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
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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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Apprentices and Masters in Arts, Trades and Disciplines, a
classical view of learning and teaching
December 28th, 2007
In many arts, trades and disciplines, the apprentices learn to follow and
apply rules and patterns, steps and methods, practices given or demonstrated by
masters, and to do so with sufficient care to obtain repeatable, reproducible
and verifiable results. The apprentice in the first instance follows the customs
and conventions of the master. In this education, rules and patterns,
steps and methods or practices may be learnt with or without explanation of why
they work or why are they are followed. But over time, the apprentice may
see or the master may demonstrate how to combine rules and patterns, steps and
methods, or practices to compound them to form further ones in a repeatable,
reproducible and hence verifiable manner. That process of combining or
compounding lends or creates a hierarchical structure to the learning and
mastery of the rules and patterns, steps and methods, or practices.
The extent to which the apprentice may meet and obtain an operational
command of art, trade or discipline may be subjective - some apprentices will
develop abilities beyond that of their master, while others will equal or
develop lesser skills. Masters and apprentices alone and in groups may
accumulate rules and patterns, steps and methods, or practices to share and
extend in a repeatable, reproducible and therefore verifiable manner. Moreover
some rules and patterns will fall into disuse or be forgotten while newer ones
arise. Each participant in the art, trade or discipline will see practices come
and go, and may in time, see why.
Intelligence within an art, trade or discipline appears and is used when or
while apprentices and masters are carefully to apply their practices, carefully,
while learning about the benefits, flexibility, limitations and origins of
elementary or compounded (combined) practices. In this, there may some be
approximations or some uncertainty known to the master, if not the apprentice,
through trial and error, and/or stories of what is feasible or not. The
master of an art, trade or discipline in meeting situations that have been
handled before or not, will look for practices that work, and try to duplicate
or refine them, and if need-be and if-possible, invent new practices to handle
new situations. Operational command of a discipline may be enhanced and advanced
by stories or theories to explain why rules and patterns work. On the
other hand, the latter may also unnecessarily inhibit and limit the operational
command. Whence not all is certain.
Over years and decades, the customs and conventions of an art, trade or
discipline in being refined may become more and more contrived and cease to be
immediately obvious to the apprentice. Whence the apprentice needs a guide
or a master to show what is possible, and self-instruction is impeded. The
operational command of an art, discipline and trade with a history of
custom and convention including a hierarchical organization in which some skills
and concepts depend on earlier ones in ways that took time and effort to
discover and perfect requires guidance from masters of the art, discipline or
trade. The apprentice is well-advised to seek that guidance and stand on the
knowledge and wisdom of others, including practical and theoretical knowledge of
the benefits, limits and origins of steps and methods, to avoid an ad hoc,
incomplete and most likely slow, construction or reconstruction of the latter
skills and concepts.
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www.whyslopes.com
Mathematics Education Essays etc
[ Back ] [ Up ] [ Next ]
Area Intro
Ideas for Better Instruction
4 Ways to Improve Reform
Theory of Knowledge
Peer Review
The Trouble With Algebra
Course Design and Delivery
How Letters Appear
Sit Down & Study
Modern Education
Key Notes and Themes
Site Lesson Plans
How This Site Differs
Site Origins
Math & Logic Puzzles
Comments on site content.
Words For Instructors
Inductive Principles
Fairness Principles
Apprentices & Masters
In for a Penny
Constructivism and Cognitive Theory
Three Remarks
For a Leaner Curriculum
Mixed Maths Curricula
Cultivating Intelligence
Reason - 3 kinds in maths
Logic in Mathematics
Science Education
Maths Instruction in General
Operational View & Values
Standards
Ends and Values
Goals & Unifying Themes
Algebra Lesson Plans
Algebra, Geometrically
Mathematics Curriculum Shifts
Teaching Tips - Fractions to Calculus
Math Ed Perils
Talk the algebra talk
Sec I - Fraction Focus
Sec II - algebra focus
Sec III - Focus on Slopes
Maps-Plans-Drawings
Math Wall Posters
Education, Empirical Art
Damage Reversal
North American Math Curriculum
Managing Reform
Essay January 2007
Educational Follies
Contructivism Incomplete
Missing the Point I
Mathematics in Context
What and When, A Challenge
Grouping Students
Teacher Certification
Education of Math Ed. Professors
Site Eurekas
Links
Help Me 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
construction, 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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