Why Study Mathematics? NAME: ______________

There are still many jobs that may not require much mathematics, except perhaps for simple arithmetic like counting money and telling time, e.g., actors and actresses, taxi drivers, administrators, historians and language teachers. How often do they use, for example, algebra, in their workplace? Why study so much mathematics when many adults do not even use it in their professions? Isn’t it a waste of time and resources?

1. What jobs have you had that required math?

2. What jobs have you had that did not require math?

The needs of the society may differ from the desires of individual students: individual students may not be interested to learn mathematics partly because they do not see the use of it, especially when most applications in the workplace are beyond their level, and partly because they may not be interested in professions that require a lot of mathematics. Therefore, there is a need to convince these students why they still need to study mathematics, and other subjects, which they may not need in their future working life.

Rationale 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.

3. What career would you like to have in the future?

4. Do you feel you have the ability to pursue that career?

5. How likely is it that you will have the opportunity to pursue that career?

6. Is this the only career ambition you have ever had?

7. What was your or were your previous career ambitions?

So, what will happen if students are allowed to specialize early? If their interests are to change later, it will be too late to switch to another subject. Moreover, some students cannot decide at this moment what job they want to do in future, so it is impossible to force them to choose now.

Therefore, this is the basis of a broad-based school curriculum, to teach students the basics of different subjects so that when they need it in their area of specialization later on, they will have some foundations to build upon.

Another reason for a broad-based curriculum is to expose students to different subjects so that they can find out where their interests lie.

8. What is your favorite subject in school right now?

9. What was your favorite subject in elementary school?

Examples of How Mathematics is Applicable in our Daily Life

Use of Similar Triangles in Radiation Oncology - 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.

Encoding of Computer Data using Large Prime Numbers

10. Do you use online banking?

11. Do you feel that your online banking data is secure?

Before computer data are sent through the Internet, especially sensitive data like online banking, they are encoded so that hackers cannot make use of the data unless they know how to decode. Ronald Rivest, Adi Shamir and Leonard Adleman have invented the very secure RSA cryptosystem, which makes use of very large primes and a complicated number theory. To break the code, hackers need to decompose a very large composite number into its two very big prime factors using trial division. Even with the fastest computers, this will take years.

Use of Differentiation in Economics

12. Can you think of a product or service that that you used to use but you stopped because the price increased?

Economics uses differentiation extensively. For example, retailers are interested to find out whether an increase in the price of a product will cause the demand to drop so drastically that the total revenue will fall? Or will the demand drop only slightly such that the total revenue will still increase? In economics, this is called the price elasticity of demand and it measures the degree of responsiveness in the quantity demanded of a commodity as a result of a change in its price.

13. Do you have GPS navigation in your vehicle or on your smart phone?

GPS (global positioning system) makes use of complex vectors and geometric trilateration to determine the positions of the objects.

An inspiring story is the ingenious plug-in called Auto-Tune that can transform mediocre singing into note- and pitch-perfect singing. The inventor is Andy Hildebrand who has worked for many years in the oil industry by providing an accurate map of potential drilling sites using sound waves sent into the ground and recording their reflections. This technique, which uses a mathematical formula called autocorrelation has saved oil companies lots of money and allowed Hildebrand to retire at 40! After retirement, at a challenge from a dinner party guest to invent something that would allow her to sing in tune, he invented Auto-Tune, which also uses autocorrelation.

Conclusion - Mathematics is of practical value in many professions. It is not just the mathematical knowledge itself but the thinking processes acquired in genuine mathematical problem solving and investigation that can be applied to unfamiliar situations in other fields. Mathematical knowledge and processes are also useful outside the workplace in everyday life to understand and interpret certain events and news reports so as not to be deceived or swayed by others’ opinions without any reasonable basis, thus improving one’s own quality of life when one is able to lead a meaningful and responsible life.