What coding should be in mathematics?

At the AAMT conference in Canberra in July, Eugene Roizman, the STEM Coordinator for Box Hill High School in Melbourne demonstrated the contexts and ideas being designed for the reSolve special topic on ‘Mathematics and algorithmic thinking’. Eugene is working with Professor Dr Bernd Meyer (Monash University) and education consultant Toan Kien Huynh.

Coding is currently a high priority topic in many schools, with several national projects, many commercial products and the new Australian Curriculum: Digital Technologies all recognising that expertise is critical to success in an ever-growing array of careers and industries.

New ways of doing mathematics

This rotating world map, based on ABS data from 2011, shows the countries of origin of Australians. 
This M.C. Escher artwork can be recreated using algorithmic methods. Image source/Fair use.

But what is the highest priority within mathematics? Working at Years 8 to 10, a reSolve special topic aims to demonstrate the capacity of computational and algorithmic thinking to complement, extend and enrich traditional mathematical approaches to authentic contexts, using approaches that show new ways of doing mathematics.

There will be three topics, each subdivided into an ‘application’ unit requiring very little prior understanding of coding and an optional ‘behind-the-scenes’ unit which develops students’ skills in modern, industry-standard tools.

Topic 1, for Year 10 or above, is ‘Understanding behaviour through simulation’. It views simulations as ‘super-charged thought experiments’ that allow us to discover unintuitive results about complex behaviours and their evolution.

Topic 2, for Year 9 and above, is ‘Understanding data through visualisation’. Students will investigate large data sets (for example, from the World Bank) and use data visualisation and computational analysis that can help us understand hidden structures (‘secrets’) in data. For example, the unit is designed so that with only a few lines of well-supported code, students can create an interactive, ‘3-dimensional’ world map that shows the countries of origin of all Australians based on Australian Bureau of Statistics data. 

Topic 3, for Year 8 and above, is ‘Understanding pattern formation through generative geometry’. It shows how patterns in nature can be understood through simple pattern generation mechanisms. The focus is on creating a bridge between numerical and visual patterns, using the former as grounding for the latter. A quick internet search on generative geometry shows some of the amazing artwork produced in this way. 

Emeritus Professor Kaye Stacey
Director of Special Topics, reSolve: Maths by Inquiry

© 2017 Australian Academy of Science