Mathematics
probably originated from man using his fingers to indicate, "How many?"
From fingers man moved to using pebbles in a relationship of one-to-one
to keep record of the number of a specific item he owned, such as a pebble
for each goat that he owned. The Egyptians and the Babylonians were among
the first to construct a device (the abacus) for computing as the need
for mathematics evolved. The history of mathematics development indicates
that the Chinese also devised an abacus which was different from the abacus
used in the Middle East. Symbols were soon devised to record the results
of the mathematics calculating on an abacus. We know that different civilizations
developed different methods for recording mathematics.
In Europe,
as an outgrowth of the abacus, a counting board was devised. It was very
difficult to manipulate on the counting board so it became necessary to
devise a computational system. History seems to indicate that the people
of India were among the first to develop a usable computation system and
then it was passed along to the Arabs. Today, we still are using the numeration
system developed at that time.
The Arabs
are probably the first to develop algorithms for calculation. Algorithms
are a set of systematic procedures for handling recurrent mathematics situations.
Today we use algorithms as the techniques in solving arithmetic situations.
We use algorithms because they are quick and efficient in producing correct
results. However, with the invention and introduction of calculators and
computers, these devices can do the calculating much more rapidly then
using paper, pencil, and algorithms.
Our definition
and understanding of what mathematics is is an outgrowth of an evolution
of the mathematics processes over hundreds of years. Computers and calculators
have revolutionized how an information world deals with mathematics and
thus has revolutionized our definition of what mathematics is.
In many classrooms,
learning is conceived of as a process in which students passively absorb
information, store it in easily retrievable fragments as a result of repeated
practice and reinforcement. The common understanding of what mathematics
is today seems to be calculating to obtain one correct answer. The procedure
seems to be that students are to memorize many mathematical facts, apply
these ideas to algorithms when they seem appropriate in order to solve
our daily mathematics needs. The procedure seems to be to memorize a group
of unrelated facts, use these facts in algorithms, follow memorized rules,
break problems into subparts, and generate a result.