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Mathematics Assessment and Evaluation
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.
Rational Numbers
Until recently there had been relatively little integration of programs of research on teaching, learning, curriculum, and assessment. However, in the last few years it has become increasingly apparent that a more unified program of research is needed to acquire an understanding of teaching and learning in schools that will inform curriculum development and assessment. The chapters in this volume represent a first step toward an integration of research paradigms in one clearly specified mathematical domain. Integrating a number of different research perspectives is a complex task, and ways must be found to reduce the complexity without sacrificing the integration. The research discussed in t...
Addition and Subtraction
A hallmark of much of the research on children’s thinking in the 1970s had been the focus on explicit content domains. Much of this research had been represented by an eclectic collection of studies sampled from a variety of disciplines and content areas. However, in the few years before this publication, research in several content domains has begun to coalesce into a coherent body of knowledge. Originally published in 1982, the chapters in this work represent one of the first attempts to bring together the perspectives of a variety of different researchers investigating a specific, well defined content domain. This book presents theoretical views and research findings of a group of international scholars who are investigating the early acquisition of addition and subtraction skills by young children. Together, the contributors bring a blend of psychology, educational psychology, and mathematics education to this topic. Fields of interest such as information processing, artificial intelligence, early childhood, and classroom teaching and learning are included in this blend.
Conversations with Educational Leaders
Educational leaders speak out in their own words--stimulating, accessible, provocative--on contemporary and controversial topics that range from differing attitudes on diversity to the debate over character education to arguments about education reform.
Integrating Research on the Graphical Representation of Functions
This volume focuses on the important mathematical idea of functions that, with the technology of computers and calculators, can be dynamically represented in ways that have not been possible previously. The book's editors contend that as result of recent technological developments combined with the integrated knowledge available from research on teaching, instruction, students' thinking, and assessment, curriculum developers, researchers, and teacher educators are faced with an unprecedented opportunity for making dramatic changes. The book presents content considerations that occur when the mathematics of graphs and functions relate to curriculum. It also examines content in a carefully considered integration of research that conveys where the field stands and where it might go. Drawing heavily on their own work, the chapter authors reconceptualize research in their specific areas so that this knowledge is integrated with the others' strands. This model for synthesizing research can serve as a paradigm for how research in mathematics education can -- and probably should -- proceed.
Mathematical Thinking and Problem Solving
In the early 1980s there was virtually no serious communication among the various groups that contribute to mathematics education -- mathematicians, mathematics educators, classroom teachers, and cognitive scientists. Members of these groups came from different traditions, had different perspectives, and rarely gathered in the same place to discuss issues of common interest. Part of the problem was that there was no common ground for the discussions -- given the disparate traditions and perspectives. As one way of addressing this problem, the Sloan Foundation funded two conferences in the mid-1980s, bringing together members of the different communities in a ground clearing effort, designed ...
Measuring What Counts
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.
Toward a New Science of Educational Testing and Assessment
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.
Betrayed
In America, more money is spent from all sources on K-12 education than on the U.S. Department of Defense. Why then are so many children suffering what amounts to educational malpractice? Why are they crippled for life with a substandard education and a life-altering vision of themselves as 'incapable'? Betrayed is a passionate, well-researched and frank accounting of how a failing public-education system continues to be forced on teachers and students, despite its nearly complete lack of supporting research or successful student outcomes. Betrayed roots out the self-styled 'stakeholders' whose personal, professional and financial interests are served by this failing system. It sympathizes with teachers_many of whom aren't allowed to do their jobs, yet are constantly threatened with removal for 'ineffectiveness' or 'insubordination.' Betrayed is an expose, but it's also a beacon of commonsense and hope. Through the 'Square of Effective Learning,' Betrayed offers practical methods for teachers, parents, advocates and legislators to stand up against this broken system, to effect positive change, and to ensure a good-quality education for all of our children.
Handbook of Research Design in Mathematics and Science Education
The Handbook of Research Design in Mathematics and Science Education is based on results from an NSF-supported project (REC 9450510) aimed at clarifying the nature of principles that govern the effective use of emerging new research designs in mathematics and science education. A primary goal is to describe several of the most important types of research designs that: * have been pioneered recently by mathematics and science educators; * have distinctive characteristics when they are used in projects that focus on mathematics and science education; and * have proven to be especially productive for investigating the kinds of complex, interacting, and adapting systems that underlie the develop...
