Appetizers and Lessons for Mathematics and Reason 
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||Définition d'une variable || Algèbre || Arithmetique || Logique ||La raison basée sur les règles et modelés||

Online Volumes (Book Orders)
1,  Elements of Reason.
1A. Pattern Based Reason 
1B. Math Curriculum Notes
2. Three Skills for Algebra
   Three Skills for Algebra
3. Why Slopes & More Math
 Avid Readers: Try Pattern Based Reason  & chs 
 1 to 12, 14,  16 & 17  in  Three Skills for Algebra.
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2. Solving Linear Equations  
3. Fractions Ratios Rates Proportions, Units
4. Euclidean Geometry
5. Analytic Geometry/Functions 
6. Number Theory
7. Calculus Introduction
8. Complex Numbers 
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14. Algebra, Odds & Ends, Etc
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17. Math Education Essays
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1. Arithmetic Reference
2. Algebra Starters 
3. More Algebra 
4. Geometry Starters
5. More Geometry
6. Calculus Modifiers 
7. Multiple Logics in Maths
8. Math Ed. Issues

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YOU are better than YOU think. Show yourself  how:  

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Read  logic chapters 1 to 5  in online volume Three Skills for Algebra  for greater skills & confidence in  work 
and study.

Learn to read notes and textbooks like a lawyer, so that no nuance, no subtlety and no clause escapes your attention.

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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
 Amazing, Amusing, Amorous,  Delicious, Delightful, Edifying, Strengthening Elixir. 
It eases work & learning difficulties Makes the hard easier. Opens eyes. Leads to greater precision.
in reading and
writing

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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Caution: Site advice is approximately correct, for some circumstances, not all. That leaves room for thought

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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.

For online automated help in senior high school maths & calculus, visit  quickmath.com  For Automatic Calculus and Algebra Help with derivatives, integrals, graphs, linear equations, matrix algebra, visit calc101.com  With  overlap, each site quickmath & calc101offers a different range of services, some free, some not, all based on webmathematica. Good luck.

Steps for Better Reason

Previous: Accidental Rules

A first step in rule- and pattern-based reason is to see and understand the difference between one-way and two-way implication rules. People too often think a one-way implication rule is a two-way implication rule. That can be confusing and misleading. It leads to false expectations and arguments. The ability to read and understand one- and two-way implication rules precisely further helps in following instructions and recipes and also in deciding which rules to apply.

A second step is to be aware of and cautious about suggestive and misleading questions. When asked a question, we politely try to answer without challenging the suggestions or assumptions made in it. Some questions take advantage of our politeness. Pause when encountering such questions. Don't always answer immediately. Rather, think if the question asked assumes too much or makes assumptions with which you are ill at ease. Those that do should be avoided or challenged. The chapter Deception, Suggestive or Misleading Questions speaks further about this issue and this second step.

A third step is to chain, link or connect implication rules together to create more implication rules for getting conclusions. (The verbs to link, to chain and to connect all have the same or similar meaning here. They are used interchangeably. Each can be used instead of any other for the sake of variety.) The chapters Chains of Reason and Longer Chains of Reason show how implication rules can be used one at a time and one after another.

The remaining chapters on reason in this book describe how patterns and implication are written and found, and how their reliability can be judged. A fourth step in logic or reason is to talk about how patterns and implication rules are found, invented and employed in daily life, technology, science and mathematics. The world is full of patterns, implications and suggestions. Some are more certain, more reliable and more correct than others, while others are completely false. We must try to identify which are which. Uncertainty is not welcome, yet not knowing what is unsure is worse. Locating weak spots in reasoning permits a search for replacements.

 

Chapter Subsections: Up ] First Puzzle ] Second Puzzle ] One- Versus Two-Way ] Talking About Logic ] Implications vs Suggestions ] One Versus Two Way Committments ] Repeatable & Reproducible ] Limits and Benefits ] Accidental Rules ] [ Steps for Better Reason ]

Next: Chapter 5: Deception, Suggestive or Misleading Questions

 

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Volume 1A, Pattern Based Reason

 Chapters 1 to 24

FOREWORD
Three Remarks

1 Introduction
2 Communication
3. Elements of Reason
4 Implication Rules
5. Deception
6 Chains of Reason
7 Longer Chains
For & From Consistency
8. Language Change
9 Next Chapters
10 Responsibility
11 Accidental Patterns
12 Knowledge Islands
13 Euclidean Logic
14 Deductive & Empirical Views of Mathematics
15 Objectivity
16 Origin of Rules
and Patterns
17 Objective Ways

18. Waking up
19. Symbols  & Logic
20. Pronouns or Symbols
21. Truth Tables I.
22. Truth Tables II
22. Biconditional
22. Contrapositive
23. IF-THEN table
24. Indirect Reason Again

To reason often means to persuade someone of the need for an idea or action. That someone could be yourself. So be careful.

1A Logic Postscripts
- online only

+Proof by Absurdity alias proof by contradiction
+How the demand for consistency supports the law of the excluded middle
+Reality versus or with the aid of Imagination
+Links for reason, logic and crtical thinking
+Three Remarks
+History Lost or Missing

There is a difference between
knowing how to spend money,
and having money to spend.

There is likewise a difference
between mastering a skill
and having meeting a situation in which it applies.

 



 


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