The Trivium & Quadrivium and Research

Powerpoint Presentation

The liberal arts education is the basis of the core curriculum required of every undergraduate student. The classical liberal arts education was (and is) meant to create a well-rounded educated person and to LIBERATE their mind from preconceived notions, prejudices, and the undue influence of others. The word LIBERATE comes from the Latin LIBER, a free person, one who is not a slave (Quadrivium 1).

The liberal arts, originally, were seven in number. Based on the ideas of Plato, Socrates, and Pythagoras, they were broken down as follows (Quadrivium 1):


  • Grammar (learning information)
  • Logic (critical thinking; evaluating information)
  • Rhetoric (communicating your ideas, conclusions)

The trivium constitutes basic learning skills and/or the basic skills needed to produce a research paper.


  • Arithmetic
  • Geometry
  • Music
  • Astronomy

The quadrivium evolved into what today we refer to as the arts, sciences, and philosophy (Quadrivium 2). The trivium constitutes the basic learning skills required before one can address advanced subject studies (Bauer 8). The trivium is also a good basic place to start discussing how research should be done.

Let's now look at the individual elements of the trivium.


The first stage of research and learning is grammar. Before you do any analysis or come to any conclusions, you must first understand the subject, learn the material, read the research on the subject (Bauer 18).

At this stage, you must work at being very open-minded. In the Quantum Physics movie, "What the Bleep Do We Know," the point is made that when Columbus first arrived in the new world, the natives could not see him or his ship. They had never seen such a thing, and so their minds simply filtered it out. You do not see up to 80% of what is visible to your eyes because your mind filters it out (Captured Light Industries). Likewise, your mind will filter out ideas unfamiliar to you unless you are very careful.

In research, it is also critical to narrow your subject to the extent that you can read almost everything written about it. If you haven't read everything about a subject, you really have only a partial view of it; you are not yet properly "informed." Without full knowledge, you cannot progress to the next stage of critical thinking, and you certainly cannot yet form an opinion.


The second stage of learning and research is logic. Logic involves using critical thinking skills to evaluate the value and meaning of the information you have gathered... Once you have read everything on the subject, "decide whether information is correct or incorrect, and make connections between cause and effect" (Bauer 18-19).


The final stage is expressing your opinions about what you have learned. This is where you would analyze and synthesize the ideas and information you have read (Bauer 19).

Write a rough draft of your ideas. Some people prefer to write an outline before their first draft.

It is critical at this stage to document every idea and piece of information. Develop a Works Cited page.

The re-writing and editing stage is where you polish both your paper and your ideas. As you re-read your paper you may well make connections that were not apparent originally. It might also, after several re-writes, be good to have a friend read your paper. Things that are clear to you may appear obscure to them when they read the paper. The paper must be clear to others, not just to you.

Writing help is available at the PAC labs.

Reading Principles

1. Read through the book or article one time without stopping. Mark difficult passages. If it is your copy, mark the passages and then note the page number in the back. "... your goal is to finish with a surface acquaintance that will deepen into true understanding as you read again to evaluate and analyze. If you don't understand..." (Bauer 43). As you read further, previous sections may become clear.

2. If it is your copy, mark the passages and then note the page number in the back. If it is not yours, note the difficult page numbers in your journal or notes. Keep reading. "The secret to reading a difficult book is simply this: Keep reading. You don't have to "get it all" the very first time through" (Bauer 42).

3. "When you first begin to read a book, read the title page, the copy on the back cover, and the table of contents. This puts you "in the picture" before you begin to read. Do NOT automatically read the preface... [it] can give you an interpretation before you even read the book -- something to be avoided... (Bauer 43)

4. "Don't take extensive notes on a first reading... Instead, stop at the end of each chapter (or substantial section) to jot down a sentence--two at the most--in your journal... summarize the chapter's content, main assertion, or most important event... You're constructing a broad outline (Bauer 44)...

5. As you read, write down questions. Also note reflections are connections which come to mind. Note page numbers beside each entry.

6. Underline important passages for review later... If it is not your book, keep a list of page and paragraph numbers/letters in your journal.

7. Go back over the important passages and your outline. Summarize for yourself what the author has done. Consider what questions you ought to ask about the work. This is also where you would question the material.

In the next section we will address statistical works in particular. Many college papers are based primarily on research articles.

Reading Research Articles

Research articles follow a typical pattern. First, they tell you the subject of their research and why the research is needed. Then they discuss their methodology -- how they collected the data. Then they give you the data. Then they discuss how they analyzed the data (usually one or more statistical methods). Finally, they discuss their conclusions based on the data and statistical analysis.

Each section of a research article can have weaknesses that destroy the validity of the conclusion. The introduction should make sense and prove that the study is both of value and interesting. The collection of data, or methodology, is often the weakest part of a research paper. There are numerous ways to go wrong. The two most common are not getting a representative or random sample, and not getting enough samples. Most pollsters in the news, for instance, imply that their conclusions are based on a random sample. However, often 70% of people refuse to answer the questions. The ones who answer the questions, therefore, are self-selecting. Self-selecting is not random.

Many medical studies reported in the news only have 10 to 20 people who were studied. This is simply not a large enough sample to be valid.

Beware of averages. You and Bill Gates have an average net worth of $35 billion. Do you feel any wealthier? My wife, my daughter and I have an average sex of female. I still don't feel female (ref).

