Employ an online or offline tutor at your own risk
from
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tutorfinder.com.au
CDN :
findatutor.ca
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CDN: Montreal
Tutors
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findatutor.co.nz
UK:
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UK: tutors4me.co.uk
USA:
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USA: ziizoo.com
or employ the site author - View
his WiZiQ profile
- Calculus students are very welcome.
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YOU are better than YOU think. Show
yourself how:
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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.
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Explore collaborative whiteboards
from groupboard,
twiddla or
scriblink.
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Chapter 3.
What is Algebra?
Previous: 3 Words Before Symbols:
What is a Variable?
There are many facets of algebra, but for most people, any subject is defined
by their first introduction to it. A broader, further ranging and more refined
definition can come later. In this light, the description and illustration of
the three skills for algebra provides an introduction and thus an initial
definition of the subject. For this author, algebra starts with the symbolic
description and formulation of calculations and continues with their symbolic
manipulation. It could be preceded by a pre-symbolic comprehension of the answer
to the question:
?
Decimal notations and operations can be regarded as part of algebra. They are
symbolic. Yet there is more to the algebraic or symbolic than this arithmetic
and concrete, most definite, use of symbols. The algebraic or symbolic process
of further mathematics involves another abstraction, namely the repeated use of
symbols as placeholders and pronouns for numbers and quantities, known or not,
constant or not. The question What is algebra? can be answered in
different ways. In past centuries, algebra may have meant all of mathematics
besides geometry. In the 20th Century, high school and college math courses,
those taught in North America especially, give the initial impression that
algebra is a mathematical subject besides say trigonometry, calculus and
possibly geometry – geometry is not often taught. But algebra is represented
by all subjects it touches, in mathematics and out.
Chapter 3 subsections: [ Up ] [ 3 Three Skills For Algebra ] [ 3 Words and Concepts Before Symbols: Variables ] [ 3. What is Algebra? ]
Next: 4 Introduction
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www.whyslopes.com
Volume 1B, Mathematics Curriculum Notes,
Foreword + Chapters 1 to 10 + 12
Area Map
Inductive Principles
1 Introduction
2 For & Against Math
3 Algebraic Thought
4 Why Slopes & SQRT of -1
5 Books & Articles to Read
6 Unruly Origins of Algebra
6. Axiomatic Civilization
7 Geometry, 2 Ways
8 Modern Instruction
9 The Two Ends
10 The Transition
10 Explaining Logic
10 Explaining Algebra
10 Why Sets in Math.
12 Four Phases
Links
Chapter 11: Primary School Mathematics
11 Primary Math
11 Cue Cards
11 Counting
11 Decimals - Addition
11 Decimals -Times
11 Decimals & Subtraction
11 Fractions and Division
11 Notational Conflict
11 Reciprocals Etc
11 Decimals - Ratios
11 Size Comparison
11 Numbers, +ve or -ve
11 Rename < Sign
11 Complex Numbers
Will provide an alternative to Chapter 11 later, most likely in the Parent's
Area: Help Your Child or Teen
Learn
Most students in high school are not heading for calculus,
but most topics in high school mathematics are present due to calculus.
Preparation for calculus demands their coverage at full strength.
See too, this site 55+, Math
Education Essays. Site areas and pages provide pieces of the a Mathematics
Education, Jigsaw Puzzle, in formation.
-Inductive
principles for course design & delivery require a clear
description of where and how skills and concepts may rest on earlier ones, so
that difficulties may be explained and remedied by looking for what was
missed or forgotten in earlier studies.
Mathematics is a demanding subject. All errors in notation
and comprehension need to be identified and corrected. In
reading, spelling and writing, students have to learn all the letters in the
alphabet, not just some. and memorize spelling. Anything less implies
difficulty.
Likewise in mathematics, students have to master key skills
and concepts, one at a time and one after another. Anything less implies
difficulty.
Modern mathematics curricula introduced an inconsistency
into course design and delivery. They did not sanction the use of decimals nor
the use of diagrams in skill and concept development but decimal arithmetic
and diagrams are needed for student comprehension and for an operational
mastery of quantitative skills. That implies the need for an mixed-math
curricula based on a systematic development of operational skills, sufficient
for applications and sufficient to provide a base & context
for the very optional study of pure mathematis.
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