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Original Site Title: Appetizers and Lessons for Mathematics and
Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept
Development with How-TOs Français: 26
pages
for college students,
gifted teens, home-tutoring and K1-12 schooling; and for avid readers in school and out. See site volumes.
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Logic
5 Chapters Arithmetic 10 Steps
Algebra 12
Starter Steps & 5
Advanced Steps
Work & Study 23 Tips Geometry
15
Steps Calculus 70 Lessons. See Site
Map
Ages 15+:
Why study slopes Polynomials
Quadratics
Why factor polynomials
Logarithms Functions
What is similarity
Euclidean geometry leanly
Coordinates + complex no.s
Vectors DC Electric
Circuits
Ages 12+:
Prime factorization
Written work formats
Decimal place value
Extend arithmetic skills orally
What is a variable
5. Fraction Operations by Raising Terms Solving Linear
Equations:
Take I
Take II
Online Volumes: 1 - Elements of
Reason, 2 -
3 Skills For Algebra, 3 -
Why Slopes and
More Math, 1A -
Pattern Based Reason, 1B -
Skill Development Principles +
Troubles
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Welcome: Site content may develop
critical thinking, improve reading and writing, and build
mathematics skills. See online chapters on
on
logic and pattern
based reason.
Teachers: This December 2011, 5-phase framework
offers a context for mathematics & logic instruction. Phases 1 to
3 focus on skills with actual or potential value for
adult & daily life. College-oriented phases 5 & 4 focus on
calculus & preparation for it. Phases 1 to 4 may also serve
trades & professions not dependent on calculus.
Site Review: Math resources ... span ... arithmetic, logic,
algebra, calculus, complex numbers, and Euclidean geometry. Lessons
and how-tos .... provide a good foundation for high school and
college ... mathematics. Read more.
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Home < Volume 2 Three Skills For Algebra << Postscript For Better Performance
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PS: For Better Performance -How To Improve Learning
Volume 2, Three Skills for Algebra
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Adopt some goals or aims for your learning. Seek and find a reason,
approximately correct, for studying a subject. Reasons may be
as crude as improving marks, or more fundamental. Ask your
instructors for reason approximately correct for studying a subject,
or topics in it. That may provide a context and motivation for
learning. That being said, a teacher saying a topic is required
because of the final examinations or course requirement could be
giving a full and honest answer. But in general we hope you and your
teachers can find reasons and a context approximately correct for
most topics in a course.
-
Mathematics mastery is best checked and proven on paper. As in
English, apart from a few mistakes, if we do not write exactly
what we mean, we do not understand what we are writing and most
likely what we are reading. Precision reading and writing, are musts
for better study skills in all subjects, mathematics
included.
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If one explanation here or elsewhere is not to your liking, hard or
nonsensical, try again and try another here or elsewhere, alone or
with help
Variety in the presentation and development of ideas means if one
explanation here or elsewhere is not to your liking, another might
be. Different people have different likes and dislikes. Another
explanation, written or in person, could be clearer.
Different authors and different teachers all provide different ways
to learn or introduce ideas and skills. So again, if one
explanation here or elsewhere is not to your liking, try
another. May will, stubbornness and patience be with
you.
-
Know-how without know-why is
incomplete in mathematics. Mastery of fraction sense and operations,
mastery of logic, mastery of algebra and mastery of geometry may help
at home and work in money problems and in construction or maintenance
problems. The know-why part of mathematics provides stories
or theories to follow, one at a time and one after another, some
independently, to provide a greater context for know-how not only
in mathematics but also in other quantitative disciplines.
-
For skill and knowledge perfection, ask your teachers or tutors
to encourage you, say what you are doing right, but also ask
that all errors in your written work, concept and notation, be
caught and corrected. Errors need to be corrected. Otherwise,
they return to slow or stop instruction.
-
In each subject, you may further focus your studies with the
question: how can I transfer or teach to others the skills and
concepts I am learning? A subject is not fully understood until
you can explain it clearly and directly.
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Teachers & Tutors: Site pages offer better or best practices for providing skills -
simpler than expected & comprehensive but for exercises. For your charges, your duty is to study them alone or in
groups and develop skill building exercises & activities to share. Start now. The effort here is the best I can do.
Others are welcome to refine or exceed it. Please do.
Secondary
Mathematics for Ages 11+, A Practical Approach for home-tutoring or -schooling, or for schools & colleges
with local curriculum control. Study how to include site content - its skill development how-TOs and innovations
into present or future lesson plans - some reading required.
