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||

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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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2. Solving Linear Equations
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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.

The following article in quoted in full from the online publication  Speaking of Learning of the Writing Center in Owens Community College. It refers to four things a student should know once posted online in the site entrance page. 


Speaking of Learning…

Teaching, Learning, and Writing
Across the Curriculum
at Owens Community College

WHAT WORKS FOR ME IN THE CLASSROOM

Volume 2, Number 1 Fall 2001

MATHEMATICS: Reality Checkup: Learning requires Effort, 

 by Jennifer Sawyer and Elsie Newman

One problem that some students encounter in learning mathematics is the misguided belief that a skill has been mastered without actual written practice. These students assume that skill mastery is based solely on the ability to understand solutions, which are modeled during classroom presentations. Without instructor intervention, these students often learn of their lack of total mastery after a poor test score. The goal of the instructor is to circumvent the notion that learning occurs without actual written skill practice before it results in student failure


Alan Selby, author of the website http://whyslopes.com, explains that students must be made to understand four things about learning math:

  1. Learning takes time and effort. 
  2. Notes and work for doing problems must be written on paper and must be written precisely. Ideas or work written incorrectly will be a source of error later – at the time of reading or further reasoning. 
  3. Use of the electronic calculator for decimal computations does not provide the exact answers that are needed for derivations of formulas in algebra and beyond. For true understanding of concepts beyond arithmetic, students must be able to perform operations with fractions. 
  4. To completely master a mathematical concept, one must be able to write calculations precisely and exactly on paper. Errors of notation create misinterpretations which when read later on lead to misunderstanding or errors of further reasoning.

Collecting student work frequently to check for correct notation is one way to identify errors early on. This also encourages students to engage in written skill practice prior to graded assignments or tests. 

These frequent checks, referred to as "attendance verification,” do not have to be lengthy: 2 - 4 problems is a convenient length because completion does not require too much class time and prompt grading is possible. Grading is not based on "percent correct"; instead it is an opportunity for students to receive feedback on their individual levels of understanding, so that errors of precise notation and calculation can be noted and corrected prior to a test or graded assignment. Complete attendance for the class session is awarded to all students who provide written effort.


Remark, October 13, 2007: The phrase  referred to as "attendance verification,”- indicates I  wrote and echoed a muse about the use of start of class work to provide attendance. Let me explain.  Attendance checks takes time in the classroom. So in place of formally taking attendance at the start of a class, give an opening set of question in the first few or fifteen minutes and insisting all students present hand in at least one answer with their name on it serves the dual purpose of (i) collecting written work for feedback (and grades too) and (b) providing a record of attendance. In that way, collecting work frequently may serve as an attendance check.  An alternate way to take attendance quickly is to have a seating chart established by the teacher or by student habits.  Then empty desks correspond to an absent student. Chart use requires students to go to their places at the start of class.  

 

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