Appetizers and Lessons for Mathematics and Reason 
www.whyslopes.com        (missing links in the exposition of both)   ( Français)  
What does it mean to use a formula forwards and backwards

 Logic mastery is key to easing or avoiding learning difficulties in work & studies. 

Online Volumes (Book Orders)
1,  Elements of Reason. 1996
1A. Pattern Based Reason  1995
1B. Math Curriculum Notes 1996
2. Three Skills for Algebra  1995
3 .Why.Slopes.&
.More.Math.1995

Links To Tutoring Services

Parents:-Help. your. child. or. teen.study

Site  Math Folders

1. Arithmetic Flash Video Lessons  11-2008
2.  Algebra Videos (to appear)
3.-Fractions-Rates-Proportns-Units-2006
4.  Algebra, Odds & Ends, HS level-2001
5. 
Solving Linear Equations  04-2005
6.-Euclidean-Geometry/Complex No.s 
7.  Analytic Geometry/Functions 2006
8.  Number Theory. 2006-7
9.  Complex Numbers More 2001. 
 
10  Exponents, Radicals & logs. 2008
11. Calculus  2005

12. Real  Analysis 1995
13. Electric Circuits Etc  2007
How-TOs/ Reference - 08- 2008
1. Arithmetic
2. Algebra 
3. More Algebra 
4. Geometry  
5. More Geometry
6. Calculus

Entrance Level


Adopt whyslopes.com/search/  for internet searches. 

Pages for Students

Proper notation & format 
makes the hard easier.

Pages For Teachers

Show a student how to learn and that helps one. Show a teacher or  tutor how to make skills and concepts easier for students and that helps many. 

Miscellaneous

Your IP Address  & how to use it

Three Links for Teachers:
(i) First Year High School Math - Lesson Plans with Fraction Focus (ii) Second Year High School Math - Lesson Plans with an algebra focus (iii) Algebra Lesson Plans

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.

YOU are better than YOU think. Show yourself  how:

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Take greater  charge of your work or studies: Read like a lawyer for better work & study skills, but do not take everything literally.

In particular, two logic puzzles  are keys to site content, and to greater work and study skills.  See if  you agree.

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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
    -new Arithmetic Folder
    - 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

First Two Reviews.

The first reviews or site descriptions 1996 were responsible for the completion of Volume 1, its second part on mathematics education, and the site author's further writings.  

1 Math Forum June 1995 Hot Spot: Alan Selby's Lessons and Appetizers for Math and Logic  

Three Skills For Algebra (a first image of mathematics after arithmetic - why letters or symbols are favored in algebra in place of numbers); Two logic puzzles to show the difference between a one-way and a two-way rule; Painless Theorem Proving; Longer Chains of Reason: What is Mathematical Induction?; Complex numbers Etc. - A geometrical story based on the addition and multiplication of arrows in the plane; Chains of Reason - math-free examples of rule-based reasoning; How Logic or Rule-Based Reason Appears in Math; VNR Concise Encyclopedia of Mathematics. Also Appetizers on Other WWW Pages.

2. Cornell Theory Center, 1995

Several puzzles and short discussions to help students understand algebra and proofs. If you don't like the first one you look at, try another; they're all quite different.


More Reviews and Site Description

3. [Math Forum], online 1996 online classifications of the then half dozen sites offering learning and teaching material..

... There are appetizers for algebra, arithmetic, logic, better learning in general, reason, theorem proving and complex numbers.  Strengths here are in Alan's explanation of mathematical concepts using words and stories: ...  

4. Magellan, the McKinley Internet Directory, 1996

Mathphobics, this site may ease your fears of the subject, perhaps even help you enjoy it. The tone of the little lessons and "appetizers" on math and logic is unintimidating, sometimes funny and very clear. There are a number of different angles offered, and you do not need to follow any linear lesson plan. Just pick and peck. The site also offers some reflections on teaching, so that teachers can not only use the site as part of their lesson, but also learn from it.

