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Standards and Assessments: Where We Are and What We Needby Linda Darling-Hammond - February 16, 2003 Standards-based reform was proposed as a means to bring coherence to the education system and trigger reforms and investments targeted at greater learning. These benefits have materialized in some states but not others, depending on their strategies for change. This article proposes mid-course corrections needed to ensure that standards-based reforms support student success, rather than punishing those who are already underserved. From one perspective, the standards-based reform movement in the United States has been extremely successful: At least 47 states have created standards for student learning; many have also adopted new curriculum frameworks to guide instruction and new assessments to test students' knowledge. Many school districts across the country have weighed in with their own versions of standards-based reform, including new curricula, testing systems, accountability schemes, and promotion or graduation requirements.
Yet not all of these initiatives have accomplished the goals that early proponents of standards-based reforms envisioned. Advocates hoped that standards outlining what students should know and be able to do would spur other reforms that mobilize resources for student learning, including high quality curriculum frameworks, materials, and assessments tied to the standards; more widely available course offerings that reflect this high quality curriculum; more intensive teacher preparation and professional development guided by related standards for teaching; more equalized resources for schools; and more readily available safety nets for educationally needy students (O’Day and Smith, 1993). This comprehensive approach has been followed in some states and districts, such as Connecticut, Kentucky, Maine, and North Carolina as well as New York’s District #2, San Diego, and New Haven, California. In these cases, investments in improved schooling and teaching have improved student achievement while enhancing teaching and taking steps to equalize educational opportunity.
However, this comprehensive approach to improving education has not been pursued everywhere. In a number of states, the notions of standards and `accountability' have become synonymous with mandates for student testing that are detached from policies that might address the quality of teaching, the allocation of resources, or the nature of schooling. In states where “high stakes testing” is the primary policy reform, disproportionate numbers of minority, low-income, and special needs students have failed tests for promotion and graduation, leading to grade retention, failure to graduate, and sanctions for schools, without efforts to ensure equal and adequate teaching, texts, curriculum, or other educational resources. A new generation of equity lawsuits has emerged where standards have been imposed without attention to educational inequalities. “Adequacy” litigation in Alabama, California, Florida, New York, South Carolina, and elsewhere has followed recently successful equity lawsuits in Kentucky and New Jersey.
There are other concerns about the quality of tests many states are using and their influence on the curriculum, about the negative effects of high stakes tests on student placements and opportunities to learn, and about the unintended consequences of incentive systems that reward or sanction schools based on average student scores rather than value-added assessments of student growth. These approaches appear to create incentives for pushing low-scorers into special education, holding them back in the grades, and encouraging them to drop out so that schools’ average scores will look better. Evidence of rising dropout rates in Georgia, Florida, Massachusetts, New York, and Texas has been tied to the effects of grade retention, student discouragement, and school exclusion and transfer policies stimulated by high stakes tests.
In addition, sanctions for low-scoring schools appear to reduce the likelihood that they can attract and keep qualified teachers. For example, Florida’s use of aggregate test scores, unadjusted for student characteristics, to allocate school rewards and sanctions led to reports that qualified teachers were leaving the schools rated D or F “in droves” (DeVise, 1999; Fischer, 1999), to be replaced by teachers without experience or training. As one principal queried, “Is anybody going to want to dedicate their lives to a school that has already been labeled a failure?''
States and districts that have relied primarily on test-based accountability emphasizing sanctions for students and teachers have often produced greater failure, rather than greater success, for their most educationally vulnerable students. More successful reforms have emphasized the use of standards for teaching and learning to guide investments in better prepared teachers, higher quality teaching, more performance-oriented curriculum and assessment, better designed schools, more equitable and effective resource allocations, and more diagnostic supports for student learning.
There are at least three areas in which mid-course corrections are needed if standards and assessments are to support improved education rather than greater inequality:
· The quality and alignment of standards, curriculum guidance, and assessments; · The appropriate use of assessments to improve instruction rather than punish students and schools; · The development of systems that assure equal and adequate opportunity to learn.
Below I discuss issues in each of these areas and then offer an example of a state that has developed a thoughtful approach to standards-based reform that provides a useful model.
