Talk the algebra talk
Arithmetic and algebraic expression, formulas and
equalities, being difficult to read aloud in ways that verbally describe
order of operations, will still is a source of silence. But the
silence can be ended, at least in part. F Online algebra chapters 8 to 14 show
(i) how to describe numbers with words apart from and besides symbols;
and show (ii) how to use describe formula usage as direct or
indirect, and describe indirect use as a numerical or algebraic
solution. There-in a new base or extension of the use of words in
algebra.
Your earlier difficulties in learning and teaching algebra come from
the lack of clear algebra talk (a clear words and terms) in
describing numbers and operations on equations and formulas.
Introducing words and terms (short descriptive phrases) to
describe and identify skills and concepts clearly codifies objectives
in algebra, present but hidden by silence, but now exposed by words
easily understood and repeated.
Arithmetic and algebraic expression, formulas and equalities, being
difficult to read aloud in ways that verbally describe order of
operations, will still is a source of silence. That silence that
may be broken or lessened by numbering, naming or giving short
descriptive phrases to identify the expressions, formulas and
equalities with written or spoken words.
If you would like to know why slopes are studied in algebra, or if
you need a simple calculus preview or two, examine this geometric preview and the
more algebraic chapters 2 to 6
in Volume 3, Why Slopes and More
Mathematics. The previews may ease or avoid algebra difficulties
in and before calculus.
The algebraic preview includes sign and monoticity analysis of factored
polynomials, and location of maxima and minima. Monoticity analysis
identifies intervals where a calculation y = f(x) is increasing or
decreasing.
This complex number starter lesson
gives a analytic geometry viewpoint - a coordinate-based
alternative to algebraic views met in pre-calculus learning and
teaching. The distributive law follows applied or mixed math-style from
the assumption that vector addition in the plane is independent of
coordinate system. Despite modern math curricula of the 1960's and
their present-day echoes, math education in trig to calculus, and
in coordinate-free Euclidean Geometry, was not pure.
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