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whyslopes.com
Entrance Level
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For Montreal Students: Head
Start Math Tutoring is available from the site author.
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.
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.
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Logic Objectives
A Skill and Concept Check List
For answers, see Volume 1A, Pattern
Based Reason, and Volume 2, Three
Skills for Algebra.
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How
to use implication rules, one at a time, and one after another, to
arrive at conclusions, one at a time or one after another. NB. the
route, how it is covered, may be of more interest than the conclusion.
-
How
two-way implication rules say more than one-way implications.
-
How
to read precisely what is written.
-
How the ability to climb a ladder or not is related to mathematical
induction.
-
How
different starting points may make a subject easier or harder to
explore.
-
How
to justify entries in truth tables for one-way implications starting
from the common notions of a rule being obeyed, disobeyed or not disobeyed.
-
How
to use the contrapositive of a one-way implication to arrive at a
conclusion (indirect reason I)
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How
proof by contradiction may be recast as using the contra-positive of a
one-way implication.
Skill and confidence in logic (rule-based
thought) comes from precisely applying implication rules, one at a time and
one after another, to arrive at conclusions, one at a time and one after
another, with the knowledge that any other thinking starting with the same
circumstances and using same implication rules, may follow your chain of
reasoning with the same result. This makes logic (how to argue you must)
repeatable and reproducible, independent of the thinker or initial discover of
a chain of reason. But an a mistake in one step of a chain of reason makes all
the rest suspect
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whyslopes.com
Entrance Level
[ Back ] [ Site Entrance & Hub ] [ Next ]
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
- Algebra
words before symbols
- direct & indirect
use of formula, numerical versus algebraic solutions - what
is a variable (more words)
- Arithmetic
- exercises
- with fractions
-
videos on primes, lcm, gcm,lcd, square roots etc
- Calculus - geometric
preview, algebraic
preview,
3 study guides,
much more
- Complex numbers
-starter lesson with java applet - easy
consequences for trig & vectors in the plane
- Education
- Empirical Course Design
& Delivery
- Fractions
- alone
- by rote
- with
algebra
- videos
- Functions - introduction
hindsight
- composition aka
substitution -
- Geometry, Euclidean - Correspondence
of triangles, Triangle
construciton, duplication & Isometry - Failure
of ASA & the // line postulate - angle
sum in triangles -//
grams - Triangle
Similarity
- Geometry-
Analytic - functions, polynomials, complex numbers, unit circle
trigonometry
- Logic
- First Steps -
Symbols in Logic
-
Occurrence &
Truth Tables - Indirect
Reason -Indirect
Reason More
- Proportionality
- Definition -
Direct & Indirect Use - Numerical versus Algebraic Solutions
- Real Analysis
- Decimal View of concepts
and of proofs
- Rules &Patterns in Science, Technology & Society
- Pattern Based Reason
- Mathematical Reasoning, empirical, inductive or deductive
- Units
- in rates & slopes &
(?) derivatives
- in ratios
& proportions - slopes & rates included
- Complex Numbers & Vectors & Trig
- trig expression for dot
& cross - cosine law
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