praphul chandra's Profile

I want to raise the general question of the mutual definition of man's
nature and the nature of modern institutions which characterizes our world
view and language.

To do so, I have chosen the school as my paradigm, and I
therefore deal only indirectly with other bureaucratic agencies of the
corporate state: the consumer-family, the party, the army, the church, the
media.

Not only education but social reality itself has become schooled.

Welfare bureaucracies claim a professional, political, and financial
monopoly over the social imagination, setting standards of what is valuable
and what is feasible. This monopoly is at the root of the modernization of
poverty. Every simple need to which an institutional answer is found
permits the invention of a new class of poor and a new definition of
poverty.

Poverty then refers to those who have
fallen behind an advertised ideal of consumption in some important respect.
In Mexico the poor are those who lack three years of schooling, and in New
York they are those who lack twelve

Equal educational opportunity is, indeed, both a desirable and a
feasible goal, but to equate this with obligator;' schooling is to confuse
salvation with the Church.

ducators
insist on packaging instruction with certification. Learning and the
assignment of social roles are melted into schooling. Yet to learn means to
acquire a new skill or insight, while promotion depends on an opinion which
others have formed

A second major illusion on which the school system rests is that most
learning is the result of teaching. Teaching, it is true, may contribute to
certain kinds of learning under certain circumstances. But most people
acquire most of their knowledge outside school, and in school only insofar
as school, in a few rich countries, has become their place of confinement
during an increasing part of their lives.

Most learning happens casually, and even most intentional learning is
not the result of programmed instruction. Normal children learn their first
language casually, although faster if their parents pay attention to them.

But the fact that a great deal of learning even now seems to happen
casually and as a by-product of some other activity defined as work or
leisure does not mean that planned learning does not benefit from planned
instruction and that both do not stand in need of improvement.

The deschooling of society implies a recognition of the two-faced nature
of learning. An insistence on skill drill alone could be a disaster; equal
emphasis must be placed on other kinds of learning.

School is inefficient in skill instruction
especially because it is curricular.

In most schools a program which is
meant to improve one skill is chained always to another irrelevant task.
History is tied to advancement in math, and class attendance to the right
to use the playground.

Schools are even less efficient in the arrangement of the circumstances
which encourage the open-ended, exploratory use of acquired skills, for
which I will reserve the term "liberal education."

Just as skill instruction must be freed
from curricular restraints, so must liberal education be dissociated from
obligatory attendance. Both skill-learning and education for inventive and
creative behavior can be aided by institutional arrangement, but they are
of a different, frequently opposed nature.

Most skills can be acquired and improved by drills, because skill
implies the mastery of definable and predictable behavior. Skill
instruction can rely, therefore, on the simulation of circumstances in
which the skill will be used. Education in the exploratory and creative use
of skills, however, cannot rely on drills. Education can be the outcome of
instruction, though instruction of a kind fundamentally opposed to drill.
It relies on the relationship between partners who already have some of the
keys which give access to memories stored in and by the community. It
relies on the critical intent of all those who use memories creatively. It
relies on the surprise of the unexpected question which opens new doors for
the inquirer and his partner.

The skill instructor relies on the arrangement of set circumstances
which permit the learner to develop standard responses. The educational
guide or master is concerned with helping matching partners to meet so that
learning can take place. He matches individuals starting from their own,
unresolved questions. At the most he helps the pupil to formulate his
puzzlement since only a clear statement will give him the power to find his
match, moved like him, at the moment, to explore the same issue in the same
context.

the unlimited opportunity for meeting among people who share an issue
which for them, at the moment, is socially, intellectually, and emotionally
important.

The Brazilian teacher Paulo Freire knows this from experience. He
discovered that any adult can begin to read in a matter of forty hours if
the first words he deciphers are charged with political meaning. Freire
trains his teachers to move into a village and to discover the words which
designate current important issues, such as the access to a well or the
compound interest on the debts owed to the patron. In the evening the
villagers meet for the discussion of these key words. They begin to realize
that each word stays on the blackboard even after its sound has faded. The
letters continue to unlock reality and to make it manageable as a problem.
I have frequently witnessed how discussants grow in social awareness and
how they are impelled to take political action as fast as they learn to
read. They seem to take reality into their hands as they write it down.

Creative, exploratory
learning requires peers currently puzzled about the same terms or problems.

The most radical alternative to school would be a
network or service which gave each man the same opportunity to share his
current concern with others motivated by the same concern.

Let me give, as an example of what I mean, a description of how an
intellectual match might work

Matching people according to their interest in a particular title is
radically simple. It permits identification only on the basis of a mutual
desire to discuss a statement recorded by a third person,

Why cannot self-identification be based also on
an idea or an issue?

Such theme-matching is by definition teacher-centered: it
requires an authoritarian presence to define for the participants the
starting point for their discussion.

