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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 Education and Critical ThinkingThe demand in modern or post-modern education theory (constructivism) for problem solving and critical thinking are undermined by course design changes which do not require drill and practice in arithmetic, so that arithmetic provides repeatable and reproducible results, and to the point that students are taught or shown that care, patience and self-discipline is required to mastery multistep methods. Allowing students to skip that care, patience and self-discipline needed to obtain repeatable and reproducible results leads to wishful and suspect critical thinking and problem solving abilities. The use and combination of rules and patterns one at a time and then one after another represents the start of deductive reason and deductive connection, construction and Euclidean codification of skills and concepts. For very critical thinking and problem solving skills demanded, students need the ability and self-discipline to follow rules and patterns in a repeatable, reproducible and thus verifiable or objective manner. But they also need the knowledge that rules and patterns, even those with seemingly repeatable, reproducible and therefore verifiable results need not be reliable. Again, That is where critical thinking appears. Further in problem solving, students should meet or be given solutions to problems previously met, so that there is not continuing need to re-invent solutions, and so that students can repeat or develop further what others have done. Students need the ability to recognize and solve open problems, but that stand on a knowledge of what has been done before and a deliberate coverage of the benefits, origins and limits of rule and pattern based processes in thought and deed. A balance is needed. Past practices should not be pushed aside. Students should learn about them, their benefits, origins and limitations, while learning to go beyond when needed. Critical thinking in science is based on statements that can be tested and the empirical accumulation of practices that work in some measure if not completely. There-in lies an behavioral approach to learning and teaching in science, mathematics included. Modern cognitive theory which says teachers and schools should not test students because (i) whatever a student thinks is valid for him or her; (ii) because rule and pattern based skills and concepts is not real learning; and because (iii) student success on one test is no guarantee of success on further tests, do so in opposition to empirical perspective of mathematics and science. |
www.whyslopes.com
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