The landing of the Perseverance rover on Mars is an excellent catalyst for a discussion with students about the nature of Mathematics. It is a chance to inspire curiosity and wonderment and to do so through a mathematical lens. The video of a small, fragile craft descending towards the surface of an alien planet, immediately captures the imagination. As the lander bobs gently beneath its parachutes and as the NASA team communicate critical moments in its descent, one is filled with a sense of awe at what is possible when we dream big and dare mighty things. By the time the lander has fired its rockets to enter a hover above the surface, and as the rover is delicately lowered to the ground on slender cables, the viewer’s mind should be awash with questions. Now is the time to invite our students to ponder the beauty and wonder revealed in the mathematics of what they are observing.
Mathematics rightly viewed possesses not only truth but supreme beauty. - Bertrand Russell (1907) The Study of Mathematics
We often overlook the mathematics that surrounds and makes so much of our daily lives possible. It is easy to think of mathematics as something that belongs inside the walls of a particular type of classroom. It is equally easy to think that mathematics is about the mere mechanics of solving a problem quickly and accurately. Contemplating the nature of the mathematics involved in landing Perseverance on Mars encourages a fresh perspective on a discipline many feel we escaped when we finished school. The Perseverance landing is awash with mathematics, and it should be readily apparent that it is mathematics that makes the whole endeavour possible. This is the mathematics of the real world, where formidable challenges are confronted with questions and creativity.
“Mathematics is not about numbers, but about life. It is about the world in which we live. It is about ideas. And far from being dull and sterile as it is so often portrayed, it is full of creativity”. - Keith Devlin - 2001
Image courtesy NASA
I had the pleasure of sharing the video of the landing with my class of Year Five students. As they watched, I invited them to notice and name the mathematics that might have been required at varying stages throughout the landing. The conversation was enlightening and evolved over time as fresh ideas emerged. From an initial focus on altitude and speed, students began to contemplate the wider range of factors that would need to be considered and included in calculations. The mass of the rover, the rate of deceleration, the gravity of Mars, the size of the parachutes, the time delay from Earth, the speed of light, the orientation of the rover in 3D space, the challenges of navigating a distant planet. We moved well beyond the traditional highly siloed approach where concepts (or curriculum outcomes) are examined in splendid isolation. Here the mathematics was meaningful, complicated, integrated and beautiful.
I’m simply stunned when I think how rarely formal learning gives us a chance to learn the whole game from early on. When I and my buddies studied basic arithmetic, we had no real idea what the whole game of mathematics was about. . . . It was kind of like batting practise without knowing the whole game. Why would anyone want to do that? - Perkins, David. (2009) Making Learning Whole
Investigating the mathematics behind Perseverance’s landing challenges our traditional approach to the discipline. School mathematics sadly has little in common with real mathematics.
Students will typically say it is a subject of calculations, procedures, or rules. But when we ask mathematicians what math is, they will say it is the study of patterns; that it is an aesthetic, creative, and beautiful subject. - Jo Boaler - (2015) Mathematical Mindsets
And, we know that our emphasis on the rote learning of mathematical processes is not facilitating the sort of deep-understanding of mathematics that our students need for success. Research from the Office of Australia’s Chief Scientist examined the approach taken to mathematics in 619 Australian schools achieving outstanding improvement in NAPLAN (a national standardised numeracy and literacy assessment) numeracy scores over a two-year period. A significant finding from this study was that “87% of case study schools had a classroom focus on mastery (i.e. developing conceptual understanding) rather than just procedural fluency.”
By removing the creative process and leaving only the results of that process, you virtually guarantee that no one will have any real engagement with the subject. - Paul Lockhart (2009) A Mathematician’s Lament
Image courtesy NASA
Hidden in Perseverance’s parachute is a beautiful example of the playful creativity of NASA’s mathematicians. Amidst the pattern designed to help NASA’s tracking systems monitor the performance of the parachute is a message only revealed by translating the visible pattern of wide and narrow segments of colour on the parachute into binary and then ASCII code. The message reads “Dare Mighty Things”. Maybe this is a message to teachers of mathematics and their students. A call for us to all dare mighty things as we explore a mathematics that is full of wonder and creativity.
By Nigel Coutts