Appetizers and Lessons for Mathematics and Reason  ( Français)  
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 Logic mastery is key to easing or avoiding learning difficulties in work & studies. 

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

External Links:  Tutoring Services

Parents: Help your child or teen learn

Site  Folders
1. Arithmetic Videos  11-2008
2.  Algebra Videos (to appear)
3. Solving Linear Equations  04-2005
4.-Fractions-Rates-Proportns-Units-2006
5.  Algebra, Odds & Ends, HS level-2001
6.-Euclidean-Geometry/Complex No.s 
7.  Analytic Geometry/Functions 2006
8.  Number Theory. 2006-7
9.  Complex Numbers More 2001. 
10  Exponents & Radicals Exactly 2008
11. Calculus  2005

12.Real  Analysis 1995
13. Electric Circuits Etc  2007
Mathematics How TOs & site 
content guides  08- 2008
1. Arithmetic
2. Algebra 
3. More Algebra 
4. Geometry  
5. More Geometry
6. Calculus
Calculus Motivation

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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Oops:  If you find an error, please report  it and  its location (URL)


 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.


Preparation for Calculus 

  • Short Form - mostly links  with very few comments, plus some rough time estimates for each part 

  • Long Form-  links with more comments.

  • Longest Form - links and many more comments.

Calculus gives the best framework for understanding calculations met in business, science and engineering. Describing the same calculation without calculus is long and shallower process.  Good preparation for college mathematics (or calculus)  requires mastery of most, but not all the topics, you meet in high school mathematics: exact arithmetic with whole numbers and fractions, algebra, geometry without and with coordinates, and trig.

Preparation for calculus prepares for most  or all arts, trades and disciplines involving mathematics. That is, preparing for calculus will help you be better than you expect in accounting, art, chemistry, drawing, English, physics, woodwork, metal work, geology, electricity, mechanics, drafting and computing etc.

Many professions apart from mathematics, for instance nursing and policing,  require mastery of mathematics, even arithmetic, as a sign of skill and intelligence in problem solving, or using rules and patterns carefully and precisely  in a repeatable and reproducible manner. Many profession far from mathematics require mathematics mastery because its mastery shows an error in one step makes it and everything after wrong. 

Preparing for calculus will help you be better than you expect in accounting, art, chemistry, drawing, English, physics, woodwork, metal work, geology, electricity, mechanics, drafting and computing etc.

Even for students who do not take calculus, preparation for calculus would or should lead to the ability to apply or use rules and patterns, one at a time and one after another, carefully with the knowledge that an error in one step makes all that follows wrong or give its a lesser value.  Students should not be surprised by the expectation that a multi-step method lead to repeatable and reproducible results when sufficient care is taken. 

Calculus even if unseen by many students,  is unifying subject in mathematics and its applications to other subjects - commerce, business, personal finance, science, technology and engineering.

Reference: The Kyrgyz-Turkish High Schools Mathematics Pages has a lot material in pdf files - look at them

Digression: A Web Guide

  •  Local material  here at www.whyslopes.com is for ages 14 to adult.  Two other sites Maths is Fun  and Math League Help Topics appear to be for ages 9 to 14 say,  site PURPLEmath appear to be for ages ages 10 to 15; and   site SOSmath.com site is for ages 16 to adult.   Two or three views of topic from different authors site put together may be clearer & more informative than one. Explore all to find examples & explanation to help yourself or someone in your care master mathematics, etc.

  •   Kyrgyz-Turkish High Schools Mathematics Pages -Here is a excellent sequence of pdf files for grades 7 to 11 going from arithmetic to calculus. Looks very complete and is well-formatted. Jealously go away.  Here is a great resource for teachers and/or students.  Includes Review ExercisesNew Link, Old Site: Earth Station 9 - a one man reference (link collection) for many, many subjects. 

  •  Free HTML Editors and WYSIWYG Web Editors - A digression

 

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Three Links for Teachers:
(i) First Year High School Math - Lesson Plans with Fraction Focus (ii) Second Year High School Math - Lesson Plans with an algebra focus (iii) Algebra Lesson Plans

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.

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

Favourite Sites:  BBC News  and mathematics portion of  English National Curriculum

All trademarks and copyrights on this page are owned by their respective owners. Copyright to comments & contributions are owned by the Poster.  The Rest © 1995 onward by site author,   Alan Selby. All Rights Reserved.  
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