Antifragility, Efficiency, and Agency in Class

I am still finishing up Nassim Taleb’s Antifragile book. I wanted to jot down some of the ways we treat students if we classified them by fragile vs antifragile.

Primer: systems are fragile if they are harmed by low-level stressors (think of a light bulb degrading over time/use); systems are antifragile if they benefit from low-level stressors (think of your cardiovascular system after progressing through difficult runs).

If we view children (students) as fragile

 If we view children (students) as antifragile

Give them constant positive feedback Barbell approach to feedback (only short corrections or high praise)
Breaking curriculum into manageable “bite-sized” portions Give them the lowest, appropriate level of information transfer (Moore method is most extreme)
Use behavioral incentives to motivate students Let students’ natural curiosities drive motivations
Use grades as incentives to motivate students Let students’ natural curiosities drive motivations
Try to plan out every moment of class time Be flexible to natural questions and connections
Stick to the specific domain of class Use human brain as a natural conduit to connect across domains (non-linear)
Ask questions with goal of efficiency and convergence Ask questions with goals of multiple approaches and nuance

I’d like to make one note on the last point on the table. When we run classrooms where students have multiple approaches to solving, we run the risk of students developing a non-optimized solution/algorithm/heuristic.

Where we have to be careful is realizing that creation and invention should be primary goals of mathematics, not efficiency. Efficient thinking is desirable and has a purpose, but it’s too easy to give (or force) students the optimal solution.

Giving pre-determined, optimized solutions has a few effects. First, we remove that student’s agency. We no longer care what you created, only what’s fastest. The main fallacy we approach with the banking model of education is that there are already millions of computers that can come up with a solution to 99.9% of high school problems.

Second, mathematics becomes something done to students, rather than students creating. See Paul Lochkhart’s Lament for a more eloquent discussion on that end.

Third, that modus operandi is bleeping boring. I know it bores me as a teacher. All I have to do is watch all of the pupils in my students’ eyes roll back when I “prescribe” optimal solutions to know students aren’t thrilled either.

Extremely Simple Example

I have seen a few different versions of this. Background: we’ve talked about some of the common conventions for the names of pairs of angles (e.g. alternate exterior) as well as which are congruent.

If the measure of angle 8 is 40 degrees, find the measure of angle 2.

Instead of recalling (or as Freire says – making a withdrawl) that alternate exterior angles are congruent, perhaps a student knows that 6 and 8 are congruent, and that 2 and 6 are congruent. So it becomes two-stepped instead of one-stepped.

However, at the cost of a small efficiency (which they will develop later independent of the teacher), the student retains agency. Instead of a memorization, there’s a bit of playfulness involved.

Giving students a chance to play with a simple transversal on a plane gives them more agency to do problems like this

image

Look at this. Already your mind is trying to parse together how you can begin solving. It’s a delicious problem.

Bottom line: if you’ve been showing kids how to solve simpler ones, if you’ve been treating them as fragile creatures instead of the wonderful, resilient, antifragile creatures that they are, then their response to your outstanding problem is this:

“Can you show me how to get started?”