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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
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.
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Four Ideas on how to be a Better Instructor
- Identify clearly the skills and concepts your students need to master.
- Develop or find lessons and lessons plans to clearly and firmly develop
those skills and concepts.
- Observe student work to correct errors and react to them - when a student
or students have difficulty, take the student or students back before the
likely source to rebuild skills and confidence, to remove the source and
then to proceed.
- Distribute a checklist of skills and concepts for students to master, and
require students to fill a binder with notes and examples that cover the
skills and concepts and demonstrate mastery of each skill and concept. Then
check that the notes are complete, photocopies are acceptable, and that the
demonstrations are correct - gaps and errors in the notes and worked
examples provide opportunity for feedback and correction, even skill and
concept development with perfection. Then marks for a given period may be
based on the percentage of skills and concepts mastered as indicated by the
binder and/or further tests. Sample and/or usable checklists for
mathematics education should appear in site pages.
Site material in 900 pages ranges from new or recycled
exposition of key skills and concepts to more theoretical discussion of
instruction, methods, ends and evaluation. That being said, Support
for inductive principles for instruction is extensive but not yet complete in
site pages. So writing will continue.
- Primary School Instructors: For mathematics instruction, year by
year, see site area for parents and see site
lesson plans for secondary I
and secondary II
mathematics. The advice and lesson plans give discipline based aims for your
mathematics lessons. In the English
National Curriculum, also see key
stages 1 and 2 and attainment
levels 1 to 5 for mathematics.
-
Secondary and Remedial College Instructors: See
Chapters 1 to 14 of Volume 2 and the site areas on solving linear equations,
or see the descriptions and appetizers for site books and further site areas
below. To learn more, see site ideas for instruction,, lessons and lesson
plans included, Also in the English
National Curriculum, also see mathematics key
stages 3 and 4 and attainment
levels 5 to exceptional performance - the latter altogether they describe
secondary school level prerequisites for calculus. Site ideas will give a
different and clearer viewpoint of what you have seen before as a teacher,
and before that as a student.
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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;
- 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
construction, 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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