Introduction
Maths Inside was a collaborative project funded by the Federal Government under the AMSPP (Australian Maths and Science Partnerships Program) competitive grants scheme and administered by a cross-faculty team at the UTS. The collaboration included UTS, the Commonwealth Scientific and Industrial Research Organisation (CSIRO) and the Australian Association of Mathematics Teachers (AAMT). The aim of the project was to show the mathematics that is “inside” industrial and scientific objects and activities, while highlighting the role of Australian scientists in their research in various fields, from radio astronomy to prawn farming, robotics to climate change, data handling for hospitals to investigating the behaviour of bees. The project team firmly believed that real world contexts can be a successful way to motivate engagement in mathematics in schools. A key element of the success of the project is that the resources include short videos of real people talking about science and mathematics, showing us their labs or their places of work; as well as classroom ready materials downloadable as word documents and Excel spreadsheets, that can be used as they are or adapted to fit any particular classroom.
The project resulted in eight modules, the first four of which are described in an earlier article for SEN: Bees with Backpacks; Big Data, Better Hospitals; Cleaner Coasts; Knowing Nutrition.
On the UTS site there is also a ninth module designed for Teacher Professional Learning, which introduces the other materials and gives an inspiring example of how one particular school, Kinross Wolaroi School in Orange, has integrated the modules into their teaching programs. There is also a link to “Pathways to Maths”, a self-assessment tool that will help users find out whether their mathematical knowledge is ready for university study in mathematics and science. This tool covers the content of the Australian Curriculum – Mathematics (Mathematics Methods).
While the modules were initially designed with the teaching of mathematics in mind, the videos in particular, and some of the classroom activities, make excellent starting points for scientific investigations as well as illustrations of Australian scientists at work solving real problems.
Maths in 3D
This was actually the first module produced by our team. Robert Zlot grew up in Canada, and came to Australia after completing a PhD in robotics. As a researcher in this field, he helped develop a portable laser scanner that oscillates on a spring. It is called “Zebedee” after a cartoon character that has a spring instead of legs. The scanner fires about 40,000 times per second and the beams are captured when they reflect off something in the environment (e.g. the walls of a cave) and back to the scanner. Using the principle of “time of flight” and knowing the speed of light, the distance from the scanner to the object is calculated. The result builds up a 3D picture of point cloud maps.
Zebedee can be used to make 3D maps of spaces such as caves, forests, old buildings, even crime scenes. To go with the video there are accompanying classroom modules that include ideas for working with speed/distance/time outdoors and indoors, and also using scientific notation to represent very large and very small numbers.
Watching the video, your students will find out that mathematics is used in many different ways in science and robotics. Robert has a particular message that is very relevant for any students who think that computers will solve the problems of the future: “Computers can do a lot of autonomous processing, crunching numbers together, but it’s really the creative aspect of developing the next generation technology that requires an understanding of the mathematical principles and a way to do new things that computers can’t do yet. You might be looking at part of your math curriculum and wondering how is this particular thing useful. And you may not know the answer to that, and your friends may not know the answer, and your teacher may not know the answer but in ten or 15 years from now you might be working in a job and a new problem comes along that you haven’t seen before and then suddenly you remember back that you have the tools for this.”
To find out more about laser scanning, the paper by Spring (2020) includes the story of Zebedee. Also, see Bosse, Zlot and Flick (2012); Zlot and Bosse (2014) and Zlot et al (2014).
Modelling Climate Changes
Michael Grose is a research scientist at the CSIRO who investigates the forces in nature that influence the weather and the climate. In the video he describes how statistics is used to build a mathematical model of the climate, using “boxes” of 100 to 200 km in each dimension. The models need to be checked against the actual changes in the weather:
The activities in this module include making a rain gauge, looking into the weather at points 200 km away from the current location of the students, and considering the difference that weather and climate make to activities such as agriculture and farming in general.
