• Buteau, C., Broley, L., Dreise, K., & Muller, E. (In Press). Students using programming for pure and applied mathematics investigations. Épijournal de Didactique et Epistémologie des Mathématiques pour l’Enseignement Supérieur.
• Gueudet, G., Buteau, C., Muller, E., Mogombelo, J., Sacristán, A. I., & Santacruz Rodriguez, M. (2022). Development and evolution of instrumented schemes: a case study of learning programming for mathematical investigations. Educational Studies in Mathematics (ESM), 353-377 DOI: 10.1007/s10649-021-10133-1
• Buteau, C., Muller, E., Mgombelo, J., Sacristán, A., & Driese, K. (2020). Instrumental Genesis Stages of Programming for Mathematical Work. Digital Experience in Mathematics Education, 6(3), 367-390. DOI: 10.1007/s40751-020-00060-w
• Buteau, C., Gueudet, G., Muller, E., Mgombelo, J., & Sacristán, A. (2019). University Students Turning Computer Programming into an Instrument for ‘Authentic’ Mathematical Work. International Journal of Mathematical Education in Science and Technology, 51(7), 1020-1041. DOI: 10.1080/0020739X.2019.1648892
• 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.
• 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, 142-166. DOI: 10.1007/s40751-016-0017-5.

Papers in Conference Proceedings

• Broley, L., Ablorh, E., Buteau, C., Mgombelo, J., & Muller, E. (Accepted). Effective Orchestration features of a project-based approach to learning programming for mathematics investigation. Proceedings of INDRUM 2022 Fourth Conference of the International Network for Didactic Research in University Mathematics. Hannover, Germany. October 2022.
• Sacristán, A.I., Santacruz-R., M., Buteau, C., Mgombelo, J., Muller, E. (Accepted). Future teachers’ appropriation of computer programming as a mathematical instrument and a resource for teaching. Accepted for presentation at the 13th ERME Topic Conference (ETC13) on Mathematics Education in the Digital Age (MEDA3) to be held 07-09 September 2022 in Nitra, Slovakia
• Mgombelo, J., Pinar Sen, A., Buteau, C., Muller, E., Sacristán, A. I., & Santacruz-Rodríguez, M. (In Press). Pre-service teachers using programming to design learning objects: A case study. Proceedings of the twelfth Congress of the European Society for Research in Mathematics Education. Bolzano, Italy.
• Gueudet, G., Buteau, C., Broley, L., Mgombelo, J., Muller, E., & Sacristán, A. I. (In Press). Understanding how students learn programming for mathematics inquiry at university: Schemes and social-individual dialectics. Proceedings of the twelfth Congress of the European Society for Research in Mathematics Education. Bolzano, Italy.
• Broley, L., Buteau, C., & Mgombelo, J. (In Press). University students learning programming-based practices for mathematics inquiry: Contributions of an institutional approach. Proceedings of the twelfth Congress of the European Society for Research in Mathematics Education. Bolzano, Italy.
• Broley, L., Ablorh, E., & Buteau, C., Mgombelo, J., & Muller, E. (2022). Effectiveness of a project-based approach to integrating computing in mathematics. Proceedings of the 2022 Annual Conference on Research in Undergraduate Mathematics Education  (pp. 72-80). Boston, MA.
• Broley, L., Buteau, C., Levay, D., Marshall, N., Muller, E., & Sardella, J. (2022). Students facing and handling challenges in programming-based mathematics inquiry projects. Proceedings of the 2022 Annual Conference on Research in Undergraduate Mathematics Education (pp. 63-71). Boston, MA.
• Mgombelo, J., Forbes, W., Buteau, C., Muller, E., & Sacristán, A. (2021). Students’ Ways of Thinking in Computer-Based Mathematics Investigation Projects. Presentation at the 14th International Congress for Mathematics Education (ICME), Shanghai (China), July 2021.
• Buteau, C., Muller, E., Gueudet, G., Mgombelo, J., & Sacristán, A. (2021). Researching the teaching and learning of programming for university mathematical investigation projects. Presentation at the 14th International Congress for Mathematics Education (ICME), Shanghai (China), July 2021.
• Buteau, C., Muller, E., Santacruz Rodríguez, M., Gueudet, G., Mgombelo, J., & Sacristán, A. (2020). Instrumental orchestration of using programming for mathematics investigations. Proceedings of the 10th ERME Topic Conference Mathematics in the Digital Age 2020 (pp. 443-450), Linz (Austria), September 2020.
• Sacristán, A., Santacruz Rodríguez, M., Buteau, C., Mgombelo, J., & Muller, E. (2020). The constructionist nature of an instructor’s instrumental orchestration of programming for mathematics, at university level. Proceedings of Constructionism 2020 (pp. 448-499), Dublin (Ireland), May 2020.
• Gueudet, G., Buteau, C., Muller, E., Mgombelo, J., & Sacristán, A. (2020). Programming as an artefact: What do we learn about university students’ activity? Proceedings of INDRUM 2020 Third Conference of the International Network for Didactic Research in University Mathematics (pp. 443-452), Bizerte (Tunisia), March 2020.
• Toor, A., Mgombelo, J., & Buteau, C. (2019). Undergraduate students’ enactment of identity in programming and mathematics learning environment. Proceedings of Congress of the European Society for Research in Mathematics Education (pp. 4867-4874), Utrecht (Netherlands), February 2019.
• Forbes, W.A., Mgombelo, J., Gannon, S., & Buteau, C. (2019). Undergraduate students’ mindsets in a computer programming mathematical learning environment. Proceedings of Congress of the European Society for Research in Mathematics Education (pp.1419-1426). Utrecht, Netherlands.
• Buteau, C., Muller, E., Dreise, K., Mgombelo, J., & Sacristán, A.I. (2019). Students’ process and strategies as they program for mathematical investigations and applications. Proceedings of Congress of the European Society for Research in Mathematics Education (pp. 2796-2803). Utrecht, Netherlands.
• Buteau, C., Muller, E., Sacristán, A.I., & Mgombelo, J. (2019). Pensée Informatique en enseignement des mathématiques post-secondaires : un cadre théorique. Proceedings of Espace mathématique francophone 2018 (pp. 1640-1648), Paris-Genevilliers (France), October 2018.
• Buteau, C., Sacristán, A.I., & Muller, E. (2018). Teaching in a Sustained Post-Secondary Constructionist Implementation of Computational Thinking for Mathematics.Proceedings of Constructionism 2018 (pp. 528-535), Vilnius (Lithuania), August 2018.
• Buteau, C, Muller, E., Mgombelo, J., & Sacristán, A. (2018). Computational Thinking in University Mathematics Education: A Theoretical Framework. Proceedings of Research in Undergraduate Mathematics Education conference (pp. 1171-1179), San Diego (USA), February 2018.

