Appetizers and Lessons for Mathematics and Reason (www.whyslopes.com)
||Définition d'une variable || Algèbre || Arithmetique || Logique ||La raison basée sur les règles et modelés||

Online Volumes (Book Orders)
1,  Elements of Reason.
1A. Pattern Based Reason 
1B. Math Curriculum Notes
2. Three Skills for Algebra
3. Why Slopes & More Math

Mathematics Course Designers: LAMP offers food for thought.
More Site Areas 
1. Help Your Child or Teen Learn 
2. Solving Linear Equations
3. Fractions Ratios Rates Proportions & Units
4. Euclidean Geometry
5. Analytic Geometry/Functions 
6. Number Theory
7. More Calculus
More Site Areas 
8. Complex Numbers 
9. Qc Maths  Education  
10. Secondary IV(?) maths
11. Real  Analysis 
12. LaTeX2HotEqn:
13. Electric Circuits Etc  
14.  Français
15. Algebra, Odds & Ends, Etc
More Site Areas 
16. Math Education Essays
17. Telling & Working with Time
18. Maps, Plans & Drawings
19. Quantitative Skills for  home, shopping and work 
20. Statistics Useful, or Not.
Try the
Twiddla Whiteboard
to work online with others.

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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.

Helping Your Child or Teen Learn

While you may hope that schools offer clear and effective instruction, you should also test and verify. not all is certain, You also need to encourage the will to learn, or the aims and goals of your charges. Then your charges may keep trying in school and cooperate with teachers, without disrupting or opposing the education of themselves and others. Good luck.

The advice offered here for helping your child or teen learn is approximately correct, for some circumstances not all. See what works.

  • Parents are the first and last teachers of their children. Where schools do not teach all, parents may intervene alone or with help to push or guide. Help your child workbooks for mathematics and other subjects may keep your child learning during school breaks and vacations, year round. Look for workbooks for math and other subjects in book shops or online.
  • If you have a teen in difficulty in school, get the teen to master logic alone or with help, if you can. Also teach him or her to be more precise and careful in school and work, by verifying or requiring your teen to learn or demonstrate mastery of exact arithmetic methods for addition, subtraction, multiplication and division of whole numbers. Mastery of logic and exact arithmetic with decimals (fractions too) will show your teen that an error in one step of a calculation or argument, lack of care and precision, sloppiness in other words,  invalidates and makes wrong the further steps and the result.  Demand from your teens that they write out answers and solutions  so that what is written serves a full record of what they thought, because they may not remember what they thought later, and because teachers in giving marks cannot read their minds.

  • Skill and knowledge mastery, perfection too, requires students to sit down and study carefully. No one else can do that for them. Encouragement or direction from parents and teachers will help.

  • North American, Educational Horror Stories: (i) A senior high school student said to me:  I met fractions in primary school and I should not need them for my studies.  His firm opinion was that I should bring  all the current course on physical science to a level where mastery of fractions was not required. After spending half-hour telling him, the course you are in requires mastery of fractions and more,  I stopped trying. He did not want to listen.  So I could not help him.  There was a question of credibility. (ii)  Another college algebra student studying to a be policeman sat at the back of my classroom. He did very little outsides of class, and inside of class spoke to his two friends, also male. While confronting his lack of effort, he explained that his mother thought mathematics after arithmetic was a waste of time. I protested, but I could not change his mind.  (iii) While giving a college, remedial algebra class, I had a student who informed me that he was high school mathematics instructor giving an algebra course. So  he needed my course   good move, but oops. (iv)  ....

Section webpages

  1. Speaking Skills suggests how to improve the speaking and listening skills of your child.
  2. Reading & Writing offers ideas for the development of these skills. 
  3. Preparing for science -Teaching a boy or girl to cook or to follow any multi-step method precisely, in a repeatable and reproducible manner, will help in science and all area of work and study.
  4. Learning Takes Time and Effort: Four Things for a Student to Know. Quote in full of an article from Speaking of Learning that refers back to words at this site, no longer online.
  5. Math Work Books for your child or young teen identifies mathematics material for your charge to use with your supervision.
  6. Math Books and Websites for Teens & Adults - besides this one.
  7. Readings for Parents -  results from a trip to a local bookstore. 
  8. Patience Please. reflects the inductive idea that learning takes time. If you see a difficulty, you need to identify the source and retreat before it in order to practice skills that restore confidence and then to practice skills that remove the source of the difficulty. Teaching, tutoring or parenting takes time and patience. Good luck. Nothing is certain.
  9. Who is in Charge? For better or worse, you the parent or guardian may be the first and longest term instructor of your child. Do your best

    Parents and teachers need to say no for small things of little consequence to build and maintain authority to say no for larger matters. Parental authority:  use it or lose it.
  10. Student Motivation Here a discussion of the challenge. Not the solution. 

