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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. |
Replies to Teacher Level Questions and Comments FollowEmail, June 8th, 2007: We've thoroughly enjoyed looking over
your site and wonder what inspired you to post it and where you are located. Reply: From fall 1983 to Spring 1989, I was aware of difficulties facing students, but as a transient college instructor, I did not have the standing to speak to colleagues about ideas for course or content reform. So I left college life in 1989, only to think in the last days of 1990, I should report my ideas to educational authorities or mathematics societies or mathematics education societies for discussion and refinement. Lack of standing for that suggested silence or self-publication. Self-publication began with one book offline in 1994, and began online in 1995, with a website, the forerunner to this domain but with the same "Appetizers and Lessons for Math and Reason" name, on the web-servers of the now defunct, non-profit society Communication Accessible Montreal. It was possession of (or was that by) ideas and lack of a venue or environment for their expression that led to self-publication and continued self-publication. I can to formulate with words today what I sensed when writing began. Namely popular, post- modern educational theories guiding education reform are tangential to content issues, the observation that course design for direct instruction mathematics is incomplete or awkward in its exposition of skills and concepts. There is a question today of what drives course design in mathematics - the rule- and pattern-based, skills and concepts in mathematics whose artful and applicable mastery may be seen as ends for instruction, or modern echoes of pre-empirical thought in theories of education which dismiss the empirical and operational mastery of rules and patterns from rote learning to proofs as sub-intelligent and too restrictive, and which dismiss the old careful role of teachers in correcting student's written work as too authoritative and not of merit since teachers (and everyone else) cannot read the minds of students to see what was thought. Modern educational theories appreciated the limitations of rule and pattern based disciplines, but not the benefits. Where ideologies are diverging, the proponents of one would not like their adherents formed by the proponents of the other. There-in lies a rational diminution of post-modern educational theories on instruction aimed at (i) developing skills and concepts in a rule and pattern based manner; and at (ii) alerting students to the limitations of the discipline's rules and patterns. |
www.whyslopes.com
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