Measuring What Counts A Conceptual Guide for Mathematics Assessment (1993) / Chapter Skim
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5 Assessing to Support Equity and Opportunity in Mathematics Learning
5 Assessing to Support Equity and Opportunity in Mathematics Learning
Pages 91-116
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From page 91... ...
Increasingly, however, educators have recognized that although status characteristics of learners may be important, they are far less important than functional characteristics are in the design of instructional strategies.' Reforms in mathematics and other areas of schooling must aim to ensure that each student, regardless of achievement level or demographic characteristics, has the opportunity to study challenging subject matter. The example on the following page, a policy statement adopted by the National Council of Teachers of Mathematics (NCTM)
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From page 92... ...
just as good instruction accommodates differences in the ways learners construct knowledge, good assessments accommodate differences in the ways that students think about mathematics and display mathematical understanding. Although all students are to be assessed on important mathematical concepts and skills, in accord with the content and learning principles, the equity principle implies that assessments must be sufficiently flexible to allow all students to show what they know and can do.
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From page 93... ...
You have constructed a 2'x 2' scale model of the mosaic, which used 120 red mosaic / A: ~ B: = C: pieces, 200 blue mosaic pieces, and 150 ~\ yellow pieces.
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From page 94... ...
Consider the response on the following page of a Ute Indian student to an assessment task.6 Rather than focusing on the mathematical question asked, the student responded to the hypothetical nature of its premise. Children who live in harsh environments in the inner cities and in remote rural areas often respond to hypothetical problems in much the same way.
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From page 95... ...
As assessments become more complex and more connected to real-world tasks, there is a greater chance that the underlying assump tions and views may not apply equally to all students, particularly when differences in bacl |
From page 96... ...
In addition, a special advisory group was created to address issues involved in administering appropriate assessment tasks and procedures for students who are not native speakers of English.8 The Center for Research, Evaluation, and Student Testing (CRESST) atthe University of California at Los Angeles also has special equity initiatives.
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From page 97... ...
Still other research suggests that group differences might be magnified when performance assessment tasks are used.~° Although the results may vary depending on the content area assessed, the nature of the specific tasks used, and whether group or individual perfomance is the focus of comparisons, it seems clear that reformers' hopes must be balanced by a spirit of empiricism: there is much more to be learned about how changes in assessment will affect long-standing group differences, one facet of equity concerns. In any event, equity implies a commitment to seek and explore the sources of any systematic performance differences that may be observed on new assessments.
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From page 98... ...
Many factors can come into play: the rater's expertise and knowledge of the specific math attend, ancT the emetics content of the task, the rater's interpretation of task requirements and scoring criteria or even similarities instruction they or differences in the backgrounds of the rater and the student being evaluated.~3 have receivecT When any of these factors contribute to systematic differ ences among definable groups, assessment results have meanings or implications that are different for some groups than for others. possible to Inferences based on results from such an assessment are said to be biased that is not equally valid for all groups.~4 , , identify · .
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From page 99... ...
PROMOTING PUBLIC INVOLVEMENT Increasingly, public dialogue is seen as an important strategy for ensuring that assessments are designed and used equitably.~7 The Urban District Assessment Coalition (UDAC) , a joint effort of Boston College and the American Federation of Teachers, organized a series of conversations about assessment reform among various groups before designing a new assessment system for the Boston schools.
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From page 100... ...
PROMOTING COMMUNITY UNDERSTANDING OF ASSESSMENT REFORM For mathematics education reform to reach each child, parents and other community members will need to understand the new vision of school mathematics. Their involvement is needed to support the efforts of the teachers, school administrators, and others who, with them, share responsibility for the education of their children.
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From page 101... ...
community Assessment tasks and their corresponding scoring criteria can be used to make this point quite convincingly. They illustrate that the knowledge and proficiency that students are being asked to demon strate are of value to all students.
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From page 102... ...
about who can For example, teachers working with researchers at the Educational Testing Service have been surprised at which students learn important do well and which do poorly on complex tasks. One of the tasks required students to explain how to set up an activity similar to a mathematics game of darts, although it involved tossing compact discs rather than darts.23 As indicated in the eaxmple below, students were to write a description that included information on how the game would be set up, chances of winning, and expected profits.
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From page 103... ...
[Bart draws lots _ _ _ _ I I I I I I ~ ~ ~ _ _ _ _ of little squares inside the original game board squares as _ _ _ _ _~- _ _ _ shown in the figure below.J I win if my dart lands in here _ _ _ _ ~- _ _ _ [referring tO his disk as a dart, and pointing to the shaded _ _ _ _ ~- _ _ _ squares in the diagram shown below.J And, I lose if the _ _ _ ~ ~- _ _ _ dart lands out here [pointing to the unshaded squaresJ. _ _ _ _ :_ - _ _ _ I've got this many chances to win, and this many to lose.
