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Michael B. Dodongan Prof. Ma. Melanie Edig

August 14, 2010

A REACTION PAPER ON HOW THE NCTM DEFINES MATHEMATICS

³Mathematics is the study of patterns and relationship.´ In studying mathematics for about 16 years since my elementary years and teaching it for about 3 years now, I find it that the subejct deals about relationship existing between one quantity with the other quantity however mathematics more than the study of relationship of things but it also deals about its relationship towards other fields of discipline. It shows that it trancends to other field of discipline by in its application. Mathematics also seeks out patterns through studying the relationship and establih new conjectures through valid logic and proof. Although mathematics can be said as the study of patterns and relationship, it doesn¶t mean the subejcts is all about the patterns and relationship. Math also includes structure, change, philosophy, logic, and space. ³Mathematics is a way of thinking.´ This definition of mathematics seems to deviate the subject from the real world since this can be said that mathematicians do have own world different from the reality. Further, this definition accounts the deviancy of the mathematicians¶ thinking from the normal person¶s thinking but this definition is true! Mathematics is a way of thinking. It is an organize way of thinking, vigilant to the relationship of things. This is not a way of thinking that only nerds and high intellect can achieve and comprehend but a way of thinking that anyone can opt to follow. Instead of understanding this definition of mathematics as a deviancy of the subject from reality, this definition must be seen as mathematics is a type of thinking patterned out from what life is. ³Mathematics is an art.´ The Webster¶s universal dictionary and thesaurus defines arts as a human creativity, a skill acquired by skill and experience. Mathematics is not born overnight. It¶s like a diamond that undergone many tough process to improve its luster and become shiny to make it more perfect and so does mathematics. It was not born overnight. It has undegone numerous logical debate and thourough analysis. It was not created by one person only but it was created by whole world for the whole world. It was created with beauty of accuracy and exactness. Mathematics is an art for it possess beauty. It the creativity of human¶s imagination. It brings patterns and connections with its elements like any other arts. Artistic pieces show what life is and so does mathematics. It shows life and its beauty.

³Mathematics is a language.´ In light with the definition of a language, mathematics must have vocabulary, grammar, community who is using it and a range of meanings in order to be considered as a language. Mathematics has both visual and symbolic vocabulary. It has different meanings for a word with general usage, like set, term, group, ring etc. Thus the field of mathematics exhibits a vocabulary with specific meanings for each word and symbol. Further, it incorporates symbols other than the alphabet like , , µ, and the like. Mathematics includes diagrams and visual in its language such as graphs, figures and the like. These visual representations have specific meanings in mathematics. In mathematics we follow certain rules such as the rule of addition of integers, properties of equality, properties of equality and algorithms. We also categorize or judge a statement whether a valid proof or not valid employing the mathematical logic. These constitute the grammar of mathematics. The rules that are contained in mathematics are the grammar of the subject. There are groups of people who are obviuosly using this language, the mathematicians. They used this in their everyday life. Students in mathematics used this language too in discovering mathematical knowledge. Mathematics conveys to us. It conveys to people who are using it. It can describe the real world by using its principles. Indeed mathematics has meaning. Indeed, mathematics is a language. ³Mathematics is a tool.´ Mathematics is the queen and servant of all sciences, thus scientists rely on mathematics for intrepretation of data they gathered through scientific processes. In this case, mathematics serves as tool behind each scientific breakthrough and sucesses. In applied mathematics, the linear programming is a powerful tool for decision making as to how many products are should

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