Algebra, some of us fear it while some of us embrace it, algebra is not â€śarithmetic with lettersâ€ť it is better described as a way of thinking. At its most fundamental level, arithmetic and algebra are two different forms of thinking about numerical issues. Many of these examples have been taken from our classroom discussions while others are examples I have discovered in my own research for this paper, several examples of each will be cited. â€śLetâ€™s start with arithmetic. This is essentially the use of the four numerical operations addition, subtraction, multiplication, and division to calculate numerical values of various things.
It is the oldest part of mathematics, having its origins in Sumeria (primarily todayâ€™s Iraq) around 10,000 years ago. Sumerian society reached a stage of sophistication that led to the introduction of money as a means to measure an individualâ€™s wealth and mediate the exchange of goods and services. There are several ways to come to an understanding of the difference between arithmetic and (school) algebra. First, algebra involves thinking logically rather than numerically. In arithmetic you reason (calculate) with numbers; in algebra you reason (logically) about numbers.
Arithmetic involves quantitative reasoning with numbers; algebra involves qualitative reasoning about numbers. In arithmetic, you calculate a number by working with the numbers you are given; in algebra, you introduce a term for an unknown number and reason logically to determine its valueâ€ť (What is algebra, 2011). For example, putting numerical values for a, b, c in the familiar formula in order to find the numerical solutions to the quadratic equation is not algebra, it is arithmetic. â€śIn contrast, deriving that formula in the first place is algebra.
So too is solving a quadratic equation not by the formula but by the standard method of â€ścompleting the squareâ€ť and factoring. When students start to learn algebra, they inevitably try to solve problems by arithmetical thinking. Thatâ€™s a natural thing to do, given all the effort they have put into mastering arithmetic, and at first, when the algebra problems they meet are particularly simple (thatâ€™s the teacherâ€™s classification as â€śsimpleâ€ť), this approach works. In fact, the stronger a student is at arithmetic, the further they can progress in algebra using arithmetical thinking.
For example, many students can solve the quadratic equation x2 = 2x + 15 using basic arithmetic, using no algebra at all. Paradoxically, or so it may seem, however, those better students may find it harder to learn algebra. Because to do algebra, for all but the most basic examples, you have to stop thinking arithmetically and learn to think algebraicallyâ€ť (What is algebra, 2011). The need for algebra does not make it any easier to learn but in todayâ€™s world with the technology it embraces, it is essential that we develop our thinking skills to match what todayâ€™s world requires.
The use a computer is one of those essential skills and being able to use that computer efficiently to do arithmetic requires algebraic thinking. Ways That Algebra Affects Business or Science There are many ways that algebra affects business and science and in several diverse approaches. These include the fields of astronomy, biology, chemistry, construction, economics, education, environment, finance, geometry, government, health/life sciences, labor, physics, sports/ entertainment, statistics/ demographics, technology and transportation.
To highlight a few for examples let us start with astronomy, astronomers use math all the time. â€śOne way it is used is when we look at objects in the sky with a telescope. The camera that is attached to the telescope basically records a series of numbers – those numbers might correspond to how much light different objects in the sky are emitting, what type of light, etc. In order to be able to understand the information that these numbers contain, we need to use math and statistics to interpret them.
Another way that astronomers use math is when they are forming and testing theories for the physical laws that govern the objects in the skyâ€ť (Real Life Applications of Algebra, 2013). Almost all consumer math involves calculating transactions. This ranges from calculating change to interest on a loan. Algebra can be used to fill in the blanks for more complex equations such as calculating the total loan and interest given a fluctuating rate, very necessary in todayâ€™s world and markets.
Yet another example is the use of algebra in the construction business, it is widely known for calculating square footage, cubic footage, and angles when building. â€śMathematics in algebra is used by construction workers in many ways. When setting out a site, mathematics is used to get the dimensions correct. It is also used calculating the amount of materials to order, and when cutting materials to size. Very few tasks do not involve some use of mathematicsâ€ť (Real Life Applications of Algebra, 2013).