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Brief History of Mathematics
2000 BC
Earlier a place value notation number system
had evolved over a lengthy period with a
number base of 60
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1700 BC
i. Phytegores theorem a2+b2 = c2
ii. Linear equations were studied in the context
of solving number problems
iii. Quadratic equations were also studied and
these examples led to a type of numerical
algebra
iv. Geometric problems relating to similar
figures, area and volume were also studiedand values obtained for
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450 BC
i. The Babylon basics of Mathematics was
developed by Greek
ii. Further mathematical discoveries were
driven by the astronomy, for example the
study of trigonometry
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300 BC to 200 AD
i. Major Greek progress in mathematics
ii. After this time progress continued in Islamic
countries
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16th Century
i. Major progress in mathematics in Europe
began again
ii. Algebraic solution of cubic and quartic
equations by Pacioli
iii. Cardan, Tartaglia, Ferrari Copernicusand
Galileo revolutionised the applications of
mathematics to the study of the universe
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17th Century
i. Napier, Briggs and others greatly extend the
power of mathematics and discover the lawof logarithms
ii. Cavalierimade progress towards the
infinitesimal calculusiii. Descartes added the power of algebraic
methods to geometry
iv. Progress towards the calculus continued withFermat, who, together with Pascal, beganthe mathematical study of probability
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18th Century
i Eulerwho, in addition to work in a wide
range of mathematical areas, was to invent
two new branches, namely the calculus of
variations and differential geometry
ii Lagrange was to begin a rigorous theory of
functions and of mechanics
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v. Newton and Barrow(Newtons teacher),
developed the calculus into a tool to push
forward the study of nature. They show theinteraction between mathematics, physics
and astronomy
vi. Newton's theory of gravitation and histheory of light take us into the 18th Century
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19th Century
In geometry Plckerproduced fundamental
work on analytic geometry and Steinerin
synthetic geometry
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The roles of Mathematics
Mathematics as a Language
What is Mathematics?
Often, people equate mathematics with arithmetic
Traditionally, the major emphasis of the K-8mathematics curriculum has been to teach childrenarithmetic
Mathematics involves more than computation
Mathematics should include experiences that helpstudents to shift their thinking about mathematics
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Mathematics as a Language
Blake wrote: "I have heard many People say,
'Give me the Ideas. It is no matter what Words
you put them into.'"
To this he replies, "Ideas cannot be Given but
in their minutely Appropriate Words."
William Blake
(quoted by J. Newman, The World of Mathematics, 1956)
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Mathematicians need to be clear and concisewhen they communicate
Our math education system pays someattention to the idea that math is a language.
For example:
Some math teachers make use ofcooperative learning(an environment thatencourages students to communicatemathematical ideas)
Some math assessment instruments requirethat students explain what it is they aredoing as they solve the math problems in theassessment.
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Mathematics as a Science
generating a formula that describes
some basic tendency of nature
use with existing theory to deduce an
unknown quantity
an analytic tool applied to experimental
data
Mathematics is important in physics and
astronomy
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Mathematics as a Way of Thinking
The process of learning mathematics
necessarily involves learning certain ways ofthinking
One of the reasons to learn problem solving
in our Mathematics curriculumSeeing connections is a big part of
mathematical problem solving and theoremproving
provide powerful support for businessdecision
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Mathematics as the Art of Calculation
Mathematics consists of techniques for
getting answers
Calculation is at the very root of
Mathematics
In China, abacus is the art of calculation.
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Mathematics is a Patterns and Relationships
Patterns and relationships are found in
aspects of math such as counting and
geometry
Number patternssuch as 3, 6, 9, 12are
familiar to us since they are among thepatterns we first learn as young students
Mathematics is especially useful when it
helps you predict, and number patterns areall about prediction
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Recognizing number patterns is also an
important problem-solving skill
If you see a pattern when you look
systematically at specific examples, you can
use that pattern to generalize what you see
into a broader solution to a problem
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Mathematics is a Tool or an instrument
Mathematics can solve abstract problem inthe mathematical problems
It also can solve daily life activities
One of the best examples is when a personis cooking