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From page 104... ...
Although not all students with histories of low academic performance produced elegant solutions in response to challenging tasks, it was not unusual to discover at least two or three such students in a typical-size classroom. It also was not unusual to find cases in which high achievers, based on traditional measures, exhibited poorer performance on such problems.26 HELPING STUDENTS UNDERSTAND AND MEET NEW EXPECTATIONS The equity principle requires that students be prepared for more challenging assessments.
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From page 105... ...
Binet could never have anticipated that his mental tests would be used to support an American hereditarian theory of intelligence and its tragic aftermath.27 More recently, states and school districts introduced For assessments to help children and to promote better minimum competency tests to ensure that each student who was graduated or promoted learned essential subjects. Some of the instruction anticipated benefits of these policies are being realized.
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From page 106... ...
Program effectiveness is judged by performance gains on those same tests. Although the basic skills gap separating Chapter students from other students has declined in the past 15 years, critics have charged that "A continued focus on remediation denies the richness of learning to those who need more, not less, of what makes education engaging and exciting."32 In mathematics, many of the children who begin remediation in third grade never catch up to their peers.
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From page 107... ...
unless it has submitted proof of the curricular validity of the test which the court defined as 'a fair test of that which was taught."' The ruling in that case and several others that dealt with high-stakes use of tests for placement established two important guidelines for fairness in educational assessment. First, assessments used to allocate different instructional treatments must be demonstrably fair tests of what students have been taught.
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From page 108... ...
Opposition has also been forthcoming on policy grounds: the burdens delivery standards might impose on states, unresolved consequences for schools that fail to satisfy standards, and unresolved questions about consequences for individual rights in high-stakes contexts when schools fail to meet delivery standards. Some of the strongest opposition to delivery standards, however, rests on the observation that remedies designed to improve schools in the past often failed precisely because the emphasis was placed on the resources schools should provide rather than the outcomes that schools should achieve.3~3 The equity principle requires that due consideration be given to the consequences of assessments for individual students.
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From page 109... ...
Second, the principle implies that assessment results must be compiled and reported in ways that support efforts to achieve greater equity among schools. Schools educating large numbers of poor and minority students have further to go and have fewer discretionary resources with which to pursue reform than do more affluent schools.
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From page 110... ...
This view is expressed quite forcefully in a statement of equity principles adopted by a number of educational leaders, reproduced here on the following page.42 MEASURING WHAT COUNTS
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From page 111... ...
Although these leaders have not always agreed on the particulars of assessment reform, they have unanimously supported the need to address equity and excellence in tandem as assessment reform moves forward. As policymakers move forward to develop new standards and assessments, they should consider including the following principles, which will help to ensure that both equity and quality are dominant themes: 1.
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From page 112... ...
O'Neil, jr., "Diversity, Assessment, and Equity in Educational Reform" (Paper presented at the Ford Foundation Symposium on Equity and Educational Testing and Assessment, Washington, D.C., I 1-12 March 1993~; Related papers presented at the same symposium were George F Madaus, "A Technological and Historical Consideration of Equity Issues Associated with Proposals to Change Our Nation's Testing Policy"; Warren Simmons and Daniel P
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From page 113... ...
. it Monty Neill, "Some Pre-Requisites for the Establishment of Equitable, Inclusive Multicultural Assessment Systems" (Paper presented at the Ford Foundation Symposium on Equity and Educational Testing and Assessment, Washington, D.C., 11 - 12 March 1993~; ]
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From page 114... ...
, 397-414. 29 The National Council on Education Standards and Testing, Raising Standards for American Education: A Report to Congress, The Secretary of Education, The National Education Goals Panel, and the American People (Washington, D.C.: ~ ~ 4 M EASE Rl NO WHAT CON NTS
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From page 115... ...
Porter, "School Delivery Standards," Educational Researcher 22:3 <1993y, 24-30. 38 "A Technological and Historical Consideration of Equity Issues Associated with Proposals to Change Our Nation's Testing Policy; "Equity Issues in Performance-Based Assessment"; "Some Pre-Requisites for the Establishment of Equitable, Inclusive Multicultural Assessment Systems." 39 Lonnie Harp, "Texas Finance Bill Signed Into Law, Challenges Anticipated," Education Week, 9 June 1993; Lonnie Harp, "Impact of Texas Finance Law, Budget Increase Gauged," Education Week, 1 6 June 1993; Millicent Lawton, "Alabama judge Sets October Deadline for Reform Remedy," Education Week, 23 June 1993.
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