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:
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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Remark 1, Fall 2005. Direct and Indirect Instruction Combined:
In the old view of mathematics education, the instructor may stand in
front of the classroom writing explanations and examples on the blackboard,
alone or with student help, to develop the skills and concepts, one at
a time and one after another. The instructor may also collect written
or walk-about the classroom to look at written work in order to correct errors
in notation and understanding. The teacher is in charge of skill development and
verification.
The newer view is that instructors should make mathematics attractive with
activities that are fun to do in which discovery and learning of skills and
concepts occurs, without the teacher standing in front of the classroom and
saying directly what should be learnt.
The old and new approaches should be combined so that students can learn or
discover through activities interesting to (engaging for) them while the
instructor states learning objectives clearly and beyond that verifies that the
desired skills and concepts have been mastered.
Remark 2, March 26, 2006. Empirical Flaw in Indirect Instruction
(Constructivism)
Older education theory calls for course outlines and materials to set forth
performance and comprehension objectives - aiming for but not always
delivery, performance and understanding in a repeatable and
reproducible fashion. Marks were based on performance. Students learn from
course material (the theory) and from loss of marks due to the
identification of errors in performance.
Modern education theory calls for students to be engaged or hooked by
open-ended, course material and investigative, authentic, realistic
activities with performance. Drill and practice, mastery of skills and concepts
in a repeatable and reproducible manner not emphasized, not demanded, and put
aside. The latter de-emphasis appears to be empirically unsound.
Remark 3. Critical Thinking - A Call in Constructivism that ain't clearly
supported.
Site material here at www.whyslopes.com
supports the development of critical thinking and problem solving skills, and a
discovery approach to learning. Critical thinking requires the ability to
follow multi-step with care, see what is available and what works, before
extraordinary or out-of-the-box or lateral thinking is required.
Re-inventing the wheel is not efficient, but problem solving situations, real
or artificial, in which students have to go the limit or beyond of their present
body of knowledge can develop thinking skills. The extreme constructivist view
that knowledge is an individual affair, not for correction, lies in
contradiction with the growth and development of technical knowledge in science,
engineering and mathematics. The latter seek and rely upon methods with
repeatable and reproducible results. The methods are learnt by trial and error,
guided by existing or extended empirical and theoretical patterns, in which
nature in a behaviorist manner may allow us to learn from mistakes - what does
not work and what recipes or methods do on a small if not a large scale.
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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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