Linear Learning

I was recently asked if “learning is linear or non-linear” by, of course, an art teacher.  We discussed his definition of “learning” for a few moments, but the main point of the question was this comparison of learning with that of a line.  We tend to define learning as a line, starting with the small child and progressing formally through high school or college or the rest of life.  And the chronological timeline notion is legitimate for many reasons.  But the best learning cannot be simply adding one new thing to the collected line of known things each day.

I happen to be working my way through a great work on Aristotle’s views of teaching (here on Amazon, though it’s out of print so if you see it in a used book store, snap it up).  In that work Aristotle does not use linear/non-linear, but deductive and inductive, which I contend are basically the same ideas, but broad enough to encompass more.

In deductive learning, or what my friend meant by “linear” learning, one adds line by line, precept upon precept new learning to what is already known.  This is the syllogistic type of learning.  Premise A is true, and Premise B is true, therefore we can deduce from those truths that something we did not know before is true (the conclusion of the syllogism).  Aristotle is often credited with formalizing this type of learning, or logic.  Certainly there is a place for this learning, and many methods can lead to its outcomes.  But often many mistake this for all there is to learning, and Aristotle soundly rejects that notion.


Inductive learning is not so linear.  In this non-linear mode, a complexity of experiences are used to learn new principles, that can in turn become perhaps the premise in a new deduction.  But induction is more like a web than a line.  It is the bringing together and comparison of many specifics to gain new categories and generalizations.  We sometimes say “connecting the dots” but two connected dots is one definition of a line.  Here is imagined a scattered group of dots, each representing a specific sense experience, and when compared, contrasted, pulled apart and thrust together, new learning occurs.

So my answer to the question about linear or non-linear is both/and.  Neither really can separate itself from the other, and the great teacher seeks to have both constantly conversing with each other and the souls in their classroom.


Overview of Specifics from “Road and Wheel”

Having stated earlier Berry’s main point with the “Road and Wheel” metaphor, I want to lay out what will be several up coming meditations on the specifics from his essay, “Discipline and Hope.”

Here is his own chart showing the contrasts between these two ways:

Linear Cyclic
Progress. The conquest of nature. Atonement with the creation.
The Promised Land motif in the Westward Movement. Black Elk’s sacred hoop, the community of creation.
Heavenly aspiration without earthly reconciliation or stewardship. The creation as commodity. Reconciliation of heaven and earth in aspiration toward responsible life. The creation as source and end.
Training, programming. Education. Cultural process.
Possession. Usufruct, relinquishment.
Quantity. Quality.
Newness. The unique and “original.” Renewal. The recurring.
Life. Life and death.

fr. Wendell Berry, Discipline and Hope, p. 137

I will develop each of these in turn by relating them to our views of education in upcoming blogs.