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What to Teach:
The Order of Learning
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Your Questions |
Our Answers |
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What is the order of learning? |
By its nature, learning begins
with poetic knowledge. It then lays its foundation
in the seven liberal arts, after which it ascends in
order through the natural sciences, the humane
sciences, and the philosophical sciences, until it
reaches its fullness in the theological sciences.
It is not possible to ascend
this ladder in any other order. Therefore, while a
curriculum can be ordered in any order the
leadership of a school desires, the student can only
learn in the order prescribed by nature. We heartily
recommend, therefore, that the school curriculum
align with the curriculum prescribed by nature and
nature's God.
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What are the great ideas? |
Of the three columns, “ideas”
provides the ordering principles and the objectives
of content and skills. The reason some content
matters more than other content matters is because
of the ideas it embodies (for example, the battle of
Gettysburg is a more important bit of historical
content than the name of Robert E. Lee’s horse
because it embodies more ideas and more significant
ideas than the name of Lee’s horse embodies; it is
also more historically decisive).
Classical education moves
toward, prioritizes, and revolves around ideas. The
great ideas are those that best help us understand
the God, humankind, and the world we live in. Since
we think both with and about ideas, the classical
school orders its instruction to and around the
great ideas.
The goal of education is to
appropriately embody ideas in our conduct, thoughts,
and creations.
Learn about the
15 ideas that
we believe every curriculum should seek to embody
and teach. |
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What are the seven liberal arts? |
The seven liberal arts are the
foundations of all later learning. The trivium (the
three verbal arts of grammar, dialectics, and
rhetoric) and the quadrivium (the four mathematical
arts of arithmetic, geometry, music, and astronomy)
comprise the seven liberal arts. Mastery of these
seven arts is the goal of pre-college education.
The seven liberal arts lay the
foundations for the sciences. A science, classically
speaking, is a mode of inquiry that leads to a
domain of knowing. The classical sciences include
the natural sciences, the humane sciences, the
philosophical sciences, and the theological
sciences.
The seven liberal arts and the
sciences are the curriculum of the classical school.
This curriculum is rooted in the nature of reality,
in the order a student must progress through to
attain higher levels of knowledge, and in the order
of knowledge apart from any application of that
knowledge.
Pierre H. Conway, O. P. and B.
M. Ashley, O.P., “The Liberal Arts in St. Thomas
Aquinas,” The Thomist vol. 22, no. 4, 1959;
Paul Abelson, The Seven
Liberal Arts, A Study in Medieval Culture,
Russell and Russell, Inc. 1965
David Wagner, Ed. The Seven
Liberal Arts in the Middle Ages, Indiana
University Press, 1983] |
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What is the Trivium? |
If you search the internet or
read books about the trivium that have been written
in the past 20 years, you will find two versions of
the trivium.
Dorothy Sayers described the
trivium as the stages of a child’s intellectual
development. Sayers’ approach to the trivium is
drawn from the ancient concept of the trivium by
analogy. As her interpretation has to do with how to
teach, you can read more about it by going to our
pages on “how to teach.”
The second view of the trivium
is the view held historically. Historically, the
trivium consists of the three verbal arts of
grammar, logic/dialectics, and rhetoric.
The liberal art of grammar is
comparable to what is now commonly called letters.
It would not be unjust to say that the art of
grammar is the art of learning to read at a very
high level. This includes formal grammar (the parts
of speech, etc.), but is by no means limited to it.
Perhaps the best and most concise description of
grammar is to say that it is the art of interpreting
symbols.
Logic/Dialectics is the art of
reasoning or thinking. The classical school
emphasized traditional logic and regards modern
logic as a valuable study for specialists later in
their studies.
Rhetoric is the art of
communicating, which can be reduced to encoding
symbols. The goal of rhetoric is the fitting
expression: to know the soul
For more information about the
trivium, we highly recommend the following
resources:
Mortimer Adler, Reforming
Education, The Opening of the American Mind,
especially Chapter 11: “What is Basic About
English?”
