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Have You Ever Wondered About the Use of Multiple Measures in Mathematics?by the California Mathematics Council State Board
One
of the current buzzwords in use in the state of California and across
the nation is multiple measures. But what does this phrase really mean
for students, teachers, schools, and districts? Quite simply by
multiple measures we mean the use of a variety of assessment formats
that allow educators to identify the strengths and weaknesses of their
students so that the curriculum can be adjusted to meet the needs of
those students.
Why Do We Need Multiple Measures?
In California, data from the Standardized Testing and Reporting (STAR)
program are being used in an attempt to answer the concerns of many
different audiences regarding the effectiveness of public education.
However, we seem to have forgotten that students come to school with
different levels of preparation for school mathematics. We also need to
remember that students may score well on a standardized test even
though they only learned a moderate amount of mathematics during the
school year; conversely, students might receive low scores on a
standardized test, but make tremendous gains in mathematics when
comparing their performance from the beginning to the end of the school
year.
Not only should stakeholders know how well students have mastered the
mathematics standards, but also how well they have progressed from the
beginning of the year. Students, parents, and teachers need to know how
students are progressing towards understanding and applying the
targeted mathematics content so the opportunities to learn can be
improved. Community members need to see how much growth has occurred
whether or not the mathematics standards have been completely mastered.
If one of the goals of assessment is to improve instruction, then it
must be done throughout the year. It would be unwise to change an
instructional program based on a single instance of feedback that comes
months after the completion of a school year. The beauty of multiple
measures is that we can learn about the progress of students within a
school year. We can revise curriculum for students as the need arises.
What Are Some Options for Multiple Measures?
The mathematics portion of the STAR program consists of standardized
and criterion-referenced tests that are given to students in grades 2
through 11 at the end of the school year. The results of these
end-of-year assessments provide information that may be used to alter
the next year’s program, rather than the current year’s program. This
is not enough to build a comprehensive assessment program that:- reflects the mathematics that students should know and be able to do;
- enhances mathematics learning;
- promotes equity;
- is an open process;
- promotes valid inference;
- is a coherent process. (NCTM 2000, 22)
Student growth must be measured throughout the year in a variety of
ways in order for stakeholders to see the full strength of an
educational program and to provide an opportunity for changing
curriculum, as needed. Hence the current mantra for multiple measures.
In California, multiple measures could make use of the STAR program at
the end of the year along with the many assessment tools teachers use
throughout the year. Teachers may routinely be using any or all of the
following forms of assessment in their classrooms:
- Homework: This provides immediate feedback on students? understandings of both concepts and skills.
- Paper/pencil Tests: These may include a variety of forms, such as true/false, multiple choice, matching, and open-ended.
- Observations:
Teachers assess on a daily basis when they observe the work students
are doing and discuss that work with the students. As a result of these
observations and discussions, teachers may be keeping anecdotal records.
- Student Reflections: These could include student journals as well as student interviews.
- Student Reports, Projects, and Presentations:
These provide opportunities for students to demonstrate understanding
of mathematical concepts and promote real-life connections to
mathematics. Students may work individually or in groups.
- Portfolios: These are used to demonstrate understanding and academic growth over time through a body of carefully selected student work.
All of these forms of assessment have as their goal to provide
information about what is happening in the classroom and thus allow for
the improvement of the educational program for students. "Just as a
photograph provides a single snapshot of a child at a given time and
place, a test measures how well a student answers a given set of
questions on a given day" (CMC, 1).
Who Will Use This Information?
Traditionally, teachers have assessed students in order to measure
student growth and communicate the information to parents. However,
with the onset of accountability, assessment has taken on the
additional task of informing a variety of audiences on the
effectiveness of public schools. Ideally, assessment should be able to
provide politicians with the information they need to develop strong
educational policies that ensure access and equity for all students.
Assessments present the general public with information regarding the
effectiveness of the schools they support financially. Data from
assessments should be used by administrators to determine the
effectiveness of curriculum materials and teachers. The data should
also be used by teachers to plan instruction, strategies, and
activities to ensure that students are meeting grade level expectations
and standards. Parents use information to monitor their children’s
progress and to select the educational setting for their children.
Students can use the assessments to demonstrate mathematical
understandings and skills, to set goals for themselves, to assume
responsibility for their own learning, and to become more independent
learners.
Given the differing perspectives of our audiences, the question
becomes: Can a single assessment meet the needs of all the
stakeholders? Obviously not.
Recommendation
The California Mathematics Council recommends that a comprehensive
assessment program in mathematics include a variety of assessments that
enhance student learning, can be used as tools for making instructional
decisions, and provide necessary feedback to a variety of stakeholders.
As Carr and Harris state in Succeeding with Standards: Linking
Curriculum, Assessment, and Action Planning: "Comprehensive assessment
is an ongoing inquiry, a process of raising questions, collecting data
to provide some possible answers, and making reasoned decisions about
necessary changes in programs, practices, and resources that will
affect student performance." As stated in the NCTM Principles and
Standards: "Assessment should not merely be done to students; rather,
it should also be done for students, to guide and enhance their
learning."
References
California Mathematics Council. How Is My Child Progressing in Mathematics? Clayton, CA: Curriculum, Instruction, and Assessment Committee, California Mathematics Council, 2000.
Carr, Judy F. and Douglas E. Harris. Succeeding with Standards: Linking Curriculum, Assessment, and Action Planning. Alexandria, VA: Association for Supervision and Curriculum Development, 2001.
Farr, Roger. "Putting It All Together: Solving the Reading Assessment Puzzle." In Reading Assessment in Practice: Book of Readings, edited by the International Reading Association, 31?42. Reston, VA: The Council, 1995.
National Council of Teachers of Mathematics. Principles and Standards for School Mathematics. Reston, VA: The Council, 2000.
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This Page was last updated: Sunday, March 7, 2004 at 11:47:29 AM
This page was originally posted: 7/4/2003; 10:05:05 AM.
Copyright 2008 cmcmath
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