Road
Safety Messages and Questions: When and why should you face
traffic when walking along a road or cycle path? Is it a good
idea to hang limbs outside of cars etc? What gives more
protection in a crash: a car, motorbike or bicycle?
See too, the BBC-Belgium story Texting and
Driving - texting & the impossible test - the article links to a gruesome utube video on the subject
The Logic of Injustice:
How Texas sent
an innocent man to his death - The wrong Carlos. Some judgments are irreversible. Procescution: Where and when prosectors play to win rather than for
justice, guilt beyond a reasonable doubt goes unrespected due to prosecutors who putting winning
first, those innocence before the law may be convicted. Some procescutors offices in continuing to accuse after a pardon
due to reasonable doubt or innocent being shown, may sucessfully oppose compensaton for false convictions
by asserting a pardon individual is still under suspicion. Then the pardoned individual or the latter's estate
is not compensation for years or decade
of improper or false imprisonment, or for execution. Site chapters on Logic
and some in Pattern
Based Reason may slowly lead to greater precision in reading, applying and
writing laws.
May 2012, Composition Starting:
Pre-School and Primary Mathematics - Quantitative Skills, An
Intellectual View, Feedback Welcome:
The 8 Most Popular Site Inlinks
Parent Center: Help your child or teen
learn:
Parent-friendly
Work Booklets for ages 3+ to 13 Use these or others to check
or build skills. Other booklets are available but these booklets
allow parents unsure of themselves in mathematics to help their
children. The selection acquired in Canada is published in the
USA. So it has a US orientation. In retrospect, the selection
shows parents what to check with the booklets or by other ways,
the choice is theirs. But in retrospect, the selection does not
cover integral and fractions liquid weights and measures - ask
the publishers to correct that! For ages 9 to 12 say, parents may
compensate by showing boys and girls how to use weights or mass,
and further measures in food preparation. Beyond that children
may be shown how to measure and calculate angles, lengths and
areas [proportional amounts too] directly or by using maps and
plans drawns to scale. Learning how to gather and measure all the
ingredients, pots and pans for a dish or a meal, along with
cleaning up sets the stage for like activities or experiments in
science courses, and in developing organizational skills,
gives boys and girls a head start. Good luck. At the other
extreme, more comprehensive than light, if your motto is
McCainian: drill, drill, drill then Toronto
mathematician and actor John Mighton's jump math organization has jump math
workbooks for at least grades 3 to 8 for at-home and in-school
use - training sessions for teachers available. Jump math has
been expanding to cover older students. Jump Math Samples: plus
Fractions for
Grades 3-4 & Grades 5-6 [Read] Free Resources grades 1 to 8
[unread - likely to be good]. and
Mathematics
Skills For Ages 3 to 14 - technical!
Skills with take
home value - A few ideas
Basic skills include
time-date-calendar Matters; money matters; map, plan and
scale diagram matters;counting, measuring and figuring;
decision making with logic and likelyhood; being careful and
being aware of the domino effect of mistakes; reading and
writing with precision.
Is your child able to add, subtract and multiply amounts
of money, work with fractions, work with clocks and calendars,
work with maps and plans, and measure length, weight-mass and
volume? Schools may promote your son or daughter without
providing basic skills in reading, writing and
arithmetic.
Arithmetic
and Number Theory Skills
Algebra
Starter Lessons
Geometry
- maps plans trigonometry vectors
More
Algebra
70
Calculus Starter Lessons
Calculus Lessons Elsewhere:
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How to Ace Calculus: Street Wise Guide - Mostly
Text.
-
Flash
Video for Calculus Phobics
They cover basic topics in ways likely to complement your
notes, your textbooks and site material. When Goldilocks
trespassed in the house of the three bears, she found three bowls
of porridge, two not to her liking, and one just right. Different
bears have different tastes. As invited guest here and elsewhere,
if one or more explanations is not to liking, try another. It may
be better or just right.
Unsolicited Advice
Learning to do and high marks if it comes to easy is often
deceptive - light rather than deep. For that reason, students
with learning difficulties determined not to let it get in their
way may go deeper and farther than those with none. High marks,
if the come easy, may be deceptive - provide a too light and not
a deep mastery. That could have been your problem in secondary
school, one that leads to comprehension shock or difficulties in
calculus and more generally in the first year of college. Bon
Appetite.
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Home < Volume 2 Three Skills For Algebra << Postscript For Better Performance
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