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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