THE QUALITY AND ALIGNMENT OF STANDARDS, CURRICULUM, GUIDANCE, AND ASSESSMENTS
Much research has found that high-stakes tests – particularly when they use limited measures of achievement – can narrow the curriculum, pushing instruction toward lower order cognitive skills and distorting the meaning of scores (Klein, Hamilton, McCaffrey & Stetcher, 2000; Koretz and Barron, 1998; Koretz, Linn, Dunbar, & Shepard, 1991; Linn, 2000; Linn, Graue, and Sanders, 1990; Stetcher, Baron, Kaganoff, & Goodwin, 1998). Recent studies cast doubt on the gains noted on the state tests in Texas, for example, finding that Texas students have not made comparable gains on national standardized tests or on the state’s own college entrance test. These studies have suggested that teaching to the test may be raising scores on the state high-stakes test in ways that do not generalize to other tests that examine a broader set of higher order skills; that many students are excluded from the state tests to prop up average scores; and that the tests have been made easier over time to give the appearance of gains (Haney, 2000; Gordon and Reese, 1997; Hoffman, Assaf, Pennington, & Paris, 1999; Klein et al., 2000; Stotsky, 1998).
While some states have developed thoughtful performance-based assessments that challenge students to demonstrate their thinking and learning in extended tasks and responses, including some that are embedded in the school curriculum, many others have settled on multiple choice tests that encourage little challenging learning and measure few of the standards. Some have adopted off-the-shelf tests that are unaligned with state standards altogether, creating a disjuncture between expectations that schools should teach to the standards and accountability systems that do not assess the standards. And the use of norm-referenced tests in some states makes it impossible to gauge progress accurately, as items are removed from the test as greater numbers of students can answer them, thus guaranteeing continuing high rates of failure, especially for certain subpopulations of students (Haney, 2002).
Early efforts at standards-based reform demonstrated that it is possible to create thoughtful standards and educationally productive assessments that are aligned to them. Connecticut, Kentucky, Maine, Maryland, Minnesota, Nebraska, Vermont, and Washington are examples of states that have developed fairly sophisticated performance-based assessment systems based on intellectually ambitious standards. They developed their systems carefully over a sustained period of time and have used them primarily to inform ongoing school improvement rather than to punish students or schools . Most policy discussions have treated tests as a “black box.” It would be useful for analyses to examine these systems and how they operate, so that others can learn from them. It would also be useful for state consortia that had once begun to form to create more thoughtful assessments, such as one launched by the Council for Chief State School Officers, to renew their efforts to allow states to collaborate in the development of standards-based criterion-referenced assessment systems that can assess the range of abilities suggested by the standards.
Finally, amendments to the new federal education legislation are needed. The legislation has already caused one state, Maryland, to drop its sophisticated performance assessment system and another, Vermont, to reject the new federal funds in order to maintain its performance assessments. The law’s current requirements for annual testing that allows cross-state comparability are likely to push states back to the lowest common denominator, undoing progress that has been made to improve the quality of assessments and delaying the move from antiquated norm-referenced tests to criterion-referenced systems. More state flexibility will be needed, along with federal supports for improving assessment systems and enabling them to assess higher order thinking and performance skills.
THE APPROPRIATE USE OF ASSESSMENTS TO IMPROVE INSTRUCTION RATHER THAN PUNISH STUDENTS AND SCHOOLS
Many unhappy outcomes of recent reforms have been associated with the inappropriate stakes associated with test scores, rather than the nature of the tests themselves. The decision to attach high stakes to tests has pushed some states back to less ambitious forms of assessment, dropping portfolio and performance tasks, even when they have been shown to support improved instruction . It has also caused a variety of dysfunctional outcomes for students when sanctions are targeted at either students or schools.
For example, grade retention and denial of diplomas have been major thrusts of some state policies, although a substantial body of research has long found lower achievement and higher dropout rates for retained students than comparable peers who move on through the grades (see e.g. Holmes and Matthews, 1984; Labaree, 1984; Meisels, 1992; Shepard and Smith, 1986; Walker and Madhere, 1987). This recent evaluation by the Consortium on Chicago School Research of a policy that retained thousands of students based on their test scores reiterates the recurrent findings:
Retained students did not do better than previously socially promoted students. The progress among retained third graders was most troubling. Over the two years between the end of second grade and the end of the second time through third grade, the average ITBS reading scores of these students increased only 1.2 GEs (grade equivalents) compared to 1.5 GEs for students with similar test scores who had been promoted prior to the policy. Also troubling is that one-year dropout rates among eighth graders with low skills are higher under this policy…. Both the history of prior attempts to redress poor performance with retention and previous research would clearly have predicted this finding. Few studies of retention have found positive impacts, and most suggest that retained students do no better than socially promoted students. The CPS policy now highlights a group of students who are facing significant barriers to learning and are falling farther and farther behind (Roderick, Bryk, Jacob, Easton, & Allensworth, 1999, pp. 55-56).
