Appetizers and Lessons for Mathematics and Reason 
What does it mean to use a formula forwards and backwards
www.whyslopes.com            ( Français)  
 Logic mastery is key to easing or avoiding learning difficulties in work & studies. 

Online Volumes (Book Orders)
1,  Elements of Reason. 1996
1A. Pattern Based Reason  1995
1B. Math Curriculum Notes 1996
2. Three Skills for Algebra  1995
3 .Why.Slopes.&
.More.Math.1995
Links For:  Tutoring Services
Notes on Public Issues

Parents:-Help. your. child. or. teen.study

Site  Math Folders

1. Arithmetic Flash Video Lessons  11-2008
2.  Algebra Videos (to appear)
3.-Fractions-Rates-Proportns-Units-2006
4.  Algebra, Odds & Ends, HS level-2001
5. 
Solving Linear Equations  04-2005
6.-Euclidean-Geometry/Complex No.s 
7.  Analytic Geometry/Functions 2006
8.  Number Theory. 2006-7
9.  Complex Numbers More 2001. 
 
10  Exponents, Radicals & logs. 2008
11. Calculus  2005

12.Real  Analysis 1995
13. Electric Circuits Etc  2007
Teaching & Tutoring How-TOs/ Reference - 08- 2008
1. Arithmetic
2. Algebra 
3. More Algebra 
4. Geometry  
5. More Geometry
6. Calculus

Economic Principles for all walks of life:
Annual income twenty pounds, annual expenditure nineteen six, result happiness. Annual income twenty pounds, annual expenditure twenty pound ought and six, result misery.

Charles Dickens, David Copperfield

Page Contents:

In good conscience,  I the site author, Alan Selby,  cannot be silent on issues of public interest. I will post concerns here with perhaps options, approximately correct, for their solution.  Educational issues are discussed outside of this folder. 

Public Health Care (Fall 2008):  

In all forms of health care, there will be a lack of resources to do the most or best for all. For example, public health care in Canada was not too costly until advances in medical treatments meant more could be done.  In the UK, local committees balance budgets between the needs of the many and the few. Yet private care in the UK retains an option for people with resources.  But triage and disappointment  in the availability and allocation of resources appears in both public and private health care.   Yet some care, dental included,  is better than none.  Both candidates in the recent US presidential election miss the point.  Insurance is not the answer. State funded health care is. With the dangers of more and more unemployment, more and more people will not be able to follow the insurance route. 

Remark: The Canadian health system initially provided an no expense is too much coverage for psychiatric patients. Then the pendulum swung the other way. Wards were closed and patients left to fend for themselves.  There has to be a middle way, 

Road Safety Question (1995?)

What side of the street should you walk on when there are no side walks?

Answer: If you have to walk along a street without sidewalks, try to walk on the side which allows you to face oncoming traffic. Then you can sidestep oncoming traffic if need be, or see what hits you. Otherwise, you are trusting that all drivers behind you, sleepy or not, will see you.

This suggestion or guideline may not apply to all circumstances. The advice here does not apply to travel in one direction along one-way streets. The advice here does not apply if you are at the head or in the middle of a column of people walking with their backs towards oncoming traffic. But the people at the rear of the column with their backs towards oncoming traffic may have cause for complaint. Caution: This advice also does not apply when following it means crossing a dangerous flow of traffic. The dangers of waling with your back to the traffic have to be balanced against the dangers of crossing the road. 

The above safety message & next may be reproduced as is, with or without acknowledgment, in any off-web forum, commercial or public.

What is the Best Way to Lose a hand or limb?

Drive with you hand or arm through a car window in all or part invites problems if the care sideswipes another object.

Alternatively drive a bicycle or a motorbike. Your protection is minimal in an accident, and other drivers may not see you before the accident. Annually, ten percent of the motorbikes in Quebec, injure their riders. And in riding a motorbike (cool, sexy or macho, whatever), unlike a car, there is metal shell to protect the rider or riders.

