26-11-2012, 12:40 PM
Why Study Mathematics? Applications of Mathematics in Our Daily Life
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Abstract
Most students would like to know why they have to study various
mathematical concepts. Teachers usually cannot think of a real-life
application for most topics or the examples that they have are
beyond the level of most students. In this chapter, I will first discuss
the purposes of mathematics, the aims of mathematics education
and the rationales for a broad-based school curriculum. Then I will
provide some examples of applications of mathematics in the
workplace that secondary school and junior college students can
understand. But students may not be interested in these professions,
so I will examine how mathematics can be useful outside the
workplace in our daily life. Lastly, I will look at how mathematical
processes, such as problem solving, investigation, and analytical
and critical thinking, are important in and outside the workplace.
Introduction
When teachers try to convince their students that mathematics is useful in
many professions, such as engineering and medical sciences, many of
their students may not be interested in these occupations. For example,
when I was a teacher, some of my students wanted to be computer game
designers instead, but they wrongly believed that this profession did not
require much mathematics: only when I demonstrated to them that
computer programming required some mathematics did they show any
interest in studying mathematics. Other students of mine aspired to be
soccer players but they did not realise that the sport could involve some
mathematics: they erroneously thought that they would have to kick the
ball high enough to clear it as far away as possible; obviously, it could
not be at an angle of 90° from the ground but they believed it to be about
60° when in fact it should be 45°. Although this is a concept in physics,
kinematics is also a branch of mathematics, not to mention that
“mathematics is the queen of the sciences” (Reimer & Reimer, 1992, p.
83) ⎯ a famous quotation by the great mathematician Carl Gauss (1777-
1855). Mathematics can also help soccer players to make a more
informed decision if they know which position on the soccer field will
give them the widest angle to shoot the ball between the goalposts (for
more information, see Goos, Stillman & Vale, 2007, pp. 50-58).
Rationales for a Broad-Based School Curriculum
Many students have ambitions but how many of them will end up
fulfilling them? Just because a student wants to be a doctor does not
mean he or she has the ability or the opportunity to become one. In
Singapore, there is a limited vacancy for studying medicine in the
university because the government does not want an oversupply of
doctors (which is a popular choice of career here) and an undersupply in
other jobs since the only asset that Singapore has is its people as there are
scarce natural resources. So, even if a student has the aptitude to become a doctor, he or she may still lose out to the more academically-inclined
students, and unless the student’s parents have the means to send him or
her overseas to pursue his or her ambition, the student will most likely
end up with another job. This is the first thing that teachers can impress
upon their students.
Applications of Mathematical Knowledge in the Workplace
What are in the Singapore secondary syllabus and textbooks are mostly
arithmetical applications such as profit and loss, discount, commission,
interest rates, hire purchase, money exchange and taxation. But what
about workplace uses of algebra, geometry, trigonometry and calculus?
Usually, many of these applications are beyond the level of most
students. However, this section will illustrate some suitable real-life
applications which teachers can discuss with their students.
Use of Similar Triangles in Radiation Oncology
Geometry plays a very important role in radiation oncology (the study
and treatment of tumours) when determining safe level of radiation to be
administered to spinal cords of cancer patients (WGBH Educational
Foundation, 2002). Figure 1 shows how far apart two beams of radiation
must be placed so that they will not overlap at the spinal cord, or else a
double dose of radiation will endanger the patient.