In high school, our math teacher was lying to the class while teaching. That was brilliant. He would spend dozens of minutes explaining concepts while we were all focused and silent. Once he was done and received our approbation, he would confess the lies. He would go back to the beginning of the explanations to show the naivety of the reasoning, pointing wrong shortcuts and inaccuracies in the demonstration.
This unorthodox methodology was hugely effective and gave me the idea to gather the principles to teach better. Teaching is key and concerns everyone. As soon as we interact with others, we transmit knowledge, whether at work or at home, orally or in writing, with a person or in front of an audience, we are confronted with it on a daily basis.
Complete is Complex
Concepts can’t always be reached in one step but instead, understanding requires small jumps. As a child for instance, you first learn that numbers start at one. It’s a poor assumption since numbers can also be null, negative, decimal, etc. but omitting the complete and complex reality avoids being overwhelmed or demotivated at a very early stage. It is in this sense that I say “Complete is complex” because they go hand in hand: you can’t have a complete and simple explanation at the same time.
Bad teachers always want to be absolutely accurate at the cost of being incomprehensible. Good teachers, on the other hand, prefer to be understood by their students at the cost of sometimes over-simplifying reality or even lying. This methodology, at first sight immoral, is very ingenious. Because the complete reality cannot be digest at once, detours bet on further clarifications.
If the truth is facing the wind and we are a sailboat, it is useless to hope to reach it directly, move away to get closer to it later. - Twitter
Learn When Needed
Another reason to omit the complete and complex reality at an early stage is simply because it is not necessary. Postpone complexity until it is needed. You understand much better how to use a screwdriver on the day you need it, instead of taking a screwdriver course out of the blue. If it’s not on a subject you like, unnecessary explanations are simply confusing.
The child who imagined that the numbers were only positive will soon reach the limit, when calculating a budget for example. This is the best time to bring the concept of zero or even negative numbers. Reaching the limits of a paradigm should be the only reason to trigger additional explanations. When teaching, complement reality only when the time is opportune.
Concrete to Abstract
Only after the concept of positive numbers has been experimented with real examples can negative numbers be addressed. Only after the concept of integers has been experimented with real examples can decimal numbers be addressed. Etc. You can’t get around all the steps at once. Start from the very concrete (1, 2, 3, etc.) before any abstraction (a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q).
No Corner Cases Upfront
Discard explanations about corner cases at the first iteration. It is just noise. You will at best overwhelm people, at worst loose them. If a child ask you how many days is contained in a year, keep the leap year for later. Start with the very nominal case (365 days) before any corner cases (365.2425 days in the Gregorian calendar).
From one Extreme to Another
- The first time you write a program, it does not contain a single comment, even though you have learned that it is important for your colleagues to understand the intent of the code.
- The first time you read your work program, you don’t understand anything. Then you promise yourself to write as many comments as possible in the future.
- The 100th time you open your code, you can’t remember if most of the comments are still valid or not. You then promise yourself not to write as much comments as possible but as much as necessary.
A great learning process swings our opinions from one extreme to the other, often before stabilizing around a reasonable one. Experimenting with one extreme and its opposite opens up the spectrum of capabilities and highlights the drawbacks of overly radical conceptions. Teaching “not to write as many comments as possible but as much as necessary” cannot be fully understood in a single step and limits the learner to a reasonable opinion only.
Teaching reasonable opinions only trains learners to remain reasonable. Teaching radical opinions allows learners to become aware of a wider range of possibilities, enabling them to make radical decisions in exceptional circumstances.
Reasonable decisions in unreasonable circumstances are not marks of reason but of folly. - Twitter
This article is no exception to these principles. I was forced to lie to you in order to simplify and radicalize my remarks with an educational objective. Read, digest, then look for its limits. Read, radicalize and then relativize.
This article is very much inspired by Principles for Better Design that I have translated for teaching. I invite you to read it and understand the general principles so that you can adapt them to your discipline: architecture, engineering, art, etc.
Do you think there’s a principle missing? Send me your comments! This list will certainly be extended and refined, subscribe to the newsletter if you wish to be notified about it.