Incarnational Teaching in Kindergarten

I am increasingly amazed at the power of classical modes of instruction to enable students and even teachers to better understand ideas.

During yesterday’s apprenticeship phone call, Buck Holler, an apprentice from Geneva School of Manhatten, described how a kindergarten teacher applied the mimetic mode to guide her kindergarten students to understand what a polygon is.

He said that when the lesson was over, the kids understood it so well they didn’t need to do a worksheet.

That launched my thoughts into a comparison of modern math programs with the classical approach. The differences are too vast to explore deeply here, but one in particular stood out to me.

As always, the difference is rooted in the priority given to ideas and therefore to thinking.

One popular math teacher, for example, stated very clearly that  he developed his math program to improve student scores on standardized tests – not, by implication, so they would be able to think better mathematically. As a result, low scoring schools have consistently found that if they switch to this program, their test scores improve.

But unless they have mathematically and pedagogically sound teachers, schools using this program have not produced a vast quantity of students who can think mathematically.

I believe the reason for this is in the developer’s approach to teaching math. His pedagogy is rooted firmly in the behavioral sciences, so he sees learning as a stimulus-response activity.

If you stimulate the mind to perform an operation and then reward it when it does it the correct way, then eventually it will perform that operation whenever confronted with a similar context. Of course, it becomes very elaborate, being the human mind and all, but that’s the fundamental idea behind this program’s techniques and its why it uses a cyclical approach. More on that in a moment.

In the classical tradition, by contrast, mathematics was treated as a contemplative activity. In other words, the students were not treated to a series of intellectual stimuli when they were taught. Instead, they were presented with types of the idea to be learned and they learned how to think by attending to those types. That probably sounds scary to an unfamiliar modern teacher, but in fact it is gloriously simple.

If the idea is polygons, then the teacher presents multiple examples of polygons to the students. The students describe them in as much detail as they can to aid their attentive perception. Then they compare them with each other. In a very short time, they will have learned what a polygon is.

If the student is being taught an algebraic principle, they are shown that principle at work in various contexts. They attend perceptively to each individual type. Then they compare the types with each other. Pretty soon, through the teacher’s guidance, they come to see for themselves, to perceive, the idea that has been embodied in the types.

The same principle applies in a literature or history class, though the ideas will be less precisely defined. For example, if a school wants a student to understand and appreciate justice, then it will ensure that students spend many years contemplating types of justice – i.e. just people, just actions, and just events: stories.

Aesop’s Fables provide priceless instances of justice embodied, which is why Martin Luther, for one instance, regarded them as priceless. “Needless to say”, the perfection of justice is embodied in Christ Himself, so the school that hopes to bear the spiritual fruit of just students will spend a great deal of time contemplating the words and actions of our Lord.

The main reason this approach to teaching has been dropped seems to be that, since Dewey, education is rooted in a behavioral psychology (even before Skinner developed the dogmas of behaviorism) in which experience is the dominant mode of learning and ideas are at best words and at worst meaningless. Combine that with the need to appear to teach large classes of students and there seems to be no motivation for contemplating ideas. Thus the cyclical approach, in which the stimulus-response sequence is stretched over time, but the students are never deliberately guided to contemplate the idea for its own sake.

This is why I often argue that, while the stages of a subject and of a child’s development are powerful concepts, the real glory of the trivium as three stages is in the individual lesson: grammar – present types; logic – compare types; rhetoric – express and apply the idea.

But when we stop contemplating ideas, we may be doing a lot of things, but one thing we are not doing is providing a classical education. Nor are we wisely leading children on the path to wisdom. So thanks, Buck, for reminding us how much children love ideas and how easily they can absorb them when we teach them the way God teaches us: incarnating what we want them to understand.