Volume 14 · Number 3 · Pages 294–309
Roles and Demands in Constructionist Teaching of Computational Thinking in University Mathematics

Chantal Buteau, Ana Isabel Sacristán & Eric Muller

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Abstract

Context: There seem to be relatively few sustained implementations of microworlds in mathematics instruction. Problem: We explore the roles of and demands on university instructors to create an environment that supports students’ constructionist learning experiences as they design, program, and use interactive environments (i.e., microworlds) for doing mathematics. Method: We draw on the experiences of instructors in programming-based courses implemented since 2001 at Brock University, Canada, as a case study, and use Ruthven’s model on the professional adaptation of classroom practice with technology to guide our analysis of these experiences. Results: We describe how, in adapting to a design of empowering students to engage in programming for authentic mathematical explorations, instructors adopt characteristics of constructionist teaching that, nevertheless, demand expertise, a shift in traditional roles, and time from instructors. Implications: The results contribute to our understanding of roles of and demands on “ordinary” instructors in classrooms, who aim to create rich environments for supporting students’ constructionist learning experiences of computational thinking for mathematics. Constructivist content: The teaching approach aligns with Papert’s constructionism: a constructivist learning theory, but also a pedagogical paradigm. However, the approach presented has two salient characteristics: it is a university-level constructionist implementation, and it is a sustained long-term authentic classroom implementation. The focus is on the roles of and demands on instructors in that kind of implementation. Through the analysis using Ruthven’s work, we enrich our understanding of constructionist teaching features.

Key words: Computational thinking, constructionism, mathematics, programming, microworlds, university, teachers.

Citation

Buteau C., Sacristán A. I. & Muller E. (2019) Roles and demands in constructionist teaching of computational thinking in university mathematics. Constructivist Foundations 14(3): 294–309. https://constructivist.info/14/3/294