 5. C-EdRes mailing list and archive, 1996

Appetizers and Lessons for Math and Reason (the web site) is based on three books by Alan Selby. It consists of 16 appetizers which could be used as starters for math lessons. The mathematics involved ranges in level of complexity from kindergarten to post secondary.

Evaluation: Every math teacher will find something of interest here. The site is designed to facilitate skipping the content that doesn't interest you. The lessons ...  were immediately usable. Some of the lessons could serve as starting point for integrating math into other curriculum areas. 

C-Edres is a joint project of the University of New Brunswick, Industry Canada, and the ERIC Clearing house on Assessment and evaluation. The number of appetizers and books online has changed. The reviewer is most likely working elsewhere.

 6. Cours de mathématiques. UbiSoft France, 1996

Si vous cherchiez un site pour apprendre, réviser ou effectuer des exercices d'arithmétique ou d'algèbre, vous l'avez trouvé. D'un bon niveau collège, il permet à tout élève de retrouver des exercices de pratique, des révisions de cours magistraux. Il peut ainsi de réviser en toute quiétude les passages plus difficiles.De très nombreux cas pratiques s'offrent aux yeux des utilisateurs, entraînant plus facilement les collégiens vers le travail que le découragement.

7. [Math Forum News Letter], 25 November 1996

ALAN SELBY's  mathematics appetizers range over arithmetic review problems, notions of what variables are, skills leading to algebra, painless theorem proving, complex numbers with some trig, the importance of slope (some calculus), a decimal perspective of error control and continuity (more calculus), and renaming the greater than sign (back to algebra). 

Advice on how to read, how to learn, why go to school, etc. is included. The tone is sometimes funny, and the writing is dense, rich, and intriguing. There are reflections on teaching, so these materials can be used in the classroom and as a place for teachers to learn. 

Alan's explanations of mathematical concepts using words and stories are particularly strong. ...

8. Waterboro Public Library, home schooling section (2000) 

Category: CRITICAL THINKING AND LOGIC

Articles and sections on topics such as how (and why) to learn mathematics in school; pattern-based reason; finding a number; solving linear equations; painless theorem proving; algebra and beyond; and complex numbers, trigonometry, and vectors. Also section on helping your child learn (which includes annotated links to other sites about math education). Lots more!

9. Education Planet Newsletter, top math sites, 2001 

What are the ideas behind most high school math? Yes indeed, I expect there were some but they are long forgotten... The commentary and online books available at this site provide a very rich guide to mathematical reasoning and high school math to calculus. The emphasis here is on the thinking part of math rather than the actual manipulations themselves. There is also information here for parents as well as teachers. Now you can help your students gain insight into mathematics rather than just helping them memorize formulas.

10. Math Forum News Letter 14, 2001   August 14, 2001.

... new sections on Complex Numbers and the Distributive Law for Complex Numbers offer a short way to reach and explain: 

  • trigonometry
  • the Pythagorean theorem
  • trig formulas for dot- and cross-products
  • the cosine law
  • a converse to the Pythagorean Theorem

There are five different ways for learning and teaching complex numbers and trig together at this website. The above links refer to the shortest of the five. Here are some ideas that are fresh or recycled.  I suspect, the above links refer to the shortest path so far found, for meeting complex numbers & trig, together or separately.  

11. Semi-Critical Review: The NSDL Scout Report for Mathematics, Engineering, & Technology -- Volume 1, Number 8 (May 24, 2002)

Site Description: Math resources for both students and teachers are given on this site, spanning the general topics of arithmetic, logic, algebra, calculus, complex numbers, and Euclidean geometry. Lessons and how-tos with clear descriptions of many important concepts provide a good foundation for high school and college level mathematics. There are sample problems that can help students prepare for exams, or teachers can make their own assignments based on the problems. Everything presented on the site is not only educational, but interesting as well. There is certainly plenty of material; however, it is somewhat poorly organized. This does not take away from the quality of the information, though.

