TABLE OF CONTENTS
COVER PAGE PAGE 1
TABLE OF CONTENTS PAGE 2
ASSIGNMENT 2 PAGE 3-12
BIBLIOGRAPHY PAGE 13
DECLARATION PAGE 14
2
, Question 1
1.1. Briefly discuss the importance of learning and teaching algebra in the
Intermediate Phase. (6)
An important part of algebra and the building of algebraic thinking is pattern. The mere
recognition of pattern is the first building block. This is done in the early years either
through simple number sequences or through pictures. The recognition of pattern is
followed by the realization that a pattern comes about through a regular and
understandable repetition or progression according to a rule. At first, learners must
describe this regular change in each consecutive term of the sequence verbally. Then
the task is to start expressing the rule mathematically – this is an algebraic ability. If
teachers use patterns to develop learners’ algebraic thinking, they lay the foundations
for the more advanced idea of functions, a mathematical concept that is mainly
concerned with relations and the rules that govern relations. A function can be
described as the relation that exists between a set of inputs and a set of outputs, where
each input is related to exactly one output.
1.2 Explain how and who came up with these algebraic concepts or used these
algebraic concepts developed over time:
1.2.1 Decimal Number System (2)
Decimals as they look today were used by John Napier, a Scottish mathematician who
developed the use of logarithms for carrying out calculations. The modern decimal point
became the standard in England in 1619.
1.2.2 Abstract symbols (2)
Humans convert virtually all direct and indirect impressions into symbols. The symbols
that humans create are words. Every word consists of two components, a denotative
and a connotative
1.2.3 Negative Numbers (2)
The English mathematician, John Wallis (1616 - 1703) is credited with giving some
meaning to negative numbers by inventing the number line, and in the early 18th
century a controversy ensued between Leibniz, Johan Bernoulli, Euler and d'Alembert
about whether \log (-x) was the same as Log(x)
1.3 Describe the stages in the development of symbolic algebra. Give at least one
example of an equation for each of the stages. (6)
Rhetorical Stage
The stage where all statements and arguments are made in words and sentences, for
example:
Lisa had two flowers and Mike bought her two more flowers, Lisa now has four flowers.
Syncopated Stage
The stage where some abbreviations are used when dealing with algebraic
expressions, for example:
Symbolic Stage
3
COVER PAGE PAGE 1
TABLE OF CONTENTS PAGE 2
ASSIGNMENT 2 PAGE 3-12
BIBLIOGRAPHY PAGE 13
DECLARATION PAGE 14
2
, Question 1
1.1. Briefly discuss the importance of learning and teaching algebra in the
Intermediate Phase. (6)
An important part of algebra and the building of algebraic thinking is pattern. The mere
recognition of pattern is the first building block. This is done in the early years either
through simple number sequences or through pictures. The recognition of pattern is
followed by the realization that a pattern comes about through a regular and
understandable repetition or progression according to a rule. At first, learners must
describe this regular change in each consecutive term of the sequence verbally. Then
the task is to start expressing the rule mathematically – this is an algebraic ability. If
teachers use patterns to develop learners’ algebraic thinking, they lay the foundations
for the more advanced idea of functions, a mathematical concept that is mainly
concerned with relations and the rules that govern relations. A function can be
described as the relation that exists between a set of inputs and a set of outputs, where
each input is related to exactly one output.
1.2 Explain how and who came up with these algebraic concepts or used these
algebraic concepts developed over time:
1.2.1 Decimal Number System (2)
Decimals as they look today were used by John Napier, a Scottish mathematician who
developed the use of logarithms for carrying out calculations. The modern decimal point
became the standard in England in 1619.
1.2.2 Abstract symbols (2)
Humans convert virtually all direct and indirect impressions into symbols. The symbols
that humans create are words. Every word consists of two components, a denotative
and a connotative
1.2.3 Negative Numbers (2)
The English mathematician, John Wallis (1616 - 1703) is credited with giving some
meaning to negative numbers by inventing the number line, and in the early 18th
century a controversy ensued between Leibniz, Johan Bernoulli, Euler and d'Alembert
about whether \log (-x) was the same as Log(x)
1.3 Describe the stages in the development of symbolic algebra. Give at least one
example of an equation for each of the stages. (6)
Rhetorical Stage
The stage where all statements and arguments are made in words and sentences, for
example:
Lisa had two flowers and Mike bought her two more flowers, Lisa now has four flowers.
Syncopated Stage
The stage where some abbreviations are used when dealing with algebraic
expressions, for example:
Symbolic Stage
3
