Figure 1. The didactic pentagram

A study of the pentagram (star) and outer and inner pentagons (polygons) can pay off handsomely.

The five points at the rim include the well known "learning material", student, and teacher and two more that often appear where persons learn something:

1. Self-help and Internet pages
2. Learner (student, pupil, anyone having a learning experience)
3. Informer (teacher, someone who informs and the like)
4. Management
5. Content (article or book on a Internet site, etc.

One or more of these are normally involved in a typical learning situation.

Some seek learning; they are "propelled" from inside. Others have learning pushed onto them; they suffer from "obligatory readings" which in many cases are killjoys to learning with interest. And learning with interest, also called "being in the flow", is a great thing.

The five sides of the pentagon are suggested, they represent different sides to education and learning:

1. Self-help instructions
2. Explanations, instructions (much as in "catechisation" in fig. 2.)
3. Rhetoric
4. Divining
5. Methodology in general

One aim of learning is to attain the fluency involved.

Example 1. A few of these sides to teaching (and learning)

Figure 2. An aspect to explore (coloured blue).

Triangle 1. The lines between 'Content', 'Management', and 'Self-help and the Internet' form a triangle which makes up one aspect, one side to teaching, or a field of teaching. The point of preponderance is in the middle, the points that "weighs more" in a study, is the focal point of a study.

(Note: A corresponding "side to learning, field of learning" is seen by the same lines, the same aspect, depending on the focus or interest. You may focus on the subject of teaching or that of learning, and view both as complementary, as you prefer. All these three are related to the red pentagon in the middle of the figure.)

Now what is such an aspect to teaching or teachings to be referred to, if at all? One of several possibilities is "Self-help management of Internet content in (public) education."

We can draw a great many supporting triangles and other polygons in order to enlarge our view of such as triangle 1 above. For example, (a) "Mangement-Content-Learner", (b) "Content-Self-help-Informer", (3) "Management-Self-help-Learner" and (4) "Management-Self-help-Informer" capture the core pentagram - the subject of teaching and learning. In this way they help us when we dive into the subject of 'Content' so as to get a focus or aim at the "real thing": teaching for learning. The preponderance of focus on one point (angle), such as 'Content', should be helped by taking into account all sides and aspects linked to it, or linked to the first triangle (fig. 2).

We can draw lines from each of the three angles in fig. 1 across the circle and back to one of them, and end up with still more triangles, that is, topics of interest, to take into account.

Triangle 2. If we draw lines between 'Content', 'Learner', and 'Informer, being informed', we get a (for most part green) triangle. It includes the red pentagon at the centre of the figure). Clarifying figure:

Figure 3. A supporting triangle to the blue triangle to explore.

The common point of both triangles is 'Content'. Further, there is an overlapping area in the middle of the first triangle. Also, the "core of teaching (red pentagram)" can be discerned more accurately by the help of the second, supplementing triangle. And that second triangle tells, in its way, how the levels and developmental needs of learners should decide how information bringers (text books, etc) is to present material or act; how learners are best informed at different stages and in different circumstances and so on. Further, the adequate content of teaching, a profitable curriculum, is at best an outcome of these two - the capactities and needs of learners and information or presentation best suited to them.

If these further sides to teaching is adequately adjusted to, the first triangle gets a more accurate direction from 'Content' into 'Teaching for learning', for example by the aid of Internet and interest managed somehow.

It goes on and on in this way. Figure 4 shows another supportive triangle, and illustrate more or less overlapping areas to be studied for a balanced overview and for a happier outcome.

Figure 4. A supporting triangle to the blue triangle to explore.

Figure 5. Another supporting triangle to figure 1. In it, the side of teaching that is called 'Divining', is a first concern. In this series it relates to 'Content'.

As may be seen, all the points of figure 1 relate to one another in an intricate way in a system of concerns, interests, and proficiencies. You may write many clarifying and helpful books on top of this one survey figure. And you could really make a difference if you stick to it.

Example 2

Try to divine the best management of curriculum (content) for study (see figure 4 to find the yellowish triangle). How can this field of teaching be made profitable? By putting the divining in the perspective of what is fit and good for the learner. It is done by drawing a support triangle between management, content, and learner, and should theoretically at least capture 'teaching outcomes' that are at least inherently profitable.

So, when we divine (guess, figure) what content and management is fit, think of the needs of growing learners, and stick to it. We may do well to adjust to these two triangles for sticking to our main subject and not getting templet to "fatten on diverted things", for example what is popular online at any time. It may be best to go for something more substantial than that. Also, "information fit for self-help" will not quite fit the formal requirements of content in almost any formal school setting.

On figure 1, putting things into perspective may be done in several ways. The one shown above used a simple "opposite" to the divining efforts.

Being diverted from a subject is simply suggested by "things" or topics ca. 90 degrees away from it.

There are still more ways to read the figure. It is found to be generally best to move with the clock (sun) for constructive outlets or outcomes, just as in the acupuncture approach to an array of system elements.

Acupuncture's system model, awarding cycle

Figure 6. Acupuncture Model.

This is a correlation: See for yourself how far such a systemic approach fits the art of teaching:

There are constructive outlets and destructive ones. Rudeness tends to belong to the destructive elements of a life.

What is called the constructive cycle of elements in ancient acupuncture is regularly applied in the treatment. Ancient Indian scriptures name what correspond to the acupuncture system elements, bhutas.

The "cycling" involved in constructive outlets is represented by a spinning sun. Anticlockwise spin on the other hand brings on wails, disorder, discord, derangement fit for destructive agents, illness and worse.

Both ways are found in nature. But adapted to good teaching, which should be a constructive activity throughout, it is the fertile, rewarding "with the sun" spin that is to made active all along.

In the next chapter three of the sides of the pentagram are told of.

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The Didactic Triangle

There are some difficult key terms below. Some of them are explained briefly further down.

Figure 7. The Didactic Triangle

Who first made the schematization behind Figure 7 is unknown. It existed in principle in the "Didactica Magna" by Jan Comenius. [Uljens 1997:201n]

Stefan Hopmann holds that one may come across the didactic triangle in several versions. [Uljens 1997:201-07]. Its three pillars and the reciprocal influence (or interaction) between them constitute didactics with content, informer, and pupil/student.

1. OF TEACHING: The heritage of rhetorics lays the foundation of the informer's presentation of the content.
2. OF WORKING ALONG: The catechization heritage influences reveal themselves in the interaction between informers and pupil/student.
3. OF LEARNING: Methodology is related to the pupil's or student's learning and his or her (learning) experiences. [All: Uljens 1997:201]