Appetizers and Lessons for Mathematics and Reason (www.whyslopes.com)
||Définition d'une variable || Algèbre || Arithmetique || Logique ||La raison basée sur les règles et modelés||

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1,  Elements of Reason.
1A. Pattern Based Reason 
1B. Math Curriculum Notes
2. Three Skills for Algebra
3. Why Slopes & More Math

Mathematics Course Designers: LAMP offers food for thought.
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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.

Search For Repeatable and Reproducible Methods

Departures From Objectivity
Chapter 15 subsection

The ideal or goal of objectivity is represented in the legal system by the idea of impartiality. Lawyers, juries and judges interpret evidence and laws. One aim is to obtain impartial, objective verdicts of guilt or innocence, and assignments of blame, damages and punishments.

Rules and laws are subject to geographic chances. In different countries, we have different legal systems. Some are impartial. In these there is an attempt to apply previously established rules and regulations objectively. In other systems, the justice may be corrupted by bribes, prejudice, etc. Even in the more-or-less impartial ones, laws and regulations differ. So what is against a law or a regulation in one location may be legal in another.

Laws, including commercial ones, often have a moral or religious basis. Moral and religious ideas often define and differentiate groups. What is considered polite, or inoffensive in one group, will be impolite or offensive in others. Laws and regulations in legal systems reflect these differences.

Laws and regulations are often, if not always, subject to human interpretation. Commercial laws are intended to control or regulate business. Laws may also define or remove previous obligations or liabilities. The economic needs, self-interest and desires of people, affect laws.

Lawmakers are further requested by interest groups to write laws in one way or another. Each group readily accepts laws to control and restrict the behavior of any other group but itself. Laws as they are being formulated may be changed minutely to the benefit of one group or another. All of us have different ideas of what is fair. Our laws themselves are compromises between the views, principles and interests of several groups, often satisfactory to none. So we cannot say in advance that a set of laws will be complete and not contradictory.

Circumstances may occur to which the laws apply, but for which the rules are not intended. Or unforeseen circumstances will occur to which the laws do not directly apply. This points to the need for a new law or new judgments about the application of existing laws. Human laws are human creations. And humans individually or collectively may err. The formulation of laws and rules and principles by people introduces the possibility of error.

Postscript 2001-01-31 (Online Only):  Rules and regulations are written or  drafted by clerks or civil servants in a government under the direction of a cabinet minister. Most law makers, following the direction of their parties,  typically do NOT read in full the laws and regulations they pass. In consequence, lawmakers do not know their own intent in passing a rule. The precise interpretation of an imprecise rule or law may be left to courts or judges. The latter try to guess the "original" intent of the law.  That is absurd. For example,  the fall  2000 US federal elections with it counting of votes and voter intent in Florida according to ambiguous or inconsistent laws and regulation  provided an instance of this, and a court battle to determine the US president.

Approximate Objectivity

Laws and regulations, however obtained, may be applied in an objective manner. Objectivity may be subject to mitigating circumstances, political interference, the ability of lawyers, the opinions or morals of judges, etc. Results may vary or differ due to different laws and mores in different locations — including your hometown; or due to ad hoc departures from objective applications and interpretations of existing laws and rules, however carefully written or not. But the ideal of objectivity with human-made and human-applied regulation remains.


 Next: Chapter 16. Origins and More Limitations of Rules and Patterns

 

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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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