Prawns for Profit
Greg Coman is a Senior Research Scientist with the CSIRO, and he works with prawns. In the video, “Prawns for profit”, he explains that a goal of his research is to find and breed prawns that grow fast, taste good, and survive well in the environment of a prawn farm. We also hear from Nick Moore, the General manager of Gold Coast Marine Aquaculture that produces Gold Coast Tiger Prawns. He describes how he ensures the best growing conditions. Calculations based on sampling are done to estimate the number of prawns in a pond. It is important to know stocking rates and “Food Conversion Ratios” to monitor the way that the prawns are eating and putting on weight.
Teachers could use this video to show students how the science of genetics is applied to a growing industry. There are also spreadsheets of prawn data from different farms, to show how statistics are used for a purpose in this industry – to make decisions about which farms a buyer might buy from depending on the time of year, and what the prawns are used for. Further details can be found in the papers written by Coman and others, for example Coman et al (2005).
Stargazing with SKA
Lisa Harvey-Smith is an astronomer. At the time of making this video, she was with the CSIRO and has since been the Australian Government Women in STEM Ambassador (2018-2024). Currently, she is a Professor of Practice in Science Communication at the University of New South Wales (UNSW). Lisa is a very effective communicator. In her video she explains some of the many ways that mathematics is used in radio astronomy, from the design of telescope dishes (parabolas) to their placement (in spirals!), and the use of complex numbers. As the project scientist for the SKA (Square Kilometre Array) venture, she communicates the significance of this project and the role that computers play in performing the many calculations (72 trillion calculations per second) that are needed to interpret the many signals received at the radio telescopes around the globe. Here are her words at the end of the video – “Maths is so much more than a load of equations. It’s everything. It’s science, it’s business, it’s finance. It can just take you anywhere. It can take you into so many careers. So, it’s so important that we understand that maths has a really important place in our world.”
My favourite part of the classroom materials written to accompany this video is the activity about making a parabolic solar trough – a sausage cooker.
Step by step instructions are given. Students need to know about the properties of the parabola to fully understand the need for the measurements, and where to place the items to be cooked.
An example of where the Maths Inside writers were able to take a start from the scientists in the videos and take it further is the set of activities based on spirals. Do you know the difference between Archimedean spirals and Logarithmic spirals? Where are they found in the world around us? This is an excellent starting point for a STEM project.
For younger students, Lisa has written popular books including “Under the stars – astrophysics for bedtime” and “When Galaxies Collide”. Both make excellent reading for all ages.
All in all, the videos and classroom activities that make up “Maths Inside” are an excellent resource for both Science and Mathematics in the secondary school. Some of the activities would also be appropriate for primary school students. And they are all completely free. You can find them here: https://www.uts.edu.au/research-and-teaching/our-research/maths-inside/maths-inside-resources
References
- Australian Association of Mathematics Teachers (2023), Maths Inside https://www.mathseducation.org.au/online-resources/maths-inside/
- Bosse, M., Zlot, R., & Flick, P. (2012). Zebedee: Design of a spring-mounted 3-d range sensor with application to mobile mapping. IEEE Transactions on Robotics, 28(5), 1104-1119.
- Coman, G. I., Crocos, P. I., Arnold, S. J., Keys, S. I., Preston, N. P., & Murphy, B. (2005). Growth, survival and reproductive performance of domesticated Australian stocks of the giant tiger prawn, Penaeus monodon, reared in tanks and raceways. Journal of the World Aquaculture Society, 36(4), 464-479.
- Spring, A. P. (2020). History of laser scanning, part 2: the later phase of industrial and heritage applications. Photogrammetric Engineering & Remote Sensing, 86(8), 479-501.
- University of Technology Sydney (2018, June 8) Maths Inside https://www.uts.edu.au/research/maths-inside
- Zlot, R., & Bosse, M. (2014). Three-dimensional mobile mapping of caves. Journal of Cave & Karst Studies, 76(3).
- Zlot, R., Bosse, M., Greenop, K., Jarzab, Z., Juckes, E., & Roberts, J. (2014). Efficiently capturing large, complex cultural heritage sites with a handheld mobile 3D laser mapping system. Journal of Cultural Heritage, 15(6), 670-678.
Note – all images are from the Maths Inside Videos and/or classroom activity material.