Advice: Take public transport instead, where possible.


What we need are car stickers to be placed on a car's rear bumper which politely says

Road walker, if you can read this, you are walking on the wrong side of the road

or says

Safety Message: Keep on the sidewalk or face traffic when you have to walk along a street.

 

Three Strikes Law in California (1995?): 

In the United Kingdom of centuries past,  stealing a loaf of bread might be punished by exile to a colony or worse.   Juries had a habit of refusing to convict because the punishment were excessive - did not fit the crime. Today in California, the three strike law is sending people to jail for 25 years to life for petty theft or infractions of the law with no  juries or common sense to prevent the resulting absurdity. The US supreme court is hearing the case of a man, now middle-aged, sentence to life for his last act, stealing video tapes worth about $134. The cost of the excessive sentence to California is $40,000 per year. About 2% of the US male population is  in jail. That may be 1.5% too much.  

Constant Retirement Rate (1999?)

A Suggestion for Human Resources

Hiring for a  constant or accelerated retirement rate in for education and the public service as means to provide more flexibility in management and greater security to the last-in. Hiring for a  constant or accelerated retirement rate may allow hiring in ways that reflect changing demographic circumstances.

Schools and colleges have had a habit of hiring young and not hiring for a constant retirement rate.  That habit has led to a hiring freeze and an extreme competition for academic posts in the last three decades, 1970 onward.  That habit has led to a shortage of retirements in education due to the too rapid hiring of faculty from one age group. Soon there may be a rapid retirement of the latter age group and a shortage of replacements.  Education reform needs to be form and hire teachers and faculty for  the sake of a constant retirement rate and a better age distribution.  A constant retirement rate would allow for the rejuvenation of schools and colleges during steady-state periods of non-growth, give the last-in more security of employment during periods of contraction, as management in place of cutting employees  immediately, with or without compensation for years of service, can wait instead for the effect of a constant retirement rate (say 3 to 5% a year). 

Any public service that hires towards a constant or accelerated retirement rate will find itself rejuvenated continuously during periods of non-growth, or periods where retirements permit new hiring's, and will find itself in a situation where its most recent hires reflect the demographics of the population it serves. Not hiring for a constant retirement rate leads to situation where the demographic face of the old employees doe not change while that of the population does. 

Hiring towards to a constant or accelerated retirement rate was  not obvious goal in times of expansion or growth. But times have changed. Hiring towards a constant or accelerated retirement rate will have advantages and disadvantages to be considered in each field of activity.  Fire fighters, those not driving a desk or a truck,  need to be physically fit and thus young. 

Economic Ideas - Skeptically given (Fall 2008): 

When I was younger,  I wanted to be a pioneer, to get away from the rat race. But then I found all the land had be claimed and rat race participation was the only option. Today, if I knew how to work for myself in a viable and independent manner, I would do so. However, for convenience or out of desperation I will am will to work in a government service and try to do it well. Possibilities follow. None are guaranteed to work. In the passage of time, each will have difficulties. Each require checks and balance to ease or avoid those difficulties.

Economic depression and lack of employment threaten many people.  Here are some ideas to consider - none guaranteed.   Age brings on skeptism.

(1) Lessening the Effect of Tough Times:  

For business and governmental lack of revenue, instead of closing or firing, share the net business and government revenue after expenses among employees, owner-operators included, in proportion to their nominal salaries or due. What that means is subject to negotiation and variation. But such proportionality might preserve jobs, business potential and avoid or lessen any depression. 

(2) Family Farm or Family Business Analogy: 

 As with a family farm , the short & long term aim is not full production. It is sustenance and occupation to avoid idle hands, with care not to exceed proven resources. Would the governments provide incentives to for-profit and non-profit businesses whose charters aim for job generation in a viable manner. See the proportionality ideas above and the above Quote of Dickens. 

