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Protest: The site author, a McGill University,
1983 Ph. D in mathematics, failed a McGill Faculty of Education B. Ed pgm 2003-5
due to
YOU are better than YOU think. Show
yourself how:
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Read logic
chapters 1 to 5 in online volume Three
Skills for Algebra for greater skills & confidence
in work
and study
Learn to read notes and textbooks like
a lawyer, so that no nuance, no subtlety and no clause escapes your
attention. |
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Logic
chapters 1 to 5 re- appear not in sequence, as is or longer,
in Volume 1A, Pattern Based
Reason, Bon Appetite.
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
Logic
mastery makes the hard, easier. Logic
mastery leads to better, stronger and richer comprehension. Logic
mastery improves reading and writing. Logic
mastery ease learning difficulties. Logic
mastery gives a headstart. In sum, logic
mastery will develops critical thinking, improve reading and writing,
and give a firmer base for work and studies at many levels. Good luck.
After logic,
(a) continue reading Three
Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving
liinear Equations ; or (b) see this calculus
starter lesson and Volume 3, Why
Slopes & More Math, chapters 2 to 6;
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Caution: Site advice is approximately
correct, for some circumstances, not all. That leaves room for thought |
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What may be learnt and when depends on how skills
and concepts are developed. Making the hard easier and clearer will allow
earlier & richer development of skills and concepts.
Try the Twiddla
Whiteboard. In principle, it allows
to people to draw and chat together online on a copy of this webpage or a clean
sheet. The chat may be via text or audio. Visit www.twiddla.com
to set up whiteboards to work with the webpage of your choice.
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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What is the Education of Mathematics Education Professors
Postscript: May 14th, 2006
Are calculus phobic Mathematics Education Professors to
blame for several hundred or a thousand hours of mathematics instruction in
pirimary and secondary schools which fail to prepare students for college
mathematics, which fail to give students an efficient fraction skills and
sense? Just as we specify the minimal mathematics background of future
secondary school teachers, should we specify the minimal subject skill and
knowledge of Mathematics Education Professors.
In the present dark ages of mathematics instruction, Professors of
Mathematics Education have not emphasized the needs of college mathematics or
calculus in the training of primary school and high school teachers, and in the
design and exposition of high school mathematics textbooks. Thus many
students graduate from primary school and even high school without efficient
fraction sense and skills, and several hundred to a thousand hours of
mathematics instruction time come to naught, less than expected, and may
be written off as a contribution to the education of many students. Site
books and further site areas point to remedies for self-application by students,
teachers and Professors of Mathematics Education. Professors of mathematics
education should teach first courses in differential and integral calculus fully
in order to know what calculus-driven standards need to be emphasized in the
mathematical formation of primary and secondary school teachers, and of students
in general.
Professors of Mathematics Education should take note
of earlier difficulties in mathematics, the introduction and
development of the shorthand algebraic way of writing and reasoning in
mathematics, and the inclusion of too many topics and directions in course
design which continue today. Professors of Mathematics education
need to read and correct textbooks in the student catch basins of their
universities, or they need to ask mathematics professors in their college or
university to perform this task for the sake of quality and perhaps a leaner
exposition of mathematics based on the needs of calculus and before the
elementary application of numbers with measures and masses - two focuses for
mathematics learning and teaching. Here again mathematicians should be
included so that key skills and topics are emphasized and the logical need for
some topics questioned. Many college calculus instructors limit or disallow
the use of calculators because its ease of use and ill-use sabotages the
intellectual component of mathematics.
Professors of mathematics education who are calculus phobic should be
extremely rare or non-existence in Education Colleges and Faculties. How common
are they?
Finally, there guidelines for the formation of secondary mathematics
instructors call for many courses in mathematics at the college level. For
the sake of consistency, mathematics education professor should have had a
similar dose of mathematics and more. Anything less calls into question
the hiring and promotion policies in schools of education.
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www.whyslopes.com
Mathematics Education Essays,
57 or so
Area Entrance & Hub 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 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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