# Về Mathigon

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.

## Active Learning

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.

## Personalisation

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.

## Storytelling

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 belief 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:

### Mindstorms: Children, Computers, and Powerful Ideas

Seymour Papert (1980)

### A Mathematician’s Lament

Paul Lockhart (2002)

### What Makes People Engage With Math – TED Talk

Grant Sanderson, 3blue1brown (2020)

### Numbers at play: dynamic toys make the invisible visible

Scott Farrar, May-Li Khoe, Andy Matuschak (2017)

### Seeing as Understanding: The Importance of Visual Mathematics

Jo Boaler et al. (2016)

### The 2 Sigma problem: The Search for Methods of Group Instruction as Effective One-to-One Tutoring

Benjamin Bloom (1984)

### Do schools kill creativity? – TED Talk

Ken Robinson (2006)

### Why books don’t work

Andy Matuschak (2019)

### Media for Thinking the Unthinkable

Bret Victor (2013)

### Magical hopes: Manipulatives and the reform of math education

Deborah Ball (1992)

PDF

### Teaching that sticks

Chip and Dan Heath (2007)

Todd Rose (2016)

## Content and Engineering

Philipp Legner
VP of Mathigon
David Poras
Director of Product
Phil DeOrsey
Software Engineer
Gabe Turow
Software Engineer
Josh Stein
Software Engineer
Kaira Imer
Software Engineer
Dmytro Ohorodnykov
Software Engineer
Sarah Page
Designer
Patrick Henning
Software Engineer
Eda Aydemir
Content Writer

Cindy Lawrence
MoMath
Wolfram Research
James Tanton
MAA
Katharine Jackson
Sage Publishing
Rich Miner
Sarah Lee
EdVentures
Simon Singh
BBC, Author

## Translations

• Catalan: David Virgili
• Chinese: iuway, Kaka, jexchan
• German: Harald March
• Italian: Michela Riganti, Letizia Diamante, Antonio La Barba
• Romanian: Claudia Dumitrascu, Ariana-Stanca Vacaretu
• Russian: Аня Никитина
• Spanish: Scott Nepple, Héctor Palacios, Carlos Ponce Campuzano, Pilar Fortuny Ayuso
• Turkish: Utku Aytaç, Can Ozan Oğuz, Ebru Nayir, Murat Uyar, Buket Eren, Eda Aydemir, Begüm Gülşah Çaktı, Ayşe Yiltekin, İsmail Kara
• Vietnamese: Ngo Thuy Anh Tuyet

## Volunteers and Supporters

We want to thank all these volunteers and supporters for their contributions, advice, proofreading, feedback or generous donations:

• Justin Baron
• Srikanth Chekuri
• Alison Clark-Wilson
• Dirk Eisner
• Susan Jobson
• Tim Knight
• Michal Kosmulski
• Wolfgang Laun
• Joel Lord
• Rose Luckin
• Samantha Marion
• Alex McCall
• Manuel Menzella
• Huw Mort
• Meenakshi Mukerji
• Andy Norton
• William O’Connell
• Antonella Perucca
• Anwit Roy
• Kostas Symeonidis
• Andre Wiederkehr
• Danny Yee
• Arul Kolla
• John Green
• Yi-Hsuan Lin
• Samuel Watson
• Enrico Poli
• Zach Geis
• Jack Kutilek
• leeyeewah
• Leif Cussen
• Chris Peel
• Sergei Kukhariev
• Alexander Shapoval
• Andrea Michi
• Troy Weets
• 安強 朱
• Howard Mullings
• Oleksandr Prokopenko
• Evgeny Sushko
• Israel Parancan Navarro
• Josep lluis Mata
• Valeri Jean-Pierre
• Alex Munger
• Jay Mitchell
• Denis Zuev
• Matematika Tivat
• Nafez Al Dakkak
• Amy Dai
• Clara Marx
• Kimberly Lilly
• Angela Bottaro
• Yolanda Campos
• rittersg
• Tom Leys
• Anuj More
• Howard Lewis Ship
• Leo
• Becca LeCompte
• Reymund Gonowon
• Axek Brisse
• Dev Karan Ahuja
• Guillaume
• Antony Mativos
• Bryan Shull
• Matthew Deren
• Georgreen Mamboleo
• Yijia Wang
• Devin Wilson
• billxiong
• dacapo
• Cyril Ghys
• charlespipin

How can we make education more about exploring and creativity, rather than rote-learning and memorising, with personalised content and engaging storytelling? These nine principles guide our team when developing great content for learning mathematics.

## 1. Learning Should Inspire

Mathematics should inspire and empower students, not scare or confuse them. We should show the surprising beauty and great power of mathematics – and that everyone can “do maths”.

## 2. Tell a Story

Storytelling can motivate students, make the content more memorable, and justify why what you’re learning is important – including real-life applications, curious puzzles, or historical background. More…

## 3. Exploration and Creativity

Allow students to explore, be creative, make mistakes, practise critical thinking, and discover new ideas – rather than just telling them the final results and procedures to memorise. More…

## 4. Mathematics is Everywhere

We are always surrounded by mathematical patterns and relationships. Students should be able to recognise these, and harness the power of maths to solve problems in everyday life.

## 5. Not Useful, but Meaningful

Not all topics in the curriculum have to be useful in everyday life (neither are Mozart or Shakespeare), but every topic should be meaningful – because of its applications or mathematical significance. More…

## 6. Mathematics is Visual

Equations are useful, but there are often much better representations of mathematical concepts and relationships. The content should be as visual and colourful as possible.

## 7. Intuition over Rigor or Fluency

Rigor is an important part of mathematics, and there is also a place for practising fluency – but the main goal should be to develop intuition, deep understanding, and general numeracy. More…

## 8. Discussion and Teamwork

Mathematics is rarely a solitary pursuit, and many real problems don’t just have a single, correct answer. Discussions, collaboration and teamwork should be a key part of every curriculum.

## 9. Mathematics is Alive

To make mathematics more relevant, it is important to portray its history, recent discoveries, and current research – as well as the diverse groups of mathematicians and scientists doing this work.