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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. |
Modern Math CurriculaDuring the late 1950s and mid-1960s modern mathematics instruction in the form of an axiomatic approach to algebra and geometry, and the explanation of sets, appeared in high school classes. In contrast to elementary instruction, in which
modern mathematics instruction puts aside the use of physical objects. Instead, it was based on logic, more precisely, the concept of derivation from first principles or axioms, on a set-based description of topics, and on a mastery of algebraic reasoning. But the latter, an algebraic way of writing and reasoning, has been employed in math classes through generations of students and teachers without a direct explanation, apart from a few paragraphs in texts to unclearly introduce the notion of a variable. My book Three Skills Leading to Algebra" offers a remedy. Postscript (September 2006):(1) The modern mathematics curricula, circa late 1950-80, introduced the advanced set theory view of pure mathematics in the classroom. While students learn to count and do arithmetic with the decimal representation of whole numbers, fractions and/or reals, exactly or approximately, the axioms for modern mathematics did not mention and hence did not sanction the decimal representation of numbers, whole to real. The modern mathematics view of calculus with its epsilon-delta codification of limits, continuity and convergence was to abstract even for many advanced students - those that did well in high school and college mathematics. The modern mathematics curricula provided logical developments with steps too large or too hard for most to follow or take. The modern mathematics curricula assumed but did not support the common knowledge in that the axiom given were not linked to the prior knowledge or experience of students and teachers, that acquired in say primary school. Masters of high school and university modern mathematics curricula (analysis included) may found themselves with two nearly separate views of the subject - the practical skills that support the common knowledge, and a theoretical view in the common knowledge of decimals plays no part. All the foregoing is in addition to the lack of a clear development for students of the algebraic way of writing and reasoning. Explore the rest of this site for remedies. Bon Appetit. Chapter Sections: Next: Chapter 15, Objective Processes, Search for Repeatable and Reproducible Results
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