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 Gods

    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