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Although assessment
is done for a variety of reasons, its main goal is to advance students’
learning and inform teachers as they make instructional decisions.
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Assessment should
enhance mathematics learning.
As an integral part of mathematics
instruction, assessment contributes significantly to all students’
learning. Because students learn mathematics while being assessed,
assessments are learning opportunities as well as opportunities
for students to demonstrate what they know and can do. Moreover,
assessments, including those external to the classroom, guide subsequent
instruction, and thus they can further enhance students’ learning.
Students can also themselves use assessments to become independent
learners. They can do so by using assessments as indicators of the
mathematics important for them to learn. Although assessment is
done for a variety of reasons, its main goal is to advance students’
learning and inform teachers as they make instructional decisions.
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"It is through our assessment that we communicate most clearly
to students which activities and learning outcomes we value."
–David
J. Clarke
(1989, p.1)
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Assessment
is a communication process in which assessors–whether students
themselves, teachers, or others–learn something about what students
know and can do and in which students learn something about what assessors
value. When the focus and form of assessment are different from that
of instruction, assessment subverts students’ learning by sending
them conflicting messages about what mathematics is valued. When instruction
pursues one set of goals and the assessment–especially if it
is for high stakes–pursues another, students are faced with a
dilemma and must assume that the goals of assessment are the ones
that count. |
| For
examples of assessment integrated with instruction, see "Listening
to Students" on page 32 and "Using Evidence to Plan Tomorrow’s
Lesson" on page 49. |
Assessment
that enhances mathematics learning becomes a routine part of ongoing
classroom activity rather than an interruption. Assessment does not
simply mark the end of a learning cycle. Rather, it is an integral
part of instruction that encourages and supports further learning.
Opportunities for informal assessment occur naturally in every lesson.
They include listening to students, observing them, and making sense
of what they say and do. Especially with very young children, the
observation of students’ work can reveal qualities of thinking
not tapped by written or oral activities. In planning lessons and
making instructional decisions, teachers identify opportunities for
a variety of assessments. Questions like the following become a regular
part of the teacher’s planning: "What questions will I ask?"
"What will I observe?" "What activities are likely
to provide me with information about students’ learning?"
Preparation for a formal assessment does not mean stopping regular
instruction and teaching to the test. Instead, for students, ongoing
instruction is the best preparation for assessment. Similarly, for
teachers, ongoing assessment is the best foundation for instruction.
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"In order
for assessment to support student learning, it must include teachers
in all stages of the process and be embedded in curriculum and teaching
activities."
–Linda
Darling-Hammond
(1994, p. 25)
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Assessment
that enhances mathematics learning incorporates activities that are
consistent with, and sometimes the same as, the activities used in
instruction. For example, if students are learning by communicating
their mathematical ideas in writing, their knowledge of mathematics
is assessed, in part, by having them write about their mathematical
ideas. If they are learning in groups, they may be assessed in groups.
If graphing calculators are used in instruction, they are to be available
for use in assessment. |
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See "Selecting
Appropriate Instructional Experiences" on page 52 for an example
of using classroom work products as assessment evidence.
For an example
of how students acquire an understanding of assessment criteria,
see "A Middle-Grades Statistics Unit" on page 30.
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Students’
classroom work, along with projects and other out-of-class work, is
a rich source of assessment data for making inferences about students’
learning. Many products of classroom activity are indicators of mathematics
learning: oral comments, written papers, journal entries, drawings,
computer-generated models, and other means of representing knowledge.
Students and teachers use this evidence, along with information from
more formal assessment activities, to determine next steps in learning.
Evidence of mathematics learning can be found in activities that range
from draft work, through work that reflects students’ use of
feedback and helpful criticism, to a polished end product. Continuous
assessment of students’ work not only facilitates their learning
of mathematics but also enhances their confidence in what they understand
and can communicate. Moreover, external assessments support instruction
most strongly when classroom work is included. When classroom work,
the teacher’s judgments, and students’ reflections are valued
parts of an external assessment, they enhance students’ mathematics
learning by increasing the fit between instructional goals and assessment. |
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For an example of self- and peer-assessment, see "Learning to
Judge One’s Own Work" on page 39.
"The assessment
of students’ mathematical disposition should seek information
about their inclination to monitor and reflect on their own thinking
and performance."
–NCTM
(1989, p. 233)
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If
students are to function as independent learners, they must reflect
on their progress, understand what they know and can do, be confident
in their learning, and ascertain what they have yet to learn. When
students work as partners with teachers and peers in the assessment
process, they learn to monitor their progress in learning. Teachers
help students become independent self-assessors by providing sample
tasks and sample criteria for judging responses, by describing how
the tasks and criteria were created, and by showing how the criteria
are applied. Students can create tasks, develop criteria of their
own, and apply the criteria to their work and to the work of others.
As the shift from teacher-centered to student-centered classrooms
occurs, students become more active participants in assessment. In
these classrooms, students learn to reflect on their work and their
learning, make critical self-judgments, critique the work of their
peers, and use productively the critiques of others.
To determine how well an
assessment enhances learning, ask questions such as these:
- How does the assessment
contribute to each student’s learning of mathematics?
- How does the assessment
relate to instruction?
- How does the assessment
allow students to demonstrate what they know and what they can
do in novel situations?
- How does the assessment
engage students in relevant, purposeful work on worthwhile mathematical
activities?
- How does the assessment
build on each student’s understanding, interests, and experiences?
- How does the assessment
involve students in selecting activities, applying performance
criteria, and using results?
- How does the assessment
provide opportunities for students to evaluate, reflect on, and
improve their own work–that is, to become independent learners?
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