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References

Artigue M. (2002) Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning 7(3): 245–274. ▸︎ Google︎ Scholar
Assude T. (2009) Teachers’ practices and degree of ICT integration. In: Pitta-Pantazi D. & Philippou G. N. (eds.) Proceedings of the fifth congress of the European Society for Research in Mathematics Education. Department of Education, University of Cyprus, Larnaka, Cyprus: 1339–1348. ▸︎ Google︎ Scholar
Barabé G. & Proulx J. (2017) Révolutionner l’enseignement des mathématiques: Le projet visionnaire de Seymour Papert. For the Learning of Mathematics 37(2): 25–30. ▸︎ Google︎ Scholar
eds.) (2004) Undergraduate programs and courses in the mathematical sciences: CUPM curriculum guide 2004. Mathematical Association of America, Washington DC. ▸︎ Google︎ Scholar
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. Volume 1. AREA, Washington DC: 25. http://web.media.mit.edu/~kbrennan/files/Brennan_Resnick_AERA2012_CT.pdf
Broley L., Buteau C. & Muller E. (2017) (Legitimate peripheral) computational thinking in mathematics. In: Dooley T. & Gueudet G. (eds.) Proceedings of the tenth congress of the European Society for Research in Mathematics Education (CERME 10) DCU Institute of Education & ERME, Dublin, Ireland: 2515–2523. ▸︎ Google︎ Scholar
Burns R. B. & Anderson L. W. (1987) The activity structure of lesson segments. Curriculum Inquiry 17(1): 31–53. ▸︎ Google︎ Scholar
Burns R. B. & Lash A. A. (1986) A comparison of activity structures during basic skills and problem-solving instruction in seventh-grade mathematics. American Educational Research Journal 23(3): 393–414. ▸︎ Google︎ Scholar
Buteau C. & Muller E. (2010) Student development process of designing and implementing exploratory and learning objects. In: Durand-Guerrier V., Soury-Lavergne S. & Arzarello F. (eds.) Proceedings of the sixth congress of the European Society for Research in Mathematics Education (CERME 6) INRP and ERME, Lyon, France: 1111–1120. ▸︎ Google︎ Scholar
Buteau C. & Muller E. (2014) Teaching roles in a technology intensive core undergraduate mathematics course. In: Clark-Wilson A., Robutti O. & Sinclair N. (eds.) The mathematics teacher in the digital era. Springer, Dordrecht: 163–185. ▸︎ Google︎ Scholar
Buteau C. & Muller E. (2016) Assessment in undergraduate programming-based mathematics courses. Digital Experiences in Mathematics Education 3(2): 97–114. ▸︎ Google︎ Scholar
Buteau C., Mgombelo J., Muller E., Rafiepour A. & Sacristán A. (2018) Authentic task features for computational thinking in mathematics. In: Proceedings of the 5th ERME topic conference MEDA 2018. University of Copenhagen & ERME, Copenhagen: 301–302. ▸︎ Google︎ Scholar
Buteau C., Muller E. & Marshall N. (2015) When a university mathematics department adopted core mathematics courses of an unintentionally constructionist nature: Really? Digital Experiences in Mathematics Education 1(2–3): 133–155. ▸︎ Google︎ Scholar
Buteau C., Muller E. & Ralph B. (2015) Integration of programming in the undergraduate mathematics program at Brock University. In: Online Proceedings of math+coding symposium, London ON. http://www.researchideas.ca/coding/docs/ButeauMullerRalph-Coding+MathProceedings-FINAL.pdf
Buteau C., Muller E., Dreise K., Mgombelo J. & Sacristán A. I. (in press) Students’ process and strategies as they program for mathematical investigations and applications. In: Proceedings of the 11th congress of the European Society for Research in Mathematics Education (CERME 11) Utrecht, Netherlands, February 2019. ▸︎ Google︎ Scholar
Buteau C., Muller E., Marshall N., Sacristán A. I. & Mgombelo J. (2016) Undergraduate mathematics students appropriating programming as a tool for modelling, simulation, and visualization: A case study. Digital Experience in Mathematics Education 2(2): 142–156. ▸︎ Google︎ Scholar
Cuoco A., Goldenberg E. P. & Mark J. (1996) Habits of mind: An organizing principle for mathematics curricula. The Journal of Mathematical Behavior 15(4): 375–402. ▸︎ Google︎ Scholar
diSessa A. A. (2000) Changing minds: Computers, learning, and literacy. MIT Press, Cambridge MA. ▸︎ Google︎ Scholar
Edwards L. D. (1995) Microworlds as representations. In: diSessa A. A., Hoyles C., Nos R. & Edwards L. D. (eds.) Computers and exploratory learning. Springer, New York: 127–154. ▸︎ Google︎ Scholar
Feurzeig W. & Lukas G. (1972) LOGO – A programming language for teaching mathematics. Educational Technology 12(3): 39–46. ▸︎ Google︎ Scholar
Grover S. & Pea R. (2013) Computational thinking in K-12: A review of the state of the field. Educational Researcher 42(1): 38–43. ▸︎ Google︎ Scholar
Healy L. & Kynigos C. (2010) Charting the microworld territory over time: Design and construction in mathematics education. ZDM 42(1): 63–76. ▸︎ Google︎ Scholar
Hoyles C. & Noss R. (1987) Synthesising mathematical conceptions and their formalisation through the construction of a LOGO-based school mathematics curriculum. International Journal of Mathematics Education in Science and Technology 18(4): 581–595. ▸︎ Google︎ Scholar