This kind of finding is not new. A decade earlier, researchers found that test-based sanctions in Georgia also led to large increases in grade retention and dropping out.
Although most of the reforms were popular, the policymakers and educators simply ignored a large body of research showing that they would not produce academic gains and would increase dropout rates. In other words, this was a policy with no probable educational benefits and large costs. The benefits were political and the costs were borne by at-risk students. The damage was psychological as well as educational, increasing the likelihood that at-risk students would drop out before receiving their diplomas; school districts were also hurt by the diversion of resources to repetitive years of education for many students (Orfield & Ashkinaze, 1991, p.139).
Recent data from the Department of Education in Massachusetts, where a similar policy has been recently enacted, show more grade retention and higher dropout rates, with the steepest increase in middle schools (a 300% increase in dropouts between 1997-98 and 1999-2000), greater proportions of students dropping out in 9th and 10th grades, more of them African American and Latino, and fewer dropouts returning to school. Meanwhile the steepest increases in test scores are occurring in schools that have the highest retention and dropout rates. For example, Wheelock (2003) shows that, in addition to increasing dropout rates, high schools receiving state awards for gains in 10th grade pass rates on the Massachusetts Comprehensive Assessment Systems showed substantial increases in prior year 9th grade retention rates and in the percentage of “missing” tenth graders (10th graders enrolled in the fall not taking the MCAS in the spring). Similar trends have been noted in Texas, where sharply increasing scores are found in schools and districts with high increases in middle school and high school dropouts (Intercultural Developmental Research Association, 1986; Haney, 2000).
The negative consequences of these policies have been exacerbated by sanctions attached to schools’ average test scores. Because these scores are sensitive to changes in the population of students taking the test and such changes can be induced by manipulating admissions, dropouts, and pupil classifications, schools have been found to label large numbers of low-scoring students for special education placements so that their scores won't "count" in school reports (Allington and McGill-Franzen, 1992; Figlio & Getzler, 2002), retain students in grade so that their relative standing will look better on "grade-equivalent" scores (Jacob, 2002; Haney, 2000); exclude low-scoring students from admission to "open enrollment" schools, and encourage such students to leave schools or drop out (Darling-Hammond, 1991; Haney, 2000; Smith et al., 1986). Smith and colleagues explained the widespread engineering of student populations that he found in his study of New York City’s implementation of test-based accountability as a basis for school level sanctions:
(S)tudent selection provides the greatest leverage in the short-term accountability game....The easiest way to improve one's chances of winning is (1) to add some highly likely students and (2) to drop some unlikely students, while simply hanging on to those in the middle. School admissions is a central thread in the accountability fabric (Smith et al., 1986, pp. 30-31).
Finally, several studies have now found that school averages are extremely volatile and that large gains from one year to the next can be followed by declines in the following year, especially in small schools, rendering decisions about school rewards and sanctions invalid (Bolon, 2001; Haney, 2002; Kane & Staiger, 2001). Because of inevitable limitations of test reliability and validity for making high stakes decisions, the American Psychological Association, American Educational Research Association, and the National Council on Measurement in Education have issued standards for the use of tests. These standards state that test scores should not be used as the sole source of information for any major decision about student placement or promotion. A recent report of the National Research Council on high stakes testing summarized appropriate policy as follows:
Scores from large-scale assessments should never be the only sources of information used to make a promotion or retention decision…. Test scores should always be used in combination with other sources of information about student achievement (Hauser & Heubert, 1999, p. 286).
