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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. |
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) |
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) |
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. |
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. |
| 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) |
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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