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8/12/2019 Liberal Arts and Learning
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1. POETICS/GRAMMER
Poetics includes grammar and literature. Literature is
imaginative (not persuasive such as a sermon or
speech) when its purpose is to delight us by telling a
story (poem, novel, play, epic, essay, etc…). Its
purpose is recreational, but superior to games or
sports. A poem stirs up our soul and then brings it to
rest by lifting up our mind and emotions above the
strains and frustrations of everyday life. It is not an
escape from life, but rather a vision of the goal ahead
which encourages us and inspires us to live more
perfectly.
The plot is the soul of the story. The characters are
also important. A beautiful book must lead us to appreciate some
truth about life which is expressed in this work of art. This is why the
books we study are important (we are trying to compile a literature
curriculum with four books per year for each grade).
The power of a story to arouse the emotions and thenbring them to rest is called catharsis (purification).
Through philosophy we can have the vision of the goal, but it comes
late in life, through poetry we can already have a similar experience
when we are young.
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2. DIALECTICS/LOGIC-It is the art of correct thinking. The students
must know the basic rules of logic. They should be able,
when reading a text, to disengage the essential from
the accidental, to see what the author is trying to
prove. They should also learn how to draw
conclusions from principles and refute false
reasoning. We must restore the disputatio in our
schools. We have sports tournaments. Why not
intellectual jousting? This exercise was a common
feature of Jesuit schools. It is excellent to sharpen the
mind. This quote from the famous Ratio studiorum
will make it clear:
The concertatio, which is usually conducted by the
questions of the master or the corrections of rivals or
by the rivals questioning each other in turn, must be
held in high esteem and used whenever time permits
so that honorable rivalry, which is a great incentive to
studies, may be fostered. Some may be sent
individually or in groups from each side especially the
officers; or one may attack several; let a private seek
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a private, let an officer seek an officer; or even let a
private attack an officer, and, if he conquers, let him
secure his honor or some other award or sign of
victory as the dignity of the class and the custom of
the place demand.
3. RHETORIC
It is the art of persuasion. It is a very practical art,
which appeals to emotions, like poetics, unlike
dialectics. What is the difference between poetics and
rhetoric? The poet is concerned with telling a good
story which excites our emotions and then brings us
to rest in the enjoyment of beauty. It leads us to
appreciate what is noble in human life. (Poetry is also
one of the fine arts, unlike rhetoric).
The rhetorician is concerned with convincing the
audience to act. They will put into practice what he
has urged them to do. (This is what a football coach
does when he gives a pep talk to his players at half
time, especially when the team is losing) Religious
sermons, political speeches, advertising, talks, etc…
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So when we are teaching math, we must make sure
our students seek to understand why an answer is
true. This means that they must trace it back to
axioms and postulates. Only then do they have
scientific knowledge. If they cannot base a conclusion
on principles known to be true, it is not real science
but mechanical skill, in the manner of an automatic
reflex. Some of our teachers seem to have found
problems with the Saxon textbooks which do not
concentrate on one concept per chapter but aim at
"programming" the student without understanding
the principles. Maybe some alternatives can be found.
5. GEOMETRY
Geometry is the science of magnitudes (discrete
quantity). When Plato opened his school, the famous
"Academy", he engraved over its portal the famous
inscription: "Let no one ignorant of geometry enter
here." It is Euclid who brought geometry to the level
of a science. In his "elements", concepts are carefully
built up in a logical way so that we can see the proper
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reasons for the conclusions.
Euclid is moving in a synthetic order from the simpler
problems to the more complex. He begins with the
simplest truths (definitions) and works in the direction
of more and more complicated theorems. On the
other hand, many of his proofs are analytical. They
begin with the conclusion and work back to the
principle on which it is based. The student then
practices syllogistic reasoning (e.g., reductio and
absurdum).
A geometry book based on Elements of Euclid is more
difficult than other textbooks, because it requires
more thinking, but it is better for the formation of the
mind.
6. MUSIC
It is applied maths. When a stretched string vibrates,
the shorter the part is, the more rapid is the vibration
and the higher the tone it emits. The scale is
therefore composed of mathematical proportions.
