Mathematics in Daily Life

Waxing eloquently on the basic importance of Mathematics in human life, Roger Bacon (1214-1294), an English Franciscan friar, philosopher, scientist and scholar of the 13th century, once stated: "Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of the world." And the ingenuity of his statement is there before us to see, in this Internet era.

However, mathematics, in itself, has all the ingredients that make it a universal language shared by all human beings irrespective of culture, religion, or gender. Pi is always 3.14159 regardless of where we are. Similarly, the elemental mathematical processes (like addition, subtraction, etc.) never get changed due to a change in the location or for any other reason whatsoever. These all say about the close intertwining of mathematics in our daily life.

At a time when even a common man is being increasingly dependent upon the application of science and technology in the day-to-day activities of life, the role of mathematics has undoubtedly been redefined. Right from getting up in early hours of the day to the ringing of an alarm, to wait for the counts of whistles of the cooker, to exchange currency at a ticket outlet while availing a public conveyance, almost every next moment we do the simple calculations at the back of our mind. Of course, these are all done pretty unconsciously without a thought being spared for the use of mathematics on all such occasions.

Reading time on a watch, rounding a date on a calendar, checking up the mileage of your car, halting at the filling station, attending to a roll call at school, getting scores in the class exams, scoring in a game, betting on a horse race, preparing a recipe in the kitchen, - the list is just endless if one goes on to note down the situations when our computational skill, or more specifically, simple mathematics comes to play a role. It scares us to certain extent to think of a life without any knowledge of calculation or computation, or in other words mathematics. In many a case, lack of a formal education hardly affects gaining a relative mastery in these computational skills which are so essential in our daily life.

At a psychological level, exposure to mathematics helps in developing an analytic mind and assists in better organization of ideas and accurate expression of thoughts. At a more general level, far away from dealing with the higher mathematical concepts, the importance of mathematics for a common man is underpinned whenever he visits banks, shopping malls, railways, post offices, insurance companies, or deals with transport, business transactions, imports and exports, trade and commerce, and the ilk. Even when we think of role of mathematics in our recreational activities, we surprisingly have a list that runs quite long: video games, computer games, puzzles, riddles, and so on.

It ensues from the above discussion that a modern life style seems completely handicapped and at times, highly improbable, in the absence of mathematics. For, unless we are well versed in the language of numbers, we would find it difficult to reach at important decisions and perform everyday tasks. Be it to shop wisely, or buy the right insurance, or refashion a home within a budget, knowledge of mathematics holds the key, and hence, barely necessary.
from http://www.articlesbase.com/k-12-education-articles/mathematics-in-daily-life-390556.html

Learning Mathematics Through Mastery of Concepts

There are many ways to learn a subject. Different people has different learning style. However, regardless of learning style, there are two particular ways to learn knowledge within any style. The first way is memory method. This way of learning focuses on remembering facts and details, and recalling them when required. The second method is to understand the underlying concepts of the facts. It is the "what" versus the "how" and "why". Either way has their merits and demerits. It depends on the education level and complexity of the subject matters. Sometimes, a hybrid of both are necessary to reap the best possible results, especially in learning mathematics.

For elementary mathematics level, the amount of mathematical facts and concepts to be learned are marginal, and only serves to lay foundation for further advancement into higher mathematics learning. At the basic level, memory method of learning may be acceptable and manageable. But how about maintaining this way when one progresses into higher mathematics studies?

At a higher level of mathematics learning, the learning taxonomy moves into the application level and beyond. Mastery of concepts becomes an important factor in analyzing and solving more complex mathematics questions. Mathematical equations and expressions get more integrated with detailed concepts. Pure memory will not be able to extract out the true meaning of these equations and expressions. A few mathematical tools may be required to solve a mathematics problem. This combination of solving methods and concepts rendered pure memory way of learning mathematics unacceptable. The scope to cover all possible combinations of solving tools and questions is far too wide to manage. Staying firm with this facts-remembering method will only cause the performance and outcome to dwindle low. This will reduce the motivation to study and may decline towards the fearful mathematics anxiety situation.

Studying mathematics is different from other subjects in that a unique language is used to present mathematical meaning. Symbols and variables are used to form relationships and conditions. Many in-depth concepts are embedded into these few symbols and variables, including mathematical operators. True mastery of the mathematics concepts is therefore needed. However, it should not be said that memorising facts are completely useless at the higher level of mathematics education. It still serves its purpose in that they are the basic ingredients for the brain to link up with the solving methods and conceptual approach. It is these linkages or bondings that retain and strengthen the acquired knowledge longer. This is real mastery of the subject and its topics. A hybid of both learning methods is therefore necessary to achieve a level of acceptable comprehension with more emphasis going towards mastery of concepts.

In conclusion, time causes facts to fade off. Memorising facts will therefore not last long. A better learning platform is to focus on relationship and concept mastery. Linking facts to solving strategy becomes a useful problem-solving skill and has the benefit that it will last longer. Understanding the "why" and "how" is better when they complement the "what". Resistance to studying advance mathematics will then be lowered when the correct method of learning mathematics through mastery of concepts is applied.
from  http://www.articlesbase.com/science-articles/learning-mathematics-through-mastery-of-concepts-246250.html