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Chapter 2, Communication of IdeasPrevious: Chapter 1, What is Reason. - Different kinds of Reason 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. This chapter describes the educational principles or pedagogy which guided the organization and content of this book on reason and its mathematical companions. DifferencesDifferences 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. Plots and SubplotsA 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 ClassroomA 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. Next: Inductive Principles for Instruction with Chapter 1 end notes. |
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Chapters 1 to 24 To reason often means to persuade someone of the need for an idea or action. That someone could be yourself. So be careful. 1A Logic Postscripts +Proof by
Absurdity alias proof by contradiction There is a difference between There is likewise a difference
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