can contribute to students opportunities to learn important
mathematics only if they reflect, and are reinforced by, high
expectations for every student."
Sciences Education Board (1993, p. 109)
should promote equity.
in assessment benefit everyone by focusing attention on each
students learning. For each student, equitable assessment
practices raise expectations, clarify what mathematics is,
and help that student learn. Equitable practices honor each
students unique qualities and experiences. Adherence
to an equity standard means that all students, including those
with special needs or talents, are expected to reach high
levels of accomplishment. It also means that each student
is given opportunities to reach those levels and the necessary
support to do so. Although professionals may disagree on ways
and means of achieving equity, its place as a goal is not
in doubt. It is not to be ignored or devalued. Equitable assessment
practices help to increase equity throughout the educational
a mathematics education that develops each students
mathematical power to the fullest.
example "Judging Progress Equitably" on page 36
for an illustration of assessment that allows all students
to demonstrate their knowledge.
In the past we wanted
all students to learn some mathematics, but we differentiated
among the types of mathematics education different groups
of students received. Now we have high expectations for all
students, envisioning a mathematics education that develops
each students mathematical power to the fullest.
In an equitable assessment,
each student has an opportunity to demonstrate his or her
mathematical power. Because different students show what they
know and can do in different ways, assessments should allow
for multiple approaches. Sometimes different assessments or
combinations of assessments are used to provide evidence of
the same mathematics learning. When students have special
needs, provision is made to ensure that they can demonstrate
their understanding. For example, assessors use English-enhancing
and bilingual techniques to support students who are learning
English. Assessment is equitable when students with special
needs or talents have access to the same accommodations and
modifications they receive in instruction.
"Listening to Students" on page 32 provides an example
of assessment that considers students unique problem-solving
cultural groups in U.S. society may have different intellectual
traditions that create different conceptions of reality than
that tapped by our testing instruments."
(1994, p. 80)
have too often ignored differences in students experience,
physical condition, gender, and ethnic, cultural, and social
backgrounds in an effort to be fair. This practice has led to
assessments that do not take differences among students into
account. The experiences each student brings to any classroom
and to any assessment are unique. Students knowledge and
ways of thinking and learning about mathematics are a complex
integration of their backgrounds with their experiences in school.
Equitable judgments about students mathematics learning
reflect the ways in which their unique qualities influence how
they learn mathematics and how they communicate that knowledge.
Students backgrounds and experiences influence how they
perceive an assessment situation and may cause them to respond
in unanticipated ways. Students may need to specify the assumptions
they are making when they communicate the results of their work.
Assessors need to be open to alternative solutions. Probing
what students are thinking, being sensitive to their experiences,
and understanding how they perceive the assessment situation
all contribute to making equitable decisions about students
the example "Understanding Variations in Performance"
on page 73, which illustrates the examination of subsets of
results are also powerful tools for monitoringat the classroom,
school, district, or state or provincial levelwhether
all students are provided equitable opportunities to learn important
mathematics. Ideally, the results will reveal no systematic
differences in performance that can be connected with characteristics
unrelated to mathematics learning. When such differences are
found, educators determine whether they have resulted from inequitable
opportunities either to learn or to demonstrate learning. In
the latter case, assessments can furnish information to guide
meaningful action by learners, teachers, and other educators
toward remedying the inequity. The burden for taking action
to ensure equitable opportunities both for teachers to teach
and for students to learn and to show their learning rests on
the entire educational system.
knowledge, experience, and the opportunity to learn are important
considerations in interpreting test results."
(1989, p. 202)
Teachers and other professionals also bring different perspectives
to the assessment process. In their role as assessors, they
need opportunities to become informed about the norms and values
of different racial, ethnic, cultural, gender, and social groups.
In responding to the needs of the students they are assessing,
however, teachers and others should recognize that each student
is a unique member of many groups and is not to be stereotyped.
Assessors sensitive to equity are willing to acknowledge and
compensate for their personal biases. Even in seemingly homogeneous
settings, assessors are constantly aware that students
views and interpretations may differ considerably from their
own. Teachers, other professionals, parents, and community members
with appropriate background and experience can provide rich
insights into students perspectives.
Equity poses many
challenges to assessment. Assessments have traditionally ignored
differences, and consequently their results have excluded
some students from opportunities to learn important mathematics.
Assessment results have also had little value in determining
and supporting instruction for certain students. An equitable
assessment process is important for removing these injustices.
Equity is not a concern for some students; it is a concern
To determine how well
an assessment promotes equity, ask questions such as the following:
- What opportunities
has each student had to learn the mathematics being assessed?
- How does the assessment
provide alternative activities or modes of response that
invite each student to engage in the mathematics being assessed?
- How does the design
of the assessment enable all students to exhibit what they
know and can do?
- How do the conditions
under which the assessment is administered enable all students
to exhibit what they know and can do?
- How does the assessment
help students demonstrate their best work?
- How is the role
of students backgrounds and experiences recognized
in judging their responses to the assessment?
- How do scoring
guides accommodate unanticipated but reasonable responses?
- How have the effects
of bias been minimized throughout the assessment?
- To what sources
can differences in performance be attributed?