In this week's article, Khan Academy founder Sal Khan discusses teaching for mastery, not test scores.
Historically in the West, education was imparted through a liberal arts education process. A tutor, or a set of tutors, were tasked with teaching a single student, which started with a review of the classics - Plato, Homer, etc - and the student retraced the development of Western Civilization.
This process was expensive and access to a liberal arts education was limited to the select privileged few who could afford access to such resources. In China, where the sheer volume of Chinese characters (around 40,000) made literacy the major impediment to education, education began, again with tutors, with three basic Confucian texts that provided the basic Chinese characters for the students to memorize rotely. All in all, the education process was personal, resource intensive, but did impart the ability to critically think for oneself, and studies were a life-long pursuit, long after guided training by tutors ended.
The modern system of public education we have today - with 30 students to a teacher, collectively progressing schoolwork, testing to rank and measure mastery - was said to be developed in Prussia in the late 18th and early 19th centuries. It was subsequently emulated by other nations and became internationally influential. Key concepts introduced by the Prussian education system in effect today include the coverage of the K-12 years (even the word Kindergarten is German), compulsory nature of basic public education and the pedogogical model of education, sometimes called the factory model of schooling. This model of education are characterized by top-down management, centralized planning, standardization, outcomes designed to meet societal needs and emphasis on efficiency in producing these results.
Public education in this manner has recorded many successes. Nations that implemented this model have reported high rates of literacy, and provided a basis for higher education and advanced research. Calculus, a high level mathematical discipline thought to be approachable after a lifetime of mathematical study in the days of Newton, is now routinely learned by high school seniors after 12 years of mathematics.
However, previous article aside about the problems associated with the standardization of curricula, current American difficulties teaching mathematics is a failure of the standardized education process to execute. Where as the last article discussed whether education should be modeled after mass production factories at all, this week's article talks about the factory's production line problems in passing students along the chain that are insufficiently prepared for the next academic step.
Nature of mathematics is such that more than any other subject, it sequentially builds on the previous lessons. A C student in math in 5th grade will have a difficult time getting an A in the next grade's mathematics, because they have only understood 70% of the previous mathematics lesson. A switch to common core will not alleviate this problem, as mathematics remains fundamentally the same, only the sequence has changed.
By the 12th year of progression in mathematics, most of the students who failed to grasp something previous will have fallen by the way side, leaving only a few students able to take on calculus or statistics, or whatever the end point mathematics course has been decided by policy. In other developed nations where this happens to a lesser degree, the school systems have picked up the slack and provided for reinforcement of missed lessons, or the cultural norms have put that responsibility on families and private education. Norway, Korea, Singapore , Finland and other nations whose students exhibit higher level of math mastery than the United States (there are 26 of them) - are mostly prosperous but less populous nations with fewer students to manage. Some of their solutions do not scale to that of the United States.
Sal Khan promotes the teaching of math based on mastery, not on getting kids to pass tests. He has also developed the Khan Academy to emphasize conceptual mastery of mathematical concepts covered in school - so that if the class has moved on without some of its kids, they have the opportunity to reinforce the missed lessons. This also allows mathematics to be what it is - a tool to study the world and to solve problems - instead of that hard thing kids struggle with in the classroom.
Video is linked below.