Poster Presentations at Scholarly Event

• Broley, L., Buteau, C., & Muller, E. (Accepted). Coding in math learning: A ‘triple instrumental genesis’ approach to support the transition from university learner to school teacher. Proceedings of INDRUM 2022 Fourth Conference of the International Network for Didactic Research in University Mathematics. Hannover, Germany. October 2022. View poster here.
• Sacristán, A.,  Rodriguez, M., Buteau, C., Mgombelo, J., & Muller E. (In Press). Computer Programming in the Professional Development of Future Mathematics Teachers. In C. Fernánndez, S. Llinares, A. Gutiérrez, & N. Planas (Eds.) Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. PME. View poster here.
• Ablorh, E., & Broley, L. (2022). Integrating Coding in Mathematics: Effectiveness of A Project-Based Approach. Fields Mathematical Education Forum (Theme: Research Day 2022.). Fields Institute for Research in Mathematical Sciences, Toronto (online), Canada, January 2022. View poster here.
• Sardella, J., & Broley, L. (2022). The Biggest Challenges Faced by Students During Course Projects, and How they Handle Them. Fields Mathematical Education Forum (Theme: Research Day 2022.). Fields Institute for Research in Mathematical Sciences, Toronto (online), Canada, January 2022. View poster here.
• Santacruz Rodríguez, M., Sacristán, A., Buteau, C., Mgombelo, J., & Muller, E. (2021). A university instructor’s orchestration for supporting his students’ programming for mathematics. In A.I. Sacristán, J.C. Cortés-Zavala, & P.M. Ruiz-Arias (Eds.), Mathematics Education Across Cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 2162–2163). Mexico: Cinvestav, AMIUTEM, PME-NA. View poster here.
• Buteau, C., Gueudet, G., Dreise, K., Muller, E., Mgombelo, J. & Sacristán, A. (2020). A student’s complex structure of schemes development for authentic programming-based mathematical investigation projects. Proceedings of INDRUM 2020 Third Conference of the International Network for Didactic Research in University Mathematics (pp. 513-514). Bizerte, Tunisia. View poster here.
• Buteau, C., Muller, E., Mgombelo, J., & Sacristán, A.I. (2019). Stages of students’ instrumental genesis of programming for mathematical investigations. In M. Graven, H. Venkat, A. Essien & P. Vale (Eds), Proceedings of the 43^rd Conference of the International Group for the Psychology of Mathematics Education (Vol 4, p.127). Pretoria, South Africa: PME. View poster here.
• Buteau, C., Muller, E., Mgombelo, J., Rafiepour, A., & Sacristán, A.I. (2018). Features of ‘authentic’ programming-based mathematical tasks. Proceedings of Mathematics Education in the Digital Age (pp.301-2). Copenhagen, Denmark. View poster here.
• Gannon, S. (2018). Undergraduate students’ sense of empowerment in programming-based mathematical explorations. Proceedings of Canadian Mathematics Education Study Group. Squamish (Canada), June 2018. View poster here.

