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This standard
connects the other standards to assessment systems, assessment
purposes, curriculum, and instruction.
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Assessment should be a coherent process.
Coherence in assessment
involves three types of agreement. First, the assessment process
forms a coherent whole; the phases fit together. Second, the
assessment matches the purposes for which it is being done.
When the design, evidence-gathering, evidence-interpreting,
and action phases of the assessment process are consistent
with one another and with the purposes of the assessment,
it has educational value. Third, the assessment is aligned
with the curriculum and with instruction. Students’ learning
connects with their assessment experiences.
A coherent mathematics
assessment system assures that assessors will develop activities
and performance criteria tailored to the purposes of each
assessment. An assessment framework is useful in judging whether
all parts of the process are in harmony, from the design stage
to the stage of reporting and using results. The assessment
process then unfolds as a logical and coherent whole.
The Coherence Standard
has several implications. Just as no single instrument section
makes a great orchestra, a coherent mathematics assessment
system cannot be based on paper-and-pencil tests alone. Instead,
a balance among appropriate and diverse assessment activities
can help all students learn.
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| See
"A Balanced Assessment System" on page 60 for an example
of assessment activities where all students can learn. |
A coherent mathematics
assessment system requires that activities be chosen that
are appropriate to the purpose at hand. A teacher would not
use a test on linear equations to assess students’ knowledge
of quadratic equations, or a test of procedural skills to
indicate students’ conceptual knowledge, or a computation
test to assess problem-solving performance.
Coherence in assessment,
however, raises broader issues than simply selecting an appropriate
test or activity. Coherence relates to all aspects of the
assessment process.
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"The
purpose of an assessment … should dictate the kinds of
questions asked, the methods employed, and the uses of the
resulting information."
–NCTM
(1989, p. 199)
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External assessment
programs are moving away from an extensive reliance on machine-scored
multiple-choice items to a greater use of performance tasks
and to the use of multiple sources of information. Assessment
activities for such programs, however, can be expensive to
develop, administer, and score. The programs may entail costs
in the form of instructional time taken away from other activities
if they are not integrated into instruction. Greater investments
of time and funding may be required, which means that people
may expect more information from the assessments. As assessment
programs change, the pressure to make a single assessment
serve multiple purposes is likely to increase. Consequently,
special vigilance may be needed to assure that all the uses
to which assessment information is being put are in harmony
with the purposes of the assessment.
Mathematics teachers
organize, conduct, and interpret assessments as part of their
ongoing mathematics instruction. When mathematics assessment
is a coherent process, teachers and students benefit because
they are not confronted by conflicting demands. Attention
to coherence underscores the principle that assessment needs
to be in step with instruction. When assessment fits the curriculum,
students can see that assessment activities not only are related
to the mathematics they have learned but also serve clear
goals. As students understand how assessment is connected
to what they are learning, an increase can be expected in
the number of students who will choose to continue their study
of mathematics.
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| "Assessment
is the guidance system of education just as standards are the
guidance system of reform."
–Mathematical
Sciences Education Board (1993, p. 2)
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Assessment developers in local and provincial or state agencies
play a vital role in making sure that the assessments of students’
mathematics learning form a harmonious whole as they progress
through school. A single assessment touches only a part of the
mathematics that students know and can use, but the totality
of the assessments students encounter provides a comprehensive
picture of their knowledge, skill, and understanding.
To determine how coherent
an assessment process is, ask questions such as these:
- How is professional
judgment used to ensure that the various parts of the assessment
process form a coherent whole?
- How do students
view the connection between instruction and assessment?
- How does the assessment
match its purposes with its uses?
- How does the assessment
match the curriculum and instructional practice?
- How can assessment
practice inform teachers as they make curriculum decisions
and determine their instructional practices?
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