Measuring What Counts A Conceptual Guide for Mathematics Assessment (1993) / Chapter Skim
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Executive Summary
Executive Summary
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Mathematics assessment must also change to ensure consistency with the goals of education. Three fundamental educational principles form the foundation of all assessment that supports effective education: THE CONTENT PRINCIPLE Assessment should reflect the mathematics that is most important for students to learn.
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In the background of public debate is the steady criticism that school mathematics is out of step with today's world and is neither well taught nor well learned. Unfortunately, these pressures often suggest inconsistent courses of action, with standards-based curriculum and instruction moving in one direction while mandated tests remain aimed in another direction, at an older, more traditional target.
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Internal assessment communicates to teachers critical aspects of their students' performance, helping them to adjust their instructional techniques accordingly. External assessment provides information about mathematics programs to parents, state and local education agencies, funding bodies, and policymakers.
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A premium was placed on assessments that were easily administered and that made frugal use of resources. The constraints rather than of efficiency meant that mathematics assessment tasks could not tap a student's ability to estimate the answer to an arithmetic calcula by eclucational tion, construct a geometric figure, use a calculator or ruler, or produce a complex deductive argument.
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Assessment should do much more than test discrete procedural skills so typical of today's topic-by-process frameworks for formal assessments. Many current assessments distort mathematical reality by presenting mathematics as a set of isolated, disconnected fragments, facts, and procedures.
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However, these considerations are essential if students are mathematics to to meet the new expectations of mathematics education standards. fit assessment, The content principle has profound implications for those who design, score, and use mathematics assessments.
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This can be done, for example, by basing assessment on a portfolio of work that the student has done as part of the regular instructional program, by integrating the use of scoring guides into instruction so that students will begin to internal ize the standards against which the work will be evaluated, or by using two-stage testing in which students have an extended opportu nity to revise their initial responses to an assessment task. Not only should all students learn some mathematics from assessment tasks, but the results should yield information that can be used to improve students' access to subsequent mathematical knowledge.
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The challenge posed by the equity principle is to devise tasks with sufficient flexibility to give students a sense of accomplishment, to challenge the upper reaches of every student's mathematical understanding, and to provide a window on each student's mathematical thinking. Some design strategies are critical to meeting this challenge, particularly permitting students multiple entry and exit points in assessment tasks and allowing students to respond in ways that reflect different levels of mathematics knowledge or sophistication.
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The mere labels "performance assessment" and "open ended" do not guarantee that a task meets sound educational principles. For example, openended problems can be interesting and engaging but mathematically trivial.
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· New performance-based assessments introduce significant challenges both for the mathematical expertise of those who score assessments and for the guidelines used in scoring. Problem solving legitimately may involve some false starts or blind alleys; students whose work includes such things are doing important mathematics and their grades need to communicate this in an appropriate fashion.
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To what extent are differences in ability to communicate to be considered legitimate differences in mathematical power? · Current assessment frameworks, derived as they were from a measurement-based tradition largely divorced from mathematics itself, rarely conform to the principles of content, learning, and equity.
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Our findings neither diminish nor reject important, time-honored measurement criteria for evaluating assessment; nor do they suggest that changes in assessment alone will bring about education reform. Clearly, they will not.
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It is time to put educational principles at the forefront of mathematics assessment. -CUTIVE SO M MARY Although the necessary change in mathematics assessment will be neither swift nor straightforward, we cannot afford to wait until ail questions are resolved.
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