Mathematics and Numeracy

Mathematics and Numeracy
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The world of maths
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Mathematics and Numeracy
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1. Mathematics
The exact definition of mathematics is a matter of debate among mathematicians and
philosophers. There exact definition of mathematics is a subject of discussion (Weyl &
Wilczek, 2009). There exist several generally accepted definitions which have been put
forward to explain the meaning of the term mathematics. According to Hersh (2013),
mathematics can be viewed as a science like physics, with an established body of facts. A
definition by Aristotle classifies mathematics as a science that deals with quantities (Peirce,
2010). Kant defines mathematics as an indispensable instrument of all physical resources.
Each of these definitions captures a certain aspect of mathematics, shedding some light into
its true nature (Hersh, 2013). The discovery of mathematical concepts is based on a method
of validation referred to as proof. Proof corresponds to carrying out an experiment as is done
to test the validity of scientific hypotheses and ideas.
Some of the mathematics characteristics from which these definitions have been derived
include:
i) Abstract
Some of the concepts expressed in mathematics cannot be experienced, felt or seen in
the actual world. For instance, no physical systems or objects can be said to be defined or
represented by negative numbers or complex numbers. Infinity which is a central idea in
mathematics cannot be experienced in practice.
ii) Intuition
Mathematics is intuitive. This means that one can be able to grasp the significance or
meaning of certain problems without relying completely on the mode of analysis. One can
then anticipate the next step in a process and how to react to it.

Mathematics and Numeracy
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iii) Logical sequence
The concepts in mathematics are inter-related and mathematical problems are
normally solved following a logical process in which each subsequent step depends on its
predecessor. Teaching and learning mathematics usually proceeds from simple to more
complicated ideas, from solid to abstract concepts.
iv) Practical applications
Mathematical concepts can be applied to solve practical problems in the physical
world. For example in the construction industry, mathematics is used to calculate the
appropriate proportions in which certain materials such as sand and cement should be mixed
to have a structure of the desired strength.
Daily applications of mathematics
Economics: Appreciation and depreciation
The field of economics is a good example in which mathematical models are used to
estimate the future value of property given a certain rate of appreciation or depreciation. For
instance, the future value of land is a function of its original value, the rate of appreciation
and elapsed time. A mathematical model can be developed using a geometric sequence to
predict the land value after a given time, given a certain rate of depreciation. One such model
takes the form given below:
Y =Y o (1+r )n
Where Y o is the initial value of the property, Y is the predicted value, n is the duration in
years and r is the rate of appreciation. For example, suppose that we are told that the initial