Everything in our world follows mathematical laws: from the motion of stars and galaxies to the transmission of phone signals, bus timetables, weather prediction and online banking. Mathematics lets us describe and explain all of these examples, and can reveal profound truths about their underlying patterns.
Unfortunately the school curriculum often fails to convey the incredible power and great beauty of mathematics. In most cases, school mathematics is simply about memorising abstract concepts: a teacher (or a video, or a mobile app) explains how to solve a specific kind of problem, students have to remember it, and then use it to solve homework or exam questions. This has changed very little during the last century, and is one of the reasons why so many students dislike mathematics.
“It is a miracle that curiosity survives formal education.”– Albert Einstein
In fact, the process of studying mathematics is often much more important than the actual content: it teaches problem solving, logical reasoning, generalising and abstraction. Mathematics should be about creativity, curiosity, surprise and imagination – not memorising and rote learning.
Mathigon is part interactive textbook and part virtual personal tutor. Using cutting-edge technology and an innovative new curriculum, we want to make learning mathematics more active, personalised and fun.
Rather than telling students how to solve new kinds of problems, we want them to be able to explore and “discover” solutions on their own. Our content is split into many small sections, and students have to actively participate at every step before the next one is revealed: by solving problems, exploring simulations, finding patterns and drawing conclusions.
We built many new types of interactive components, which go far beyond simple multiple choice questions or textboxes. Students can draw paths across bridges in Königsberg, run large probability simulations, investigate which shapes can be used to create tessellations, and much more.
As users interact with Mathigon, we can slowly build up an internal model of how well they know different related concepts in mathematics: the knowledge graph. This data can then be used to adapt and personalise the content – we can predict where students might struggle because they haven’t mastered all the prerequisites, or switch between different explanations based on students’ preferred learning style.
A virtual personal tutor guides you step-by-step through explanations and gives tailored hints or encouragement in a conversational interface. Students can even ask their own questions.
Using Mathigon requires much more effort and concentration from students, compared to simply watching a video or listening to a teacher. That’s why it is important make the content as fun and engaging as possible.
Mathigon is filled with colourful illustrations, and every course has a captivating narrative. Rather than teaching mathematics as a collection of abstract facts and exercises, we use real life applications, puzzles, historic context, inter-disciplinary connections, or even fictional stories to make the content come alive. This gives students a clear reason why what they learn is useful, and makes the content itself much more memorable.
All these goals are difficult to achieve in a classroom, because a single teacher simply can’t offer the individual support required by every student. Of course, we don’t want to replace schools or teachers. Mathigon should be used as a supplement: by students who are struggling and need additional help, students who want to go beyond what they learn at school, or even by teachers in a blended learning environment.
The ideas of active learning and personalised education are nothing new – teachers and researchers have been experimenting and writing about it for many years. Mathigon is one of the first implementations on a fully digital platform, which means that we can reach a much larger number of students. Of course, we are just getting started and there is still a long way to go.
One of the key underlying concepts is constructivism, the believe that students need to “construct” their own mental models of the world, through independent exploration, discovery and project-based learning. Constructionism was first developed by psychologist Jean Piaget (1896 – 1980), and then extended by mathematician, computer scientist and educator Seymour Papert (1928 – 2016).
There is plenty of research and evidence supporting this approach to teaching mathematics, and many existing ideas or examples we use as inspiration:
Seymour Papert (1980)
Paul Lockhart (2002)
Benjamin Bloom (1984)
Bret Victor (2013)
Scott Farrar, May-Li Khoe, Andy Matuschak (2017)
Ken Robinson (2006)
Andy Matuschak (2019)
Jo Boaler et al. (2016)
Deborah Ball (1992)
Chip and Dan Heath (2007)
Todd Rose (2016)
6 May 2020
London City Hall, November 2018
Philipp studied mathematics at Cambridge University, and mathematics education at the UCL Institute of Education in London. He previously worked as software engineer at Google, Bloomberg, Wolfram Research and Goldman Sachs. Philipp also consults for educational organisations like MoMath and IMAGINARY, regularly speaks at conferences all around the world, and was ISTE STEM educator of the month in January 2020.
Cindy is the Executive Director and CEO of MoMath, the National Museum of Mathematics in New York City, where she works to change public perceptions of mathematics.
Conrad is the co-founder and CEO of Wolfram Research Europe, the makers of Mathematica and Wolfram|Alpha. He also founded the Computer-Based Math Project, to reform maths education.
James is the founder of Global Math Week and mathematician-at-large for the Mathematical Association of America. He is committed to sharing the delight and beauty of the subject.
Mike is the founding CEO of National Numeracy, a non-profit dedicated to helping everyone use numbers and data in their daily lives. He also led the scale up of Numicon, and has a background in international sport and the military.
Rich is a co-founder of Android, partner at Google Ventures, and director at Google, where he works on new products for students and teachers.
Sarah is a former startup founder with over 16 years of experience scaling exceptional education programs and schools, and coaching founding teams of EdTech Startups globally.
We want to thank all these volunteers and supporters, and many others, for their contributions, advice, proofreading, feedback and generous donations: