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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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Site Origins
As a secondary school student 1965-9, I suspected
difficulties in algebra were due to its incomplete introduction. That is, the
algebraic shorthand roles of letters and symbols were used, required, but not
clearly nor fully explained. So I watched for a remedy. In fall 1983 as a
novice instructor, I gave three lessons, namely three
skills for algebra, why
slopes and two logic puzzles to
make algebra & calculus simpler to understand and explain; to improve
reading, writing & reasoning skills; and to hint at the role of logic in
mathematics. Since then, I have been trying to tell to fellow instructors
how difficulties in mathematics might be addressed but my ideas not wanted, were
dismissed before being heard.. Today, I am still trying. Parallel to views
that difficulties in mathematics can be eased by use of indirect instruction to
engage or interest students, my 1965-9 suspicion has slowly become a proposition
for a clearer, fuller, wordier development of algebraic skills, concepts
and themes. Site material shows how in ways motivated by inductive
principles for instruction met in 1981 outside of mathematics. Site material
also spring from examples of guest speakers 1975-82 at McGill University
of different ways to understand and develop skills and concepts in mathematics
and physics.
Writing only began in the last days of 1990 as I saw no hint in
mathematics education literature and practice of the remedies I saw or
sensed for common difficulties. Prior to that my writings aimed at
advancing mathematics itself and not mathematics education. The mathematic
education literature with its focus on delivery matters obscures the question of
what should be taught. It appears that cognitive theories of learning dismissive
of the rule-based fashion in which mathematicians see their discipline lead
course design and delivery in North America. Sequences of skills and
concepts which could be leaner, which mathematicians see as
preparation for calculus are being obscured or diluted by cognitive theories,
dominant or authoritative in their own way, which say students should find and
construct their own knowledge instead of following authoritative (textbook)
accounts.. This opposition to authority in name of developing critical thinking
undermines them instead as the ability to follow rules and patterns in a
repeatable and reproducible manner is needed before and besides the question of
whether or not particular rules and patterns are valid.
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www.whyslopes.com
Mathematics Education Essays etc
[ Back ] [ 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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