To view the posters, click here.

Videos

• Balt, K., & Buteau, C. (2020a, September 4). Illustrating the web of schemes: A student’s process when engaging in using programming for pure or applied math investigation [Video]. YouTube. https://youtu.be/teJAd3TDw9E
• Balt, K., & Buteau, C. (2020b, September 4). Using programming for pure/applied mathematics investigation: Mandelbrot set and running in the rain illustrations [Video]. YouTube. https://youtu.be/irTlCE-eXhc
• Buteau, C. & Muller E. (2017, July 4). A university mathematics department’s adoption of constructionist math courses [Video]. YouTube. https://www.youtube.com/watch?v=SNvTdaG04gc&t=27s

Journal Articles and Book Chapters

• Buteau, C., & Muller, E. (2016). Assessment in Undergraduate Programming-Based Mathematics Courses. Digital Experiences in Mathematics Education, 3(2): 97-114. DOI 10.1007/s40751-016-0026-4.
• Buteau, C., Muller, E & Marshall, N. (2015). When a university mathematics department adopted course mathematics courses of unintentionally constructionist nature – really? Digital Experience in Mathematics Education,1(2-3), 133-155. DOI 10.1007/s40751-015-0009-x
• Buteau, C., & Muller, E. (2014). Teaching Roles in a Technology Intensive Core Undergraduate Mathematics Course. In  Clark-Wilson, O. Robutti, N. Sinclair (eds): The Mathematics Teacher in the Digital Era (pp. 163-185). Springer Netherlands.
• Marshall, N. & C. Buteau (2014). Learning by designing and experimenting with interactive, dynamic mathematics exploratory objects. International Journal for Technology in Mathematics Education, 21 (2), 49-64.
• Gueudet, G., Misfeld, M., Mesa, V., & C. Buteau (2014): Technologies, resources and instruments in university mathematics education. Research of Mathematics Education, Special Issue:  Institutional, sociocultural and discursive approaches to research in university mathematics education, 16 (2), 139-155.
• Marshall, N., Buteau, C. & Muller, E. (2014). Exploratory Objects and Microworlds in University Mathematics Education. Teaching Mathematics and its Applications, 33, 27-38. DOI: 10.1093/teamat/hru004
• Martinovic, D., E. Muller & Buteau, C. (2013). Intelligent partnership with technology: Moving from a math school curriculum to an undergraduate program. In Computers in the Schools, 30:1-2, pp.76-101. DOI: 10.1080/07380569.2013.768502
• Muller, E., & C. Buteau (2012). An Innovative Integration of Evolving Technologies in Undergraduate Mathematics Education. In Essays on Mathematics and Statistics, Vol. 2, Akis, V. (Ed.), Athens Institute for Education and Research (publisher), 117-122.
• Muller, E., Buteau, C., Ralph, B., Mgombelo, J. (2009): Learning mathematics through the design and implementation of Exploratory and Learning Objects. In International Journal for Technology in Mathematics Education , 16 (2), pp. 63-74.
• Mgombelo, J. & Buteau, C. (2009): Prospective Secondary Mathematics Teachers Repositioning by Designing, Implementing and Testing Learning Objects: A Conceptual Framework. In International Journal of Mathematical Education in Science and Technology, 40 (8), 1051-1068. DOI: 10.1080/00207390903236459
• Muller, E. and C. Buteau (2006): Un nouveau rôle de l’informatique dans la formation initiale des enseignants. In Bednarz, N., Mary, C. (Eds.), “L’enseignement des mathématiques face aux défis de l’école et des communautés”, Actes du colloque EMF 2006, Sherbrooke: Éditions du CRP [CD-ROM], 17 pp.

