Learning How to Learn

I remember lying awake at night, waiting for an email containing my grades. I had never studied so hard in my life. The email arrived. My phone lit up the room. The results were 6, 6, 6. On a seven-point scale, that's good. But I knew people who did four subjects and surpassed me with ease. I was disappointed for a moment.

Then I reflected on what had happened. In my first year of engineering, I failed half of my subjects. I even started a different degree, thinking I just couldn't handle engineering. When I returned, I pushed hard to make it work. And it did work. I had succeeded for the first time, through sheer brute force. Compared to myself 18 months prior, I was a raging success.

Later I met Marty (not his real name), also a mature-age student. Marty had long hair and wore Slayer and Megadeth t-shirts. He used to be a software developer and had a diploma he called a "Corn Flakes box degree". Now, he studied pure mathematics. Marty quietly scored high distinctions across the board every semester. We often studied together, sharing the same extreme work ethic. Marty was a different beast though. He put in long hours, but not to ace the exam.

"I don't even bother trying to remember anything" he said. "The point of this is solving problems you've never seen before. Good luck memorising that."

Marty's approach was different. Most of us treated assignments like chores and tried to "get them done." Marty treated them like spirit guides on an LSD trip. He would dive deep for long periods. When he returned to mundane reality, he'd come out with some mind-blowing insight.

One day, he showed me a piece of paper with a square drawn on it. There was a function written underneath the square.

"If you change the way you measure space" he said, pointing to the function. "This meets the definition of a circle."

I was stunned. Then I burst out laughing. Studying with Marty was fun. His playful approach showed me that learning was not just blood, sweat and tears.

That summer, Marty and I hit the library to study a Dover book on algebraic topology. The book showed me the power of thinking about invariants. It might sound strange to study on your holidays, but I remember it fondly. It was a privilege.

It reminded me of David from my English night class a few years prior. He was a man of 40 who — like myself and everybody else in the class — had never finished high school. David loved mathematics and had taught himself well into the university level. He wanted to study formally, but this was his third time trying to pass English. He soon dropped the class and gave up on his dream. That was not uncommon. Most people who quit high school never return to formal education. I felt grateful, because there I was, well on my way to a four-year degree.

We got lunch, then Marty went home. I stayed to browse the social sciences library. I found a book called Learning How to Learn, by Joseph Novak. I could not put it down.

The author framed conceptual learning as a cycle of differentiation and integration. Differentiation is dividing an abstract concept into a hierarchy of subordinate concepts. Integration is articulating the relationships between those concepts. The analogy to calculus was intriguing.

I set about building concept maps just as prescribed. It was a great method for building big-picture understanding. You understand a domain by figuring out the entities (differentiation) and how they relate (integration). Building the maps took time, but the process boiled complexity down to its essence. Concept mapping gave me a whole new level of clarity. This introduced me to the power of being systematic.

Toward the end of my studies, I came across another decades-old, overlooked gem called Thinking Mathematically by John Mason. The book detailed a complete problem-solving process. I would do the problems in the book at night after work. It was monotonous, but that was the idea: practice being systematic.

The book was not really about mathematics. It was about behaviours. It talked about defining the problem, gathering what you know, specialising, generalising, conjecture, skepticism, contemplation, monitoring your emotions and asking questions. It talked about persevering when you feel stuck and reflecting on the emotional journey. Ultimately, you learn that the emotions pass. Then you develop confidence. The practice worked. The improvement in my problem-solving ability was absolutely phenomenal.

As I monitored and reflected, I saw that getting stuck triggered spiraling negative emotions. This limited my cognitive capacity. Avoiding my emotions would drive counter-productive behaviours like jumping to conclusions, rushing, wild goose chases and giving up.

All this time, my difficulties with education were not cognitive. I merely lacked insight into my emotional state during learning. Learning how to feel had shown itself to be even more important than learning how to learn.

My goal was originally to improve my performance, but that's only half the picture. An athlete must rest and recover to become faster and stronger. Likewise, you must be willing to heal to improve.