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

The Inductive Approach

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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