Statistical Implicative Analysis: Theory and Applications


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Research focused on these arenas will enhance understanding of practical matters related to how students learn and how learning can best be measured in a variety of school subjects.

Recommendation 6: Developers of assessment instruments for classroom or large-scale use should pay explicit attention to all three elements of the assessment triangle cognition, observation, and interpretation and their coordination. All three elements should be based on modern knowledge of how students learn and how such learning is best measured. Considerable time and effort should be devoted to a theory-driven design and validation process before assessments are put into operational use.

When designing new tools for classroom or large-scale use, assessment developers are urged to use the assessment triangle as a guiding framework, as set forth and illustrated in Chapters 5 , 6 , and 7. As discussed under Recommendation 1 above, a prerequisite for the development of new forms of assessment is that current knowledge derived from research be conveyed to assessment and curriculum developers in ways they can access and use.

A key feature of the approach to assessment development proposed in this report is that the effort should be guided by an explicit, contemporary cognitive model of learning that describes how people represent knowledge and develop competence in the subject domain, along with an interpretation model that is compatible with the cognitive model. Assessment tasks and procedures for evaluating responses should be designed to provide evidence of the characteristics of student understanding identified in the cognitive model of learning.

The interpretation model must incorporate this evidence in the assessment results in a way that is consistent with the model of learning. Assessment designers should explore ways of using sets of tasks that work in combination to diagnose student understanding while at the same time maintaining high standards of reliability. The interpretation model must, in turn, reflect consideration of the complexity of such sets of tasks. An important aspect of assessment validation often overlooked by assessment developers is the collection of evidence that tasks actually tap the intended cognitive content and processes.

Starting with hypotheses about the cognitive demands of a task, a variety of research techniques, such as interviews, having students think aloud as they solve problems, and analysis of errors, can be used to explore the mental processes in which examinees actually engage during task performance.

Conducting such analyses early in the assessment development process ensures that the assessments do, in fact, measure what they are intended to measure.

Statistical Implicative Analysis 2008

Recommendation 7: Developers of educational curricula and classroom assessments should create tools that will enable teachers to implement high-quality instructional and assessment practices, consistent with modern understanding of how students learn and how such learning can be measured. Assessments and supporting instructional materials should interpret the findings from cognitive research in ways that are useful for teachers. Developers are urged to take advantage of opportunities afforded by technology to assess what students are learning at fine levels of detail, with appropriate frequency, and in ways that are tightly integrated with instruction.

The committee believes a synthesis of cognitive and measurement principles has particularly significant potential for the design of high-quality tools for classroom assessment that can inform and improve learning. However, teachers should not be expected to devise on their own all the assessment tasks for students or ways of interpreting responses to those tasks.

Some innovative classroom assessments that have emerged from this synthesis and are having a positive impact on learning have been described in preceding chapters. A key to the effectiveness of these tools is that they must be packaged in ways that are practical for use by teachers. Recommendation 8: Large-scale assessments should sample the broad range of competencies and forms of student understanding that research shows are important aspects of student learning.

A variety of matrix sampling, curriculum-embedded, and other assessment approaches should be used to cover the breadth of cognitive competencies that are the goals of learning in a domain of the curriculum. Large-scale assessment tools and supporting instructional materials should be developed so that clear learning goals and landmark performances along the way to competence are shared with teachers, students, and other education stakeholders. The knowledge and skills to be assessed and the criteria for judging the desired outcomes should be clearly specified and available to all potential examinees and other concerned individuals.

Assessment developers should pursue new ways of reporting assessment results that convey important differences in performance at various levels of competence in ways that are clear to different users, including educators, parents, and students. Though further removed from day-to-day instruction than classroom assessments, large-scale assessments also have the potential to support instruction and learning if well designed and appropriately used.

Deriving real benefits from the merger of cognitive and measurement theory in large-scale assessment requires finding ways to cover a broad range of competencies.

Game Theory: The Science of Decision-Making

Alternatives to the typical on-demand testing scenario—in which every student takes the same test at a specified time under strictly standardized conditions—should be considered to enable the collection of more diverse evidence of student achievement. Large-scale assessments have an important role to play in providing dependable information for educational decision making by policy makers, school administrators, teachers, and parents. Large-scale assessments can also convey powerful messages about the kinds of learning valued by society and provide worthy goals to pursue.

If such assessments are to serve these purposes, however, it is essential that externally set goals for learning be clearly communicated to teachers, students, and other education stakeholders. Considerable resources should be devoted to producing materials for teachers and students that clearly present both the learning goals and landmark performances along the way to competence.

Writing the Discussion Section

Those performances can then be illustrated with samples of the work of learners at different levels of competence, accompanied by explanations of the aspects of cognitive competence exemplified by the work. These kinds of materials can foster valuable dialogue among teachers, students, and the public about what achievement in a domain of the curriculum looks like.

The criteria by which student work will be judged on an assessment should also be made as explicit as possible. Curriculum materials should encourage the use of activities such as peer and self-assessment to help students internalize the criteria for high-quality work and foster metacognitive skills. All of these points are equally true for classroom assessments. The use of assessments based on cognitive and measurement science will also necessitate different forms of reporting on student progress, both to parents and to administrators.

Reports on student performance could also provide an important tool to assist administrators in their supervisory roles. Such information could help administrators determine where to focus resources for professional development. In general, for the information to be useful and meaningful, it will have to include a profile consisting of multiple elements and not just a single aggregate score. Recommendation 9: Instruction in how students learn and how learning can be assessed should be a major component of teacher preservice and professional development programs.

