Effective learning requires self-awareness, and self-awareness requires (self-) assessment. Often we consider formal – so called, “summative” – tests to be the metric by which we discern our own knowledge. Tests, I mean. We take tests, and based on the number assigned by the professor determine whether we “know” the content or not. But tests are actually quite terrible metrics for assessing knowledge, as they are so easily hacked by logical reasoning, inference, eliminating answer choices, cramming, rote regurgitation, or plug-and-play memorization of formulae. Richard Feynman relays a story of Princeton physics students leaving a lecture on leverage and motion who were unable to open the large antique door of the hall because they misunderstood how to push relative to the hinges. Princeton students get good scores on tests, but did they know physics or did they know equations? Einstein, meanwhile, failed entrance exams to the most elite schools, and had his most monumental discoveries in a patent office, daydreaming. So clear was Einstein’s understanding that he did not require a lab or library, and could simply play with the ideas in his mind. His discovery of relativity occurred long before his proof or paper, long before his famed equations and prizes and posts. Technical formalization and academic performance are at best minor components of true knowledge—at the end of the day, notational descriptions of motion won’t get the door open.
So, how do you know if you truly know (or if your students do)? Here are the five tests that I use to assess the quality of understanding and instruction, both for myself and others:
The Feynman Test
Though associated with the joking professor, other great explainers like Grant Sanderson, Khalid Azad, Richard Maybury, and, yes, Einstein have reformulated this sentiment, with the essence being: “Can you explain this to a bright child?” The essence of calculus is slopes and areas, and they’re calculated by making increasingly small lines or boxes. A smart sixth-grader should have little difficulty grasping the logic, as well as some of the basic computations and proofs. Ponderous explications of differentiation and limits at infinity and the power rule won’t cut through, and if that’s all you have to offer, you probably don’t get it yet.
The Dennett Test
Daniel Dennett coined the term “Intuition Pump” some years ago, and I largely prefer that to related terms like “analogy” and “thought experiment.” My rationale is subtle and not really important, and analogies and thought experiments are sufficiently close concepts to proceed. The essence of the Dennett Test is: “Can you tell me a story, describe an example, or offer a comparable process that links the concept to something I already understand.” A perfect mapping isn’t necessary, only something about the mechanics of what you are explaining that is sufficiently similar to something familiar, such that you trip my intuition into “Aha!” mode. The general format should run something like: “You know how…when you…it does…--this is like that.”
The Twain Test
From Mark Twain’s famed dictum: “Eschew superfluous verbiage.” Often we use the convenient obfuscation created by esoteric language to mask our shallowness of understanding (counting on the other guy not knowing the terms either). Indeed, we can often convince even ourselves that we comprehend something because we can throw impressive argot around. But technical language is created to indicate extremely fine distinctions; the majority of the concept is contained within much simpler stuff. The Twain Test asks: “Can you explain this without the deployment of any technical language or notation?” Try writing or articulating a few sentences that start with “Basically, its…” For example, rather than “A tariff is a <insert references to Keynesian monetary policy and supranational protectionism reflective of supply chain …>…”, try “Basically, it’s a tax to sell something in a different country.”
The Trifecta Test
Simple: “Can you explain this in at least three different ways.” Deep understanding situates a concept within a mental schema – a framework of mental model that reflects lots of operations and relationships across your conscious experience. A shallow understanding leaves the information very poorly linked to a broader network of information. Think about a language—in English (a language I’m deeply fluent in), I can state: “Where’s the bathroom?” or “Can you point me to the restroom?” or “Is there a men’s room I can use on this floor?” or “Do you mind showing me to the lavatory?” or any other of dozens of reiterations of the same essence. In Spanish (a language I’m only somewhat familiar with), I can only offer “Donde esta el bano?”
The “Feynman’s Classmate” Test
With reference to the story about Feynman above, this test assesses whether you can get the door open or not. When something is meaningfully understood, life presents challenges where that information is recognized as being useful to the solution. Engineers don’t study calculus to take bizarre integrals on exam sheets – they learn it to discern how to build bridges, measure light waves and gravitational forces, and keep airplanes in the air. Consider: “Given a puzzle/challenge/task, can I recognize that X is the tool I need to solve the problem?” I won’t even say that you ought to be able to (necessarily) do X, but if you don’t see that this is the tool to solve this kind of problem, then you probably don’t get it beyond words on a page.
Comments