Note: The poor organization has since been corrected or succeeded.  

12. Math Forum  Internet Newsletter No. 10.8 (21 Feb 2005)

Alan Selby has added a new section called Solving Linear Equations to his site "Appetizers and Lessons for  Mathematics and Reason." The section introduces stick diagrams as a way
to "provide a concrete context for many of the rules or patterns for solving equations -- a context that may develop equation solving skills and confidence informally before the algebraic statement of the rule and patterns for solving equations."

13. The NSDL Scout Report for Mathematics Engineering and Technology-- Volume 4, Number 4 (February 25, 2005)

Site Description: This section of the website, Appetizers and Lessons for Mathematics and Reason, written by Alan Selby, PD. (see also Scout Report for Math, Engineering, and Technology, May 24, 2005) offers lesson ideas for teaching linear equations in high school or college. The approach uses stick diagrams to solve linear equations because they "provide a concrete or visual context for many of the rules or patterns for solving equations, a context that may develop equation solving skills and confidence." The idea is to build up student confidence in problem solving before presenting any formal algebraic statement of the rule and patterns for solving equations. Links to related chapters from his book, "Three Skills for Algebra," are also provided.

Remark: See also May 24, 2005 issue might refer to May 24, 2002 and not a forthcoming issue.

15. All.info Science and Health - Math - Books - (Found April 14, 2005) 

Appetizers and Lessons for Math and Reason -Entrance
Since July 1995, this book-based website has been offering appetizers and lessons to aid and REFORM instruction in mathematics, logic and science. One book is online in full. Math-free lessons on Euclidean Logic may lessen gullibility while developing precision reading and writing. Site produced by: an Expert/Specialist  Site contains: Academic Content


16. Irem Lyon-Sites-Outils mathématiques (Found April 2005)

Site Description: Un ensemble de ressources assez disparates : de l'utilisation du programme NetMeeting à de très nombreux liens et renvois. Pour les mathématiques, ce site veut nous ouvrir l'appétit; noble objectif qui est réalisé par des cours de tous niveaux, de l'addition de trois naturels à des choses plus élaborées ( par exemple un cours sur les nombres complexes avec une appliquette efficace). On peut même parcourir le site en mettant en bruit de fond des conseils mathématiques (en anglais !). A noter aussi la présence de trois leçons en français.
17. The World-Wide Web Virtual Library Education by Country - Canada
November 1, 2005.

Why Slopes: Appetizers and Lessons for Math and Reason. This online classroom offers appetizers and lessons for math from arithmetic to calculus or why slopes; for deductive reason (logic) and critical thinking; and for learning in general. Included here are opinions on the communication of skills and mathematics instruction. The logic appetizers are math free. Each appetizer is different. If one is not to your liking try another. Most are from three books on understanding and explaining math and reason. 

URL: http://www.whyslopes.com/  Complete Record Details

 

18. From Math Help Online (Found Oct 29th, 2006) at Trenton Public School District Teacher Network 

Effective Algebra Lesson Plans (here at whyslopes.com)A bit dry at first, but contains some great tips on teaching Algebra in different ways. See solvingLinearEquations first for best samples.

19. From The 100 top sites in EEVL mathematics section (Copied Oct 29th, 2006)

Title:
Appetizers and Lessons For Mathematics and Reason
URL:
http://whyslopes.com/
Alternative URL:
http://whyslopes.com/francais/index.html
Description:
This site is aimed at the age group 14 and up. It features videos, online books, guides for learning and teaching and some extras such as an introduction to complex numbers and tips for parents to assist children in learning mathematics. The videos require RealPlayer. The site has been developed by Alan Selby.
Keywords:
teaching units, draft lessons, instruction, teaching, manuals, planning aids, problem books, Arithmetic, Logic, Algebra, Calculus, Complex Number, Euclidean Geometry
Resources:
Full Text Documents - E-Books
Full Text Documents - General
Image/Video
Learning Material/Courseware
Mathematics Classification:

 

 

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