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 has fun and engaging as possible.
Mathigon is filled with colourful illustrations, and every chapter 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)
Jo Boaler et al. (2016)
Deborah Ball (1992)
Chip and Dan Heath (2007)
Todd Rose (2016)
As part of developing Mathigon, we regularly give talks at conferences on mathematics or education.
Philipp studied mathematics at Cambridge University, and mathematics education at the UCL Institute of Education in London. Before Mathigon, Philipp worked at Google, Bloomberg, TouchPress, Wolfram Research and Goldman Sachs. He regularly gives talks at conferences on education, and has volunteered with MoMath, Code Club, ReachOut! and many similar projects
Philipp created Mathigon while volunteering with an outreach project at Cambridge University, that sent university students to local primary and secondary schools. The initial goal was simply to show how fun and colourful mathematics is. Over time, Mathigon has grown from a spare time project into a platform with thousands of users and numerous awards.
We are grateful to all of the following for their contributions, support, proofreading and testing:
London, September 2017 – Mathigon is an award winning new mathematics education platform for students aged 12 to 18. Part textbook and part virtual personal tutor, it is available online at mathigon.org and completely free. Using cutting-edge technology and an innovative new curriculum, Mathigon wants to make learning mathematics more fun and more interactive.
Rather than just telling students how to solve standardised problems, we want them to actively explore and discover solutions on their own. Every chapter has countless illustrations and a captivating narrative that makes the content more accessible and memorable – from real life applications to puzzles, historic context or fictional stories.
Teachers can link their students’ accounts and see detailed analytics on their progress, or specific topics they struggled with. We also have a range of other classroom resources – from mathematical origami to a treasure hunt.
Mathigon was created by Philipp Legner, who studied mathematics at Cambridge University, mathematics education at the Institute of Education in London, and worked as software engineer at Google and Bloomberg. In addition to fantastic feedback from students and teachers, Mathigon has received multiple awards:
Mathigon is still in beta, and we are constantly adding new features and additional content. Please contact firstname.lastname@example.org for additional information.