I have to admit that I have never been one of the students to ask a teacher ‘Why do we have to learn this?’ Perhaps I already saw the applications of Mathematics at an early age or knew that I would need these concepts to succeed in University Mathematics courses. More likely, I was good at math and liked doing the ‘drill and kill’ problems. I didn’t think I had to have a reason for learning it other than there was a ‘right’ answer and I enjoyed finding it. Most students, however, are not like me at all. I have been lucky enough, or probably just do not have enough experience yet, never to have had a student ask me The Question (which ‘Why do we have to learn this?’ will be referred to from now on in this post).
Depending on the student and the situation, I think I would have different answers.
For a student that I think would respond to humour, I would direct them to the following article:
and make a joke about them not wanting to be an uneducated or uninformed consumer.
For a student that enjoys English, I would direct them to this article and make a joke about how even authors incorporate mathematical concepts in their writing.
If the whole class was having a problem with what we were doing, I would explain that understanding mathematics allows us to:
· Manage our time and money
· Understand patterns in the world
· Solve problems using reasoning skills
· Use technology
· Be aware of what makes the objects around us work (search engines, technology, motion, etc.)
If students needed a more concrete answer than the one previously mentioned, I would explain how the following topics that are covered in the Pre-Calculus stream of mathematics in my province are/should be relevant to them.
Trigonometry (specifically the use of radians) – Who decided there were 360 degrees in a circle? Isn’t this arbitrary? Radians are not an arbitrary measuring unit. They are based on the intrinsic properties of a circle. Therefore, many complicated trigonometric expressions can be easily reduced and simplified with the use of radians.
Function Transformations – Function transformations relate a function to its corresponding graph. Functions describe many real life phenomena and the graphs of these functions are sometimes more easily interpreted than the function itself. These graphs show you a picture of what is happening. With knowledge of function transformations, you can determine how the different parts of a function (coefficients, degrees, positive or negative) affect the graph of a function, and therefore the interpretation of the data a function represents.
Exponents and Logarithms – The functions have many applications including modelling population growth, exponential growth and decay, logarithmic scales eg. Richter scale, pH scale, and they are even used to model the cooling of a dead body (what student wouldn’t find a crime scene application interesting?).
Radical & Rational & Polynomial Functions – used to model real world phenomena
Permutations and Combinations – The ordering of groups and the number of different grouping possibilities has many applications, especially those related to probability, e.g. the probability that a certain arrangement of runners will win a race. Permutations and combinations can also help you discover the number of different locker combinations, the number of different license plate numbers, and the number of different poker hands.
Of course, all of the above information will never answer ‘The Question’ for a student who doesn’t want to see the necessity or use of mathematics around them. For those students, I have no answer ...