www.whyslopes.com
Appetizers and Lessons for Mathematics and Reason
a calculus, preparation for calculus and math ed reform etc., website

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
calculus preview/intro &review

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.

 

||Définition d'une variable || Algèbre || Arithmetique || Logique ||La raison basée sur les règles et modelés||
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Protest:  The site author, a McGill University, 1983 Ph. D in mathematics, failed a McGill Faculty of Education B. Ed pgm 2003-5 due to


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.

What is the Education of  Mathematics Education Professors

Postscript: May 14th, 2006

Are calculus phobic Mathematics Education Professors to blame for several hundred or a thousand hours of mathematics instruction in pirimary and secondary schools which fail to prepare students for college mathematics, which fail to give students an efficient fraction skills and sense? Just as we specify the minimal mathematics background of future secondary school teachers, should we specify the minimal subject skill and knowledge of Mathematics Education Professors. 

In the present dark ages of mathematics instruction, Professors of Mathematics Education have not emphasized the needs of college mathematics or calculus in the training of primary school and high school teachers, and in the design and exposition of high school mathematics textbooks.  Thus many students graduate from primary school and even high school without efficient fraction sense and skills, and several hundred to a thousand hours of mathematics instruction time come to naught,  less than expected, and may be written off as a contribution to the education of many students.  Site books and further site areas point to remedies for self-application by students, teachers and Professors of Mathematics Education. Professors of mathematics education should teach first courses in differential and integral calculus fully in order to know what calculus-driven standards need to be emphasized in the mathematical formation of primary and secondary school teachers, and of students in general.  

Professors of Mathematics Education should take note of  earlier difficulties in mathematics,  the introduction and development of the shorthand algebraic way of writing and reasoning in mathematics, and the inclusion of too many topics and directions in course design which continue today.   Professors of Mathematics education need to read and correct textbooks in the student catch basins of their universities, or they need to ask mathematics professors in their college or university to perform this task for the sake of quality and perhaps a leaner exposition of mathematics based on the needs of calculus and before the elementary application of numbers with measures and masses - two focuses for mathematics learning and teaching.  Here again mathematicians should be included so that key skills and topics are emphasized and the logical need for some topics questioned. Many college calculus instructors limit or disallow the use of calculators because its ease of use and ill-use sabotages the intellectual component of mathematics. 

Professors of mathematics education  who are calculus phobic should be extremely rare or non-existence in Education Colleges and Faculties. How common are they?

Finally, there guidelines for the formation of secondary mathematics instructors call for many courses in mathematics at the college level.  For the sake of consistency, mathematics education professor should have had a similar dose of mathematics and more.  Anything less calls into question the hiring and promotion policies in schools of education.

 

  www.whyslopes.com
Mathematics Education Essays, 57 or so 

Area Entrance & Hub
Ideas for Better Instruction
4 Ways to Improve Reform
Theory of Knowledge
Peer Review
The Trouble With Algebra
Course Design and Delivery
How Letters Appear
Sit Down & Study
Modern Education
Key Notes and Themes
Site Lesson Plans
How This Site Differs
Site Origins
Math & Logic Puzzles
Comments on site content.

Words For Instructors
Inductive Principles
Fairness Principles
Apprentices & Masters
Three Remarks
For a Leaner Curriculum
Mixed Maths Curricula
Cultivating Intelligence
Reason - 3 kinds in maths
Logic in Mathematics
Science Education
Maths Instruction in General
Operational View & Values
Standards
Ends and Values
Goals & Unifying Themes
Algebra Lesson Plans
Algebra, Geometrically
Mathematics Curriculum Shifts
Teaching Tips - Fractions to Calculus
Math Ed Perils
Talk the algebra talk
Sec I  - Fraction Focus
Sec II -  algebra focus
Sec III - Focus on Slopes
Maps-Plans-Drawings
Math Wall Posters
Education, Empirical Art
Damage Reversal
North American Math Curriculum
Managing Reform
Essay January 2007
Educational Follies
Contructivism Incomplete
Missing the Point I
Mathematics in Context
What and When, A Challenge
Grouping Students
Teacher Certification
Education of Math Ed. Professors
Site Eurekas
Links

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
    - 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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