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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. |
Missing or Lost History of Science, Technology and Mathematics
Imagine a sequence of buildings, each self-contained and sufficient by itself, each serving as a removable scaffolding for the next. The removal of the scaffolding leaves a construction whose history or origin may be mysterious. Technical disciplines may lead to a sequence of methods and theories, each of which serves as a removable scaffolding for the next. The result may be a discipline, logically or empirically developed and refined, whose history has been lost. In mathematics, self-standing thought-based developments and justification of skills and concepts are possible without reference to historical meanderings that led to the ideas, but some historical references are needed in education to point out the progress or evolution and/or pruning of skills and concepts. And in the physical sciences, the history of ideas and concepts in past times can be provided - they were fewer workers than - but modern times have seen a great expansion in physical and technical knowledge which leaves the scientist, engineer and technician in a plug and play, division of labour, situations. Here the technical and scientific trial and error methods are followed with inherited components and theories which are used, combined and followed until their limits are reached and invention. Here artists can arrive at repeatable and reproducible results with tools and materials inherited or mysteriously manufactured by others. So society, science, engineering and many technical disciplines live in a flow of methods and results which appear to be repeatable and reproducible, a flow that may expand and continue until perhaps a collapse, only to begin again. |
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