Thursday, August 16, 2012

Algebra: An Art of Rational Thinking

Algebra is commonly viewed as a generalized arithmetic which is meant only for middle and high school level students. A more comprehensive definition says that it is a separate branch of mathematics in which letters and other symbols are used to represent numbers and quantities in formula and equations. Therefore today's teachers regard it as the laws of number and imparting it in a wrong way into their students mind, restricting them to have a true understanding of the subject.
Algebra is only for Older Students- A Myth
But our modern day scholars in mathematics believe that Algebraic formulas are not about laws of number, but it deals with the laws of rational human thinking which is discovered in the course of investigating on numbers. It has been proved that Algebra is a gateway to enhance the logical thinking ability of mind and higher mathematical learning. That's why it is more essential for the elementary students to learn the basic algebraic concepts for the development of their brains. In fact young children are far more capable of reasoning thinking than what we adult can do and this is the right age when their brain can be developed to its fullest potential. So it is of vital importance that Algebraic concepts should be included in the elementary curriculum and the teachers should be properly trained for it.
Algebra as a Mathematical Thinking Tool
"Algebra is a language. This language has five major aspects. They are unknowns, formulas, generalized patterns, placeholders and relationships. At any time that these ideas are discussed from kindergarten upward, there is opportunity to introduce the language of algebra." as quoted by Zalman Usiskin, the well known educator and director of the University of the Chicago School of Mathematics.
Algebra basics can be divided into three broad categories as problem solving skills, representation skills, and reasoning skills. It is amusing to know that these thinking tools are used in our daily lives as habits of mind on a regular basis.
Problem solving is all about deciding what and how to do in a particular given situation using tools like guess and check, make a list, work backwards etc. While mathematical representations can be expressed in many forms like visually (diagrams, pictures, graphs), numerically (tables, lists), symbolically, and verbally. The ability to create, interpret, and translate these representations can actually boosts the logical thinking of brain. Lastly, the reasoning ability which involves real life cases helps to identify patterns and relate them to a particular problem.

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