Nabeel Qureshi is a biomedical software engineer at Palantir who studied Philosophy, Politics & Economics at Oxford. In his recent essay How To Understand Things, he argues that “understanding is not a binary “yes/no”. It has layers of depth.” Qureshi’s insights fit well with our learning philosophy here at Demme Learning, and in this post, I highlight some of his most compelling ideas for building understanding.
Qureshi begins his essay by recounting the following:
The smartest person I’ve ever known had a habit that, as a teenager, I found striking. After he’d prove a theorem, or solve a problem, he’d go back and continue thinking about the problem and try to figure out different proofs of the same thing. Sometimes he’d spend hours on a problem he’d already solved.
The Benefits of Deep Learning
When we are learning new things, it’s tempting to be satisfied with a superficial understanding. We memorize a solution or formula and then speed onto the next topic. But rushing through the learning process robs us of the opportunity to really gain conceptual mastery. Deep learning is a slow, deliberate process that rewards careful attention and precise thinking.
Qureshi observes that “intelligent people simply aren’t willing to accept answers that they don’t understand.” Instead, like the mathematician who continued to find alternative solutions for problems, those who wish to deeply comprehend do not rest with easily won answers. Rather they spend additional time forming better questions that are harder to answer but whose answers hold much revelatory power. Importantly, intelligence is not a fixed, innate trait, and the speed of reading or the rate at which you can process new information has no bearing on the character traits of tenacity and determination required for deep learning. Qureshi thus argues that “what we call ‘intelligence’ is as much about virtues such as honesty, integrity, and bravery, as it is about ‘raw intellect’.”
Regarding integrity, Qureshi warns that it is “so easy to think that you understand something when you actually don’t. So even figuring out whether you understand something or not requires you to attack the thing from multiple angles and test your own understanding.” Most of us do not relish the feeling of confusion or ignorance, and so we rush to persuade ourselves that we have mastered material long before we actually have gained mastery. As Qureshi explains, “it is uniquely easy to lie to yourself because there is no external force keeping you honest; only you can run the constant loop of asking “do I really understand this?” And so to become lifelong learners, we have to foster a desire for authenticity, an “honesty, or integrity: a sort of compulsive unwillingness, or inability, to lie to yourself.”
Helpful Study Habits
Qureshi provides the following practical advice for the kinds of study habits that can really help to foster the virtues needed for authentic learning:
Read slowly, think slowly, really spend time pondering the thing. Start by thinking about the question yourself before reading a bunch of stuff about it. A week or a month of continuous pondering about a question will get you surprisingly far. And you’ll have a semantic mental ‘framework’ in your brain on which to then hang all the great things you learn from your reading, which makes it more likely that you’ll retain that stuff as well.
This is a demanding vision for education and one that foregrounds good character alongside the domain-specific body of knowledge. If Qureshi is correct, it is not possible to be a truly great student if you are not also actively becoming a good person. And that means what happens outside the “classroom” is every bit as important as what transpires within it. This might seem too daunting as a model for education. The great news though is that virtue provides us with its own rewards. As our understanding begins to expand and deepen, the internal experience of coherence and clarity more than makes up for all the hard toil required to reach that point. In much the same way that we feel a thrilling rush after hiking to a summit with a beautiful view, the moment of “eureka” is the greatest reward for the authentic and honest work of building genuine understanding.
Here at Demme Learning, all of our curricula are designed to “build understanding.” Like Qureshi, we recognize that authentic learning is about far more than mere memorization. We seek to empower our students to move at their own pace, only advancing to the next sequential concept when they are able to demonstrate mastery of the current concept. In this way, we help students to build that robust mental framework through which to integrate all their learning. Whether it’s math, spelling, or grammar, we enable students to gain conceptual depth and be able to creatively apply what they are learning.
• One of Nabeel Qureshi’s key insights is that virtue is intrinsic to authentic learning. Francis Su, the former president of the Mathematical Association of America, agrees that virtues enable learning, but he also believes that studying mathematics can also help foster the virtues needed for a good life.
• Qureshi’s essay is a great example of the importance of epistemology – the branch of philosophy that deals with what we know and how we can know it. Mathematics is intimately connected to epistemology.
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