Mathematics
Curriculum
Notes
Printed in Canada
ISBN 0-9697564-6-1
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This folder has a tree like structure. The
child, same level and parent level webpages for this webpage follow..
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
1. Introduction
2 For & Against Math
3 Algebra
4 Why Slopes & Complex No.
5 References - Past Efforts
6 Euclidean Logic
7 Geometry in 2 Ways
8 Modern Instruction
9 The Two Ends
10 The Transition
11 Primary School Math
12 Four Phases
Book Entrance
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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] [ 1. Introduction ] [ 2 For & Against Math ] [ 3 Algebra ] [ 4 Why Slopes & Complex No. ] [ 5 References - Past Efforts ] [ 6 Euclidean Logic ] [ 7 Geometry in 2 Ways ] [ 8 Modern Instruction ] [ 9 The Two Ends ] [ 10 The Transition ] [ 11 Primary School Math ] [ 12 Four Phases ]
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