Chapter 2. Communication of Ideas

Initial Assumption

No area of knowledge is properly mastered until it can be readily explained to others. Each subject needs paths (or curricula) passing through easily described and easily repeated ideas and skills. Each such path permits those who have traveled along it to tell others what to expect and hopefully why. The existence of such paths may show that an area is well-understood.

Differences

Differences in our alertness, how awake we are, imply that a lecture, a book, a picture, or a film is seen and understood differently by each of us, depending on the time of day, etc. All of us are witnesses. Some witnesses see more than others. In describing and explaining ideas to several people, we need to speak in a way that each listener (or witness) will understand as much as possible. When we speak to several people, our words will be understood by each differently. In communication, especially in teaching, these differences need to be considered.

Principles for Instruction

For learning and teaching in all disciplines, the following overlapping principles appear self-evident, at least once stated.

• Each discipline needs to be taught or presented, so that students understand what they are learning and why. Without a knowledge or an opinion of why, students may lose interest and not go further. The why could be approximate a little uncertainty leaves room for thought.

• Pathways through easily described and repeated ideas may extend knowledge of any discipline, area of thought or belief. One or more paths through easily described and easily repeated topics may allow those who travel further to tell others willing to listen, what to expect and possibly why. Of course, differences of opinion exist on which disciplines should be taught or what pathways in them should be followed.

• Awkwardness with an idea or skill often signals difficulty with previous ones. It may indicate at least one earlier skill has been missed or forgotten. When an awkwardness is felt or seen, learners should go or be taken back to practice the missing skills, and possibly the ones just before them. This retreat aims to restore confidence and build skills, so that the learner can go further. This requires a diagnostic skill and a knowledge of or opinion on how the topics in question can be organized and taught. Here again, opinions may differ.

• Each collection of mental and physical skills could be organized into a ladder-like sequences of steps with the basic ones first and the more advanced ones second. Learning in any subject stumbles when a first or succeeding step is not easily reachable from those before them. To climb a ladder, the initial steps must be reachable, and each further step must be reachable from the one or ones before it.

  [1] The latter summarizes an educational analog of the principle of mathematical induction. in chapter 7, Longer Chains of Reason.

  Explanations should follow chains of reason or persuasion which begin at the level of the student before advancing further.

Remark 1. An alternative to ladder-like structure is a tree-like structure. Here skills and ideas are represented by the branches of a tree or bush. The tree can be climbed when those branches closest to the ground are accessible while the higher ones are accessible from branches below. For ease of exposition and comprehension, the organization of ideas into a flat tree-like structures where each branch can be reached via a few lower branches or directly from the ground is to be preferred to the case in which most branches are high and can be reached only from the one just below it. This is to simply observe that short chains of reasoning are better for explanation and comprehension than longer ones.

Remark 2. These words or thoughts on communication of skills echo a course on how to be a cross-country ski instructor. The course was taught one weekend early in 1981, by an instructor-trainer from CANSKI, the CANadian association for Nordic, that is cross-country, SKIing. The course gave a piece by piece approach to instruction. The objective was to build both the confidence and ability of students. The course emphasized that difficulty with a skill signaled the need for a retreat to, or even before, previously mastered skills. The detailed structure provided turned cross-country ski instruction into an art. Arts of this kind are required in other areas of instruction.

Plots and Subplots

A writer normally offers a main plot along with a few or several subplots. The main plot and ideas should be obvious to everyone the first time. After the main plot is noticed, the subplots themselves and links between them may become apparent. On reading for the first time a book or an article, we grasp and master some of its ideas. The rest remains to be found. Others ideas and messages just pass us by. A second or third reading may help us see them.

In the Classroom

A teacher has to explain ideas to students with different backgrounds and knowledge. One approach to this is to divide students into groups, and to speak to each group separately. A second approach is to speak to all in a way that speaks to each group at its own level without being too imprecise. A teacher may try to explain and broadcast ideas or knowledge at several levels at once. The intent here is to allow each listener to tune to the level most suited to him or her with reinforcing echoes from the other levels.

Echoes can be provided by the repetition of words and phrases with similar, like or related meanings. They can be used one after another in a single sentence. Familiarity with one word or phrase leads to an understanding of the others. The latter in turn favors variety instead of monotony in speech. Multiple themes and multiple levels of meanings may challenge the listener or student and take some beyond what was expected of them. Some redundancy and repetition in communication is fine. Too much may be boring.

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