About Mathigon

2. Tell a Story

Rather than presenting mathematics as an abstract collection of results, we should introduce every new topic with an interesting narrative that shows students why what they are about to learn is useful and worthwhile doing. This is not just more interesting and motivating, but it also makes the content much more memorable.

Stories could be based on real-life applications (“predicting the weather”), historical events (“measuring the height of Mount Everest”), a mathematical puzzle (“which shapes tessellate”) or even fictional characters. There could even be some suspense and plot twists, where students don’t initially know where the story might lead, and are later surprised with an unexpected mathematical result.

3. Exploration and Creativity

In mathematics, the process of learning is often more important than the actual results and knowledge: it teaches students problem-solving, logical reasoning, critical thinking, abstraction and generalisation. These skills are transferable to many other parts of life, even if the specific mathematical topics have no real-life applications.

To make this most effective, students should be able to freely explore and be creative. With the guidance of a teacher or tutor, they should be able to discover new patterns and ideas on their own, and not just be the consumers of pre-packaged results and procedures.

5. Not Useful, but Meaningful

A large part of the mathematics that students learn at school won’t be useful in everyday life, even if they end up working as a scientist or software engineer. And that’s ok – as we’ve seen in principle 3, one of the reasons to study mathematics is to learn transferable skills like problem-solving and critical thinking. There are many other subjects in school that are also not “useful”, from Shakespeare’s Sonnets to Mozart’s Symphonies, and even Newton’s laws of motion. Instead, these subjects tell us about culture and history, or they help us understand and make sense of the world around us.

However, a lot of the existing mathematics curriculum is also not meaningful – and that is a problem. Rather than teaching about boring and essentially meaningless topics like long division, rationalising denominators or two-column geometry proofs, we should teach about networks, chaos, data science, cryptography, or game theory: topics which are exciting and beautiful, and which have a direct impact on all our lives. They help students better understand the world we live in, even if they are not directly useful in everyday life.

7. Intuition over Rigor or Fluency

When mathematicians think about their subject, they might primarily associate the rigor and formality of proofs. When high-school students think about mathematics, they might associate fluency problems when preparing for exams. In reality, neither of these two approaches are what we need from school mathematics.

The focus should be much more on mathematical intuition and understanding: estimating the answer to problems or verifying an existing answer, recognising and generalising patterns, deriving procedures and equations which you don’t remember exactly, and being aware of common mistakes and misconceptions (especially in topics like probability and statistics).

Many concepts in mathematics have a wide range of different representations (e.g. fractions as shaded areas, decimals, percentages, groups or rates). Students should be familiar with as many representations as possible, understand their relationships, and be able to decide which one is most suitable for a specific problem.