Given my efforts in “How to Turn Every Child into a ‘Math Person’” to figure out something helpful to say about math education, I was delighted not too long after to run across Barbara Oakley’s Wall Street Journal op-ed
(As with all Wall Street Journal articles, if you hit the paywall, just google the title. The Wall Street Journal lets you jump the paywall if you come from Google.) Here is the key passage:
True experts have a profound conceptual understanding of their field. But the expertise built the profound conceptual understanding, not the other way around. There’s a big difference between the “ah-ha” light bulb, as understanding begins to glimmer, and real mastery.
As research by Alessandro Guida, Fernand Gobet, K. Anders Ericsson and others has also shown, the development of true expertise involves extensive practice so that the fundamental neural architectures that underpin true expertise have time to grow and deepen. This involves plenty of repetition in a flexible variety of circumstances. In the hands of poor teachers, this repetition becomes rote—droning reiteration of easy material. With gifted teachers, however, this subtly shifting and expanding repetition mixed with new material becomes a form of deliberate practice and mastery learning.
I also especially like her conclusion:
Understanding is key. But not superficial, light-bulb moment of understanding. In STEM, true and deep understanding comes with the mastery gained through practice.
For anyone learning math, the key to learning is patience—patience with both with the mental training needed to become good at working through details and with moments of confusion that come along the way. Believe me, those who do math for a living (as I do in important measure) face many moments of confusion in our work. What makes a mathematician is patience and persistence through those moments—and often hours or days, and sometimes months—of confusion, as well as the hours of honing skills for getting mathematical details straight.
I agree 100%.
One of the things people forget about John Stuart Mill’s On Liberty is that he lays down rules for when society can appropriately apply social pressure against bad behavior as well as when society can appropriately use the apparatus of law to punish people. When what is at issue is the appropriate use of the powerful apparatus of social pressure, John feels it is appropriate to act against a wide range of anti-social acts and character flaws. The following passage from On Liberty, Chapter IV, “Of the Limits to the Authority of Society over the Individual” paragraph 6, is an important list of antisocial acts and character flaws. I think we would have a better society if we all took seriously this list of things for which society can appropriately apply “moral reprobation”:
What I contend for is, that the inconveniences which are strictly inseparable from the unfavourable judgment of others, are the only ones to which a person should ever be subjected for that portion of his conduct and character which concerns his own good, but which does not affect the interests of others in their relations with him. Acts injurious to others require a totally different treatment. Encroachment on their rights; infliction on them of any loss or damage not justified by his own rights; falsehood or duplicity in dealing with them; unfair or ungenerous use of advantages over them; even selfish abstinence from defending them against injury—these are fit objects of moral reprobation, and, in grave cases, of moral retribution and punishment. And not only these acts, but the dispositions which lead to them, are properly immoral, and fit subjects of disapprobation which may rise to abhorrence. Cruelty of disposition; malice and ill-nature; that most anti-social and odious of all passions, envy; dissimulation and insincerity, irascibility on insufficient cause, and resentment disproportioned to the provocation; the love of domineering over others; the desire to engross more than one’s share of advantages (the pleonexia of the Greeks); the pride which derives gratification from the abasement of others; the egotism which thinks self and its concerns more important than everything else, and decides all doubtful questions in its own favour;—these are moral vices, and constitute a bad and odious moral character: unlike the self-regarding faults previously mentioned, which are not properly immoralities, and to whatever pitch they may be carried, do not constitute wickedness. They may be proofs of any amount of folly, or want of personal dignity and self-respect; but they are only a subject of moral reprobation when they involve a breach of duty to others, for whose sake the individual is bound to have care for himself. What are called duties to ourselves are not socially obligatory, unless circumstances render them at the same time duties to others. The term duty to oneself, when it means anything more than prudence, means self-respect or self-development; and for none of these is any one accountable to his fellow creatures, because for none of them is it for the good of mankind that he be held accountable to them.
This is a nice article by Callum Williams in the Economist, picking up on Ken Rogoff’s pitch for abolishing cash.
For clarity, I wanted to distinguish my approach from Ken Rogoff’s. I wrote in "Q&A: Apple Pay and the Future of Electronic Money"
I think physical cash is likely to play a minor role for a long time after it has been mostly eclipsed by electronic payment. For example, I think the strong demand for anonymity for certain kinds of purchases will make it very hard to eliminate paper money entirely. (If we tried to abolish paper dollars entirely, people would start using paper euros or yen or pounds for the purchases they wanted to make anonymously.)
So it is important to make some provision for what happens with paper currency rather than just assuming it can be abolished.
I was impressed with Uwe Reinhardt when I met him in person some years ago. And I like what he says in this abstract about occupational licensing. You can get Uwe’s full review at the link above.
Abstract: The licensing of occupations—a very forceful intervention in markets—is pervasive and growing in modern economies. Yet the attention paid to it by economists and economics textbooks has been small. Highly welcome, therefore, has been the extensive and intensive work on this subject by Morris Kleiner. Kleiner’s latest book, titledStages of Occupational Regulation: Analysis of Case Studies(2013), explores the progression of occupational regulation, from mere registration to certification to outright licensing—three distinct stages. Kleiner carefully selects for his analysis a series of occupations representing the stages of regulation, devoting a chapter to each occupation. He uses a variety of statistical approaches to tease out, from numerous databases, what the impact of mild to heavy regulation on labor markets appears to be. Kleiner’s work leads him to call for a pervasive review of occupational regulation in the United States, with a view towards replacing occupational licensure, which introduces the most inefficiency and welfare loss, with mere certification of occupations. That recommendation gains plausibility in an age where cheap computation and data mining makes it possible to protect consumers from low-quality and possibly dangerous services by providing robust, user-friendly information on the quality of services delivered by competing occupations, such as doctors and nurse practitioners.