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?