Conference Proceedings

• Mamolo, A., Buteau, C., & Muller, E. (forth.). Prospective mathematics and sciences teachers’ views on coding and computational thinking. American Educational Research Association (AERA) Annual Meeting, Toronto, ON, April 2019.
• Gannon, S., with Buteau, C. (2018). Integration of Computational Thinking in Canadian Provinces. In Online Proceedings of the Computational Thinking in Mathematics Education Symposium, UOIT (Scarborough), October 2017.
• Broley, L., Buteau, C., & Muller, E. (2017). (Legitimate peripheral) computational thinking in mathematics. Proceedings of the Congress of European Society for Research in Mathematics Education (CERME), Dublin (Ireland), February 2017.
• Buteau, C., Gadanidis, G., Lovric, M., & Muller, E. (2017). Computational Thinking and Mathematics Curricula/La pensée computationnelle et le programme de mathématiques. Proceedings of the Canadian Mathematics Education Study Group (CMESG) 2016 Annual Conference, Kingston (Canada), June 2016, 119-135.
• Buteau, C. & Muller, E. (forth.). Systemic integration of programming in undergraduate mathematics: from implementation to theory. International Congress on Mathematical Education 2016, Hamburg (Germany).
• Buteau,  (2016). Undergraduates Learning of Programming for Simulation and Investigation of Mathematics Concepts and Real-World Modelling. Online proceedings of Didactics of Mathematics in Higher Education as a Scientific Discipline, Hanover (Germany), December 2015.
• Buteau, C., Muller, E., & Ralph, B (2015). Integration of Programming in the Undergraduate Mathematics Program at Brock University. In the Online Proceedings of Math+Coding Symposium, London (Ontario), June 2015.
• Buteau, C., Marshall, N., & Muller, E. (2014). Learning university mathematics by creating and using fourteen ‘microworlds’. In G. Futschek & C. Kynigos (Eds.), Constructionism and Creativity. Proceedings of the 3rd International Constructionism Conference 2014 (pp. 401-406). Vienna, Austria: Österreichische Computer Gesellschaft (OCG).
• Buteau, C., Marshall, N., & Muller, E. (2014). Perception on the Nature of Core University Mathematics Microworld-Based Courses. In G. Futschek & C. Kynigos (Eds.), Constructionism and Creativity. Proceedings of the 3rd International Constructionism Conference 2014 (pp. 379-389). Vienna, Austria: Österreichische Computer Gesellschaft (OCG).
• Buteau, C., Muller, E., & Marshall, N. (2014). Competencies Developed by University Students in Microworld-type Core Mathematics Courses. In Proceedings of Joint Meeting Int. Group Psychology Mathematics Education (PME 38), Vancouver, Canada, 2014, pp. 209-18.
• Marshall, N., Buteau, C. & E. Muller (2013): Exploratory Objects and Microworlds in University Mathematics Education. In Proceedings of the 11th International Conference on Technology in Mathematics Teaching, Bari (Italy), 187-193.
• Mgombelo, J. & Buteau, C. (2012): Learning Mathematics for Teaching Through Designing, Implementing, and Testing Learning Objects. Issues in the Undergraduate Mathematics Preparation of School Teachers: The Journal, Vol 3. 16pp.
• Muller, E., & C.Buteau (2012). An Innovative Integration of Evolving Technologies in Undergraduate Mathematics Education. In Essays on Mathematics and Statistics, Vol. 2, Akis, V. (Ed.), Athens Institute for Education and Research (publisher), 117-122.
• Buteau, C. & E. Muller (2010): Student Development Process of Designing and Implementing Exploratory and Learning Objects. In Proceedings of the Sixth Conference of European Research in Mathematics Education 
Lyon, France – Jan. 28th – Feb. 1, 2009, 1111-1120.
• Mgombelo, J. & Buteau, C. (2010): Mathematics Teacher Education Research and Practice: Researching Inside the MICA Program. In Proceedings of the Sixth Conference of European Research in Mathematics Education (CERME 6), 
Lyon (France), 2009, 1901-1910.
• Buteau, C. & Muller, E. (2006). Evolving technologies integrated into undergraduate mathematics education. In L. H. Son, N. Sinclair, J. B. Lagrange, & C. Hoyles (Eds.), Proceedings for the Seventeenth ICMI Study Conference: Digital Technologies and Mathematics Teaching and Learning: Revisiting the Terrain, Hanoi University of Technology, 3rd-8th December, 2006, Hanoi (Vietnam) (c42)[CD-ROM], 8 pp.

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• 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.
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