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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.



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



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…



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



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



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



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



(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



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



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



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.

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