Appetizers and Lessons for Mathematics and Reason 
www.whyslopes.com - mathematics as an art and discipline, step-by-step  Parents: See Help Your Child/ Teen Learn 
Français
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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.
More Site Areas 
1. Help Your Child/ Teen Learn 
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 
More Site Areas 
9. Quebec Maths Education  
10. Secondary IV(?) maths
11. Real  Analysis 
12. LaTeX2HotEqn:
13. Electric Circuits Etc  
14. Algebra, Odds & Ends, Etc
16  LAMP - Course re Design Plans
17. Math Education Essays
Teacher-Tutor Info & How-TOs
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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Protest:  The site author, a McGill University, 1983 Ph. D in mathematics, failed a McGill Faculty of Education B. Ed pgm 2003-5 due to


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.

Learning Takes Time and Effort

Students must be made to understand four things about learning math:
  1. Learning takes time and effort. 
  2.  Notes and work for doing problems must be written on paper and must be written precisely. Ideas or work written incorrectly will be a source of error later – at the time of reading or further reasoning.
  3.  Use of the electronic calculator for decimal computations does not provide the exact answers that are needed for derivations of formulas in algebra and beyond. For true understanding of concepts beyond arithmetic, students must be able to perform operations with fractions. 
  4. To completely master a mathematical concept, one must be able to write calculations precisely and exactly on paper. Errors of notation create misinterpretations which when read later on lead to misunderstanding or errors of further reasoning.

 

 

  www.whyslopes.com
Mathematics Education Essays, 57 or so 

Area Entrance & Hub
Ideas for Better Instruction
4 Ways to Improve Reform
Theory of Knowledge
Peer Review
The Trouble With Algebra
Course Design and Delivery
How Letters Appear
Sit Down & Study
Modern Education
Key Notes and Themes
Site Lesson Plans
How This Site Differs
Site Origins
Math & Logic Puzzles
Comments on site content.

Words For Instructors
Inductive Principles
Fairness Principles
Apprentices & Masters
Three Remarks
For a Leaner Curriculum
Mixed Maths Curricula
Cultivating Intelligence
Reason - 3 kinds in maths
Logic in Mathematics
Science Education
Maths Instruction in General
Operational View & Values
Standards
Ends and Values
Goals & Unifying Themes
Algebra Lesson Plans
Algebra, Geometrically
Mathematics Curriculum Shifts
Teaching Tips - Fractions to Calculus
Math Ed Perils
Talk the algebra talk
Sec I  - Fraction Focus
Sec II -  algebra focus
Sec III - Focus on Slopes
Maps-Plans-Drawings
Math Wall Posters
Education, Empirical Art
Damage Reversal
North American Math Curriculum
Managing Reform
Essay January 2007
Educational Follies
Contructivism Incomplete
Missing the Point I
Mathematics in Context
What and When, A Challenge
Grouping Students
Teacher Certification
Education of Math Ed. Professors
Site Eurekas
Links

Help Me Learn/Teach;

  1. Algebra
    words before symbols - direct & indirect use of formula, numerical versus algebraic solutions - what is a variable (more words)
  2. Arithmetic
    - exercises
    - with fractions
    - videos on primes, lcm, gcm,lcd, square roots etc
  3. Calculus - geometric preview, algebraic preview,
    3 study guides,
    much more
  4. Complex numbers
    -starter lesson with java applet - easy consequences for trig & vectors in the plane
  5. Education
    - Empirical Course Design & Delivery
  6. Fractions
    - alone
    - by rote
    - with algebra
    - videos
  1. Functions - introduction
    hindsight - composition aka
    substitution
    -
  2. Geometry, Euclidean - Correspondence of trianglesTriangle construction,  duplication & Isometry - Failure of ASA & the // line postulate - angle sum in triangles -// grams - Triangle Similarity
  3. Geometry- Analytic - functions, polynomials, complex numbers, unit circle trigonometry
  4. Logic
    - First Steps -
    Symbols in Logic -
     Occurrence & Truth Tables - Indirect Reason -Indirect Reason More
  5. Proportionality
    - Definition - Direct & Indirect Use - Numerical versus Algebraic Solutions
  6. Real Analysis
    - Decimal View of concepts and of proofs
  7. Rules &Patterns in Science, Technology & Society - Pattern Based Reason
  8. Mathematical Reasoning, empirical, inductive or deductive
  9. Units
    - in rates & slopes & (?) derivatives
    - in ratios & proportions - slopes & rates included
  10. Complex Numbers & Vectors & Trig
    trig expression for dot & cross - cosine law

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