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

 (Optional Book Orders)
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.
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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.

Student Motivation

Some students study because they do well with their marks or because they like learning. Many more become cynical about the value of education. How do we help them?   

An advisor should not give direct advice. The advisor instead offers open or multi-choice problems for others, interested parties, students, sons or daughters,  to solve.  Then they have a say in what to do.  No one likes to be told. 

 Here are a few questions or problems for your teen to consider.

D What to do in School and Why  
E. How to Study  Mathematics

While some teenagers may skip the terrible teens and remain polite and serious, the terrible teens arrive sooner or later for most. During that period parents can do no right.  And during that period if not before,  school may become less attractive.  Elementary students may be motivated by the notion that school attendance helps them grow-up or mature, but after several years of schooling from ages 6 to 13 say, school loses it appeal.  It is compulsory, parent and teachers may not be say clearly why school is necessary except for bureaucratic need for a high school graduation as a ticket to further studies if not employment. 

Compulsory instructions may seem pointless for some students. The question of why go or why stay does not have a clear nor immediate answer.  The reward if any lies in the future. 

One way to motivate students is to say that studying is a job and to support that view with pay or pocket money for performance and attitude.  That is, students could be given an immediate reward for their effort. (As an instructor, I would not object to informing students that their pay in my class depends on their work habits and work presentation - In the presence of a demanding and rigourous curriculum, students may not see point of the long preparation. Some way to get students to behave in class with motivation would be welcome. 

My subject properly taught can be rather dry despite efforts on my part to lighten the subject and provide a context for it. Kid who lack motivation slow learning for themselves and will sooner or later not cooperate in their own education,. and may even rebel.  

Students in the past and today have been expected to bring their own motivation. That motivation may be inherited from parents.  Students with motivation, regardless of source, will go further than students with out.  The will to learn is important. 

Teachers and school may provide encouragement. Instruction in not leading to definite ends,  but in leading to general ends cannot say to a student in concrete terms why he or she should work at their studies and take those studies seriously.  General statements of the importance of education may lack specifics. So education itself may mean following a dream or path with no definite aims nor ends.  And in those circumstances, loss of interest in school may be a sign of intelligence. Parents and Course Designers need to consider the question of leadership, the question of how to  provide motivation for learning.  

Attempt to provide motivation are provided by the appendices in site volume three skills for algebra on what to do in school and why, and on how to study mathematics and why.  Besides those appendices, parents may give their teens and younger charges a message, namely that mastery of logic and arithmetic (fraction sense) is provides the intelligence needed to follow multi-step methods in many arts and disciplines at school, home and work.  The knowledge that an error in one step makes all that follow wrong or likely to be wrong is a sign of intelligence and application provided by the mastery of logic and arithmetic. 

Remark: In mathematics, the key to success is fraction sense and fraction skills. If you have a teen in difficulty in mathematics, see if you can convince him or her to consolidate basic skills.  The site area Solving Linear Equations with Stick Diagrams and Fractions may help.

 

 

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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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a 1983 McGill. Ph. D. in mathematics
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