Sister Miriam Joseph, The
Trivium: The Liberal Arts of Logic, Grammar, and
Rhetoric.
Also, see our resource page to
see resources for each of the three arts of the
trivium. |
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What is the Quadrivium? |
The Quadrivium consists of the
four liberal arts of arithmetic, geometry, music,
and astronomy, sometimes referred to as the
mathematical arts.
The art of arithmetic is the
mastery of the properties of numbers. It begins with
counting and calculating (with a strong emphasis on
the work a student does in his own mind) and
progresses to a detailed enjoyment of watching how
numbers behave in various situations.
The art of music is concerned
with the applications of what is learned in
arithmetic, especially with ratios and proportions.
The art of geometry is the
mastery of the properties of shapes or space. While
arithmetic is concerned with discrete numbers (i.e.
counting), geometry is concerned with continuous
numbers (i.e. measuring).
The art of astronomy is
concerned with the applications of geometry,
especially with shapes moving. Since the stars
provide the most regular observable and measurable
movement of shapes, they are the preferred way to
study the movement of shapes.
Geometry literally means the
measure of the earth. Astronomy literally means the
laws of the stars.
Mastery of the quadrivium
enables us to know the world around us. |
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When should we begin the study of the sciences? |
This is a tricky question,
because so much turns on the way you are using the
word science. Strictly speaking, a student can study
any of the sciences, using the term classically,
only to the degree to which he has mastered the
seven liberal arts. So in one sense, it is not
possible to study the sciences before around 11th
grade.
Does that mean lower school
children should not study the sciences at all in any
way? No. A younger student is able to study the
sciences for at least three reasons:
One, he has some mastery of the
seven liberal arts, so he can study them to some
degree. For example, he can, in varying degrees,
read, so he can read about the sciences.
However, the teacher must
understand that a student is not learning to do
science when he is reading about science. He is
learning how to read (grammar) and he is learning
about science, but until he is able to engage in
scientific inquiry he is not doing science.
Two, he is human, so he can
study them poetically (whole, living, organic—with
mind and senses together).
The second reason is by far the
most important and helpful. The “grammar level”
student should poetically encounter the world he
lives in. That is, he should experience it whole and
alive through his senses. Later he will dissect dead
things and engage in other analytical studies.
But when he is young he should
experience natural things naturally, not, as we
might say today, “scientifically.” He should have a
garden plot, climb trees, splash in rivers and
creeks, catch frogs, etc.
Reading about science should be
limited and should be controlled by students’
experiences, not the marketing designs of textbook
publishers.
We highly recommend
photographs, drawings, recordings and other sensual
aids to learn about groups of natural objects, such
as rocks, clouds, insects, etc.
In the Dialectic years,
students can begin to study the natural world more
analytically, but they mustn’t lose touch with the
wonder of it. This is a great age for collections.
The various scientific categories can be introduced
at this age. Children can learn words like geology,
physiology, zoology, etc.
In the dialectic years, we
recommend that students learn the more concrete
sciences first.
During the upper school
(rhetoric stage) years, your students should be
ready for the more abstract sciences of physics,
biology, and chemistry. Once they have mastered the
seven liberal arts (ideally, around tenth grade),
they can be set free on the natural sciences as
natural sciences.
The humane, philosophical, and
theological sciences are beyond the capacity of a
high school student to master. The high school
teacher, however, must understand them as well as
possible as they will necessarily inform all his
instruction (see below, the order of being).
In addition, the high school
student must be told what the authorities have to
say about these matters because only by imitating
the authorities can they ever become authorities
themselves.
For example, moral authorities
have always taught that fornication is unethical.
The student is not in a position to thoroughly
understand the arguments for and against this
position. He is, therefore, required by necessity to
follow an authority. It is the duty of the
teacher/parent to ensure that this authority is
genuinely authoritative as the health of the child's
soul depends on it.
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What is a science? |
Science comes from the Latin
word “scientia” and means knowledge or a realm of
knowledge.
