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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.
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Helping Your Child or Teen Learn
While you may hope that schools offer clear and effective
instruction, you should also test and verify. not all is certain, You also
need to encourage the will to learn, or the aims and goals of your charges.
Then your charges may keep trying in school and cooperate with teachers,
without disrupting or opposing the education of themselves and others. Good
luck.
The advice offered here for helping your child or teen learn is approximately
correct, for some circumstances not all. See what works.
- Parents are the first and last teachers of their
children. Where schools do not teach all, parents may intervene alone or
with help to push or guide. Help your child workbooks for mathematics and
other subjects may keep your child learning during school breaks and
vacations, year round. Look for workbooks for math and other subjects in
book shops or online.
-
If you have a teen in difficulty in
school, get the teen to master logic
alone or with help, if you can. Also teach him or her to be more precise and
careful in school and work, by verifying or requiring your teen to learn or
demonstrate mastery of exact arithmetic methods for addition, subtraction,
multiplication and division of whole numbers. Mastery of logic and exact
arithmetic with decimals (fractions too) will show your teen that an error
in one step of a calculation or argument, lack of care and precision,
sloppiness in other words, invalidates and makes wrong the further
steps and the result. Demand from your teens that they write out
answers and solutions so that what is written serves a full record of
what they thought, because they may not remember what they thought later,
and because teachers in giving marks cannot read their minds.
-
Skill and knowledge mastery, perfection
too, requires students to sit down and study carefully. No one else can
do that for them. Encouragement or direction from parents and teachers will
help.
-
North American, Educational Horror
Stories: (i) A senior high school student said to me: I met
fractions in primary school and I should not need them for my studies.
His firm opinion was that I should bring all the current course on
physical science to a level where mastery of fractions was not required.
After spending half-hour telling him, the course you are in requires mastery
of fractions and more, I stopped trying. He did not want to
listen. So I could not help him. There was a question of
credibility. (ii) Another college algebra student studying to a be
policeman sat at the back of my classroom. He did very little outsides of
class, and inside of class spoke to his two friends, also male. While
confronting his lack of effort, he explained that his mother thought
mathematics after arithmetic was a waste of time. I protested, but I could
not change his mind. (iii) While giving a college, remedial algebra
class, I had a student who informed me that he was high school mathematics
instructor giving an algebra course. So he needed my
course good move, but oops. (iv) ....
Section webpages
- Speaking Skills suggests how to improve
the speaking and listening skills of your child.
- Reading & Writing offers ideas for
the development of these skills.
- Preparing for science -Teaching a boy or girl
to cook or to follow any multi-step method precisely, in a repeatable and
reproducible manner, will help in science and all area of work and study.
- Learning Takes Time and Effort: Four
Things for a Student to Know. Quote in full of an article from Speaking
of Learning that refers back to words at this site, no longer online.
- Math Work Books for your child or young
teen identifies mathematics material for your charge to use with your
supervision.
- Math Books and Websites for
Teens & Adults - besides this one.
- Readings for Parents -
results from a trip to a local bookstore.
- Patience Please. reflects the inductive
idea that learning takes time. If you see a difficulty, you need to identify
the source and retreat before it in order to practice skills that restore
confidence and then to practice skills that remove the source of the
difficulty. Teaching, tutoring or parenting takes time and patience. Good
luck. Nothing is certain.
- Who is in Charge? For better or worse,
you the parent or guardian may be the first and longest term instructor of
your child. Do your best
Parents and teachers need to say no for small things of
little consequence to build and maintain authority to say no for larger
matters. Parental authority: use it or lose it.
- Student Motivation Here a discussion
of the challenge. Not the solution.
Students with parents who say mathematics mastery is
important, or education in general is important, will often have more
goals, more will and more staying power in school and college - no
guarantees here -but is part of the solution.
- Talk to Your Child or Teen.
For many, those without learning difficulties, the will to learn is
often more important than ability. Encourage the will. That is part of
the solution.
- Primary and High School Mathematics
describes or lists the skills and ideas met primary school to the first year
of high school, and points to a context
for high school mathematics.
Ages 5 or 6
Ages 6 or 7 Ages
8 or 9 Ages 10 to 13 Ages
14 plus.
Knowledge of them will allow you to judge the skills of your charge and
the math and logic work books or reading for your charges. You will see
where they are going.
- Links for Kids and their Guides
Problems in Education
Students should construct skills and knowledge and
learn to be critical thinkers in social and technical subjects by mastering
existing rules and patterns, that is be able to follow and apply rules and
methods in a repeatable and reproducible manner, while learning about the
benefits, origins and limitations of rule- and pattern-based methods. Sixth
Message to Repeat
Ideally students will have clear and precise reading material, that is text
and exercises, to follow or do, one at a time and one after
another. Albeit, some school authorities may impose math textbooks of the
scatter-brained type on teachers and students, a professional embarrassment for
the teachers which puts students and parents. Not all is
ideal. To help improve school textbooks, ask local mathematicians, domain
experts with doctorates in mathematics to identify in public
newspapers and in university mathematics department websites, the rational and
irrational elements in local mathematics textbooks for local schools,
primary to secondary. Do some muckraking. .
What Sabotages Education: Pre-university education
theory (constructivism) says mastery of rules and patterns starting with
arithmetic is not a sign of intelligence But later studies in senior high
school, college and university instruction in mathematics, science,
medicine, trades, technology and law prize & require that mastery or
ability. So education K1-9 may be inconsistent with later requirements
for study and work. - Work and most arts & disciplines are rule- and
pattern-based. The ability to use rules and patterns carefully and diligently,
one at a time, one after another, alone or in combination, is needed to
to arrive at a results that are repeatable and reproducible for better and
worse in our pollution age societies. Rule and pattern mastery is a
mixed blessing but a necessary one for your offspring.
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Tutors - All Subjects
(use at your own risk
AU:
tutorfinder.com.au
CDN :
findatutor.ca
CDN: .i-tutor.ca
NZ: findatutor.co.nz
UK:
tutorhunt.com
USA: wiziq.com
USA: ziizoo.com
www.whyslopes.com
Help your Child or Teen Learn:
Area Intro
1. Speaking Skills
2. Reading & Writing
3. Preparing for Science
4. Learning Takes Time and Effort
5. Math Books: kids & teens
6. Math Books: teens & adults
7. Readings for Parents
8. Patience Please
9. Who is in Charge
10. Motivation
11. Will to Learn
12. Math K1-20
13. Links For Parents
14. JumpMath WorkBooks
15. Discipline in Schools
Maths for Ages 5+
D
What to do in School & Why
E.How to Study Mathematics
To read, write and spell, your children need to
learn and memorize the alphabet. Anything less would be absurd. That being
said, learning and using mathematics demands that your children meet key
skills and concepts, and not skip any. Where local schools do not provide the
latter, you need to provide remedies.
Care and Precision: If your child can learn
to follow multi-step methods carefully and precisely in arithmetic, he or she
may do so in other subjects, as well. Get your child or teen, if you
can, to sit down and study. Suggest he or she aim for skill and concept
development and perfection for their own sake, not that of their teachers.
The will to learn is the key to success in
school. Parents do have to be educated to support or guide their
children and teens. What matters more is support for the will to learn, for
children and teens to be told to try to learn and to ask teachers, their
schools or classmates for help and more help, as needed. Teachers and parents
need to push students, help them find the will to learn, teamwork helps.
The main reason and focus for high school
mathematics is or should be preparation for calculus. That requires skill and
knowledge perfection with fractions, algebra, geometry, trig and functions.
Many high school programs do not provide this. Make sure alone or with
help that your children and teens have a good command of
fractions.
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