Research Interests in Mathematics Education

My main interests are the use of digital technology in teaching and learning of mathematics, including computational thinking and programming technology, university mathematics education, and teacher education.

Ongoing and past projects and collaborations include:

• Extended ongoing SSHRC (2017-22), Buteau, Mgombelo, & Sacristán: Educating for the 21st Century: post-secondary students learning ‘progmatics’ (computer programming for mathematical investigation, simulation, and real-world modeling).
• Mathematics Knowledge Network (2016-22), funded by the Ontario Ministry of Education.
• SSHRC Partnership Development (2016-18), Gadanidis, Sinclair et al.: Computational Thinking in Mathematics Education
• SSHRC International Opportunities Fund (2007-10), Jarvis, Buteau, & Lavicza: Computer Algebra Systems (CAS) in University Instruction: An International Research Study on CAS Usage and Sustainability.

Events include:

• PD-Day & Symposium on Coding, Computational Modeling, and Equity in Mathematics Education. Brock University, St. Catharines, 26-29 April 2023.
• International Online Seminar Series on Programming in Mathematics Education. June-August 2020.
• Symposium on Computational Thinking in Mathematics Education. University of Ontario Institute of Technology (UOIT), Toronto (Canada), October 13-15, 2017.
• Atelier sur l’intégration de la technologie dans l’enseignement post-secondaire aux étudiants en mathématiques. Centre de recherches mathématique (CRM), Montreal, October 2010/ Workshop on Technology Integration in Teaching Undergraduate Mathematics Students. Fields Institute for Research in Mathematical Sciences, Toronto (Canada), October 2010.

Publications (selection – for more, see here):

• Gueudet, G., Buteau, C., Muller, E., Mgombelo, J., Sacristán, A., & 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. https://doi.org/10.1007/s10649-021-10133-1
• 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) 1007/s40751-015-0009-x

Research Interests in Mathematical Music Theory

My interests have been deterministic modeling of music analysis and structure and computational music analysis. I am particularly interested in modeling motivic (melodic) structure and analysis of musical compositions through a topological approach.

Publications (selection)

• Buteau, C., & C. Agnagnostopoulou (2012): Mathematical and Computational Modeling Within a Music Analysis Framework: Motivic Topologies as a Case Study. In Journal of Mathematics and Music, 6 (1), pp. 1-16.
• Buteau, C. & G. Mazzola (2008): Motivic Analysis Regarding Rudolph Réti: Formalization Within A Mathematical Model. In Journal of Mathematics and Music, 2 (3), pp. 117-134.

Selected Refereed Book Chapters

• Modeste, S., Broley, L., Buteau, C., Rafalsaka, M., & Stephens, M. (2024). Computational thinking and mathematics. In B. Pepin, G. Gueudet, & J. Choppin (Eds.), Handbook of Digital (Curriculum) Resources in Mathematics Education. Springer.
• Buteau, C., Muller, E., Santacruz Rodiguez, M., Mgombelo, J., & Sacristán, A., Gueudet, G., (2023). Instrumental orchestration of using programming for authentic mathematics investigation projects. In Clark-Wilson, Robutti, & Sinclair (eds): The Mathematics Teacher in the Digital Era (2^nd Edition) (pp. 289-322). Springer Netherlands.
• Buteau, C., & Muller, E. (2014). Teaching Roles in a Technology Intensive Core Undergraduate Mathematics Course. In Clark-Wilson, Robutti, & Sinclair (eds): The Mathematics Teacher in the Digital Era. Springer Netherlands, 163-185.
• Assude, T., Buteau, C., & Forgasz, H. (2009). Factors Influencing Implementation of Technology-Rich Mathematics Curriculum. In L. H. Son, N. Sinclair, J.-B. Lagrange, & C. Hoyles (Eds.), Mathematics Education and Technology —Rethinking the terrain: The 17th ICMI Study. New York: Springer, 405-419.

Journal Special Issues

• Stephens, M., & Buteau, C., Eds (2023). Special Issue on Computational thinking and Mathematics teaching and learning, Journal for Pedagogical Research, 7(2).
• Anagnostoupoulo, C. & Buteau, C., Eds (2010). Computational Music Analysis [Special Issue]. Journal of Mathematics and Music, 4 (2).

