Mathematics

Below are some general notes about teaching this subject as a whole.

Mathematics is really about three things: Logic, (Mental) Calculation, and Algebra.

• Logical thinking (like pattern recognition or problem solving) is a crucial skill that anyone should keep training all their life. At the same time, it’s not the same as Mathematics. You can have logical problems without any numbers, for example. That’s why we mostly moved it into its own subject, as part of Science.
• (Mental) Calculation comes down to repetition and automation. There’s not much else to it and no way around it. You have to calculate a variety of things over and over until it becomes second nature and you can do it automatically in your head.
• Algebra encompasses the idea of numbers, of counting, and all the extra tools that Mathematics gives you to solve problems. This is about understanding a system. It’s not rote memorization, it’s about building an intuition for how to manipulate numbers.

Truly effective Mathematics education should teach all three things in equal measure. Our resources aim to help you with that.

Puzzles, escape rooms, games, they all teach these three things effectively. They ask you to logically problem solve. They ask you to really understand a problem, because it’s just too impossible (or mysterious) to brute force your way to the solution.

Even the repetitive “automation” part is made fun and exciting. These tools are great for throwing a variety of challenges at players. If you play a board game against other players, you never know what they might do, so the numbers you’re calculating with are always different.

Maths education is done right when the Apprentice naturally starts solving new problems. They deeply understand what they’ve been shown and can thus apply it to things they’ve never seen before.

As stated, things like logic and programming/coding are part of Science. Mathematics focuses on the journey towards Calculus.

Perhaps surprisingly, this subject also has stories, like all subjects. Those stories are meant for the Algebra part only: they often present a mystery or a tense adventure in which the protagonist really has to understand some mathematical idea to crack it. They’re a great tool for this. (Stories are not the best fit for the other two parts.)

We also see no reason to do what’s been done before. Free websites like Khan Academy have great digital, interactive tools that can literally throw infinite calculation challenges at you. We don’t do that. We focus on what we can do best: puzzles, games, social activities, and other physical challenges to teach deep understanding of mathematical concepts.