By contrast, matching by the title of a book, film, etc., in its pure
form leaves it to the author to define the special language, the terms, and
the framework within which a given problem or fact is stated; and it
enables those who accept this starting point to identify themselves to one
another.

Why not let the identification of match
seekers include information on age, background, world view, competence,
experience, or other defining characteristics?

Why not provide match seekers with incidental
assistance that will facilitate their meetings-with space, schedules,
screening, and protection?

The equal right of each man to
exercise his competence to learn and to instruct is now pre-empted by
certified teachers.

Incidental education cannot any longer return to the forms which
learning took in the village or the medieval town. Traditional society was
more like a set of concentric circles of meaningful structures, while
modern man must learn how to find meaning in many structures to which he is
only marginally related. In the village, language and architecture and work
and religion and family customs were consistent with one another, mutually
explanatory and reinforcing. To grow into one implied a growth into the
others. Even specialized apprenticeship was a by-product of specialized
activities, such as shoemaking or the singing of psalms. If an apprentice
never became a master or a scholar, he still contributed to making shoes or
to making church services solemn. Education did not compete for time with
either work or leisure. Almost all education was complex, lifelong, and
unplanned.

Karl Marx

outlaw child labor. He opposed the proposal in the interest of the
education of the young, which could happen only at work. If the greatest
fruit of man's labor should be the education he receives from it and the
opportunity which work gives him to initiate the education of others, then
the alienation of modern society in a pedagogical sense is even worse than
its economic alienation.

Some words become so flexible that they cease to be useful "School" and
"teaching" are such terms.

For this purpose I shall define "school" as the
age-specific, teacher-related process requiring full-time attendance at an
obligatory curriculum.

School groups people according to age. This grouping rests on three
unquestioned premises. Children belong in school. Children learn in school.
Children can be taught only in schoo

School is an
institution built on the axiom that learning is the result of teaching.

We have all learned most of what we know outside school. Pupils do most
of their learning without, and often despite, their teachers.

Everyone learns how to live outside school. We learn to speak, to think,
to love, to feel, to play, to curse, to politick, and to work without
interference from a teacher.

probability" allows us to predict unknown outcomes based on known parameters, "likelihood" allows us to estimate unknown parameters based on known outcomes.

In a sense, likelihood works backwards from probability: given B, we use the conditional probability P(A|B) to reason about A

a likelihood function is a conditional probability function considered as a function of its second argument, with its first argument held fixed

given outcome A, use the likelihood function L(B|A) to reason about parameter B.

The numerical value L(b | A) alone is immaterial; all that matters are likelihood ratios of the form

where x is the observed outcome of an experiment. In other words, when f(x | θ) is viewed as a function of x with θ fixed, it is a probability density function, and when viewed as a function of θ with x fixed, it is a likelihood function.

If p is a probability then p/(1 − p) is the corresponding odds, and the logit of the probability is the logarithm of the odds; similarly the difference between the logits of two probabilities is the logarithm of the odds ratio (R), thus providing a shorthand for writing the correct combination of odds-ratios only by adding and subtracting:

An explanation of logistic regression begins with an explanation of the logistic function:

The variable z represents the exposure to some set of risk factors, while f(z) represents the probability of a particular outcome, given that set of risk factors. The variable z is a measure of the total contribution of all the risk factors used in the model and is known as the logit.

β₀ is called the "intercept" and β₁, β₂, β₃, and so on, are called the "regression coefficients" of x₁, x₂, x₃ respectively. The intercept is the value of z when the value of all risk factors is zero

Each of the regression coefficients describes the size of the contribution of that risk factor. A positive regression coefficient means that that risk factor increases the probability of the outcome, while a negative regression coefficient means that risk factor decreases the probability of that outcome; a large regression coefficient means that the risk factor strongly influences the probability of that outcome; while a near-zero regression coefficient means that that risk factor has little influence on the probability of that outcome.

Logistic regression is a useful way of describing the relationship between one or more risk factors (e.g., age, sex, etc.) and an outcome, expressed as a probability, that has only two possible values, such as death ("dead" or "not dead").

The Ising model is defined on a discrete collection of variables called spins, which can take on the value 1 or −1. The spins S_i interact in pairs, with energy that has one value when the two spins are the same, and a second value when the two spins are different.

Spins become randomized when thermal energy is greater than the strength of the interaction.

The spins can be thought of as living on a graph, where each node has exactly one spin, and each edge connects two spins with a nonzero value of J. If all the Js are equal, it is convenient to measure energy in units of J. Then a model is completely specified by the graph and the sign of J.

The probability of each configuration of spins is the Boltzmann distribution

Like the familiar Fourier transform, the Legendre transform takes a function ƒ(x) and produces a function of a different variable p. However, while the Fourier transform consists of an integration with a kernel, the Legendre transform uses maximization as the transformation procedure.