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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. |
Site OriginsAs a secondary school student 1965-9, I suspected difficulties in algebra were due to its incomplete introduction. That is, the algebraic shorthand roles of letters and symbols were used, required, but not clearly nor fully explained. So I watched for a remedy. In fall 1983 as a novice instructor, I gave three lessons, namely three skills for algebra, why slopes and two logic puzzles to make algebra & calculus simpler to understand and explain; to improve reading, writing & reasoning skills; and to hint at the role of logic in mathematics. Since then, I have been trying to tell to fellow instructors how difficulties in mathematics might be addressed but my ideas not wanted, were dismissed before being heard.. Today, I am still trying. Parallel to views that difficulties in mathematics can be eased by use of indirect instruction to engage or interest students, my 1965-9 suspicion has slowly become a proposition for a clearer, fuller, wordier development of algebraic skills, concepts and themes. Site material shows how in ways motivated by inductive principles for instruction met in 1981 outside of mathematics. Site material also spring from examples of guest speakers 1975-82 at McGill University of different ways to understand and develop skills and concepts in mathematics and physics. Writing only began in the last days of 1990 as I saw no hint in mathematics education literature and practice of the remedies I saw or sensed for common difficulties. Prior to that my writings aimed at advancing mathematics itself and not mathematics education. The mathematic education literature with its focus on delivery matters obscures the question of what should be taught. It appears that cognitive theories of learning dismissive of the rule-based fashion in which mathematicians see their discipline lead course design and delivery in North America. Sequences of skills and concepts which could be leaner, which mathematicians see as preparation for calculus are being obscured or diluted by cognitive theories, dominant or authoritative in their own way, which say students should find and construct their own knowledge instead of following authoritative (textbook) accounts.. This opposition to authority in name of developing critical thinking undermines them instead as the ability to follow rules and patterns in a repeatable and reproducible manner is needed before and besides the question of whether or not particular rules and patterns are valid.
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www.whyslopes.com
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