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Evaluation of students' achievement is an essential part of mathematics education.
Monitoring and evaluation are necessary to assess students' readiness for new learning,
to give teachers feedback on the success of their methods and approaches, and to assist
planning for new learning.
Evaluation includes diagnostic assessment procedures which enable teachers to discover
difficulties that individual students may be having. Appropriate diagnostic assessment
may reveal that the reason for a particular student's lack of progress is a lack of
understanding achieved at some earlier time, and the difficulty may be relatively easily
addressed. Diagnosis may also reveal that the student is very talented and is simply
bored by lack of stimulation. Diagnostic assessments enable teachers to plan further
learning activities specifically designed to meet the learning needs of individual
students. Worthwhile diagnosis is very often carried out by simple question and answer
interaction in the classroom.
Assessment should focus both on what students know and can do, and on how they
think about mathematics. It should involve a broad range of mathematical tasks and
problems and require the application of a number of mathematical ideas. Skills
assessed should include the ability to communicate findings, to present an argument,
and to exploit an intuitive approach to a problem.
Assessment should, as far as possible, be integral to the normal teaching and
learning programme. Continuing assessment as part of the teaching and learning programme
increases the range and quality of assessment which can be carried out for good diagnosis,
and avoids the artificial intrusion on learning and teaching time which is associated
with separate assessment sessions. Assessment should involve multiple techniques including
written, oral, and demonstration formats. Group and team activities should also be assessed.
Teachers should avoid carrying out only tests which focus on a narrow range of skills
such as the correct application of standard algorithms. While such skills are important,
a consequence of a narrow assessment regime which isolates discrete skills or knowledge
is that students tend to learn in that way. Mathematics becomes for them a set of separate
skills and concepts with little obvious connection to other aspects of learning or to their world.
Assessment should also be undertaken to provide students and their parents with an indication
of a student's progress. In summarising the results of evaluations of students' achievement,
teachers should report what students have been working on, what they have achieved, and how well
they have achieved it. A grade, level, or mark alone is insufficient.
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