Assessment Of Authentic Performance In School Mathematics

This book is the result of a conference sponsored by the Educational Testing Service and the University of Wisconsin's National Center for Research in Mathematical Sciences Education. The purpose of the conference was to facilitate the work of a group of scholars whose interests included the assessment of higher-order understandings and processes in foundation-level (pre-high school) mathematics. Discussions focused on such issues as the purposes of assessment, guidelines for producing and scoring "real-life" assessment activities, and the meanings of such terms as "deeper and higher-order understanding," "cognitive objectives," and "authentic mathematical activities." Assessment was viewed as a critical component of complex, dynamic, and continually adapting educational systems. During the time that the chapters in this book were being written, sweeping changes in mathematics education were being initiated in response to powerful recent advances in technology, cognitive psychology, and mathematics, as well as to numerous public demands for educational reform. These changes have already resulted in significant reappraisals of what it means to understand mathematics, of the nature of mathematics teaching and learning, and of the real-life situations in which mathematics is useful. The challenge was to pursue assessment-related initiatives that are systematically valid, in the sense that they work to complement and enhance other improvements in the educational system rather than act as an impediment to badly needed curriculum reforms. To address these issues, most chapters in this book focus on clarifying and articulating the goals of assessment and instruction, and they stress the content of assessment above its mode of delivery. Computer- or portfolio-based assessments are interpreted as means to ends, not as ends in themselves. Assessment is conceived as an ongoing documentation process, seamless with instruction, whose quality hinges upon its ability to provide complete and appropriate information as needed to inform priorities in instructional decision making. This book tackles some of the most complicated issues related to assessment, and it offers fresh perspectives from leaders in the field--with the hope that the ultimate consumer in the instruction/assessment enterprise, the individual student, will reclaim his or her potential for self-directed mathematics learning.

This book is the result of a conference sponsored by the Educational Testing Service and the University of Wisconsin's National Center for Research in Mathematical Sciences Education. The purpose of the conference was to facilitate the work of a group of scholars whose interests included the assessment of higher-order understandings and processes in foundation-level (pre-high school) mathematics. Discussions focused on such issues as the purposes of assessment, guidelines for producing and scoring "real-life" assessment activities, and the meanings of such terms as "deeper and higher-order understanding," "cognitive objectives," and "authentic mathematical activities." Assessment was viewed as a critical component of complex, dynamic, and continually adapting educational systems. During the time that the chapters in this book were being written, sweeping changes in mathematics education were being initiated in response to powerful recent advances in technology, cognitive psychology, and mathematics, as well as to numerous public demands for educational reform. These changes have already resulted in significant reappraisals of what it means to understand mathematics, of the nature of mathematics teaching and learning, and of the real-life situations in which mathematics is useful. The challenge was to pursue assessment-related initiatives that are systematically valid, in the sense that they work to complement and enhance other improvements in the educational system rather than act as an impediment to badly needed curriculum reforms. To address these issues, most chapters in this book focus on clarifying and articulating the goals of assessment and instruction, and they stress the content of assessment above its mode of delivery. Computer- or portfolio-based assessments are interpreted as means to ends, not as ends in themselves. Assessment is conceived as an ongoing documentation process, seamless with instruction, whose quality hinges upon its ability to provide complete and appropriate information as needed to inform priorities in instructional decision making. This book tackles some of the most complicated issues related to assessment, and it offers fresh perspectives from leaders in the field--with the hope that the ultimate consumer in the instruction/assessment enterprise, the individual student, will reclaim his or her potential for self-directed mathematics learning.

