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maths zone
sums will set you free -
at abelard.org


Maths, or sums, are often misunderstood.

Language is used for communication between humans. Mathematics is a more precise means for communicating than everyday language, but it is important to realise that mathematics is not different in type from English.

In the sums will set you free zone, abelard offers articles that can help demystify this language, and so enable the user to understand and to master much in their physical and social environment.

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abstracts of articles

how to teach a person number, arithmetic, mathematics
pages have simple, illustrated explanations

Numbers are labels assigned to real objects, with particular labels assigned to different sized groupings of objects.

counting and addition
Tools to learn and to master manipulation of numbers and counting.

subtraction & more counting
Separating one or more objects from a group is the start of subtraction. Continuing with basic number and sums. Includes sections on counting in the real world, placeholders, subtraction, equals, category - logic blocks

Multiplication can be regarded as repeated addition, or constant addition. But often, instead of adding just one each time, a collection or set of items is added again. Continuing basic number and sums.

Division is constant subtraction, with smaller groups of items are removed from a larger collection. Continuing basic number and sums.

writing down sums
When teaching basic arithmetic to pre-literate people, it is less confusing for the learner to grasp the writing of, and the reading of, numbers separately.
Step by step illustrated explanations, in clear language, for additioon, subtraction, multiplication, division, as well as long multiplication and long division sums.

quadratic equations, with model answers
Four worked examples of how to answer questions with quadratic equations from 1970, compared with a question from 2010. With commentary.

sums.fractions, decimals, percentages and ratios 1
fractions, decimals, percentages and ratios are all effectively the ‘same’ thing. This first page concentrates on what are fractions and how to do simple additions and subtractions with fractions

fractions, decimals, percentages and ratios 2
This second page on fractions and decimals focuses on how to do various multiplications and divisions with fractions.

prime numbers and factors, the sieve of Eratosthenes
Prime numbers and factors of numbers are important concepts to understand when doing sums with fractions.

orders of magnitude, indices and logarithms
Step by step explanations, in clear language, of some important tools in maths.

writing down logarithms
Step by step explanations, in clear language, for using logarithm tools. They may be regarded as historic, but slide rules and log tables help learners understand how maths works more deeply.

writing down stats : using the standard normal distribution table graph
Step by step explanations, in clear language, for calculations using the normal distribution graph or bell curve, as well as discussion on aspects of standard distribution and statistics in general.

simultaneous equations, with model answers
Working with simultaneous equations is working with more than one equation at a time [simultaneously], and with more than one variable. Worked examples with commentary, illustrations.

‘equality’ or ‘same as’
“There ain’t no such thing as equality.”

equality and equations
Keeping sums in balance.

minus and zero, dealing with no-thing and less than nothing!
If taught sloppily or incorrectly, zero becomes the foundation for much difficulty and confusion. abelard clarifies what is zero.

understanding graphs and charts
What are graphs and charts? Let's show you how they work

abelard’s maths educational counter
Count up, count down, in binary, in decimal, in hexadecimal, or whatever you choose. Even count backwards in negative decimals. An excellent, fluent and very useful tool for all sums learners and teachers.

understanding, calculating, and changing bases
Numbers are counted in groups called bases, to make it easier to count larger groups (or sets) of numbers. A simple explanation of how to count in different bases using abelard’s educational counter, together with some everyday examples

understanding sets and set logic
A set is another name for a box into which you group similar or dissimilar objects. How to handle sets.

writing down sets and set logic equations
Including truth tables and how to work out compound truth values, logic equations.

why aristotelian logic does not work
Aristotelean logic is the shaky foundation of western thinking and is the cause of conflicts throughout western culture. A primer to thinking sanely.

Metalogic – A: The Confusions of Gödel
An analysis of the multiple problems and unsound foundations involved in Gödel’s theorems (in four parts).
A1: Gödel and sound sets
The requirement for sound sets.
A2:Gödel and sound numbers

Just what are numbers?
A3:Gödel and the ‘paradoxes’
Removing the confusions known as ‘paradoxes’.
A4:The Return of the Gödel
Are Gödel’s theorems just a dog’s breakfast?
Supplement: Who were these people - logic and madness – in preparation

‘intelligence’: misuse and abuse of statistics – abelard
The generalised tool of statistics is widely mis-applied to individual cases and decisions, a process that varies somewhere between fraught and outrageous.

cause, chance and Bayesian statistics
The methods of empiric statistics. improving judgements.

Is Intelligence Distributed Normally? By Cyril Burt, 1963
A paper on the distribution of high IQ.

Statistical inquiries into the efficacy of prayer - Francis Galton, 1872
In 1872, Francis Galton, a cousin of Charles Darwin, published this study on the efficacy of prayer. Also in this document are Galton's ingenious method for visualising a million and a short biography of Galton.

Laying the foundations for sound education
Teaching the basics of psychology, including the difference between reality and the words in their heads, to children and adults. This is also the intent of 'meditation' properly understood.

the sum of a geometric sequence: or the arithmetic of fractional banking
Explains fractional banking for the ordinary reader. Sum of a geometric sequence formula, how to derive/use it explained with real world examples and simple language.

oppression, poverty and life expectancy
Oppression leads to poverty. Poverty leads to earlier death. Meanwhile socialist dictatorships also murder in bulk.With explanations of Loss of Life Expectancy (LLE) and logarithms.

calculating moving averages
One way of dealing with the problems where trends are uncertain is to do what is called a moving average. A possible tool to help understand today’s volatile money markets.

how to teach a person to read using phonics
A clear and simple explanation of how to teach reading rationally and systematically. Aimed at teachers and parents. NOT look-say.





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