The authors of this book question the assumptions of the psychometric paradigm that underlie virtually all criterion-referenced and standardized tests used in North American schools. They make a compelling case for a new science of educational testing and assessment, one that shifts decision making from central administration to individual schools and communities. Harold Berlak argues that the concept of tests as scientific instruments validated by technical experts is anachronistic and self-contradictory. He makes a case for a contextual paradigm, an approach which assumes that consensus on educational goals and national testing programs is neither possible nor desireable. Assessment practices in a democratic society must acknowledge and affirm differences in values, beliefs, and material interests among individuals and groups over the purposes and practices of schooling.
Summarizing data derived from a four-year combined longitudinal/ cross-sectional comparative study of the implementation of one standards-based middle school curriculum program, Mathematics in Context, this book demonstrates the challenges of conducting comparative longitudinal research in the reality of school life. The study was designed to answer three questions: What is the impact on student performance of the Mathematics in Context instructional approach, which differs from most conventional mathematics texts in both content and expected pedagogy? How is this impact different from that of traditional instruction on student performance? What variables associated with classroom instruction account for variation in student performance? The researchers examined a range of variables that affected data collection. These variations highlight the need to study the effects of the culture in which student learning is situated when analyzing the impact of standards-based curricula on student achievement. This book is directed to educational researchers interested in curriculum implementation, mathematics educators interested in the effects of using reform curriculum materials in classrooms, evaluators and research methodologists interested in structural modeling and scaling of instructional variables, and educational policy makers concerned about reform efforts.
This easy-to-understand textbook presents a modern approach to learning numerical methods (or scientific computing), with a unique focus on the modeling and applications of the mathematical content. Emphasis is placed on the need for, and methods of, scientific computing for a range of different types of problems, supplying the evidence and justification to motivate the reader. Practical guidance on coding the methods is also provided, through simple-to-follow examples using Python. Topics and features: provides an accessible and applications-oriented approach, supported by working Python code for many of the methods; encourages both problem- and project-based learning through extensive examples, exercises, and projects drawn from practical applications; introduces the main concepts in modeling, python programming, number representation, and errors; explains the essential details of numerical calculus, linear, and nonlinear equations, including the multivariable Newton method; discusses interpolation and the numerical solution of differential equations, covering polynomial interpolation, splines, and the Euler, Runge–Kutta, and shooting methods; presents largely self-contained chapters, arranged in a logical order suitable for an introductory course on scientific computing. Undergraduate students embarking on a first course on numerical methods or scientific computing will find this textbook to be an invaluable guide to the field, and to the application of these methods across such varied disciplines as computer science, engineering, mathematics, economics, the physical sciences, and social science.
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 volume takes an in-depth look at the problems and practices involved in conducting formative assessments in middle school mathematics classrooms. In these chapters, researchers and teachers identify the challenges teachers faced as they attempted to implement new assessment procedures, moving from more traditional methods to an emphasis in the quality of student work. This authoritative book: Documents the shift from traditional ways of judging student performance (tests to measure what students know) to reform notions of mathematical literacy (documenting students' growth in understanding specific content domains); Discusses four key steps in the change process that helped teachers to accomplish the necessary shift in assessment practices. Includes two chapters written by teachers that describe their personal experiences with implementing these new practices in the classroom and outlines a professional development program that evolved as a consequence of the work done by the teachers and students discussed in this book.
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