[RUME] Secondary Mathematics, A Practical (Skill-Oriented) Approach.

[Alan Selby]

My site www.whyslopes.com  has   a new section
"Secondary Mathematics for Ages 11+, a Practical Approach". There is a
link to it from the top border of every page. Its URL is

www.whyslopes.com/index.php/0400Secondary_Mathematics_-_A_Practical_Approach/

Section material provides a coherent guide to technical innovations in  
other site
sections aimed at simplify and easing the learning and teaching of  
arithmetic and number
theory practices, elementary and advance algebra, elementary and advanced  
geometry, plus
two calculus previews with a description of a light calculus course, more  
descriptive
than deductive, aimed at introducing the key ideas in differential and  
integral
calculus. An appendix "Calculus with Proofs for the Keen or Gifted"  
describes
how to reform calculus, limit it to Lipshitz continuous functions, all in  
a manner
that makes proofs simpler and more accessible, at least for the keen and  
gifted,
without loss to calculus skill and concept development in senior secondary  
or college
level mathematics.

As of April 14th, the site has a new title "Logic and Mathematics Skill &  
Concept Development"
to better reflect its extent and intent. The site has outgrown its original
title "Appetizers and Lessons for Mathematics and Reason" in use since site
birth in June 1995. The new section covers key skills and concepts, and  
shows
how to employ site material, 1200 pages in 70 plus sections, in secondary  
level skill
and concept building in mathematics, logic and more generally quantitative  
skills.
The new section results from the study of topics European and American  
mathematicians were considering
in the 1960s for the preparation of university-bound students in commerce,  
science and
engineering. It further results from the somewhat ad hoc of a hundred plus  
textbooks and
exercise books in use from the mid-1960s to the present in primary and  
secondary schools.
Initially, the aim was to reform modern mathematics curricula of the  
period 1960-1990, the content
of which essentially implies the content of today's secondary curricula  
apart from the inclusion of
statistical methods. But the result is very different. The discovery of  
technical innovations
including methods for the systematic development of algebra skills in  
secondary mathematics
and calculus led to more practical, skill-oriented approach, one that may  
be use in home-schooling,
in home-tutoring, and in independent schools with control over the  
curricula they use.
Finally, some pages are slow to appear properly due to the use of  
web-based LaTeX tools MathJax and its younger
form jsMath for dynamically typesetting formulas and equations properly.  
The new section and site
as a whole is also the result of the thought in my 1966 onward highschool  
days that words were missing
in the introduction of algebra. In the last four plus decades, I have seen  
how to remedy most of the difficulties
I saw and add multiple innovations, all to make skill development simpler  
and stronger.

There is no pleasing everyone. See what you like. If one site element is  
not to your liking,
try another.  Bon Appetite.


Alan Selby
Montreal, Quebec
April 16, 2012
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