(3)  Quality not Quantity:  

Security of income (quality) with care not to live beyond one means is more important than quantity.  Quantity is only important when income is not certain.  In developed countries, farm mechanization and energy supplies in the last century implied that 2% of the population in place of 80% could generate all the food necessary for the whole population. There is more than enough labor in most lands to provide all the services needed and to provide food, clothes, shelter, education,  health care and production, essential or not. 

(4) Too many hands, for too little work B: 

The main economic problem is not distribution of wealth, but distribution & assignment of work in an ecological sound manner.  People may belong to the flow of energy, money,  bartering or local script necessary to purchases those goods and services in society that government services, when and where they exist, do not provide.   Money has become a local, national and international  mechanism to enable the exchange of goods and services. Yet local scripts in a deliberate make work manner could be deployed in in a region or small community with a surplus of labor and materials, energy included, could be used to test to protect and foster the local exchange of goods and services, and the development of production facilities. Economic units, large and small need to  

(5)  Slowing Down with Style:  

Economies may surf waves of free market expansions and contraction. In times of growth and expanding consumerism, people find employment. No thought or planning is needed. Employment needs no protection.  That being said, in the late 1800s and early 1900's,  The government in each land has a responsibility to its shareholders, it stake holder, the inhabitants of the land and its cities. Times have changed. Production and consumption need to be limited to produce what is essential, but also to protect or reverse environmental damage.  The full-speed ahead model of the economy, the need to encourage consumption, needs to be throttled. It needs to be replaced for the sake of sustainability by a slower pace of life in which work is distributed. The provision, distribution and protection of work is more important for the quality of life than efficiency or excess quantity and with that destruction of the environment or a speedier depletion of resources.  There is no guarantee that resources will expand indefinitely, that advances in technology will provide answers. We may hope for that, and be happy if that transpires. But we should not count on it. The standard of living has advanced and retreated in lands around the world. So a little prudence may be advised. The question is how.  

(6)  Channeling the Flow of Goods and Services:

 Governments at many levels taxes goods, property and services to fund the provision of further goods and services - health, education and emergency services included. Wherever there is a flow of energy (oil etc for transportation, sun light to grow plants for food and even fuel, and electricity to provide lighting, whatever the source) people may work to buy or produce food, shelter and services. Subject to checks and balances to be determined and change as well in response to changing circumstances,  it is possible to combine a free market economy where ambition and energy are free to produce non-essential goods and services with multi-level government driven systems? Even in so called free market systems, government spending funds and dominates many areas of the free or not so free market.   Further government systems  services or systems provides essential services in the form of education, various forms of care and regulation enforcement (limits on freedom, so that people respect each others properties and the commons) in a manner that distributes work and so provide income to people not fully in the free-market.   That needs to be done in a sustainable manner.  

The free market economy has one advantage over government delivery systems.  Free market systems that do not have a monopoly, will fail if they lose their clients.  In contrast, government departments appear to be forever. The latter leads to bureaucratization.  It might be an idea to periodically close and reopen government departments regionally and at different levels.  The re-opening again under a new administration with a mix of new and old people in new and different positions would shake up the cobwebs. Otherwise, the channels of power may become fossilized.  Care would have to be taken so that the foregoing periodic closures and reshuffling leads to revitalization while preserving know-how. 

(7) Distributing  and Generating Work 

In developed and developing countries, I suspect the efficiency of production (not a bad thing in itself and much appreciated) leads to idle hands and the problem of distributing work. 
Economic sustainability principle:
Annual income twenty pounds, annual expenditure nineteen six, result happiness. Annual income twenty pounds, annual expenditure twenty pound ought and six, result misery.
- Charles Dickens, David Copperfield

The foregoing quote of Dickens applies to individuals, to for profit and non-profit enterprises, and to departments in schools, hospitals, governments and companies. There is a need to live within budgets. 

