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Have your gifted students read logic
chapters 1 to 5 in online volume Three
Skills for Algebra for greater skills & confidence
in work
and study.
tell students to read notes and textbooks like a lawyer, so that no nuance, no
subtlety and no clause escapes their 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
Tell students that 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. In Volume 2, Three
Skills for Algebra, a 4th skill for algebra appears in Chapter 14. It
provides a unifying theme for high school mathematics - equations and formulas
may be used forwards and backwards, directly and indirectly, numerically in arithmetic
solutions & with literals in algebraic solutions.
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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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- Ten Commandments for
Mathematics Teachers
| US, UK and Canadian Mathematics Curriculums, Etc
The UK link below includes all subjects and not just mathematics.
Course or curriculum discussions in one location may and should
influence discussions elsewhere. UK efforts are well-written. The
Quebec English curriculum for mathematics identifies well the
geometric requirements of upper high school instruction.
UK Resources for Education
All Years, Most Subjects. The UK
1996-20000 National Curriculum gives a detailed view of
English, Mathematics, Science, Design and technology,
Information and communication technology, History, Geography, Modern
foreign languages, Art and design, Music, Physical education,
Citizenship, and ???
The material is online in html format and in pdf files. The html
format is well-well organized.
The details of the mathematics curriculum offer a checklist or
attainment levels for what should be covered and when from elementary
school to the last years of high school. This site should be explored
for completeness if you are teaching one of the subjects it mentions. Here
is a reference for standards or course design elsewhere. The treatment
of history is notable - British history no longer call Britain great.
The absence of that pretension is welcome. The UK experience in
mathematics is different from that of the US experience - how should
be determined if you are interested in mathematic course design. A
divergence was present in the 1960's. UK schools in then did not
emphasize the set theoretic, axiomatic development of modern
mathematics.
The UK mathematics curriculum for 1995 was very detailed and
mostly written in plain English with very few platitudes. The 1995
version mentions that the study of the infinite in mathematics gave
the subject a spiritual value. One could also say that mathematics
has a great spiritual value as it becomes a great mystery for most
high school and college graduates. Other than that I did not see the
spirituality.
US Resources for Education
The following links provide detailed checklists for skills and
ideas to be covered in mathematics and/or other subjects.
Identification of what should be covered is more important than when.
What is high school material in one location may be college material
in another.
1. The first 5 years. The Talbot
County Framework page in a two or three page, well-written
table, includes mathematics
framework for preschool to grade 5, one grade or year per column.
Each curriculum item is accompanied by an action to support or reach
it. The resulting path gives a very clear checklist for what should be
covered in Pre-School to Grade 5, and when. Read this first if
you teaching these grades, or preschool. This checklist is close to
providing a script for instruction.
2. Years 6 and 7. The Talbot
County Framework page also also offers a mathematics
framework for grades 6 & 7. This table provides another check
list as well, not yet as clear as the pre-school to grade 5 one. Read
this short item second if you teaching these grade 1 to 8.
3. All Years, Most Subjects. The Massachusetts Department of
Education offers frameworks
for many subjects including mathematics. The Massachusetts August 2000
mathematics framework, is comprehensive for grades 1 to 12.. Read it third if you are
interested in US elementary and high school instruction. It provides a
detailed, well-written checklist for mathematics instruction from
primary school to college. This checklist follows and improves on the
"Standards" of the National Council of
Teachers of Mathematics.
4. Offline, The Mathematical
Association of America, CUPM Panel on Teacher Training, in 1983
published Recommendations for on the Mathematical Preparation of
Teachers, ISBN 0-99385-052-4. The recommendations are still worth
reading. Here CUPM stands for Committee on Undergraduate
Program in Mathematics. Compare or contrast this
reference with more recent efforts.
5. For Better or Worse. The US
National Committee of Teachers of Mathematics has an Illuminations
Website to illustrate it principles
and standards, online from 1989 onward. American Mathematics
Society, Mathematical Association of America, and the Society for
Industrial and Applied Mathematics have all permitted or designated
the US National Council of Teachers of Mathematics to take the lead in
defining what should be taught at the US national level. But so far, I
have found the committee written material of the National Council of
Teachers of Mathematics too wordy, and for the most part, I find
exploration of its principles and standards, a chore and not a
pleasure. That should not be the case.
Canadian Resources for Education.
1. Offline, The Ontario Curriculum Guideline for Mathematics,
Part 3, Intermediate and Senior Divisions, 1985, is well-written. It
describes well what could or should be mastered in grades 7 to 12.
Compare or contrast it with more recent efforts.
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www.whyslopes.com
Volume 1B, Mathematics Curriculum Notes,
Foreword + Chapters 1 to 10 + 12
Book Entrance
Inductive Principles
1 Introduction
2 For & Against Math
3 Algebraic Thought
4 Why Slopes & SQRT of -1
5 Books & Articles to Read
6 Unruly Origins of Algebra
6. Axiomatic Civilization
7 Geometry, 2 Ways
8 Modern Instruction
9 The Two Ends
10 The Transition
10 Explaining Logic
10 Explaining Algebra
10 Why Sets in Math.
12 Four Phases
Links
Chapter 11: Primary School Mathematics
11 Primary Math
11 Cue Cards
11 Counting
11 Decimals - Addition
11 Decimals -Times
11 Decimals & Subtraction
11 Fractions and Division
11 Notational Conflict
11 Reciprocals Etc
11 Decimals - Ratios
11 Size Comparison
11 Numbers, +ve or -ve
11 Rename < Sign
11 Complex Numbers
Will provide an alternative to Chapter 11 later, most likely in the Parent's
Area: Help Your Child or Teen
Learn
Most students in high school are not heading for calculus,
but most topics in high school mathematics are present due to calculus.
Preparation for calculus demands their coverage at full strength.
See too, this site 55+, Math
Education Essays. Site areas and pages provide pieces of the a Mathematics
Education, Jigsaw Puzzle, in formation.
-Inductive
principles for course design & delivery require a clear
description of where and how skills and concepts may rest on earlier ones, so
that difficulties may be explained and remedied by looking for what was
missed or forgotten in earlier studies.
Mathematics is a demanding subject. All errors in notation
and comprehension need to be identified and corrected. In
reading, spelling and writing, students have to learn all the letters in the
alphabet, not just some. and memorize spelling. Anything less implies
difficulty.
Likewise in mathematics, students have to master key skills
and concepts, one at a time and one after another. Anything less implies
difficulty.
Modern mathematics curricula introduced an inconsistency
into course design and delivery. They did not sanction the use of decimals nor
the use of diagrams in skill and concept development but decimal arithmetic
and diagrams are needed for student comprehension and for an operational
mastery of quantitative skills. That implies the need for an mixed-math
curricula based on a systematic development of operational skills, sufficient
for applications and sufficient to provide a base & context
for the very optional study of pure mathematis.
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