The Learning Standard
Assessment in Mathematics Classrooms
an excerpt from Assessment Standards for School Mathematics
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.
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.
Students' classroom work, along with projects and other outofclass
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, computergenerated 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.
Reprinted with permission from Assessment Standards for School
Mathematics, copyright 1995 by the National Council of Teachers of
Mathematics. Order from NCTM, 1900 Association Drive, Reston, VA 22091.
Telephone 18002357566.
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