Improper notation in mathematics points to and leads to difficulties.
If your teacher solves equations ¾ = (¼)x by writing =3 besides the x,
transfer to another class. Proper notation allows you to record,
develop and report arithmetic and algebraic ideas in writing instead
of in your head. If you cannot write mathematics properly, your
mathematics education is at risk.
A) Arithmetic Troubles. People have difficulty in
mathematics due to a poor command of arithmetic - See these
arithmetic problems with
hints of algebra. If you have trouble with them see the RealPlayer
webvideos in Three Skills
for Algebra. For further help leave this site to explore aaamath. and Purplemath carefully
and then return. the following Math League Help Topics
(help from another Ph. D in math for grades 4 to 8) provide more site
exits.
|| Whole
numbers & their basic properties || Decimals,
whole numbers & exponents || Using data and
statistics || Fractions
|| Geometry ||
Ratio and
proportion || Percent and
probability || Integers ||
Metric units
& measurement || Introduction to
algebra || Positive &
negative numbers || (help topics here go beyond arithmetic, and may
be useful by themselves or with site coverage of similar topics).
Novices: The ability to do arithmetic with whole numbers
and fractions not in your head but on paper efficiently and
written with proper notation is needed in algebra, geometry, trig
and probability. Mastery of fractions and radical without a
calculator may not be useful in daily life but it is required for
further learning in mathematics. Old curriculums in mathematics said
mastery of arithmetic was needed for algebra. But today requiring less
points to folly in mathematics instruction with many victims - high
marks in mathematics courses where arithmetic skills are not developed
mislead students and lead to to remedial mathematics courses for many
first year students in North American colleges and universities.
Arithmetic skills should lead to unique results - In arithmetic, if
you regularly obtain different results than others then your
arithmetic skills need urgent repair.
B) Algebra Troubles. Intelligent people have difficulty with
algebraic reason, the shorthand roles of letters and symbols in
mathematics, due to awkward or absence explanations - too much is
assumed and not enough is explained.
The following site pages offer a remedy which requires arithmetic
skills slowly and not suddenly - so student weak in arithmetic may
follow most immediately.
Logic Chapters (3
Chains of Reason 4
Longer Chains 2
Logic Puzzles 5
Knowledge Islands) Algebra Chapters ( 8 Three Skills for Algebra
9
The First Skill 10.Two.More.Skills 11 Why Shorthand)
Essay:
What is a Variable Algebra Chapter: 14, Compound Interest,
Arithmetic Skills (Problems & More
Problems, Solving Linear
Equations) Algebra Chapters (Solving linear Equation - a
second go, 16 Painless
Theorem Proving 17
Pythagorean Theorem - Chinese Square Proof)
The remedy begins with logic chapters to test or develop reading,
writing and study skills. Strong reading and writing are needed in
mathematics and for learning in general. The remedy continues with
lessons and insights not found elsewhere to provide a fuller and
clearer view of algebra. The First Skill
for algebra and the essay
What is a Variable offer a simpler and clearer ways to understand
not only symbols but also words in mathematics from arithmetic to
calculus and beyond. Remember: Fraction sense (comprehension)
and arithmetic with fractions is needed for algebra.
C) Calculus Troubles - Students
starting calculus often have difficulties with algebra, arithmetic and logic skills. Calculus
courses may compound difficulties by demanding not only well developed
arithmetic skills, but also algebraic ways of writing and reasoning at
full strength too quickly. Site links and site pages point to
remedies to ease or
avoid difficulties, besides further topics to enrich skills and
knowledge.
Site pages on algebra, arithmetic, logic, better
learning in general, reason, theorem proving and complex
numbers offer appetizers and lessons that may be
added to the start or middle of calculus to ease or avoid perils. Some
may be met before calculus to provide a context for slopes and
polynomials. All gradually introduce the full strength role of algebra
in elementary to advance topics in a ways that may avoid difficulties
and enrich knowledge.
Calculus is the subject of slope related
computations, direct or reversed, along with interpretations and
applications. Many formulas for perimeters, areas and volumes met
before calculus can be justified by slope (a.k.a derivative)
computations, direct and reversed.
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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:
-
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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