|
YOU are better than YOU think. Show yourself how:
|
-/[]\- 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;
|
-/[]\- 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. | Preparing for Analytic GeometryWith diagram and sketches, this site area provides a thought-based development of geometry before or without coordinates and in doing so provides a base for right triangle trigonometry and the coordinate-free discussion of parallelograms. The further development of geometry with the aid of coordinates goes further by standing on the skills and concepts covered above. The use of coordinates in geometry introduces arithmetic and the properties of arithmetic into the development of skills and concepts. The further development is based on the assumption that is a correspondence between what can be drawn and what can be described with numbers. The latter assumption, not part of pure mathematics, is a basis for applied mathematics. With it, models can be made of geometric or physical situations. The switch to coordinate- or numerical-based reasoning simplifies the development of ideas in geometry and avoids the need for drawing and extrapolating from diagrams. The switch replaces drawings or suggestive sketches by more certain or more precise consideration and in doing so avoids bad or misleading sketches in arriving at conclusions. Mathematics reasoning in geometry and physical situations may motivate and lead to arithmetic skills and patterns of an empirical kind. But the assumption and use of those skills and patterns in turn leads to a numerical description and development of geometrical skills and concepts in which the properties of numbers and not sketching ability count. That is, once the accounting rules are established via the use of coordinates, the ability to sketch become illustrative only.
|
|
|
|