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.


8 Responses

  1. This model also obeys the 5th Law of Teaching by inspiring the student to “discover” the answer to the question him or herself.

    • Joseph, you are exactly right. In fact, I’ll assert right here that this approach easily and naturally obeys all seven laws of teaching and it is the only way to obey them all.

  2. grammar – present types; logic – compare types; rhetoric – express and apply the idea.

    This very helpful summary is a very good way to represent the way children acquire their native language. What implications might that have for teaching them to acquire their second language? hmmm, very interesting.

  3. Both/And not Either/Or … balance, the older I get, the more balance seems to be the key 🙂

  4. OK, I’m thinking more and more and becoming even more interested in this idea. I’ve been researching the “what to teach” classically side for a while now, but am starting into the actually teaching part and have recently been starting to think on the “how to teach” classically, so this is really right up my alley at the moment. (and many of the articles on CiRCE have been extremely helpful … unfortunately, I’m not a very good questioner as I found out when I student taught. But, I digress.)

    Anyway, I read all sorts of people saying they “classically home school” but that just means they follow the WTM recommendations or some other schedule, but are not necessarily teaching using classical methodology in their every-day lessons. This is a pitfall I want to avoid, so structuring lesson plans around “grammar, logic, and rhetoric – Evans and Littlejohn would really hate that! – is a helpful first thought.

    OK, for the second stream of thoughts (semi-related to the first):

    I’m interested that on the CiRCE site, you say that math for grammar stage should be “Drill”, but the example in your above post would be far from “drill.” I’m curious how “drill” fits into the experiential mental attendance described above.

    It seems to me that this would call for math that follows more along the lines of “living math.” Living Math ( is the idea that math should be taught in the context in which it was developed (integrating history and biographies of mathematicians into the actual solving of problems) Secondly, if math is taught from this more “example oriented” perspective, it seems the homeschool (esp in the grammar stage) would provide many opportunities to provide real life examples for students. It also seems that manipulative use in math would be greatly beneficial. Math on the Level would be a good example of a curriculum that is currently on the market teaching like this. (I’m not expecting you to comment on the curricula above, I’m partially trying to put your thoughts into my context [grin])

    No real question here, I already told you I’m a bad questioner, but am I on a remotely right track or am I blogging after having been awake too many hours in a row? [grin]

    • Dawn,

      You obviously are a very thoughtful person, which means that you obviously are very good at asking questions. I haven’t closely examined either Living Math or Math on the Level, but I can tell you I have a worry about any new math program. Some are all about drill and some are all about experience. But both are needed and the idea must remain the goal.

      Having said that, there is nothing you can do to replace the need for math drills, though they can either be a blast or a – um – drill. You do want to use manipulatives in the early years, but only until they can see that 4+2 = 6 without them. When the mind’s eye sees it, the body’s eye can rest.

      So yes, use manipulatives (good teachers always have), but don’t eliminate drill.

  5. Wow Dawn! Thanks!

    I’m truly grateful it was useful as my life has no real meaning apart from helping people teach. Except of course for my family, friends, and church, but it’s all the same thing really.

    This approach is what The Lost Tools of Writing is built on too, which helps explain why it’s so effective at teaching kids how to think.

    You’ve made my day.


  6. “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.”

    Perfect! This is the exact kind of pedagogical aide that I need!!!!!!!!!!! “(I am not usually an excess exlamation point user, either) This article will be printed, delicioused, passed around and regularly referred to.

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