According to research, mathematics teaching is both an art and a science. An effective teacher integrates theory with practice. It is the theories about teaching and learning that provide a framework for analyzing learning situations and improving classroom instruction. To develop one’s philosophical framework for teaching mathematics, we begin by understanding the nature of mathematics.

The National Council of Teachers of Mathematics (NCTM), the largest organization of mathematics teachers in the world, defines the nature of mathematics as follows:

1. Mathematics is a study of patterns and relationships.

Mathematics ideas are interwoven with each other. Students must explore the recurring ideas or the patterns, and discover the relationships between and among them.

2. Mathematics is a way of thinking.

The problem solving activities and various lessons in mathematics train us to think logically. In a way, mathematics provides us with the thinking skills needed to confront everyday problems.

3. Mathematics is an art.

Mathematics is characterized by order and internal consistency. Numerous patterns can be found in numbers and geometric figures. Tessellations, weaving, and tiling are a few explicit examples of mathematics in art. By exploring the orderliness and consistency of mathematics, we learn to appreciate its beauty.

4. Mathematics is a language.

It is used to communicate complex processes and thoughts efficiently using symbols and specific and precise terms. Mathematics has its own register or special vocabulary, which students have to learn to be able to communicate well about mathematics and to speak and think like mathematicians. Teachers should not use “equal,” “congruent,” and “similar” interchangeably as these terms mean different things.

5. Mathematics is a tool.

Many occupations require the knowledge of mathematics. Scientists, engineers, businessmen, and many other professions use a great deal of mathematics to do their work.

By: Ms. Patricia B. Mojica | Teacher II | Sto. Domingo Elementary School

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