Selected Refereed Journal Papers

• Gueudet, G., Buteau, C., Broley, L., Mgombelo, J., Muller, E., Sacristán, A., & S.-Rodriguez, M. (2023). Learning programming for mathematical investigations: An instrumental and community of practice approach. In Research in Mathematics Education journal, 1-26. DOI: 1080/14794802.2023.2239195
• Broley, L., Buteau, C., & Sardella, J. (2023). When Preservice and Inservice Teachers Join Forces: A Collaborative Way to Support the Enactment of New Coding Curricula in Mathematics Classrooms. In Stephens, M. & Buteau, C. (Eds): Special issue on Computational thinking and Mathematics teaching and learning, Journal for Pedagogical Research, 7(2), 21-40.
• Gueudet, G., Buteau, C., Muller, E., Mgombelo, J., Sacristán, A., & 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. https://doi.org/10.1007/s10649-021-10133-1
• Buteau, C., Muller, E., Mgombelo, J., Sacristán, A., & Dreise, K. (2020). Instrumental Genesis Stages of Programming for Mathematical Work. Digital Experiences in Mathematics Education (DEME), 367-390. DOI: 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, 1020-10 DOI: 10.1080/0020739X.2019.1648892
• Buteau, C., Sacristán, A.I., & Muller, E. (2019).Roles and Demands for Constructionist Teaching of Computational Thinking in University Mathematics. Constructivist Foundations 14(3): 294-309. https://constructivist.info/14/3/294
• Broley, L. Buteau, C. and Muller, E. (2017). Struggles and Growth in Mathematics Education: Reflections by Three Generations of Mathematicians on the Creation of the Computer Game E-Brock Bugs. Journal of Humanistic Mathematics, 7(1), 62-86. (DOI) 10.5642/ jhummath.201701.06.
• 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, 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), 142-166. (DOI) 10.1007/s40751-016-0017-5.
• Broley, L., Buteau, C., & Muller, E. (2015). E-Brock Bugs©, an Epistemic Math Computer Game. Journal of Humanistic Mathematics, 5(2), 3-25.
• 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) 1007/s40751-015-0009-x
• 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., C. Buteau, Mesa, V., & Misfeld, M. (2014). Instrumental and documentational approaches: from technology use to documentation systems 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.
• Buteau, C., Jarvis, D. & Lavicza Z. (2014). On the Integration of Computer Algebra Systems (CAS) by Canadian Mathematicians: Results of a National Survey. In Canadian Journal of Science, Mathematics and Technology Education, 14(1), 35-57.
• Marshall, N., Buteau, C. & Muller, E. (2014). Exploratory Objects and Microworlds in University Mathematics Education. Teaching Mathematics and its Applications, 33, 27-38.
• Martinovic, D., E. Muller & C. Buteau (2013). Intelligent partnership with technology: Moving from a math school curriculum to an undergraduate program. In Computers in the Schools, 30 (1-2), 76-101.
• Marshall, N., C. Buteau, D. Jarvis & Z. Lavicza (2012). Do mathematicians integrate Computer Algebra Systems in university teaching? Comparing a literature review to an international survey study. Computers & Education, 48(1), 423-424.
• Buteau, C. & G. Mazzola (2008). Motivic Analysis Regarding Rudolph Réti: Formalization Within A Mathematical Model. In Journal of Mathematics and Music, 2 (3), 117-134.

Past Teaching Assignments

• MATH 1P11 Linear Algebra I
• MATH 1P12 Applied Linear Algebra
• MATH 1P40 Mathematics Integrated with Computers and Applications (MICA) I
• MATH 1P97 Calculus with Applications
• STAT 1P98 Basic Statistical Methods
• MATH 2P12 Linear Algebra II
• MATH 2P95 Mathematics and Music
• MATH 3P41 Visual and Interactive Mathematics Through Programming (MICA III for future teachers)
• MATH 4/5P96 Technology and Mathematics Education

• Learning Objects developed by the Department
• Learning Objects developed by Brock students

Awards:

• Brock University Award for Distinguished Teaching, 2023
• Brock University Research Capacity Program Award, 2023-25 Cycle
• Brock Faculty of Mathematics and Science Distinguished Research Award, 2022