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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. |
In the first part of your mathematics education, rules and patterns may be accepted because they work in a repeatable, reproducible and thus verifiable manner. What is right or wrong is thus clear, or can be checked. The careful mastery of rules and patterns, one at a time and one after another, with repeatable and reproducible results, is a sign of intelligence and gives an operational viewpoint of mathematics and its mastery by rote or with explanation. Explanation in mathematics may be based on giving examples to suggest or illustrate and confirm a rule and pattern. Explanation in mathematics may be based on combining rules and patterns to arrive at new ones. Explanation in mathematics may also be based on logic - the direct and indirect use of implication rules or patterns B IF A. Finally, with practice, mathematics can be codified via logic:
Most students will appreciate the use of logic in mathematics when it gives new results or patterns. Students will see as redundant and not necessary the explanation of what has worked before and been.. So mathematics education may mix a previous operational command of earlier rules and patterns with a proof-based command of new material. That may be sufficient for many students - as the logical codification of mathematics take time and effort, and interest too. Remark: Along side the axioms for pure mathematics, there should also be included in education for mathematics and quantitative disciplines (accounting, physics, chemistry), extra applied mathematics supporting axioms or assumptions that formally sanction for students, the manipulation of units of measurement in calculations, and the geometric use of coordinates. Just a thought: The full Euclidean style axiomatic codification and derivation of pure mathematics and its applied mathematics extension with units and coordinates might be left to after a mixed mathematics mastery of calculus.
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