    Students with parents who say mathematics mastery is important, or education in general is important, will  often have more goals, more will and more staying power in school and college - no guarantees here -but is part of the solution.
  11. Talk to Your Child or Teen. For many, those without learning difficulties, the will to learn is often more important than ability. Encourage the will.  That is part of the solution.
  12. Primary and High School Mathematics  describes or lists the skills and ideas met primary school to the first year of high school, and points to a context for high school mathematics.  

    Ages 5 or 6 Ages 6 or 7 Ages 8 or 9 Ages 10 to 13 Ages 14 plus.

    Knowledge of them will allow you to judge the skills of your charge and the math and logic work books or reading for your charges. You will see where they are going. 
  13. Links for Kids and their Guides

Problems in Education

Students should construct skills and knowledge and learn to be critical thinkers in social and technical subjects by mastering existing rules and patterns, that is be able to follow and apply rules and methods in a repeatable and reproducible manner, while learning about the benefits, origins and limitations of rule- and pattern-based methods. Sixth Message to Repeat

Ideally students will have clear and precise reading material, that is text and exercises,  to follow or do,  one  at a time and one after another. Albeit, some school authorities may impose  math textbooks of the scatter-brained type on teachers and students, a professional embarrassment for the teachers which puts students and parents.   Not all is ideal.  To help improve school textbooks, ask local mathematicians, domain experts with doctorates  in mathematics  to identify in public newspapers and in university mathematics department websites, the rational and irrational elements in local mathematics textbooks for local schools,  primary to secondary. Do some muckraking. .

What Sabotages Education: Pre-university education theory (constructivism) says mastery of rules and patterns starting with arithmetic is not a sign of intelligence But later studies in senior high school, college and university instruction in mathematics, science, medicine,  trades, technology and law prize & require that mastery or ability. So education K1-9 may be  inconsistent with later requirements for study and work. - Work and most arts &  disciplines are rule- and pattern-based. The ability to use rules and patterns carefully and diligently, one at a time, one after another, alone or in combination, is needed to  to arrive at a results that are repeatable and reproducible for better and worse in our pollution age societies.  Rule and pattern mastery is a mixed blessing but a necessary one for your offspring. 
 

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www.whyslopes.com
Help your Child or Teen Learn:


Area Intro
1. Speaking Skills
2.  Reading & Writing
3. Preparing for Science
4. Learning Takes Time and Effort
5. Math Books: kids & teens
6. Math Books: teens & adults
7. Readings for  Parents
8. Patience Please
9. Who is in Charge
10. Motivation
11.  Will to Learn
12. Math K1-20
13. Links For Parents
14. JumpMath WorkBooks
15. Discipline in Schools

Maths for Ages 5+



D What to do in School & Why  

E.How to Study Mathematics


To read, write and spell, your children need to learn and memorize the alphabet. Anything less would be absurd. That being said, learning and using mathematics demands that your children meet key skills and concepts, and not skip any. Where local schools do not provide the latter, you need to provide remedies.

Care and Precision: If your child  can learn to follow multi-step methods carefully and precisely in arithmetic, he or she may do so  in other subjects, as well. Get your child or teen, if you can, to sit down and study. Suggest he or she aim for skill and concept development and perfection for their own sake, not that of their teachers.

The will to learn is the key to success in school.  Parents do have to be educated to support or guide their children and teens. What matters more is support for the will to learn, for children and teens to be  told to try to learn and to ask teachers, their schools or classmates for help and more help, as needed. Teachers and parents need to push students, help them find the will to learn, teamwork helps.

The main reason and focus for high school mathematics is or should be preparation for calculus. That requires skill and knowledge perfection with fractions, algebra, geometry, trig and functions. Many high school programs do not provide this. Make sure alone or with help that your children and teens have a good command of fractions. 

 

 



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The Rest © 1995 onward by site author,   Alan Selby,
a 1983 McGill. Ph. D. in mathematics
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