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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. |
Remarks for TeachersThe thought-based development here is semi-formal. Too much formality or rigour would make the inductive-to-deductive development of advance concepts too unwieldy - inaccessible. The principal objective is to develop the algebraic way of writing and reasoning, and computational skills, needed to further in mathematics and quantitative disciplines in science, technology and business. All that is to be done without overwhelming students with formalities, that is proofs for all properties and assertion, but with a sufficient amount of mathematical reasoning to lay a found foundation for calculus and beyond that. As seen here, the role of mathematics courses from arithmetic to advance calculus is to inductively develop skills, knowledge and computational confidence in logic and applied or mixed mathematics, so that students see mathematics in context with mixed applications. The context-free development of mathematics is not for beginners nor for students who have no intention of learning pure mathematics. While trigonometry and distance concepts in the plane can be developed and formalized without diagrams in advanced mathematics (analysis), the high school student accessible introduction and use of trig requires diagrams and geometric drawings inconsistent with the idea that context-free, exposition of mathematics is possible in the introduction of secondary and junior college mathematics. Since instruction relies on diagrams in the introduction of trig, instruction can also rely on diagrams in others matters and on decimals for arithmetic and beyond that the discussion of limits and continuity from arithmetic to calculus in mathematics course design and delivery. |
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