Parents: Help your child or teen

Online Volumes (Book Orders)
1,  Elements of Reason. 1996
1A. Pattern Based Reason  1995
1B. Math Curriculum Notes 1996
2. Three Skills for Algebra  1995
3.
_Why_Slopes_&_More_Math_1995

More Site Areas 
1.  Solving Linear Equations  2005
2.-Fractions-Rates-Proportns-Units-2006
3.  Algebra, Odds & Ends, HS level-2001
4.-Euclidean-Geometry/Complex No.s 
5.  Analytic Geometry/Functions 2006
6.  Number Theory. 2006-7
7.  Complex Numbers More 2001
8.  Calculus Introduction 2005
More Site Areas 
9   Real  Analysis 1995
10. Secondary IV? maths 2006-7
11. Math Education Essays  2006-7
12. LaTeX2HotEqn: 2004
13. Electric Circuits Etc  2007
14. Quebec Math Education 2004
15-Prequel-to-the-How-TOs-06-2008
How TOs/ Ref.-08- 2008
1. Arithmetic Reference
2. Algebra 
3. More Algebra 
4. Geometry  
5. More Geometry
6. Calculus
7. Logics in Maths


Employ an online or offline tutor at your own risk from 

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UK:   tutorhunt.com 
UK:  tutors4me.co.uk
USA:  wiziq.com
USA: ziizoo.com

YOU are better than YOU think. Show yourself  how:

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 For better work & study skills, read logic chapters 1 to 5  in  Three Skills for Algebra. Sooner is better. Good luck.

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 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

Do not leave here without it -  Logic mastery  will develops critical thinking, improve reading and writing, and give a firmer base for work and studies at many levels. Good luck.

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Caution: Site advice is approximately correct, for some circumstances, not all. Site How-TOs are logically developed, but not tried and tested. That leaves room for thought and refinement..

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After logic  (a) continue reading Three Skills for Algebra, chapters 8 to 14  and do so alongside site area on solving linear2007 Equations ; or (b) see this calculus starter lesson and Volume 3, Why Slopes  & More Math, chapters 2 to 6;


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.


Explore collaborative whiteboards from groupboardtwiddla  or scriblink.


Deductive, Inductive or Empirical Reason

Previous: Linking or Chaining Several Rules Together

Deductive reason uses or chains together supposedly (or preferably) never-disobeyed implication rules to suggest, to make or to reach conclusions. See the examples above. The implication rules in question may come from assumptions. The assumptions may be tentative.

The phrase inductive reason has one role in mathematics and another outside of mathematics. To induce (or induct) literally means to draw or extract. When you see a rule or pattern that no one has suggested, you are extracting or drawing that pattern from your observations. This process of recognizing rules and patterns that may hold, accidentally or not, is called inductive reasoning. Inductive reason outside of mathematics refers to the identification and recognition of rules and patterns from data and observations. Here rules and patterns may hold accidentally.

Reason which relies on a single or several, experience-found, rules and patterns to arrive at conclusions is called empirical. The underlying problem of inductive, empirical reason is to extract (infer, draw, induct or identify) from experience, in particular, data and observations, rules and patterns not satisfied merely by accident and which appear to be reliable. Self-deception needs to be avoided here.

Inductive reason inside mathematics refers to another process, namely, the extraction or drawing of conclusions from ladder-like chains of reason. See the next chapter for a more precise image or explanation. The rules or assumptions here are usually so certain, that we deliberately ignore the experience-based origins of mathematical reason.

Criteria for the recognition of reliable, non-accidental rules and patterns are described later in the chapter Origin of Rules and Patterns.

 


Chapter Subsections: Direct and Indirect Usage of a Single Rule ] Linking and Chaining Two Rules Together ] Linking and Chaining Several Rules Together ] [ Deductive, Inductive or Empirical Reason ] Chapter 6, Chains of Reason (Deductive Reason), Pattern Based Reason ] Linking and Chaining ] Putting Several Rules Together ] [ Deductive ]

Next: Chapter 7, Longer Chains of Reason

 

 

www.whyslopes.com
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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