|
YOU are better than YOU think. Show yourself how:
|
-/[]\- Logic chapters 1 to 5 re- appear not in sequence, as is or longer, in Volume 1A, Pattern Based Reason, Bon Appetite. Logic
Mastery 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;
|
-/[]\- 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. |
|
| Introducing and emphasizing our ability or skill of talking about and describe numbers apart from doing arithmetic and writing formulas adds a verbal dimension to mathematics. That compensates for most or many arithmetic and algebraic expression being better seen and understood silently than being read aloud symbol by symbol, in a linear and sequential, one dimension manner. |
While pictures and formulas are each worth a thousand words or a few hundred, pictures can be seen and understood usually without an explanation of their ingredients. In contrast, the shorthand role of letters and symbols, and the technical use of words in mathematical subjects needs explanation, a clear introduction. To that end students and teachers should invest time in the multi-page site essay on What is a Variable:
Introduction
Variation between Examples
Variation of Letters
A letter denotes a variable
Cases of Double Variation
Three Notions of a Variable
Constants, Parameters and Variables
Talking about numbers
Dependent
or Independent
Variable, a Matter of Choice
To learn more and to extend or consolidate your understanding of what is a variable, of the algebraic way of writing and reasoning, see Chapters 8, 9, 11 and 12 in site Volume 2, Three Skills for Algebra.
8
The Three Skills
9 First
Skill
11
Why Shorthand
12
Shorthand Usage
Chapter 11 or 12 in Three Skills for Algebra explore the use and reuse of letters in examples, a use and reuse akin to the use and reuse of pronouns in a sentence or characters in a story. In speaking apart from mathematics, in each context, the pronouns, say it, he & she, should refer to different objects or persons. Otherwise there is confusion. And in plays, each character is normally played by a different actor, or single actor wearing different hats (superscripts if you wish). That is to say, students to need learn that in each context each letter or compound symbol or expression needs to have a unique role, albeit the same role (through the notion of equality) may be played by the same letter or compound symbol or expression.
Food for thought: Mathematics relies too much on diagrams, arithmetic expressions and algebraic formula and equations to the exclusion of the greater or clearer use of words in mathematics to describe numbers, amounts and quantities and to describe or introduce the shorthand role of letters and symbols and even diagrams. The readings above point to a correction.
Volume 2, Three Skills for Algebra, was misnamed. A fourth skill, the forward and backward use of equations, appears in Chapter 14 on the Compound Interest Formula. My aim in writing the chapters was to expand the algebraic way of writing and reasoning. Only later, much later, did I realise that the forward and backward use of formulas in that chapters could be identified as unifying theme for secondary mathematics in the use of all equations and formulas and in working with proportional relations or equations. Before the latter can be applied directly, they have to be used backwards or indirectly to obtain the value of the proportionality constant.
See the next lesson: Solving Equations with Literals
www.whyslopes.com
Lesson & Lesson Plans for
Sec IV (Maths 436)
a reference for learning and teaching functions, polynomials, solving linear systems,
powers + exponents + bases + radicals (roots) , quadratic formulas, equations of straight lines
1A. Master Logic 1B. Problems Solving Method 2A Solve Linear Equations i 2B.Solve Linear Equation II 2C Use Equal Sign Properly 2D. Perfect Arithmetic Skills 3 Words & Symbols 3 Goals to Set for Students 4 Use Equations Backwardly 5. Master Functions & Relations 6. Exponents & Radicals I 6 Exponents & Radicals II 7. Straight Lines 8. Polynomials (x,/,+/-) 9. Quadratics 10 Prove it 13 Similarity Scale Factors 12 Trig & Triangles 14 Statistics MEQ Intermediate Objectives Remarks for Teachers
Sit down and study - no one else can do that for you.
Advice and Directions
What to do in School & Why
How to Study Maths & WhyGood News: If you can learn to follow a multi-step methods in any subject precisely, you should be able to do so in other subjects, as well. Hint: Start with arithmetic
Words Before Symbols:
What is a Variable?
Level: Secondary II to VI, or Grades 7 to 12)
Introduction
Variation between Examples
Variation of Letters
A letter denotes a variable
Cases of Double Variation
Three Notions of a Variable
Constants, Parameters
& Variables
Talking about numbers
Dependent or Independent
Variable, a Matter of ChoiceComplex number starter lesson
Arithmetic Videos
Fractions
Primes
Greatest Common Divisors
Least Common Multiples
Square Root SimplificationArithmetic Videos
Decimal Addition Methods
Decimal Subtraction Methods
Decimal Multiplication Methods
Decimal Division Methods
Fraction Starter Lesson
(simplify, multiply, divide &
then add or subtract)
|
[Top of this Page][ All trademarks and copyrights
on this page are owned by their respective owners. |