This past weekend's WSJ had an interesting article by Stephen Hawking ("A Brief History of a Best Seller"), in which he discusses his famed book's origin. His editor pestered him to make it more readable (which actually was Dr. Hawking's objective, as he wanted a book that could reach the masses).
I found the following of interest: "I am sure that nearly everyone is interested in how the universe operates, but most people cannot follow mathematical equations. I don't care much for equations myself." (emphasis added) Wow! "I don't care much for equations myself."
He continues "This is partly because it is difficult for me to write them down, but mainly because I don't have an intuitive feeling for equations. Instead, I think in pictorial terms, and my aim in the book was to describe these mental images in words, with the help of familiar analogies and a few diagrams."
Hawking and I are in agreement on the benefit of using "images in words," "familiar analogies, and "diagrams" to communicate ideas.
In our training classes, for example, we use the following graphic to discuss attribution's effects:
To explain "macro attribution," I came up with
We use a series of graphics, culminating in
I love metaphors, and use them frequently. And, I even cite a few episodes from Seinfeld and an occasional Doonesbury comic strip to communicate ideas.
Hawking isn't saying that formulas aren't needed, because they clearly are; however, there are often better ways to communicate ideas than relying solely on the math.
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Excellent points, as always, very insightful thoughts. If there is any competence these times call for, it is adaptability. Adaptability requires the flexibility to take into account multiple perspectives on a given situation. But the problem here is that your innovating approach and teaching techniques are not important to professionals who seek to acquire the CFA or any other designation. Simply because the exams test your breadth of knowledge, not your depth of knowledge!
ReplyDeleteCandidates therefore need to learn a little of a wide ranging of topics, without ever mastering any single field. Just memorize a few formulas and you’ll do well, we are often told.
My belief is that we are all exposed to, and have generally accepted, a certain line of standard learning techniques. This is why I think we see more and more candidates straight out of college passing the exams than multi-year professionals. Consider the difference between judging on process and judging on results. College students focus on the process, the structure of the actual test. In contrast, professionals on the field are judged on the application of their knowledge. In the real world the structure is often unknown and ever changing.
In other words, the test taker does not need to dig deeper; he/she already knows the question structure and even has the chance to take sample exams with the exact format used in the actual exam. Perhaps if the exam structure was different every time, your approach would be significant enough for the candidate.
Your analysis and conclusions are correct because they reflect how we actually learn. We first experience something and get to know how it behaves. We then visualize and verbalize what we know. This is where pictures come in. The power of these pictures is in their universality; they bridge the differences between our tendency towards unique expressions of a common reality. Only when we have established a common understanding of something do we apply literacy, which may be in the form of written words or mathematical expressions of the relationships between the particular variables that express the thing we are studying. In other words: a picture is worth a thousand words.
ReplyDeleteSteve, "spot on" (not patting myself on the back; it's re. the broader points). After one is quite comfortable with the math/functions/formulae/ideas, then they can translate it into a graphic, metaphor, etc. Some folks will never get the math, but they may get the ideas when expressed in this form; and, that's usually all that matters.
ReplyDeleteTake care not to confuse "modeling" with "equations" -- for example, object modeling via influence diagrams or process figures are essential -- however, the relationship between objects is still best expressed via an equation -- one without the other is methodologically unsound -- hope these thoughts are useful...
ReplyDeleteInteresting point; these models are each constructed from equations. Perhaps some standalone equations cannot easily be portrayed pictorially, but I would suspect that the use of metaphors, analogies, and the like can still hold in some cases.
ReplyDeleteThe book "Basic Economics" by Thomas Sowell is just like this - describes the fundamentals of economics without a single graph or table. Reading it made me get a MS in Econ. I wish the classes were as straight forward as that book.
ReplyDeleteThanks, Miles ... sorry for the delay in publishing; it got lost.
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