Aristotle includes music in a liberal education. He
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mathematics (whether pure or applied) begins as the
study of a practical art and ends as a speculative
science. Astronomy is a good way to have the
students apply their knowledge of geometry to
physical reality (the movement of celestial bodies).
The observation of stars and planets with a telescope
is also a great way to awaken wonder in their minds
and leads them to appreciate the beauty of God’s
creation.
CONNECTIONISM (EDWARD THORNDIKE)
The learning theory of Thorndike represents the
original S-R framework of behavioral psychology:
Learning is the result of associations forming between
stimuli and responses. Such associations or "habits"
become strengthened or weakened by the nature and
frequency of the S-R pairings. The paradigm for S-R
theory was trial and error learning in which certain
responses come to dominate others due to rewards.
The hallmark of connectionism (like all behavioral
theory) was that learning could be adequately
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explained without refering to any unobservable
internal states.
EDWARD THORNDIKE'S EXPERIMENTS
Thorndike investigated learning in animals by using
cats. A hungry cat was confined in a puzzle box with
food visible on the outside. He presented it a
problem, which required the cat to manipulate some
devices, which would open the gate of the puzzle box.
Bits of food were placed outside the box as an
incentive for the cat to open the gate. From such
experiments, Thorndike made the following
observations.
The cat first behaved aimlessly as if doing things by
trial and error.
It then responded correctly by accident (chance
success) and finally, repeated the successful
operation
Consuming the food (satisfier) rewarded it. Getting
the reward strengthens the connection between the
stimuli and the response made just before the reward
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(satisfier) was given. From the above observations.
Thorndike formulated three major laws, namely: law
of effect, law of readiness and law of exercise
LAW OF EFFECT
The law of effect states that the association between
a stimulus and a response will strengthen or
weakened depending on whether a satisfier or an
annoyer follows the response (Gibson, 1980). An act,
which is followed by satisfaction in a given situation,
will generally
Become associated with that situation; so that when
it recurs the act will also be likely to recur (Curzon,
1981). On the other, an act, which results in
discomfort, tends to be disassociated from the
situation, so that when the situation recurs, the act
will be less likely to recur.
The greater the satisfaction or discomfort
experienced, the greater the degree to which the S-R
bond will be strengthened or loosened.
After research studies have showed that this
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explanation was inadequate, Thorndike propounded
another law, the truncated law of effect. This law
added the idea that while satisfiers always
strengthens the bond between a stimulus and a
response, the effect of annoyers
Is much less predictable; sometime they weaken the
bond, but sometimes they do not.
LAW OF EXERCISE
The law of exercise states that response to a situation
may be strongly connected with the situation
depending on the number of times it has been so
connected and to the average strength and duration
of the connection. The exercise here refers to
practice. Practice they say makes
Perfect. In a later revision of the law, Thorndike
asserts that practice in itself did not make perfect,
but practice in circumstances that allowed the learner
to be informed or given comments about his progress
could be valuable in strengthening the S-R links
LAW OF READINESS
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The law of readiness states that a learner's
satisfaction determined by the extent of his
preparatory set, that is, his readiness for action. This
law was summarized into two:
When someone is ready to perform an act to do so is
satisfying.
When someone is ready to perform some act, not do
so is annoying. An interference with goal-directed
behavior causes frustration and making someone to
do something he does not want to do is frustrating
SUBSIDIARY LAWS
Thorndike also outlines other subsidiary law (Curzon,
1981). They include the following:
Law of Multiple Responses. A response, which fails
to produce satisfaction, will trigger off another until
success results and learning becomes possible
Law of Set. The individual's total attitude or
disposition affects learning.
Law of Response Analogy. A Person's response to
a novel situation is determined by innate tendencies
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to respond and by elements in similar situations to
which he has acquired responses in the past.
Law of Selectivity of Response. As an animal
learns, it becomes capable of ignoring some aspects
of a problem and responding to others.
Law of Associative Shifting. A learner first
responds to a given stimulus, then transfers the
responses, but association, to another stimulus.
Law of Spread Effect. If an act had pleasurable
consequences, the pleasure tended top become
associated with not only the act and the eliciting
stimulus, but also with other actions, which occurred
approximately, the same point in time.