The natural scientists claimed
that only what they study should be called a science
because they argued that only scientific knowledge
is true knowledge. This is not how classical thought
perceives the matter and it is an idea that is
fading from the education debates.
A science is a domain of
knowing that arises from a mode of inquiry. In other
words, when we ask a certain kind of question, it
will give rise to a certain kind of knowledge. As we
think about the knowledge the questions give rise
to, it is natural to order that knowledge. So a
science can be said to be an ordered body of
knowledge (a domain of knowing) that arises from
asking a certain kind of question (a mode of
inquiry).
Every science is distinguished
by and ordered by its causes.
The kind of questions one asks
and the sort of material one will accept as valid
for answering the given questions determine what can
be known using a given mode of inquiry. See, for
example, the definition of the natural sciences
below.
One can be considered a master
of a science when he understands the causes of that
domain of knowing (science) so well that he is able
to order and to judge rightly the matter of that
science.
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What are the Natural Sciences?
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The natural sciences are the
domains of knowing (sciences) that arise when the
questioner uses empirical and mathematical modes of
inquiry. Following these modes of inquiry, inquirers gain
empirical and mathematical knowledge.
The foundational natural
sciences are biology, or the study of living things,
physics, or the study of force and movement, and
chemistry, or the study of the fundamental physical
elements of things.
We highly recommend a thorough
study in physiology as a fine intersecting point for
the three basic sciences and as preparation for the
humane sciences.
The natural sciences inquire
into the physical causes of things.
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What are the Humane Sciences? |
The humane sciences are the
sciences of human behavior and the soul and are
sometimes called the moral sciences.
All of the humane sciences can
be summarized in two broad and rich categories:
ethics (answering the question: How do we become
virtuous in the soul?) and politics (How do we
become virtuous in community?).
History, literature, and the
arts are properly known only when they are
understood as humane sciences, that is to say, as
responsible human activities.
The humane sciences inquire
into the causes of human behavior, especially the
mystery of the human will, with the driving question
being, "How does one become virtuous - that is,
fully human?".
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What are the Philosophical Sciences? |
The philosophical sciences are
those realms of inquiry that go beyond what can be
learned from the natural and humane sciences. The
natural and humane sciences necessarily assume
philosophical conclusions. The philosophical
sciences establish them.
For example, both humane and
natural sciences assume being and essence, cause and
effect, the law of non-contradiction, etc. The
philosophical sciences establish these foundations.
The philosophical sciences can
be summed up as ontology (the science of being
itself) and metaphysics (the study of first causes).
Peter Kreeft defined philosophy as “the science that
seeks to understand all things by knowing their
causes by natural reason.” [summa 28]
While many natural scientists
have argued that the philosophical sciences are an
obstacle to progress and many Christians have
dismissed them as idle speculation, the fact is that
humans want to know the foundations of truth and
being.
Whether we raise it to a
science or not, all of us live in and speculate
about this realm of being whose science is called
philosophy. For this reason, to fail to honor the
science is to fail to honor human nature and to have
an incomplete curriculum and it is to leave sincere
students sincerely unsatisfied.
The philosophical sciences
inquire into the causes of all things and into the
nature of cause itself. |
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What are the Theological Sciences? |
Theology is the study of the
first cause, God. In theology we inquire into what
goes beyond the capacity of our reason to discover,
but has been revealed by God in the sacred
tradition.
Every religion or perspective
has a theology, and that theology is the central
unifying principle of its view of everything. For
Christians, Christ the Logos is the central unifying
principle. He is the only adequate unifying
principle, which leads to disintegration, cynicism,
chaos, and even despair for every other
philosophical or religious system.
While the order of learning
moves from the bottom to the top or from the outside
to the inside of the curriculum, the order of being
proceeds from the top to the bottom or from the
center to the outside. |
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How can I learn more about the order of learning? |
Retreat talks
Aristotle
Books
Poetic knowledge |
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