This training should be linked to actual experience in classrooms in assessing and interpreting the development of student competence. Research on the integration of cognition and measurement also has major implications for teacher education. Teachers need training to understand how children learn subject matter and how assessment tools and practices can be used to obtain useful information about student competence. Both the initial preparation of teachers and their ongoing professional development can incorporate insights and examples from research on the integration of cognitive and measurement science and equip teachers with knowledge and skills they can use to employ high-quality assessments.

At the same time, such learning opportunities can enable teachers to transform their practice in ways that will allow them to profit from those assessments. If such assessments are to be used effectively, teacher education needs to equip beginning teachers with a deep understanding of many of the approaches students might take toward understanding a particular subject area, as well as ways to guide students at different levels toward understanding Carpenter, Fennema, and Franke, ; Griffin and Case Teachers also need a much better understanding of the kinds of classroom environments that incorporate such knowledge NRC, b.

Typically, teacher education programs provide very little preparation in assessment Plake and Impara, Yet teaching in ways that integrate assessment with curriculum and instruction requires a strong understanding of methods of assessment and the uses of assessment data.

This does not mean that all teachers need formal training in psychometries. However, teachers need to understand how to use tools that can yield valid inferences about student understanding and thinking, as well as methods of interpreting data derived from assessments. In addition, school administrators need to provide teachers with ample opportunities to continue their learning about assessment throughout their professional practice. Professional development is increasingly seen as a vital element in improving of practice, for veteran as well as new teachers. Cohen and Hill, ; Elmore and Burney, This continued learning should include the development of cognitive models of learning.


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In that approach, teachers develop lessons on their own, based on a common curriculum. They try these lessons out in their classrooms and share their findings with fellow teachers. They then modify the lessons and try them again, collecting data as they implement the lessons and again working collaboratively with other teachers to polish them. The resulting lessons are often published and become widely used by teachers throughout the country. Recommendation Policy makers are urged to recognize the limitations of current assessments, and to support the development of new systems of multiple assessments that would improve their ability to make decisions about education programs and the allocation of resources.

Important decisions about individuals should not be based on a single test score. Policy makers should instead invest in the development of assessment systems that use multiple measures of student performance, particularly when high stakes are attached to the results.

Assessments at the classroom and large-scale levels should grow out of a shared knowledge base about the nature of learning. Policy makers should support efforts to achieve such coherence. Policy makers should promote the development of assessment systems that measure growth or progress of students and the education system over time and that support multilevel analyses of the influences responsible for such change. Recommendation The balance of mandates and resources should be shifted from an emphasis on external forms of assessment to an increased emphasis on classroom formative assessment designed to assist learning.

Another arena through which research can influence practice is education policy. This is a particularly powerful arena in the case of assessment. Policy makers currently are putting great stock in large-scale assessments and using them for a variety of purposes. There is a good deal of evidence. Research on the integration of cognition and measurement can affect practice through policy in several ways. Most directly, the research can enhance the assessments used for policy decisions. Furthermore, the decisions of policy makers could be better informed than is the case today by assessments that provide a broader picture of student learning.

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Since test developers respond to the marketplace, a demand from policy makers for new assessments would likely spur their development. A range of assessment approaches should be used to provide a variety of evidence to support educational decision making. There is a need for comprehensive systems of assessment consisting of multiple measures, including those that rely on the professional judgments of teachers and that together meet high standards of validity and reliability.

Single measures, while useful, are unlikely to tap all the dimensions of competence identified by learning goals. Multiple measures are essential in any system in which high-stakes decisions are made about individuals on the basis of assessment results NRC, a.

Statistical Implicative Analysis

Currently, assessments at the classroom and large-scale levels often convey conflicting goals for learning. As argued in Chapter 6 , coherence is needed in the assessment system. A coherent assessment system supports learning for all students. If a state assessment were not designed from the same conceptual base as classroom assessments, the mismatch could undermine the potential for improved learning offered by a system of assessment based on the cognitive and measurement sciences.

To be sure, coherence in an educational system is easier to wish for than to achieve—particularly in an education system with widely dispersed authority such as that of the United States. In many ways, standards-based reform is a step toward achieving some of this coherence. But current content standards are not as useful as they could be. Cognitive research can contribute to the development of next-generation standards that are more effective for guiding curriculum, instruction, and assessment—standards that define not only the content to be learned, but also the ways in which subject matter understanding is acquired and develops.

Theory and Applications

Classroom and large-scale assessments within a coherent system should grow from a shared knowledge base about how students think and learn in a domain of the curriculum. This kind of coherence could help all assessments support common learning goals. Assessments should be aimed at improving learning by providing information needed by those at all levels of the education system on the aspects of schooling for which they are responsible.

Statistical Implicative Analysis: Theory and Applications Statistical Implicative Analysis: Theory and Applications
Statistical Implicative Analysis: Theory and Applications Statistical Implicative Analysis: Theory and Applications
Statistical Implicative Analysis: Theory and Applications Statistical Implicative Analysis: Theory and Applications
Statistical Implicative Analysis: Theory and Applications Statistical Implicative Analysis: Theory and Applications
Statistical Implicative Analysis: Theory and Applications Statistical Implicative Analysis: Theory and Applications
Statistical Implicative Analysis: Theory and Applications Statistical Implicative Analysis: Theory and Applications

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