Measuring What Counts A Conceptual Guide for Mathematics Assessment (1993) / Chapter Skim
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2 A Vision of Mathematics Assessment
2 A Vision of Mathematics Assessment
Pages 29-40
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From page 29... ...
External assessments provide information about mathematics programs to state and local agencies, funding bodies, policymakers, and the public. That information can be used either to hold program managers accountable or to monitor the program's level of performance.
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From page 30... ...
The written tests administered by the Boston School assessment Committee in 1845 led to rankings of schools by level of achieve ment and to recommended changes in instructional methods.2 The must change in New York State Regents Examinations were set up primarily to maintain standards by showing teachers what their students needed ways that will to know 3 The traditional view of many Americans that tests and examinations can do more than measure achievement is reflected in both support this quotation from a 1936 book on assessment prepared for the American Council on Education: "Recently increasing emphasis has and be been placed upon examinations as means for improving instruction, and as instruments for securing information that is indispensable for consistent with the constructive educational guidance of pupils." 4 other changes Researchers are beginning to document more thoroughly the effects of assessment, determining, in effect, whether this traditional under way in view is justified. A 1992 study by the Center for the Study of Testing, Evaluation, and Educational Policy at Boston College examined the mathematics content of the most commonly used tests embedded in textbooks and standardized tests in mathematics and science for grades 4 to 12 and education.
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From page 31... ...
Reformers have proposed a host of innovative approaches to assessment, many of which are described in subsequent sections of this report. Leaders in the educational policy community are joining the chorus, arguing that minimum competence tests and basic skill assessments, like those commonly seen today, work against efforts to improve schools.6 Low-level tests give coarse and deceptive readings of educational progress.
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From page 32... ...
· ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ · ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ P R ~ N C ~ P ~ E S F O R A s s E S S ~ N G M A T H E M A T ~ C S E A R N ~ N G In this chapter, three educational principles based on content, learning, and equity are set forth to guide changes in mathematics assessment. Underlying these three principles is the fundamental premise that assessment makes sense only if it is in harmony with the broad goals of mathematics education reform.
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From page 33... ...
Assessment tasks can be designed so that they are virtually indistinguishable from good learning tasks by attending to factors that are critical to good instructional design: motivation, opportunities to construct or extend knowledge, and opportunities to receive feedback and revise work. Assessment and instruction can be combined, either through seamlessly weaving the two kind of activities together or by taking advantage of opportuni VISION OF MATHEMATICS ASSESSMENT Assessment makes sense only if it is in harmony with the broac!
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From page 34... ...
The equity principle aims to ensure that assessments are designed to give every student a fair chance to demonstrate his or her best work and are used to provide every student with access to challenging mathematics. Equity requires careful attention to the many ways in which understanding of mathematics can be demonstrated and the many factors that may color judgments of mathematical competence from a particular collection of assessment tasks.
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From page 35... ...
The constraints of efficiency meant that mathematics assessment tasks could not tap a student's ability to estimate the answer to an arithmetic calculation, construct a geometric figure, use a calculator or ruler, or produce a complex deductive argument. A narrow focus on technical criteria primarily reliability The content, learning, and equity principles challenge the clominance, not the importance, of traditional also worked against good assessment.
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From page 36... ...
Broadening the domain of important mathematics to include these skills may make it difficult to separate general cognitive skills from the outcomes of mathematics instruction, which may undermine validity as it is traditionally understood. i2 Other open technical issues relate to the difficulty of estab lishing that assessment tasks actually evoke the higher-order pro cesses they were designed to tap.~3 The array of solutions to high quality mathematics tasks is potentially so rich that expert judge ments will not be sufficient.
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From page 37... ...
Reordering priorities so that these new principles provide a foundation on which to develop new assessments puts student learning of mathematics ahead of other purposes for assessment. It is bound to have dramatic implications for mathematics assessment, not all of which can be foreseen now.
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From page 38... ...
7 Raising Standards for American Education; Edward Silver, "Assessment and Mathematics Education Reform in the United States, InternationalJournal of Educational Research, in press; Andrew C Porter, "Assessing National Goals: Some Measurement Dilemmas," The Assessment of National Educational Goals: Invitational Conference Proceedings (Princeton, N]
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From page 39... ...
, Division of Science, Technical and Environmental Education, UNESCO; Edward Silver and Patricia Kenney, "Sources of Assessment Information for Instructional Guidance in Mathematics," in Thomas Romberg, ea., Reform in School Mathematics and Authenic Assessment, (in press) ; Edward Silver, Patricia Kenney, and Leslie Salmon-Cox, The Content and Curricular Validity of the 1 990 NAEP Mathematics Items: A Retrospective Analysis (Pittsburgh, PA: Learning Research and Development Center, University of Pittsburgh, 1991~; Richard Lesh and Susan ]
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