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
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UK:
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USA: wiziq.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.
|
Explore collaborative whiteboards from groupboard,
twiddla or
scriblink.
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Welcome. The ends, means and values of mathematics education represent a
jigsaw puzzle with some pieces missing, or as yet undefined. In this site area
is a depository for some of the pieces, and ideas on how to find the missing
ones.
For navigation, click on the next or back buttons, or return to this area
entrance to select another essay. Bon Appetite.
About this Site
- Site History and Content
- through site reviews 1995 onward.
- Site Eurekas - Site Highlights, an
old view
- How this Site Differs
- Reactions to Site
Material - comments & questions, good and bad.
- Site Origins
- About Site Lesson Plans
- Another tour of Site Content
Challenges for Education Reform
- Managing Reform - Assigning
Responsibilities. (Should anyone be responsible? Should anyone be in
charge? Is reform headless?)
- Mathematics in Context -
What Context?
- What Should
be Learnt and When?
- Grouping
Students - Streaming?
- Learning Takes Time and Effort
- Making the Hard Easier but
Ignoring how and so missing the Point
- Hook, Line and
Sinker - Mathematics Education Inconsistencies Reform in North America
- More on Mathematics Education:
Covers: For a leaner curriculum, Education an empirical art,
More on testing, Constructivism versus Empirical Methods.
- Four Skeptical
Essays on Constructivism Revisited - Incompleteness
- Euclidean Model for
Development. Damage Reversal
- Educational Follies -
Learning By Discovery incomplete, cannot work, compound difficulties.
- An Educational
Inconsistency.
- Modern Education
But teaching by indirect instruction requires not only a knowledge of what
can be taught directly, but also a knowledge of how to explain all elements
indirectly. Anything less invites or compound difficulties. Ouch.
Ideas and Principles For Instruction and Educational Reform
- Inductive Principles For
Instruction - systematic skill and concept development.
- Fairness
in Education - requires systematic development of all skills and
concepts.
Can education be fair if students are tested on natural
talents instead of developed ones? Mastery of a skill, say the
algebraic way of writing and reasoning, is regarded as a natural talent when
and only when we do not know how to systematically develop that skill
or concept. Site material reduces the number of natural talents required in
the mastery of mathematics. Find the four skills for algebra in
chapters 8 to 14 of Volume 2, Three
Skills for Algebra, to see how to artificially and artfully develop the
algebraic way of writing and reasoning, and thus make mathematics fairer.
- Apprenticeship
in art, trades and disciplines, a classical view.
- Education is an Empirical
Art
- Key Notes and Themes
- Three Remarks
- For a Leaner
Mathematics Curriculum
- Need for a
Mixed Mathematics Curricula
- Extent and Need
for Quantitative Skills depends on your society
- Ways to be a Better
Instructor - Ideas and Methods - try with caution
- Four Ways to
Improve Education Reform, and avoid disaster.
Lesson Plans, Aims and Goals (Ends, Values and Means?)
- Three Aims for
Students - Ends and Values
- Three Goals
for Mathematics Education, etc - Ends, Values, Unifying Themes
- Lessening or
Avoiding Algebra Difficulties
- Algebra Lesson
Plans
- Algebra,
Geometrically
- Mathematics Curriculum
Shifts
- Advice and Suggestions for
Course Design and Delivery
- Teaching Tips - from fractions to
Calculus
- Math Education Perils
(Arithmetic, Algebra, Calculus)
- Talk the algebra talk
- First Year High School
Math - Lesson Plans with Fraction Focus
- Second Year High School
Math - Lesson Plans with an algebra focus
- Third Year High School
Math - Lesson Plans with a Focus on Slopes
- Math Wall Posters
- How Letters Appear in Mathematics
- Map, Plans and Drawings, a multi-year
project
Links
- Links - Just
a few.
- Activities to Engage
Students - links to explore
Logic and Reason in Mathematics
Mixing Rote & Thought-Based Development
- Cultivating Intelligence
- Why value careful mastery of rules and patterns, steps and methods,
practices, in a repeatable and reproducible manner.
- Multiply Kinds
of Reason in mathematics - Essay I
- Multiply Kinds
of Reason in Mathematic- Essay IIs - On the hierarchical development of
rules and patterns, steps and methods, and practices in pure and applied
mathematics (mixed mathematics). What is proof? What options are there for a
thought-based development and verification of college and pre-college
mathematics?
- Theory of Knowledge -
Stories, Longer and longer
- Formal or Informal
Peer Review
- Education
in Mathematics, Science and Technology - All based on empirical
verification and empirical skill development and verification. But in
mathematics we can offer a full thought-based development while in science
and technology, we can introduce the scientific method and introduce lab
equipment, but can only provide a full-thought based development through
visits to the lab and library. The lab alone is insufficient.
- Maths Instruction
in General - Three Goals A B and C to Set for Student, Supporting those
goals and why rewrite the curriculum
- Operational
Viewpoint - Aim for an Operational Command of Mathematics First.- For
students with no immediate interest in the know-why, a focus on the
practice, an operational command of key skills and concepts may make
comprehension later of the know-why easier and more appealing. The calculus
teacher may says to students - learn to do now and to understand later.
- How to Set Standards
for textbooks and course materials - Need for Inspection by
University Domain experts outside of Education Faculties to ensure
bureaucratic course design and textbook composition does not lead to
nonsense in mathematics education.
Teacher Training
- Teacher Certification Issues
and Cautions
- Math Ed. Professors
- Training, Education of
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www.whyslopes.com
Mathematics Education Essays etc
[ 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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