Employment in some government services, the employment of last resort or not,  would not involve a fixed salary. Instead, salaries would be proportional to  points or shares, the number of might depend on the qualifications of the employee, the job, and even the number of hours worked.. There would be no limit on the number of employers. But the would be an amount budgeted for total pay of all employees, and  each employee would receive as a pay amount proportional to the number of points or shares. Each government service would then have to justify its budget in term of the value of that service and the value of hiring people to deliver it.  The government in this matter might be local, regional or national. Terms of employment may demand or require some work habits or ethics.  

The size of a government department in which proportionality applies is not specified. Suffice to say in a small department where employers there may some resistance among existing employees to expanding their ranks due to wage dilations - for every ten percent expansion in employees, there might a nine percent salary or income reduction. Key employees, if their salaries are not protected, are not exempted from dilations may leave.  On the other hand, some government departments may be created to distribute word and hence remuneration on a everyone is welcome basis.

(8) Saving the Environment:  

An individual, company or region that cannot see alternatives will continue in its ecological affects.  Each and every human on being born affects the environment and all innocence makes demands on it. If the only way to sustain an economy is to produce and consume more and more in the hope that employment will benefit everyone then the environment and human kind is doomed.  The economy needs to relax. The distribution and generation of work in economy where due to mechanical advances in production, the needs of the many can be served by the labor of a few,  the needs of the many for work and personal productivity need to be considered in a way that is sustainable.  


 


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Take greater  charge of your work or studies: Read like a lawyer for better work & study skills, but do not take everything literally.

In particular, two logic puzzles  are keys to site content, and to greater work and study skills.  See if  you agree.

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Pages For Teachers

Site Notes for Instructors
Permissions for Instructors
Lesson Plans - Sec I
Lesson Plan, Sec II
Lesson Plans - Sec III
Secondary Maths, Core Elements
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Vol 1. Elements of Reason

Show a student how to learn and that helps one. Show a teacher or  tutor how to make skills and concepts easier for students and that helps many. 

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Your IP Address  & how to use it

Pages for Students

Complex No.s Intro.,.
A Site Map
Public Affaires

Three Links for Teachers:
(i) First Year High School Math - Lesson Plans with Fraction Focus (ii) Second Year High School Math - Lesson Plans with an algebra focus (iii) Algebra Lesson Plans

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.

Help Me Learn/Teach;

  1. Algebra
    words before symbols - direct & indirect use of formula, numerical versus algebraic solutions - what is a variable (more words)
  2. Arithmetic
    -new Arithmetic Folder
    - exercises
    - with fractions
    - videos on primes, lcm, gcm,lcd, square roots etc
  3. Calculus - geometric preview, algebraic preview,
    3 study guides,
    much more
  4. Complex numbers
    -starter lesson with java applet - easy consequences for trig & vectors in the plane
  5. Education
    - Empirical Course Design & Delivery
  6. Fractions
    - alone
    - by rote
    - with algebra
    - videos
  1. Functions - introduction
    hindsight - composition aka
    substitution
    -
  2. Geometry, Euclidean - Correspondence of trianglesTriangle construction,  duplication & Isometry - Failure of ASA & the // line postulate - angle sum in triangles -// grams - Triangle Similarity
  3. Geometry- Analytic - functions, polynomials, complex numbers, unit circle trigonometry
  4. Logic
    - First Steps -
    Symbols in Logic -
     Occurrence & Truth Tables - Indirect Reason -Indirect Reason More
  5. Proportionality
    - Definition - Direct & Indirect Use - Numerical versus Algebraic Solutions
  6. Real Analysis
    - Decimal View of concepts and of proofs
  7. Rules &Patterns in Science, Technology & Society - Pattern Based Reason
  8. Mathematical Reasoning, empirical, inductive or deductive
  9. Units
    - in rates & slopes & (?) derivatives
    - in ratios & proportions - slopes & rates included
  10. Complex Numbers & Vectors & Trig
    trig expression for dot & cross - cosine law

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