematics Education 55, 1315–1329 (2023). https://doi.org/10.1007/s11858-023-01509-z
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DOI: https://doi.org/10.1007/s11858-023-01509-z