Mid-course corrections should encourage states to follow these professional standards for the uses of tests, as a number of states already have. (See, for example, discussion of Connecticut’s policies below.) Interestingly, despite the common view that tests will only be meaningful if they are used to allocate rewards and punishments to individuals and organizations, these states have seen growth in student performance without the inappropriate use of test scores for purposes they cannot serve well. States should be encouraged to:
· Use local, school-based measures (including first-hand assessments of performance) as an important component of all placement and graduation decisions; · Prohibit the use of test scores as single arbiters of decisions about students, teachers, or schools; · Use analyses of (value-added) individual gain scores over time in lieu of aggregated cross-sectional measures (such as grade level averages or proportions of students meeting cut scores) for understanding school trends. Include multiple measures of learning and participation in school for evaluating school trends; · Use assessment data to trigger additional supports for students who are struggling and for schools in need of additional supports rather than for allocating sanctions.
THE DEVELOPMENT OF SYSTEMS THAT ASSURE EQUAL AND ADEQUATE OPPORTUNITY TO LEARN
Finally, and most obviously, students will not learn to higher levels unless they experience good teaching around appropriate curriculum with adequate resources. Most of the students who are struggling are students who have long experienced suboptimal schooling and those with special learning needs that require higher levels of expertise from teachers. A developmental view of assessment seeks to create the conditions that enable responsive practice. These include teacher knowledge, school capacity for improvement and problem-solving, flexibility in meeting the actual needs of real students, and policy structures that provide equitable resources and encourage inclusive education. Because this nation has not invested heavily in teachers and their knowledge, the capacity to teach all students to high levels is not widespread. Furthermore, because of funding inequalities, low-income and minority students are routinely taught by the least experienced and least-prepared teachers in schools where curriculum resources are inequitable as well (Ferguson, 1991; Oakes, 1990; National Commission on Teaching and America’s Future, 1996). Investments in teaching quality will be required before changes in assessment strategies result in more challenging and effective instruction for currently underserved students. This, in turn, will require changes in school funding so that schools serving poor and minority students are able to recruit well-prepared teachers and support them with organizational designs that permit the curriculum focus, assessment information, and personalized instruction that undergird high-quality teaching.
California’s new Master Plan proposal, for example, advocates “Opportunity to Learn Standards” that specify what the state and school districts must provide all schools: qualified teachers, a curriculum consistent with the state’s standards, texts and materials needed to support learning of the standards, and clean, safe schools. An Opportunity to Learn index is proposed to complement the state’s Academic Performance Index, and an irrational state funding system would be replaced with a model that fairly and adequately funds the cost of a standards-based system, with formula adjustments for cost of living and pupil needs.
A CASE EXAMPLE - CONNECTICUT
Connecticut provides an especially instructive example of how state level policy makers have used a standards-based starting point to upgrade teachers’ knowledge and skills as a means of improving student learning. Since the early 1980s, the state has pursued a purposeful and comprehensive teaching quality agenda, using teaching standards, followed later by student standards, to guide investments in school finance equalization, teacher salary increases tied to higher standards for teacher education and licensing, curriculum and assessment reforms, and a teacher support and assessment system that strengthened professional development (Wilson, Darling-Hammond, & Berry, 2001).
By 1998, Connecticut’s 4th grade students ranked first in the nation in reading and mathematics on the National Assessment of Educational Progress (NAEP), despite increased student poverty and language diversity in the state’s public schools during that decade (NCES, 1997; NEGP, 1999). In addition, the proportion of Connecticut 8th graders scoring at or above proficient in reading was first in the nation; Connecticut was also the top performing state in writing and science. The achievement gap between white students and the large and growing minority student population has been shrinking, and the more than 1/4 of Connecticut’s students who are black or Hispanic substantially outperform their counterparts nationally (Baron, 1999).
Connecticut’s preparation, licensing, and mentoring requirements – which are tightly connected to its student standards – ensure that all entering teachers have strong content and pedagogical knowledge to enable them to teach a wide range of diverse learners well – including those who have special education needs and those who are English language learners. In addition to strong standards for preservice education and initial licensing, portfolio assessments for beginning teacher licensing, modeled on the National Board process, examine how a teacher can teach to Connecticut’s student learning standards in each content area in which the teacher is assigned.
Student assessments are aimed at higher order thinking and performance skills embedded in state standards and are used to evaluate and continually improve practice. While the highly public reporting system places strong pressure on districts and schools to improve their practice, the student assessments are not used for rewards or punishments for students, teachers, or schools. In evaluating the reasons for Connecticut’s success, a National Education Goals Panel report noted the benefits of the state’s low-stakes testing approach, which precludes the use of test scores for graduation or promotion. This has allowed the measurement of more ambitious skills and the encouragement of more strategies for examining student performance. The state requires that each district develop its own assessment criteria for graduation, which criteria must include but “may not be exclusively based on” the results of the 10th grade mastery examination. The use of multiple measures, including local assessments and curriculum-embedded performances, is encouraged .
