Abstract
D.Ed.
During the past few years the teaching of mathematics has been characterized by a move
away from the traditional teaching methods. With a view to improving the effectiveness
of teaching and learning mathematics, the emphasis has shifted from the product to the
process. The mathematical skills that need to be developed in pupils include strategies for
the solving of real problems. This represents a shift from the application of mathematics
to solve problems to problem solving as a teaching method. The application of a problemcentred
approach in the teaching of mathematics has given rise to a need for instruments
that will facilitate multidimensional assessment. This requires the revision, adaptation and
expansion of the structure of existing assessment techniques. A need was identified for
the formulation of clear guidelines for the assessment of pupils' mathematical competericies.
Data obtained from relevant literature and from questionnaires designed for the purpose
of this study were used to compile guidelines for the assessment and evaluation of mathematics
pupils. New assessment methods make new demands on the designers and users of assessment
instruments, and the assessment of pupils' problem solving skills make high demands on
mathematics teachers. It requires a thorough knowledge of, and insight into how pupils
learn mathematics. The teacher is a facilitator, a catalyst and a provider of information
who teaches pupils the language of mathematics by teaching them the necessary terminology
and symbolism. Because of the diversity that is present in the way pupils respond,
the assessment of their problem-solving ability is a complex process. It is therefore very
important that mathematics teachers be equipped with extensive assessment skills.
Assessment is a complete reporting on the knowledge of the pupils; it is the tool employed
to measure progress. It describes the present situation by collecting the data required for
evaluation. Evaluation can be defined as the awarding of a value to progress made and
conclusions arrived at on the basis of the total body of information collected. Every single facet that influences the pupils' achievement in mathematics must be
assessed in order to form a complete image of their mathematical abilities. It is therefore
essential to assess both cognitive and the affective facets. To ensure the reliability of the
data collected with a view to assessment, a variety of assessment techniques need to be
employed.
Any report on the pupils' demonstration of the achievement of the desired outcomes must
be more comprehensive than a single mark or symbol. Separate reports must be compiled
in respect of cognitive progress and affective aspects. Pupils should receive clear guidelines on what the expected outcomes are, and on how
and when assessment will be conducted. Criteria for monitoring the standard of assess .-
ment must be formulated by the teacher, whose duty it is to inform the pupils fully on
these. Validity and reliability are important considerations in testing. Assessment serves
to emphasize the most important mathematics to be learned.
The choice of assessment techniques is extremely important. A policy of continuous
assessment ensures that the final decision is not based on the result of a single examination.
However, promotion or the awarding of credits must be based on more than the
result of a continuous formative assessment. Summative final examination assessment
place the final stamp on knowledge, without which it would have been impossible to conduct
an evaluation.