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Appetizers and Lessons for Mathematics and Reason 
||Définition d'une variable || Algèbre || Arithmetique || Logique ||La raison basée sur les règles et modelés||
 Calculus, Preparation for Calculus and Math Ed Reform etc 

Online Volumes (Book Orders)
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.
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. More Calculus
More Site Areas 
8. Complex Numbers 
9. Qc Maths  Education  
10. Secondary IV(?) maths
11. Real  Analysis 
12. LaTeX2HotEqn:
13. Electric Circuits Etc  
14.  Français
15. Algebra, Odds & Ends, Etc
More Site Areas 
16. Math Education Essays
17**. Telling & Tracking Time
18**. Maps, Plans & Drawings
19**. Quantitative Skills for  
     home and  work, etc, etc 
20**. Statistics .
** Means Under-construction.

Test the Twiddla Whiteboard

whyslopes.com
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For Montreal Students:  Head Start Math Tutoring  is available from the site author.  Head start tutoring is for students whose parents are not satisfied with math ed in Quebec.

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  
Then seek 4 skills for algebra in it.

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 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.


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;

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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.


George Orwell:   Is it nonsense for arts and disciplines based on and respected for carefully  mastery of rules and methods, alone and combined, to face education reforms based on the supposition that mastery of rules and methods is not a sign of intelligence.  Would you like to rewrite 1984 to include that angle?


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 twiddla.com to set up whiteboards to work with the webpage of your choice.

Precalculus sites mathsisfun & purplemath are visually more appealling than this one.  Do not go. 

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.

 

 

Quantitative Skills - Ideas for a New Site Area

This site area to grow will cover or point to numerical skills and concepts appearing in all walks of life at work, at home and in-between.  The aim is to include common calculations of potential interest on a daily or long-term basis.  For example, one of the books I am reading or have read on learning French gives many examples of visiting a places, a store or restaurant, a train station, etc, and introducing  the words needed or likely to met in such a place or situation. This site area will offer examples (vignettes) where we describe the calculation likely to occur in each place or activity. Any place, trade or activity in which elementary mathematics appears provides material for a webpage in this (future) area. These examples may be useful for instruction and self-instruction. 

Money Matters

The site pages provide an elementary to advance view of money related calculations.  

[Compound Interest Formula] 14 The Formula ] 14 Direct Use ] 14 Indirect Use I ] 14 Indirect Use II ] 14 Further Notes ] 21 What's Next ] 22. Sums ] 22 Arithmetic Sums ] 22 Geometric Sums ] 23 Sum Shorthand ] 24 Your Money ] 24 Periodic Deposits ] 24 Account Tracking ] 24 Pension Plans ] 25 Inductive Proof.Eg ] 25 Factorial Definition ] 25 Product Notation ] 25 Notation for Sums ]

The further pages review arithmetic and try to teach some algebra and logic 

2. Implication Rules ] [ 3. Chains of Reason ] 5 Knowledge Islands ] 4. Induction (Longer Chains) ] A  Arithmetic Problems ] Solutions ] B Caclulator Problems ] Solutions ] C More  Arithmetic Problems ] Solutions ] D Algebra Problems ] Solutions ]

Logic Lessons 2 to 5 could and should lead to precision reading and writing, two musts for studies and work!

These consumer and money mathematics lessons are in the online work Three Skills for Algebra 

Site Content Guide

Chapter 14 on the  Compound Interest Formula shows there is more to mathematics than doing arithmetic. Formulas can be used directly and indirectly. This chapter shows how. In this discussion of the compound interest formula, I just want to show you how to use it and how to manipulate or change it to extract other formulas from it. Examples with and without numbers will be given. Explanations of why the compound interest works may be found elsewhere. When times permits, the explanation why will be posted here.

The next group of chapters

  1. Geometric Sums Etc,
  2. Notation For Sums,
  3. Personal Money Computations, and
  4. Some Finite Mathematics
describe ideas and mathematical methods which can be used in money computations. The methods should be used carefully. Errors here could be costly. Opinion: Everyone regardless of academic or work destination, should meet and master such calculations because they might be useful in daily life.

The first two chapters Geometric Sums Etc and Notation for Sums and describe the mathematical ideas and methods needed in to explain the calculations involving compound interest, loans and pensions in the chapter Personal Money Matters. Note this chapter provides only one motivation for mastering the mathematical ideas and methods employed or shown.

The chapter Some Finite Mathematics shows how the principle of mathematical induction can be used to justify or confirm again the summation shortcut formulas given earlier. (Mathematicians favor math induction in place of more relaxed methods of justification.) The ideas and methods in this chapter Some Finite Mathematics are re-cycled or re-used in many further parts of mathematical thought.

 

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Tutors - All Subjects
(use at your own risk)
AU:  tutorfinder.com.au
CDN :  findatutor.ca 
CDN: .i-tutor.ca
CDN: Montreal Tutors
NZ:   findatutor.co.nz
UK:   tutorhunt.com
USA:   wiziq.com
USA: ziizoo.com

Pages For Teachers

Site Entrance & Hub
Permissions for Instructors
Lesson Plans - Sec I
Lesson Plan, Sec II
Lesson Plans - Sec III
Secondary Maths, Core Elements
About Site Books & Areas
Site History/Content
Site Reviews
Vol 1. Elements of Reason
Maps Plans Drawings
Quantitative_Skills/index.html
Order  Site Books

HIP, HIP, HIP, Hooray for site
content & history. Hype, Hype,
Hype, Hoorary,
for deception.

Your IP Address  & how to use it

Pages for Students

Site Entrance & Hub
Head Start Page
25 hours per tear
More Advice & Directions
Aims to adopt to aid
Arithmetic Check List
Fraction Skill and Concept Check List
Site History and Content
Books to Read
Complex No.s Intro.,.
Calculus Motivation
Calculus. Guide Short
Calculus. Guide-Long
Calculus Guide - Longest
Links - Many Subjects
Links - Games/Activities
Long Site Intro
Still More Advice
Logos Cafe
Logic Check List
Mathematics Cafe
Math CheckList
Site Areas by Age and Subject
A Site Map
Advice for Secondary I Students
Three Ways to be a Better Student
Reason for HS Mathematics
Montreal Tutors

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

 

Help U 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
  7. Functions - introduction
    hindsight - composition aka
    substitution
    -
  8. Geometry, Euclidean - Correspondence of trianglesTriangle construciton,  duplication & Isometry - Failure of ASA & the // line postulate - angle sum in triangles -// grams - Triangle Similarity
  9. Geometry- Analytic - functions, polynomials, complex numbers, unit circle trigonometry
  10. Logic
    - First Steps -
    Symbols in Logic -
     Occurrence & Truth Tables - Indirect Reason -Indirect Reason More
  11. Proportionality
    - Definition - Direct & Indirect Use - Numerical versus Algebraic Solutions
  12. Real Analysis
    - Decimal View of concepts and of proofs
  13. Rules &Patterns in Science, Technology & Society - Pattern Based Reason
  14. Mathematical Reasoning, empirical, inductive or deductive
  15. Units
    - in rates & slopes & (?) derivatives
    - in ratios & proportions - slopes & rates included
  16. Complex Numbers & Vectors & Trig
    trig expression for dot & cross - cosine law

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