Jenson J. & Rose C B. (2006) Finding space for technology: Pedagogical observations on the organization of computers in school environments. Canadian Journal of Learning and Technology 32(1) https://www.learntechlib.org/p/42798/
Kafai Y. B. & Resnick M. (1996) Constructionism in practice: Designing, thinking, and learning in a digital world. Erlbaum, Routledge, Mahwah NJ. ▸︎ Google︎ Scholar
Kynigos C. & Grizioti M. (2018) Programming approaches to computational thinking: Integrating turtle geometry, dynamic manipulation and 3D space. Informatics in Education 17(2): 321–340. ▸︎ Google︎ Scholar
Kynigos C. (2015) Constructionism: Theory of learning or theory of design? In: Cho S. J. (ed.) Selected regular lectures from the 12th international congress on mathematical education. Springer, Cham: 417–438. ▸︎ Google︎ Scholar
Lave J. & Wenger E. (1991) Situated learning: Legitimate peripheral participation. Cambridge University Press, New York NY. ▸︎ Google︎ Scholar
Leinhardt G., Putnam T., Stein M. K. & Baxter J. (1991) Where subject knowledge matters. Advances in Research in Teaching 2: 87–113. ▸︎ Google︎ Scholar
Lim K. H. & Selden A. (2009) Mathematical habits of mind. In: Swars S. L., Stinson D. W. & S. Lemons-Smith (eds.) Proceedings of the thirty-first annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Georgia State University, Atlanta: 1576–1583. ▸︎ Google︎ Scholar
Marshall N. & Buteau C. (2014) Learning by designing and experimenting with interactive, dynamic mathematics exploratory objects. International Journal for Technology in Mathematics Education 21(2): 49–64. ▸︎ Google︎ Scholar
Monaghan J. (2004) Teachers’ activities in technology-based mathematics lessons. International Journal of Computers for Mathematical Learning 9(3): 327–357. ▸︎ Google︎ Scholar
Muller E., Buteau C., Ralph B., Mgombelo J. (2009) Learning mathematics through the design and implementation of Exploratory and Learning Objects. International Journal for Technology in Mathematics Education 16(2): 63–74. ▸︎ Google︎ Scholar
Noss R. & Clayson J. (2015) Reconstructing constructionism. Constructivist Foundations 10(3): 285–288 https://constructivist.info/10/3/285
Noss R. & Hoyles C. (1996) Windows on mathematical meanings: Learning cultures and computers. Kluwer, Dordrecht. ▸︎ Google︎ Scholar
Noss R. & Hoyles C. (2017) Constructionism and microworlds. In: Duval E., Sharples M. & Sutherland R. (eds.) Technology enhanced learning: Research themes. Springer, Cham: 29–35. ▸︎ Google︎ Scholar
Papert S. (1971) Teaching children to be mathematicians vs. teaching about mathematics. Memo No. 249. Artificial Intelligence Lab, MIT. http://hdl.handle.net/1721.1/5837
Papert S. (1980) Computer-based microworlds as incubators for powerful ideas. In: Taylor R. (ed.) The computer in the school: Tutor, tool, tutee. Teacher’s College Press, New York: 203–210. ▸︎ Google︎ Scholar
Papert S. (1980) Mindstorms: Children, computers, and powerful ideas. Basic Books, New York NY. ▸︎ Google︎ Scholar
Papert S. (1991) Situating constructionism. In: Hare I. & Papert S. (eds.) Constructionism: Research reports and essays 1985–1990 by the MIT Media Laboratory, Epistemology and Learning Research Group. Ablex, Norwood NJ: 1–12. http://www.papert.org/articles/SituatingConstructionism.html
Papert S. (1993) The children’s machine: Rethinking school in the age of the computer. Basic Books, New York. ▸︎ Google︎ Scholar
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. ▸︎ Google︎ Scholar
Ralph B. (2001) Mathematics takes an exciting new direction with MICA program. Brock Teaching 1(1): 1. http://www.brocku.ca/webfm_send/18483.
Rasmussen C. & Kwon O. N. (2007) An inquiry-oriented approach to undergraduate mathematics. The Journal of Mathematical Behavior 26(3): 189–194. ▸︎ Google︎ Scholar
Ruthven K. (2009) Towards a naturalistic conceptualisation of technology integration in classroom practice: The example of school mathematics. Education & didactique 3(1): 131–159. ▸︎ Google︎ Scholar
Trouche L. (2004) Managing the complexity of human/machine interactions in computerized learning environments: Guiding students’ command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning 9: 281–307. ▸︎ Google︎ Scholar
Wagh A., Cook-Whitt K. & Wilensky U. (2017) Bridging inquiry-based science and constructionism: Exploring the alignment between students tinkering with code of computational models and goals of inquiry. Journal of Research in Science Teaching 54(5): 615–641. ▸︎ Google︎ Scholar
Weintrop D., Beheshti E., Horn M., Orton K., Jona K., Trouille L. & Wilensky U. (2016) Defining computational thinking for mathematics and science classrooms. Journal for Science Education and Technology 25: 127–147. ▸︎ Google︎ Scholar
Wing J. M. (2008) Computational thinking and thinking about computing. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366(1881): 3717–3725. ▸︎ Google︎ Scholar
Wing J. M. (2014) Computational thinking benefits society. Social Issues in Computing, 40th Anniversary Blog, University of Toronto. http://socialissues.cs.toronto.edu/index.html%3Fp=279.html

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