The assessment system emphasizes reporting and analysis strategies that focus on curriculum and teaching reforms, including widespread professional development; the use of authentic measures of reading and writing on the state tests; the wide dissemination of the standards and test objectives along with widespread professional development around literacy and the teaching of reading; and support to districts and schools to disaggregate and analyze their data in ways that permit diagnosis of student needs and curriculum effects (Baron, 1999). The state then provides targeted resources to the neediest districts to help them improve, including funding for professional development for teachers and administrators, preschool and all-day kindergarten for students, and smaller pupil-teacher ratios. Rather than pursue a punitive approach that creates dysfunctional responses without generating learning, Connecticut has made ongoing investments in improving teaching and schooling through high standards and high supports.
CONCLUSIONS
Mid-course corrections to standard-based reforms are needed to develop more productive systems of accountability for student learning. These should focus on
· assessing meaningful learning using high-quality measures tied to standards and supplemented by local indicators of learning; · using assessment data to inform curriculum reform and guide invests rather than to punish students and schools for low-performance; · developing high-quality teaching in schools that provide equitable access to curriculum that can enable students to learn the standards.
References Allington, Richard L. and Anne McGill-Franzen (1992). Unintended effects of educational reform in New York. Educational Policy, 6 (4), 397-414.
Baron, J. B. (1999). Exploring High and Improving Reading Achievement in Connecticut. Washington, DC: National Educational Goals Panel.
Bolon, C. (2001). Significance of test-based ratings for metropolitan Boston schools. Education Policy Analysis Archives, 9 (42), http://epaa.asu.edu/epaa/v0n42.
Darling-Hammond, L. (1991, November). The implications of testing policy for quality and equality. Phi Delta Kappan, 73 (3), 220-225.
Ferguson, R. F. (1991). Paying for public education: New evidence on how and why money matters. Harvard Journal on Legislation, 28 (2), 465-98.
Figlio, D.N. & Getzler, L.S. (2002, April). Accountability, ability, and disability: Gaming the system? Cambridge, MA: National Bureau of Economic Research.
Gordon, S.P. & Reese, M. (1997, July). High stakes testing. Worth the price? Journal of School Leadership, 7, 345-368.
Haney, W. (2000). The myth of the Texas miracle in education. Education Policy Analysis Archives, 8 (41), http://epaa.asu.edu/epaa/v8n41/
Haney, W. (2002). Lake Woebeguaranteed: Misuse of test scores in Massachusetts, Part I. Educational Policy Analysis Archives, 10 (24), Available at http://epaa.asu.edu/epaa/v10n24/
Hoffman, J. V., Assaf, L., Pennington, J., & Paris, S. G. (1999). High stakes testing in reading: Today in Texas, tomorrow? The Reading Teacher 52, 482-492.
Holmes, C.T. and K.M. Matthews (1984). The effects of nonpromotion on elementary and junior high school pupils: A meta-analysis. Review of Educational Research 54, 225-236.
Intercultural Development Research Association (1986, October). Texas school survey project: A summary of findings. San Antonio, TX: Author.
Jacob, B. A. (2002). The impact of high-stakes testing on student achievement: Evidence from Chicago. Working Paper. Harvard University.
Kane, T. & Staiger, D. (2001, April). Volatility in school test scores: Implications of test-based accountability systems. Cambridge, MA: National Bureau of Economic Research. Available at http://www.nber.org/papers/w8156.
Klein, S.P., Hamilton, L.S., McCaffrey, D.F., & Stetcher, B.M. (2000). What do test scores in Texas tell us? Santa Monica: The RAND Corporation.
Koretz, D., & Barron, S. I. (1998). The validity of gains on the Kentucky Instructional Results Information System (KIRIS). Santa Monica, CA: RAND, MR-1014-EDU.
Koretz, D., Linn, R. L., Dunbar, S. B., & Shepard, L. A. (1991, April). The effects of high-stakes testing: Preliminary evidence about generalization across tests, in R. L. Linn (chair), The Effects of High Stakes Testing. Symposium presented at the annual meeting of the American Educational Research Association and the National Council on Measurement in Education, Chicago.
