Why we Learn not to Learn

In this article, we’ll cover:

• Procedures vs abstract understanding
• Apparent short-term progress vs short-term struggle w/ long-term benefit
• Context-switching as a way of nudging out abstract understanding

The Problem

For many, the process of learning mathematics is not one of deep understanding but instead rote memorization of the procedures required to solve particular problems. This is because, in the short term, learning a procedure that functionally enables one to solve a problem is faster and easier than taking the time to acquire real understanding. To make matters worse, this type of learning is being incentivized in schools today.

A common lesson plan will take each subject sequentially and focus on a particular aspect for a short period. In Algebra, for example, one might progress from a basic linear equation to one containing exponents or square roots, and then to systems of equations, and so on. Every so often, a quiz or test will validate the contents of the current learning block. Besides the final exam, these quizzes and tests usually won’t contain any sort of review questions — instead focusing exclusively on the most recent subject having been learned. What this means is students are incentivized to study for short periods of time just before the test (“cramming”). Our short term memories allow us to hold this information just long enough to pass the test, but in the long-term it isn’t retained.

What’s more, the questions are usually either ones that the student has seen before, or are some simple variation on a theme, where the student is able to recognize the pattern and apply the correct procedure. This does not facilitate true creativity or problem solving, or even understanding. Actually, no understanding is necessary. Besides answering questions on a test, the student very likely has acquired little to no ability to apply the strategies in any other context.

The Solution

As a remedy, there are several research-backed methods which are proven to facilitate learning and retention, some of them counter-intuitive.

The first is that simply increasing the amount of time between rehearsals increases learning. A study asked three groups to memorize a list of words. The first group studied the list and then was allowed to recite the list immediately after. The second was given 15 to study the list before repeating it. The last was distracted by simple math problems before repeating the list. In this trial, the first group did the best, followed by the second and third. A bit later, when the groups thought they were finished, they were asked to recite the words again. This time the third group did the best. Just by the increased effort of struggling to hold the words in memory while working on another task, long term retention was improved even though short term performance suffered. This goes to show our intuitions about performance can be biased to favor short term demonstrable results over long term learning acquisition.

Next is that more struggle equals more learning. The US Air Force has a scholarship program that grants a full-ride with a pledge to do 8 years of service. It includes a core curriculum with Calculus I&II. Participants in a study were assigned teachers randomly, each with the same curriculum and testing procedure. It was found that the teachers rated best gave the best short-term performance in Calculus I, but not necessarily the best performance in Calculus II. In converse, the worst rated professors had lower short term performance metrics, but better long term performance. It goes to show that, although the fastest, most efficient way to pass a test in the short term gives the sense of satisfaction of having learned more, it is not necessarily the best way to establish a strong, enduring foundation of knowledge that will generalize into the future.

Finally, a technique called “interleaving” helps improve learning. When context doesn’t shift at all, the same procedure can be unthinkingly applied. By mixing learning blocks with review concepts, the flexibility required to apply rules abstractly in differing situations is challenged and reinforced. Research supports both that interleaving increases learning and retention, but also that people rate their learning lower for interleaved study blocks, yet on examination actually perform better.

I think humans are naturally creatures of habit. It is more comfortable and parsimonious for us to stick with known patterns and approaches for dealing with the world. Why waste energy seeking deep understanding when a simple algorithm will do just as well? But in certain contexts, this tendency inhibits us. By not stepping back from what we are trying to learn for a period, and by taking shortcuts and avoiding struggle, we prevent a sturdy foundation of knowledge from taking root. Proper scaffolding to support later knowledge requires enough time and enough connections in order to form sturdily.

As a side note, I would differ with the author somewhat in his sharp differentiation between specific and generalized learning. I think specific learning, in other words learning a procedure, can be a way to abstract a general principle. Seeking to understand the general principle in the absence of any concrete applications might be as difficult/harmful as only seeking solutions without general understanding.

If you found this useful, please feel free to comment in the section below. See ya!

References:

1. Range — Why Generalists Triumph in a Specialized World, David Epstein (Amazon Link)