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11 Cue Cards 11 Counting 11 Decimals - Addition 11 Decimals -Times 11 Decimals & Subtraction 11 Fractions and Division 11 Notational Conflict 11 Reciprocals Etc 11 Decimals - Ratios 11 Size Comparison 11 Numbers, +ve or -ve 11 Rename < Sign 11 Complex Numbers
Foreword 1. Introduction [4] 2 For & Against Math 3 Algebra [3] 4 Why Slopes & Complex No. [2] 5 References - Past Efforts 6 Euclidean Logic 7 Geometry in 2 Ways 8 Modern Instruction 9 The Two Ends 10 The Transition [3] 11 Primary School Math [13] 12 Four Phases
Book Entrance
This explanation
of What
is a Variable differs from the common view (letters in algebra are
variables) and is compatible with the pure math view (variable in maths are placeholders for
element of a set).
Amazon Link: The VNR Concise
Encyclopedia of Mathematics
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Chapter 11
Elementary Instruction
There is no single route in primary school for the teaching or learning of
arithmetic and geometry, the associations between them, and their uses. Any
route followed will I suspect circle around the same or related concepts and in
the act cover more detail with much redundancy.
This chapter constructs an image, approximately correct perhaps, of primary
instruction, that is, the explanation or description of mathematics before
deductive reasoning and algebraic thought are emphasized and relied upon. This
image is intended not only for elementary school teachers but also for the
teachers of intermediate and advanced mathematics. The image approximately
represents [1] the background
and expectations of students at the finish of primary math instruction.
The initial aim of primary math instruction is descriptive and corroborative.
It suggests patterns from experience. It gives rules for calculation and shows
how to verify results. The rules and patterns may involve geometric or
arithmetic ideas. The rules and patterns are not derived from first principles
but, altogether, the rules and patterns set a stage. They introduce some rule-
and pattern-based reason together with the observation that rules and patterns,
if applied without error, lead to repeatable, reproducible and thus verifiable
results. Such use of rule and pattern-based methods precedes deductive reasoning
and is for many people a secure substitute. Deductive reasoning itself
represents a refined attachment to repeatable, reproducible and thus verifiable
results. Ideas on and for primary mathematics instruction follow.
Sections: [Chapter Entrance] [ Foreword ] [ 1. Introduction [4] ] [ 2 For & Against Math ] [ 3 Algebra [3] ] [ 4 Why Slopes & Complex No. [2] ] [ 5 References - Past Efforts ] [ 6 Euclidean Logic ] [ 7 Geometry in 2 Ways ] [ 8 Modern Instruction ] [ 9 The Two Ends ] [ 10 The Transition [3] ] [ 11 Primary School Math [13] ] [ 12 Four Phases ]
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1, Elements of
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3 .Why.Slopes.&.More.Math.1995
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