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Philosophy of Teaching Mathematics

When I was in grade school, we learned mathematics by doing problems from our math books. As a result of this, I never really liked math. To me, math consisted of books and worksheets, not of real world problems. Mathematics is an abstract concept, one that is difficult for many children to grasp. However, mathematics is one of the most relevant subjects students can learn. Mathematics has been called "the universal language," the one language that everyone in our world can speak.

The system that taught me how to do mathematics is not an effective system. Children learn various mathematical concepts, however they do not understand the reasoning behind these concepts. In order for our society to produce a new generation of mathematicians and people who love math, we must change our manner of teaching this subject.

Jean Piaget, Jerome Bruner, and Richard Skemp have all developed theories of development that say that individuals pass through various stages as they develop intellectually. Basically, these three theories parallel each other. The beginning stages all focus on the manipulation of objects. Children at these stages learn by working with objects and making connections with their hands. The next stage of learning is the pictorial. Children at this stage are learning how to move beyond manipulation and represent their objects pictorially. The final stage of learning is the abstract stage. At this stage, children are able to comprehend those abstract ideas that they could not grasp during their earlier stages. They can look at the world theoretically, understanding different concepts without having to use manipulatives or pictures. This stage is the true stage of understanding.

As teachers, we should use these ideas to teach our children mathematics. Math is not an easy concept for many children. Simply seeing numbers on a page does not help them to understand the concepts behind those numbers. In order for comprehension to take place, we must first introduce a concept using manipulatives. After students can demonstrate an idea using manipulatives, we should then move to the pictorial stage, allowing students to depict the concepts. When both of these stages have been mastered, students can then advance to the abstract stage of learning. Because students understand the concepts behind the numbers, they can easily transition into this abstract stage of learning.

If math becomes a hands-on experience, students will begin to appreciate mathematics and understand the concepts. Mathematics might become fun for students again. Too many students dislike mathematics because they do not understand it. By teaching mathematics to our students in this manner, we may open the doors to a whole new world. After all, if math is the "universal language," shouldn’t we teach this language in a manner that children can understand?


Kennedy, L. and Tipps, S. (2000). Guiding children’s learning of mathematics—Ninth edition. Belmont, CA: Wadsworth/Thompson Learning.


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