modelling

COMPUTATIONAL MODELLING

This eBook is about modelling with code, a.k.a. computational modelling, in the context of teaching and learning mathematics.

Use the drop-down menus above to access activities.

More activities will be added on a regular basis: this eBook is a work in progress.

 

Computation in our society

Our societies are growing in complexity, in large part because of the intertwining connections afforded by new technologies. The use of computational tools to model phenomena, processes and relationships is becoming a prerequisite to scientific progress and economic success, as evidenced by the emergence of numerous computational modelling fields, such as computational biology, computational mathematics, computational finance, computational medicine, to name a few examples. (Gadanidis, Hughes, Namukasa & Scucuglia, forthcoming)

The authentic computational modelling practices of scientists and professionals involve solving real-world problems and building knowledge – to learn – through computational “conversation” and “interaction” with their field (Barba, 2014) “with and across a variety of representational technologies” (Wilkerson-Jerde, Gravel and Macrander, 2015, p. 396).

“It’s a source of power to do something and figure things out, in a dance between the computer and our thoughts. The inversion, starting with computing as a formal thing to understand and then come to the application later, takes away its power.” (Barba, 2016)

 

Computational modelling in mathematics education

A focus on computational modelling in education, which is not isolated but integrated with mathematics (and with other subjects), not only prepares students for future success; it also provides students a powerful learning tool with which to design, test and refine conceptual schema and build powerful understandings of mathematics they are studying. (Gadanidis, Hughes, Namukasa & Scucuglia, forthcoming)

See a video of George Gadanidis discussing how computational affordances can help us teach mathematics better: imaginethis.ca/educating-young-mathematicians-3-five-as-for-coding-math

 

Mathematics education reform

The table below illustrates how computational affordances may map onto mathematics education reform goals (Gadanidis, 2017; Gadanidis, Clements & Yiu, 2018).

 

References

Bandura, A. (1997). Self-efficacy: The Exercise of Control. New York: W. H. Freeman.

Barba, L.A. (2014). Computational thinking is computational learning. Keynote address at SciPy (Scientific Computing with Python) Conference, Austin, Texas. Video retrieved 5/01/17 from http://lorenabarba.com/gallery/prof-barba-gave-keynote-at-scipy-2014

Barba, L.A. (2016). Computational Thinking: I do not think it means what you think it means. Blog post, retrieved 6 January 2018 from http://lorenabarba.com/blog/computational-thinking-i-do-not-think-it-means-what-you-think-it-means.

Boyd, B. (2009). On the origin of stories: evolution, cognition, and fiction. Cambridge, MA: Harvard University Press.

Burton, L. (1999). The practices of mathematicians: what do they tell us about coming to know mathematics? Educational Studies in Mathematics, 37, 121-143.

Dissanayake, E. (1992). Homo aestheticus. New York: Free Press.

Gadanidis, G. (2018). Math + coding = natural fit? Yes, through computational modelling (Keynote address). Association for Computer Studies Educators Conference, 24 February 2018, York Campus of Seneca College.

Gadanidis, G. (2017). Five affordances of computational thinking to support elementary mathematics education. Journal of Computers in Mathematics and Science Teaching 36(2), 143-151.

Gadanidis, G., Hughes, J., Namukasa, I. & Scucuglia, R. (forthcoming). Computational Modelling in Mathematics Education.

Gadanidis, G., Borba, M., Hughes, J. & Lacerda, H. (2016). Designing aesthetic experiences for young mathematician: a model for mathematics education reform. International Journal of Mathematics Education Research 6(2), 225-244.

Gadanidis, G., Clements, E. & Yiu, C. (2018). Group theory, computational thinking and young mathematicians. Mathematical Thinking and Learning 20(1), 32-53.

Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. New York, NY: Basic Books.

Papert, S. (1993). The children’s machine. Rethinking school in the age of the computer. New York, NY: Basic Books.

Wilkerson-Jerde, M.H., Gravel, E.G. & Macrander, C.A. (2015). Exploring shifts in middle school learners’ modeling activity while generating drawings, animations, and computational solutions of molecular diffusion. Journal of Science Education and Technology 24, 396-415.