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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Modern Education and Critical Thinking
The demand in modern or post-modern education theory
(constructivism) for problem solving and critical thinking are undermined by
course design changes which do not require drill and practice in arithmetic,
so that arithmetic provides repeatable and reproducible results, and to
the point that students are taught or shown that care, patience and
self-discipline is required to mastery multistep methods. Allowing
students to skip that care, patience and self-discipline needed to obtain
repeatable and reproducible results leads to wishful and suspect critical
thinking and problem solving abilities. The use and combination of rules
and patterns one at a time and then one after another represents the start of
deductive reason and deductive connection, construction and Euclidean
codification of skills and concepts. For very critical thinking and problem
solving skills demanded, students need the ability and self-discipline to follow
rules and patterns in a repeatable, reproducible and thus verifiable or
objective manner. But they also need the knowledge that rules and patterns, even
those with seemingly repeatable, reproducible and therefore verifiable results
need not be reliable. Again, That is where critical thinking appears. Further in
problem solving, students should meet or be given solutions to problems
previously met, so that there is not continuing need to re-invent solutions, and
so that students can repeat or develop further what others have done. Students
need the ability to recognize and solve open problems, but that stand on a
knowledge of what has been done before and a deliberate coverage of the
benefits, origins and limits of rule and pattern based processes in thought and
deed. A balance is needed. Past practices should not be pushed aside. Students
should learn about them, their benefits, origins and limitations, while learning
to go beyond when needed.
Critical thinking in science is based on statements that can be
tested and the empirical accumulation of practices that work in some measure if
not completely. There-in lies an behavioral approach to learning and
teaching in science, mathematics included. Modern cognitive theory which
says teachers and schools should not test students because (i) whatever a
student thinks is valid for him or her; (ii) because rule and pattern
based skills and concepts is not real learning; and because (iii) student
success on one test is no guarantee of success on further tests, do so in
opposition to empirical perspective of mathematics and science.
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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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