Labaree, D.F.. (1984). Setting the standard: Alternative policies for student promotion. Harvard Educational Review, 54 (1), 67‑87.
Linn, R. L. (2000). Assessments and accountability. Educational Researcher, 29 (2), 4-16.
Linn, R. L., Graue, M. E., & Sanders, N. M. (1990).Comparing state and district test results to national norms: The validity of claims that "everyone is above average." Educational Measurement: Issues and Practice, 9, 5-14.
Meisels, S. (1992, June). Doing harm by doing good: Iatrogenic effects of early childhood enrollment and promotion policies. Early Childhood Research Quarterly, 7 (2), 155‑74.
National Center for Education Statistics (NCES) (1997). NAEP 1996 mathematics report card for the nation and the states. Washington, DC: US Department of Education.
National Commission on Teaching and America's Future (NCTAF) (1996). What Matters Most: Teaching for America's Future. New York: Author.
National Education Goals Panel (NEGP) (1999). Reading achievement state by state, 1999. Washington, DC: U.S. Government Printing Office.
Oakes, Jeannie (1990). Multiplying inequalities: The effects of race, social class, and tracking on opportunities to learn mathematics and science. Santa Monica: The RAND Corporation.
O'Day, J. A. & Smith, M.S. (1993). Systemic school reform and educational opportunity, in S. Fuhrman (ed.), Designing coherent education policy: Improving the system. San Francisco: Jossey-Bass.
Orfield, G., & Ashkinaze C. (1991). The closing door: Conservative policy and black opportunity. Chicago: University of Chicago Press, p. 139.
Roderick, M., Bryk, A.S., Jacob, B.A., Easton, J.Q. & Allensworth, E. (1999). Ending social promotion: Results from the first two years. Chicago: Consortium on Chicago School Research.
Sergi, T.S. (2001). Circular Letter C-3, 2001-2002, August 17, 2001, Local Graduation Competency Requirements, New Legislation. Hartford, CT: Connecticut State Department of Education.
Shepard, L. and Smith, M.L. (1986, November).Synthesis of research on school readiness and kindergarten retention, Educational Leadership, 44 (3), 78-86.
Smith, F., et al. (1986). High School Admission and the Improvement of Schooling. NY: New York City Board of Education.
Stecher, B. M., Barron, S., Kaganoff, T., & Goodwin, J. (1998). The effects of standards-based assessment on classroom practices: Results of the 1996-97 RAND Survey of Kentucky Teachers of Mathematics and Writing (CSE Technical Report 482). Los Angeles: Center for Research on Evaluation, Standards, and Student Testing.
Stotsky, S. (1998). Analysis of Texas reading tests, grades 4, 8, and 10, 1995-1998. Report prepared for the Tax Research Association. Available at http://www.educationnews.org/analysis_of_the_texas_reading_te.htm
Walker. E. & Madhere, S. (1987). Multiple retentions: Some consequences for the cognitive and affective maturation of minority elementary students. Urban Education, 22, 85-89.
Wilson, S., Darling-Hammond, L., & Berry, B. (2001). A case of successful teaching policy: Connecticut’s long-term efforts to improve teaching and learning. Seattle: Center for the Study of Teaching and Policy, University of Washington.
Wheelock, A. (2003). School Awards Programs and Accountability in Massachusetts:
Kentucky, for example, dropped aspects of its portfolio and performance assessments because of the concerns associated with high stakes judgments based on these more open-ended components. New York ended portfolio assessment development plans because of concerns for standardization associated with the stakes to be attached to test results. Kentucky, for example, dropped aspects of its portfolio and performance assessments because of the concerns associated with high stakes judgments based on these more open-ended components. New York ended portfolio assessment development plans because of concerns for standardization associated with the stakes to be attached to test results. Circular Letter C-3 (Sergi, 2001) notes that: “The results of the 10th grade CAPT cannot be used as the sole basis for the graduation criteria but must be included as one alternative… to meet a district’s mathematics competency, the district might decide that a student meet a district determined score on the mathematics portion of CAPT, or satisfactorily complete a district performance task in mathematics, or achieve a minimum grade in a specific course, or achieve a specified score on a national or … local exam in mathematics” (p. 2).
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