This document was created because of the need for new assessment strategies and practices to be developed to enable teachers and others to assess students' performance in a manner that reflects the NCTM's reform vision for school mathematics. Instead of assuming that the purpose of assessment is to rank students on a particular trait, the new approach assumes that high public expectations can be set that every student can strive for and achieve, that different performances can and will meet agreed-on expectations, and that teachers can be fair and consistent judges of diverse student performances. The first sections of the document discuss six mathematics assessment standards: (1) The Mathematics Standard, (2) The Learning Standard, (3) The Equity Standard, (4) The Openness Standard, (5) The Inferences Standard, and (6) The Coherence Standard. The use of the assessment standards is then discussed in the context of different purposes such as monitoring students' progress, making instructional decisions, evaluating students' achievement, and evaluating programs. The next section discusses what should happen next with regard to mathematical assessment. The document concludes with a glossary and a selected assessment bibliography with 116 citations. Contains 28 references. (MKR)

To achieve national goals for education, we must measure the things that really count. Measuring What Counts establishes crucial research- based connections between standards and assessment. Arguing for a better balance between educational and measurement concerns in the development and use of mathematics assessment, this book sets forth three principlesâ€"related to content, learning, and equityâ€"that can form the basis for new assessments that support emerging national standards in mathematics education.

Today new ways of thinking about learning call for new ways for monitoring learning. Reform in School Mathematics builds from the vision that assessment can become the bridge for instructional activity, accountability, and teacher development. It places teachers in key roles while developing the theme that we cannot reform the way in which school mathematics is taught without radically reforming the ways the effects of that teaching are monitored. Among others, this volume addresses the issues of the specification of performance standards, the development of authentic tasks, the measure of status and growth or a combination, the development of psychometric models, and the development of scoring rubrics. The new models proposed in this book give teachers a wealth of nontraditional assessment strategies and concrete ways to obtain measures of both group and individual differences in growth.

This book is the result of a conference sponsored by the Educational Testing Service and the University of Wisconsin's National Center for Research in Mathematical Sciences Education. The purpose of the conference was to facilitate the work of a group of scholars whose interests included the assessment of higher-order understandings and processes in foundation-level (pre-high school) mathematics. Discussions focused on such issues as the purposes of assessment, guidelines for producing and scoring "real-life" assessment activities, and the meanings of such terms as "deeper and higher-order understanding," "cognitive objectives," and "authentic mathematical activities." Assessment was viewed as a critical component of complex, dynamic, and continually adapting educational systems. During the time that the chapters in this book were being written, sweeping changes in mathematics education were being initiated in response to powerful recent advances in technology, cognitive psychology, and mathematics, as well as to numerous public demands for educational reform. These changes have already resulted in significant reappraisals of what it means to understand mathematics, of the nature of mathematics teaching and learning, and of the real-life situations in which mathematics is useful. The challenge was to pursue assessment-related initiatives that are systematically valid, in the sense that they work to complement and enhance other improvements in the educational system rather than act as an impediment to badly needed curriculum reforms. To address these issues, most chapters in this book focus on clarifying and articulating the goals of assessment and instruction, and they stress the content of assessment above its mode of delivery. Computer- or portfolio-based assessments are interpreted as means to ends, not as ends in themselves. Assessment is conceived as an ongoing documentation process, seamless with instruction, whose quality hinges upon its ability to provide complete and appropriate information as needed to inform priorities in instructional decision making. This book tackles some of the most complicated issues related to assessment, and it offers fresh perspectives from leaders in the field--with the hope that the ultimate consumer in the instruction/assessment enterprise, the individual student, will reclaim his or her potential for self-directed mathematics learning.

Are current testing practices consistent with the goals of the reform movement in school mathematics? If not, what are the alternatives? How can authentic performance in mathematics be assessed? These and similar questions about tests and their uses have forced those advocating change to examine the way in which mathematical performance data is gathered and used in American schools. This book provides recent views on the issues surrounding mathematics tests, such as the need for valid performance data, the implications of the Curriculum and Evaluation Standards for School Mathematics for test development, the identification of valid items and tests in terms of the Standards, the procedures now being used to construct a sample of state assessment tests, gender differences in test taking, and methods of reporting student achievement.

It describes each strategy and clarifies its advantages and drawbacks. Also included is a large sample of classroom-tested examples along with sample student responses. These examples can be used "as is" - or you can customize them for your own class. This book will help prepare your students for standardized tests that include items requiring evidence of conceptual understanding. The strategies reflect the assessment Standards benchmarks established by the NCTM. In addition, an entire chapter is devoted to help teachers use these assessments to arrive at their students' grades.