Abstract
M.Ed.
Our world is becoming more mathematical. We are constantly surrounded by
mathematical situations and are regularly required to make mathematical
decisions. These decisions require number sense, estimation skills, ability to
analyse data intelligently, knowledge of two and three-dimensional geometry and
many other abilities not often taught in school. Halpern (1992:1) states:
"...as a nation we not only need competent scientists and engineers, we also need
a citizenry that is literate in mathematics issues."
Reyes and Stannic (1998:26) support this view as they state:
"Knowledge of mathematics is essential for all members of our society. To
participate in our democratic processes and to be unrestricted in career choice and
advancement, people must be able to apply mathematical ideas."
Learners leaving school need to be able to use available technology and to reason
mathematically, be confident of their abilities, be able to communicate mathematically
and be problem solvers.
The introduction of technology into the lives of many people has called upon their
background of mathematics to cope with mathematical problems and manipulating
technological instruments. The relationship between mathematics and technology
is emphasised by Dowling and Noss (1990:24) when they say: "New technology is
a powerful tool which opens up new areas of mathematics and changes the way in
which society makes use of mathematics in the factory, office and home".
The Cockcroft Committee (1982), in their report on an inquiry into the teaching of
Mathematics in schools, sees the main task of mathematics teachers as:
"Enabling each learner to develop within his own capabilities the mathematical
understanding and skills required for adult life, for employment and further study".
The most important contribution for the purpose of this study, was the emphasis
placed on cognitive aims to equip learners with numerical understanding and skills.
Other contributions were to develop logical thinking and to expand their ability to
look for patterns and explain them and to develop an awareness of the link
between mathematics and everyday situations. This report (1982) motivated the
researcher to review how teachers are teaching. This means that there will be an
investigation into how children learn mathematics and not just what should be
taught. Naidoo, Smit and Van Heerden (1995:7) also emphasise this by stating
that "...the advance in technology at this time changed educational thinking more,
making it even more important to further investigate how children actually learn."
Yildirim (1994:28) argues that "... improving student's thinking ability is accepted as
an important goal of education, and schools are considered places where thinking
skills can be promoted. However, ways in which this should be done is a matter of
controversy among educators." He further postulates that the best way to improve
student thinking involves deep and thoughtful subject matter instruction in which
students are encouraged to think reflectively rather than to merely cite the facts.
The central characteristics of mathematical thinking are the determination of
relationship and their application. It includes the ability to analyse a given situation
or experience; to distinguish between applicable data and those which are not
applicable; to classify and arrange these data; to abstract relationships from them,
and finally to symbolize them for future use and application in new situations.
Therefore it is important and essential for students to be taught how to approach
the problems. This is one way of encouraging inquisitive and creative
mathematics. Well-developed thinking skills are useful in almost every life
situation, therefore there is a need to design instructional programmes that focus
on the acquisition and uses thinking skills that are needed to find and solve
mathematical problems.