Antifragility and mathematics education

This summer I’ve really tried to get back into reading offline (a difficult task at times). I’ve missed dabbling in some science fiction, a little spreadsheet modeling, and some texts from some modern great thinkers.

One book I am currently reading is Antifragile by Nassim Taleb. I really began making the strangest connections between some of these dynamic systems and mathematics education. I was pretty familiar with his earlier works The Black Swan and Fooled by Randomness, but I had not had a chance to read his newest treatise.

The basics

First a primer: the basic premise of the book is that systems can be classified in three ways: fragile, robust, and antifragile. The method of classification is fairly simple – how they perform under low-level stressors and volatility.

For an illustration, think of airplanes. Recently I was traveling to the Dominican Republic. I had to take a series of two flights to get there. Since flying involves getting into small metal tubes at 500+ mph, I wanted the minimal amount of stressors (e.g. turbulence, delays, sudden drops in pressure) as possible. I am in a fragile system.

However, the airline industry as a whole can be considered antifragile. Consider that although thousands of flights occur each day, and millions each year the recent fatal in San Francisco was the first domestic US flight with fatalities in 3 full years. With closer examination of the weather conditions, the habits of the flight crew, the integrity of the plane, and other factors (or stressors), the airline industry as a whole benefits from these tragedies. The probability of a crash of subsequent plane trips will go down – they are not independent. This is an example of an antifragile system.

A robust system merely one that is not fragile or antifragile. It neither benefits or is harmed by volatility.

Obviously this is a summary of a much longer work, but the entire text is available as a free pdf at Below is one additional table that gives some more illumination on the matter.


Obviously, because I have trouble relaxing on tropical vacations in the Dominican, I began thinking about this core tenet I have regarding children and learning. Although I am not a parent yet, my students have often referred to me as something of a tiger mom. I question, demand, instigate, rile up, needle, and question some more. Since beginning teaching, I have developed a bimodal approach – a movement to be more highly critical or more encouragingly praising with little small talk in between. This is partly due to my personality and partly due to the loving nature of my school. Someone has to show tough love… right?

But my reason for bringing this up now (and hopefully when I get back to blogging more regularly) is that we tend to think of students as fragile. Fragile systems need to be protected, they grow weaker with stressors and volatility and maintain their strength with order and predictability.

I completely reject this notion. Children as autonomous learners are antifragile. They need low level stressors coupled with respite in between. They don’t need their meal cut up for them. In fact they don’t even need you plating the meal or telling them “Dinner is ready!”. This metaphor isn’t perfect, and I would like to get into critical theory and the oppressive nature of some curriculum, but I digress.

Low-level stressors

Treating students as fragile is a disservice. Here is an off-the-top-of-my-head list of mathematical low-level stressors that will cause temporary discomfort (think of the temporary discomforts of a long run) that benefit students in the long term (i.e. increasing maximal distance, heart health).

  • not asking questions that are quickly answered
  • not answering questions that students can easily acquire
  • asking students to explain in detail, like with actual words
  • asking students to reflect on best practices
  • asking students questions which you might not know the answer
  • asking students to work in unfamiliar environments (new tools, software, physical spaces)
  • being direct with them when they are not working hard

There are probably better lists on beneficial stressors. Send me some @brandondeanprice if you have them.