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YOU are better than YOU think. Show yourself how:
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-/[]\- Logic chapters 1 to 5 re- appear not in sequence, as is or longer, in Volume 1A, Pattern Based Reason, Bon Appetite. Logic
Mastery Logic mastery makes the hard, easier. Logic mastery leads to better, stronger and richer comprehension. Logic mastery improves reading and writing. Logic mastery ease learning difficulties. Logic mastery gives a headstart. In sum, logic mastery will develops critical thinking, improve reading and writing, and give a firmer base for work and studies at many levels. Good luck. After logic, (a) continue reading Three Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving liinear Equations ; or (b) see this calculus starter lesson and Volume 3, Why Slopes & More Math, chapters 2 to 6;
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-/[]\- What may be learnt and when depends on how skills and concepts are developed. Making the hard easier and clearer will allow earlier & richer development of skills and concepts. Try the Twiddla
Whiteboard. In principle, it allows
to people to draw and chat together online on a copy of this webpage or a clean
sheet. The chat may be via text or audio. Visit www.twiddla.com
to set up whiteboards to work with the webpage of your choice. |
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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