Statistical analysis is a hard subject to judge because even experts cannot agree about what might be the appropriate statistical method to apply in any particular situation.

Conclusions can also be landmines of fallacious thinking. Unfortunately, most scientists go into an experiment with a conclusion in mind. This typically skews their thinking and their methodology. It is not uncommon, in addition, to read conclusions that simply do not follow from the data and analysis. The best advice is to use your common sense and critical thinking skills.

For more on research methods, see Stat Lies. You might also want to look at the book, A Mathematician Reads the Newspaper, by John Allen Paulos. It is filled with examples of statistics and analysis gone wrong.

Critical Thinking

Critical thinking involves keeping an open mind and insisting on reasons being given for conclusions. You have been shaped by your childhood, your environment, your home, and many other factors. These can all serve to blind you to new, and especially novel, information. Keeping an open mind is difficult to do and requires practice to perfect.

Always demand sources. Compare different sources on the same information to see if they correspond. If not, you will have to determine which sources you trust.

Watch for mistakes in logic and reasoning. Also, watch for historical mistakes. For detailed information on critical thinking, see a series of lectures I have stored on the Web.

Finally, be suspicious. The Web and Libraries are filled with mistakes and errors. Don't be fooled.

For details of critical thinking strategies, see this web site.


Synthesizing is the opposite of analyzing, or the scientific method. Analyzing requires that you take something apart to understand it by studying its several components or parts. Synthesizing involves putting things TOGETHER to arrive at something that didn't exist before.

Often referred to as the "holistic" viewpoint, this approach often points to human beings as a perfect example of the failure of analysis and the superiority of synthesis. If you cut a person up into pieces, you don't have much. You certainly don't understand the person better. A human being is much more than their mechanical parts.

One of the steps in decision making is to generate alternatives -- possible answers to the problem. Often an additional and even better step is to try to COMBINE the alternatives into a solution which is better than any individual alternative... a win/win solution, as it were.

The Quakers are famous for their synthetic approach to decision making and meetings. In their meetings, if they are unable to come to a unanimous decision -- if even a single person disagrees -- they will avoid making a decision. Their worry is that the one person disagreeing may be right. Therefore, everyone in the meeting is required to re-think the alternatives and possible solutions, trying to find a combination of elements which will satisfy everyone. In mentally wrestling with the alternatives, they often come up with a new alternative, better than all the other previously considered.

Another popular method of coming up with new and unique answers, often synthetic in nature, is through mind mapping. This approach has you draw out on a piece of paper the relationships between the different ideas and assumptions and solutions that you are considering. Looking at the physical relationships sometimes triggers new ideas and possibilities. If you are intrigued, do a search for mind mapping on the web.

Mind Shift--You will notice that each of the synthetic methods requires a shift in viewpoint or ideas to arrive at new, unique solutions that were not initially considered. This "mind shift" has been since ancient times referred to as "metanoia."

Metanoia is an awakening, a fundamental shift or change of the mind, a transcendence. The word has a rich history. For the Greeks, it meant a fundamental shift or change, or more literally transcendence ("meta" --above or beyond, as in "metaphysics") of mind ("noia," from the root "nous," of mind). In the early (Gnostic) Christian tradition, it took on a special meaning of awakening shared intuition and direct knowing of the highest, of God. "Metanoia" was probably the key term of such early Christians as John the Baptist. In the Catholic corpus the word metanoia was eventually translated as "repent"" (Senge 13). "To grasp the meaning of "metanoia" is to grasp the deeper meaning of "learning," for learning also involves a fundamental shift or movement of the mind" (Senge 13).

"The problem [is that] "learning" has lost its central meaning in contemporary usage. Most people's eyes glaze over if you talk to them about "learning".. Little wonder -- for, in everyday use, learning has come to be synonymous with "taking in information."

""Yes, I learned all about that at the course yesterday." Yet, taking in information is only distantly related to real learning. It would be nonsensical to say, "I just read a great book about bicycle riding--I've now learned that"" (Senge 13).

"Real learning gets to the heart of what it means to be human. Through learning we re-create ourselves. Through learning we become able to do something we never were able to do. Through learning we reperceive the world and our relationship to it. Through learning we extend our capacity to create..." (Senge 14). The basic meaning of the "learning person" or the "educated person" is that they are continually expanding their capacity to create their future.

"To create NEW answers, you must ask NEW questionns" (KnCell Technologies slogan--

For more on metanoia, see the website.

Once you have reached metanoia--once your mind has shifted and you see the world in a different way, then you are ready to write about what you have read. You have a real opinion to express.

Works Cited

Bauer, Susan Wise. The Well-Educated Mind: A Guide to the Classical Education You Never Had. NY: W.W. Norton, 1999. [See notes.]

Captured Light Industries. "What the Bleep Do We Know!?" A Lord of the Wind Film. See material at, accessed Feb. 8, 2005.

Paulos, John Allen. A Mathematician Reads the Newspaper. NY: Doubleday, 1995.

"The Quadrivium.", accessed 2-8-05. [See notes.]

Senge, Peter M. THE FIFTH DISCIPLINE: The Art and Practice of the Learning Organization. NY: Doubleday, 1990. ISBN 0-385-26094-6.

Colby Glass, MLIS