I've commented on Mathematics in the past but some recent discussion are moving me towards it again. Last time I discussed reasons people may despise math. This time, I would like to look at why math is considered a critical skill college - or at least critical enough to be required for general education. The most well known course for the Quantitative Literacy requirement is MATH 1050 - College Algebra, but it may be one of up to five course options. The office I work in has been tasked with enforcing the math completion policy for our university, so I hear plenty of students complete about, berate, and in so many other way despise the policy, math, math teaching, and everything else related. As the messengers of this policy our staff has be metaphorically shot at on a regular basis. This was the catalyst of the previous post, but I would like to provide an answer to those students who may ask, "When will I ever use this?" It is a fair question and deserves an answer.
My high school math teacher, when confronted with this question used to say, "You won't [use this]. This is to make you think." I feel that this is the most accurate answer to the proffered question. There is a lot in mathematics that is either specialized for specific calculations, or they are more abstract concepts that are the foundation for those specific calculations. With that said, that instructor taught my trigonometry class and as well as other classes required for calculus. Algebra, the basis for all other advanced mathematics, is used more often. I would like to split the usage into two areas: unconscious calculations and intentional calculations.
Unconscious calculations are the ones that you do without even thinking about it. Every time you get in a car and drive you brain is processing velocity, acceleration, position, distance, and time equations faster than your reflexes can even respond. The same is true of any physical activity or sport - to catch a ball is an exercise in those same factors so you know where to move your hand. The world you live in can be described in numbers, vectors, shapes, solids, and velocities. Without your brain's ability to do math people would never had killed enough food to evolve past subsistence level of living. All of this is algebra. This is not to say that if you have difficulty in solving algebra problems in your math book that you are a bad driver. The math that our brain does without thinking about it is intuitive. But if we consider those calculations that we do intuitively - then the answer to our questions is, "Every moment of every day."
Intentional calculations are the ones we actively choose to do or the ones that our math classes require us to do. Even thought these are a active choice there are certain calculations we do all the time without thinking about it. Anytime you look at a clock to see how much time you have, you are doing algebra.
available funds - (original price * discount percentage) = new available funds
These two examples may be obvious to most people. Those same people may come back and say that use calculations do not require exponents or fractions. That is true, for the most part - some purchases may be very complex. Even if such calculations are not very complex by studying algebra you are practicing skills that you use every day. The more practice you have the better you get at them, the better you get the more consistently accurate you are and the fast you are. Until such equations, no matter how complex may be.
There are other areas where intentional calculations come into play. Many hobbies that people do use math, including: wood workings (or other building hobbies - measuring, scale, etc.), cooking (one of the few places that people intentionally calculate fractions), gambling (probability), and many other games of all kinds (angles in strategy games, keeping and maximizing score, fields of view, the list goes on.) Again, these may not require exponents or logs, etc, but those develop complexity and give practice. You cannot be good at something unless you are stretched.
The last place that I want to mention that people use algebra every day is in problem solving. I don't think it's a coincidence that the individual calculations that we are required to solve in math classes are referred to as math problems and that the process of resolving difficulties as problem solving. I don't know which came first, perhaps it's an example of the chicken vs. the egg, but regardless math problems and problem solving go hand in hand. Just like we can describe the vast majority of our physical world in terms of mathematics many of our social, emotional, and mental situations can also be labeled in terms of mathematics.
Perhaps next week I'll go into the biggest reason that math is taught in college in what I call the unknown expectation of college. But until then, I think this is sufficient.
My high school math teacher, when confronted with this question used to say, "You won't [use this]. This is to make you think." I feel that this is the most accurate answer to the proffered question. There is a lot in mathematics that is either specialized for specific calculations, or they are more abstract concepts that are the foundation for those specific calculations. With that said, that instructor taught my trigonometry class and as well as other classes required for calculus. Algebra, the basis for all other advanced mathematics, is used more often. I would like to split the usage into two areas: unconscious calculations and intentional calculations.
Unconscious calculations are the ones that you do without even thinking about it. Every time you get in a car and drive you brain is processing velocity, acceleration, position, distance, and time equations faster than your reflexes can even respond. The same is true of any physical activity or sport - to catch a ball is an exercise in those same factors so you know where to move your hand. The world you live in can be described in numbers, vectors, shapes, solids, and velocities. Without your brain's ability to do math people would never had killed enough food to evolve past subsistence level of living. All of this is algebra. This is not to say that if you have difficulty in solving algebra problems in your math book that you are a bad driver. The math that our brain does without thinking about it is intuitive. But if we consider those calculations that we do intuitively - then the answer to our questions is, "Every moment of every day."
Intentional calculations are the ones we actively choose to do or the ones that our math classes require us to do. Even thought these are a active choice there are certain calculations we do all the time without thinking about it. Anytime you look at a clock to see how much time you have, you are doing algebra.
current time + (how much time) = target time.Any time you use money, particularly cash, you use algebra. This is very true when figuring out a tip, a discount, or other promotions.
available funds - purchase price = new available funds
original price * discount percentage = new priceFactor that into the original equation:
available funds - (original price * discount percentage) = new available funds
These two examples may be obvious to most people. Those same people may come back and say that use calculations do not require exponents or fractions. That is true, for the most part - some purchases may be very complex. Even if such calculations are not very complex by studying algebra you are practicing skills that you use every day. The more practice you have the better you get at them, the better you get the more consistently accurate you are and the fast you are. Until such equations, no matter how complex may be.
There are other areas where intentional calculations come into play. Many hobbies that people do use math, including: wood workings (or other building hobbies - measuring, scale, etc.), cooking (one of the few places that people intentionally calculate fractions), gambling (probability), and many other games of all kinds (angles in strategy games, keeping and maximizing score, fields of view, the list goes on.) Again, these may not require exponents or logs, etc, but those develop complexity and give practice. You cannot be good at something unless you are stretched.
The last place that I want to mention that people use algebra every day is in problem solving. I don't think it's a coincidence that the individual calculations that we are required to solve in math classes are referred to as math problems and that the process of resolving difficulties as problem solving. I don't know which came first, perhaps it's an example of the chicken vs. the egg, but regardless math problems and problem solving go hand in hand. Just like we can describe the vast majority of our physical world in terms of mathematics many of our social, emotional, and mental situations can also be labeled in terms of mathematics.
If X happens, then Y will occur. But if I don't want Y to occur, then I must do Z.Anytime you have a situation with any number of possible outcomes the ability to reason is key. That reasoning is often termed logic and is the basic language of mathematics. The ability that you gain in learning how to arrange, manipulate, and see the relationships in numbers translates to other kinds of problems as well. So even though you may never use numbers in your future equations, algebra is again proven to be helpful in everyday interactions and situations.
Perhaps next week I'll go into the biggest reason that math is taught in college in what I call the unknown expectation of college. But until then, I think this is sufficient.
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