Employ an online or offline tutor at your own risk
from
AU:
tutorfinder.com.au
CDN :
findatutor.ca
CDN: .i-tutor.ca
CDN: Montreal
Tutors
NZ:
findatutor.co.nz
UK:
tutorhunt.com
UK: tutors4me.co.uk
USA:
wiziq.com
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 4
Complex Numbers and Why Slopes
Reason itself appears in mathematics whenever we draw a conclusion from a
calculation, a diagram or from some implications rules employed in mathematical
definitions and assertions. The physicist Richard Feynman (1918-1988)
gave three public lectures at McGill University in 1979 (Printed version says
1976 in error). His work on physics has been followed by many scientists and
students[1].
[1] Apart from his more serious works, he
is the author of two light books, Surely You are Joking, Mr. Feynman!
Adventures of a Curious Character, 1985 and What Do You Care About What
Other People Think? Further Adventures of A Curious Character, 1988, both
distributed by Norton, New York.
In the lectures, most likely tongue-in-cheek, he suggested that physics was
based on two easily described operations, namely the addition and multiplication
of arrows in the plane. His description of arrow addition and multiplication for
a general, non-mathematical audience was a model for the informal, very
visual, yet also adequate, presentation of mathematical ideas. He gave it under
the guise of describing physics. And he avoided panic among the mathematically
shy by not saying that the arrows, with their addition and multiplication,
represent what pure and applied mathematicians (since Gauss) regard as the
complex numbers.
Two Topics, Easily Described
Talking about arrows, vectors and slopes are further parts of mathematics
besides rule-based reason and the algebraic way of writing and thinking. The
on-paper presentation of these glimpses is somewhat technical. They are much
easier to understand from a live presentation[2].
[2] What is not immediately understood below could be
left for as subject further inquiry – questions for someone more familiar
with late high school or early college math.
Links to the two topics (the next Chapter sections)
4 Complex Numbers
- how to add and multiply points or arrow in the plane
4 Why Slopes - how to
ease or avoid calculus difficulties
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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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