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
1,  Elements of Reason.
1A. Pattern Based Reason 
1B. Math Curriculum Notes
2. Three Skills for Algebra
3. Why Slopes & More Math

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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
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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

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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.


Speaking Skills

Explain to your child, that every object in the home and in the street has a name. In pointing to objects, in your spare moments, you can ask your child to identify or name them. This can be done before or besides lessons on reading and writing. (This is done accidentally while your child is hearing the conversation in your house.) Identification should a game with rewards (a treat, a smile or the word good perhaps, but no penalties).

Once a week, it could be an ongoing game or task to introduce say three or several new words to your child. In this game, you say a word. If your child can say what the word means, you provide a small reward, and if not, you explain it. Playing this game may require a dictionary as an aid, if the game lasts a long-time. Feel free to introduce unexpected words, ones not in use locally or in the present time, or ones for which are several possible meanings. (You may also explain how the meaning of words changes. To be brave today has a noble meaning, but in previous centuries, to be called brave was to be called a fool. Meanings do change.) Note in some school districts, an elementary school teacher who with good intentions introduces new vocabulary weeks or a year before it is scheduled to be introduced may be cautioned or fired. This word game might fill a gap in your child's education.

Speaking and listening skills can also be developed by reading or telling your child or children, a short story, and then asking him or her to summarized it. Around a table with many children, you may ask one or more to summarize or repeat the main points of a story just told or read. Later summaries may improve or corrupt the story. The changes in detail may be most interesting or amusing -- politeness required. The youngest children present may be asked first, or given a chance to improve their stories by giving their summaries after an older individual. After all the summaries, the short story can be read in full, once more yourself or one of the older children. Have fun. Once children have learnt to read and write, this speaking activity should be retained as a family gathering, but variations may be tried. Listeners can write their summaries or notes down before reading them aloud. But the game lies in the presentation of the summaries. Beyond this, game children or those present can be asked to create stories, or repeat others from memory.

The communication of ideas is based on story telling. The story can be fiction, nonfiction or, in a stretch, it can describe how to do this or that. A repertoire of stories, those of others in the first place, provide examples for the development of further stories. Stories provide a second hand experience of this or that real or imagined situation.

Speaking and listening skills may also be improved by asking your children around the dinner table, after supper or before: what happened in school today, what was unusual, what new ideas and words were met and understood, what words or ideas were met and not understood. This questions can be applied to English courses, history courses, science courses and mathematics courses etc. This habit of reporting what has pasted the day should be cultivated or introduced slowly, not suddenly. Each child should be given a chance to speak, and should be listened to, politely.

Again, reporting and summarizing what was met or learnt in school could be and should be introduced and cultivated slowly as a pleasant duty. Negative reactions might require your backing off. With luck, older children may lead the discussion and allow parents to depart. Children or teens from neighboring families could also come together in study groups. Your home could be a one room, supplementary school house. Good luck. (The demands of modern life and TV watching may be a distraction, and meeting once a week instead of everyday may well be necessary.

 

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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