The first is one of the biggest education reform initiatives to predate the current era. It had striking parallels to many of the current initiatives and was often supported by almost identical rhetoric but it seems to have dropped down the memory hole.
New Mathematics or New Math was a brief, dramatic change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries, during the 1960s. The name is commonly given to a set of teaching practices introduced in the U.S. shortly after the Sputnik crisis in order to boost science education and mathematical skill in the population so that the perceived intellectual threat of Soviet engineers, reputedly highly skilled mathematicians, could be met.
Mathematicians describe interesting objects with set-builder notation. Under the stress of Russian engineering competition, American schools began to use textbooks based on set theory. For example, the process of solving an algebraic equation required a parallel account of axioms in use for equation transformation. To develop the concept of number, non-standard numeral systems were used in exercises. Binary numbers and duodecimals were new math to the students and their parents. Teachers returning from summer school could introduce students to transformation geometry. If the school had been teaching Cramer's rule for solving linear equations, then new math may include matrix multiplication to introduce linear algebra. In any case, teachers used the function concept as a thread common to the new materials.
Philosopher and mathematician W.V. Quine wrote that the "rarefied air" of Cantorian set theory was not to be associated with the New Math. According to Quine, the New Math involved merely..."the Boolean algebra of classes, hence really the simple logic of general terms."
It was stressed that these subjects should be introduced early. The idea behind this was that if the axiomatic foundations of mathematics were introduced to children, they could easily cope with the theorems of the mathematical system later.
Other topics introduced in the New Math include modular arithmetic, algebraic inequalities, matrices, symbolic logic, Boolean algebra, and abstract algebra. Most of these topics (except algebraic inequalities) have been greatly de-emphasized or eliminated in elementary school and high school since the 1960s.
The second is a widespread though perhaps fading approach to running a business. Outside of various questionable theories of incentives, it might be the most influential set of private sector ideas in the reform movement. (For a more detailed account of the relationship, check out this article by Shawn Gude)
Its development began with Frederick Winslow Taylor in the 1880s and 1890s within the manufacturing industries. Its peak of influence came in the 1910s; by the 1920s, it was still influential but had begun an era of competition and syncretism with opposing or complementary ideas.
Although scientific management as a distinct theory or school of thought was obsolete by the 1930s, most of its themes are still important parts of industrial engineering and management today. These include analysis; synthesis; logic; rationality; empiricism; work ethic; efficiency and elimination of waste; standardization of best practices; disdain for tradition preserved merely for its own sake or to protect the social status of particular workers with particular skill sets; the transformation of craft production into mass production; and knowledge transfer between workers and from workers into tools, processes, and documentation.
Scientific management's application was contingent on a high level of managerial control over employee work practices. This necessitated a higher ratio of managerial workers to laborers than previous management methods. The great difficulty in accurately differentiating any such intelligent, detail-oriented management from mere misguided micromanagement also caused interpersonal friction between workers and managers.
The third is rather specific and it's perhaps more up-and-coming than big, but it has some powerful supporters and is already having a having a major impact, particularly in mathematics education.
Psychologist K. Anders Ericsson, a professor of Psychology at Florida State University, has been a pioneer in researching deliberate practice and what it means. According to Ericsson:
"People believe that because expert performance is qualitatively different from normal performance the expert performer must be endowed with characteristics qualitatively different from those of normal adults." "We agree that expert performance is qualitatively different from normal performance and even that expert performers have characteristics and abilities that are qualitatively different from or at least outside the range of those of normal adults. However, we deny that these differences are immutable, that is, due to innate talent. Only a few exceptions, most notably height, are genetically prescribed. Instead, we argue that the differences between expert performers and normal adults reflect a life-long period of deliberate effort to improve performance in a specific domain."
One of Ericsson's core findings is that how expert one becomes at a skill has more to do with how one practices than with merely performing a skill a large number of times. An expert breaks down the skills that are required to be expert and focuses on improving those skill chunks during practice or day-to-day activities, often paired with immediate coaching feedback. Another important feature of deliberate practice lies in continually practising a skill at more challenging levels with the intention of mastering it. Deliberate practice is also discussed in the books, "Talent is Overrated," by Geoff Colvin, and "The Talent Code," by Daniel Coyle, among others.
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