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HIP,
HIP, HIP, Hooray
YOU are better than YOU think. Show yourself how:
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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
liinear2007 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.
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Early 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.
First two inlinks to this site (at its old location)
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.
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 Inlinks
[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: ...
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.
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.
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.
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. ...
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!
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.
... 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.
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.
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."
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.
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
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.
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
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.
| 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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whyslopes.com
Entrance Level
Montreal Area Tutors
Pages For Teachers
Site Entrance & Hub
Permissions for Instructors
Lesson Plans - Sec I
Lesson Plan, Sec II
Lesson Plans - Sec III
Secondary Maths, Core Elements
Site History/Content
Site Reviews
Vol 1. Elements of Reason
Maps Plans Drawings
Quantitative_Skills/index.html
Order Site Books
McGill-Quebec Nonsense & BS
HIP, HIP, HIP, Hooray for
site
content & history. Hype, Hype,
Hype, Hoorary, for deception.
Your IP Address & how to use
it
Pages for Students
Site Entrance & Hub
25 hours per course
Site Areas by Age and Subject
Montreal Tutors
Entrance Continued
Still More Advice
Head Start Page
More Advice & Directions
Aims to adopt to aid
Arithmetic Check List
Fraction Skill and Concept Check List
Site History and Content
Books to Read
Complex No.s Intro.,.
Calculus Motivation
Calculus. Guide Short
Calculus. Guide-Long
Calculus Guide - Longest
Links - Many Subjects
Links - Games/Activities
Long Site Intro
Logos Cafe
Logic Check List
Mathematics Cafe
Math CheckList
A Site Map
Advice for Secondary I Students
Three Ways to be a Better Student
Reason for HS Mathematics
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
Help U Learn/ Teach
- Algebra
words before symbols
- direct & indirect
use of formula, numerical versus algebraic solutions - what
is a variable (more words)
- Arithmetic
- exercises
- with fractions
-
videos on primes, lcm, gcm,lcd, square roots etc
- Calculus - geometric
preview, algebraic
preview,
3 study guides,
much more
- Complex numbers
-starter lesson with java applet - easy
consequences for trig & vectors in the plane
- Education
- Empirical Course Design
& Delivery
- Fractions
- alone
- by rote
- with
algebra
- videos
- Functions - introduction
hindsight
- composition aka
substitution -
- Geometry, Euclidean - Correspondence
of triangles, Triangle
construciton, duplication & Isometry - Failure
of ASA & the // line postulate - angle
sum in triangles -//
grams - Triangle
Similarity
- Geometry-
Analytic - functions, polynomials, complex numbers, unit circle
trigonometry
- Logic
- First Steps -
Symbols in Logic
-
Occurrence &
Truth Tables - Indirect
Reason -Indirect
Reason More
- Proportionality
- Definition -
Direct & Indirect Use - Numerical versus Algebraic Solutions
- Real Analysis
- Decimal View of concepts
and of proofs
- Rules &Patterns in Science, Technology & Society
- Pattern Based Reason
- Mathematical Reasoning, empirical, inductive or deductive
- Units
- in rates & slopes &
(?) derivatives
- in ratios
& proportions - slopes & rates included
- Complex Numbers & Vectors & Trig
- trig expression for dot
& cross - cosine law
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