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It has been alleged that few American students can use their knowledge effectively in thinking and reasoning. This study urges teachers to give more attention to student abilities in analyzing, classifying, comparing, formulating hypotheses, and drawing conclusions--that is, thinking skills essential to reasoning processes. Designed to familiarize secondary classroom teachers with one model of instruction for developing students' reasoning abilities, this book gives practical assistance in learning how to use the inductive approach, a teaching approach that actively involves students in the use of their own reasoning while learning content area material. Each chapter of the book includes a section that asks readers to recall experience pertinent to the material in the chapter, a set of questions to answer as the material is read, and a series of activities designed to lead readers through the developmental stages of the learning process. Chapters of the book are: (1) What is the inductive approach? (2) Why use the inductive approach? (3) How to use the inductive approach for concept development; (4) How to use the inductive approach for principle formation; (5) Inductive reasoning in English; (6) Inductive reasoning in mathematics; (7) Inductive reasoning in science; and (8) Inductive reasoning in social studies. A 90-item bibliography is attached. (RS)
For too many students, mathematics consists of facts in a vacuum, to be memorized because the instructor says so, and to be forgotten when the course of study is completed. In this all-too-common scenario, young learners often miss the chance to develop skills—specifically, reasoning skills—that can serve them for a lifetime. The elegant pages of Teaching Mathematical Reasoning in Secondary School Classrooms propose a more positive solution by presenting a reasoning- and discussion-based approach to teaching mathematics, emphasizing the connections between ideas, or why math works. The teachers whose work forms the basis of the book create a powerful record of methods, interactions, and decisions (including dealing with challenges and impasses) involving this elusive topic. And because this approach shifts the locus of authority from the instructor to mathematics itself, students gain a system of knowledge that they can apply not only to discrete tasks relating to numbers, but also to the larger world of people and the humanities. A sampling of the topics covered: Whole-class discussion methods for teaching mathematics reasoning. Learning mathematical reasoning through tasks. Teaching mathematics using the five strands. Classroom strategies for promoting mathematical reasoning. Maximizing student contributions in the classroom. Overcoming student resistance to mathematical conversations. Teaching Mathematical Reasoning in Secondary School Classrooms makes a wealth of cutting-edge strategies available to mathematics teachers and teacher educators. This book is an invaluable resource for researchers in mathematics and curriculum reform and of great interest to teacher educators and teachers.
First released in the Spring of 1999, How People Learn has been expanded to show how the theories and insights from the original book can translate into actions and practice, now making a real connection between classroom activities and learning behavior. This edition includes far-reaching suggestions for research that could increase the impact that classroom teaching has on actual learning. Like the original edition, this book offers exciting new research about the mind and the brain that provides answers to a number of compelling questions. When do infants begin to learn? How do experts learn and how is this different from non-experts? What can teachers and schools do-with curricula, classroom settings, and teaching methodsâ€"to help children learn most effectively? New evidence from many branches of science has significantly added to our understanding of what it means to know, from the neural processes that occur during learning to the influence of culture on what people see and absorb. How People Learn examines these findings and their implications for what we teach, how we teach it, and how we assess what our children learn. The book uses exemplary teaching to illustrate how approaches based on what we now know result in in-depth learning. This new knowledge calls into question concepts and practices firmly entrenched in our current education system. Topics include: How learning actually changes the physical structure of the brain. How existing knowledge affects what people notice and how they learn. What the thought processes of experts tell us about how to teach. The amazing learning potential of infants. The relationship of classroom learning and everyday settings of community and workplace. Learning needs and opportunities for teachers. A realistic look at the role of technology in education.
Teaching Mathematics in Grades 6 - 12 by Randall E. Groth explores how research in mathematics education can inform teaching practice in grades 6-12. The author shows preservice mathematics teachers the value of being a "researcher—constantly experimenting with methods for developing students' mathematical thinking—and connecting this research to practices that enhance students' understanding of the material. Ultimately, preservice teachers will gain a deeper understanding of the types of mathematical knowledge students bring to school, and how students' thinking may develop in response to different teaching strategies.
In the mid 1980s, the International Commission on Mathematical Instruction (ICMI) inaugurated a series of studies in mathematics education by comm- sioning one on the influence of technology and informatics on mathematics and its teaching. These studies are designed to thoroughly explore topics of c- temporary interest, by gathering together a group of experts who prepare a Study Volume that provides a considered assessment of the current state and a guide to further developments. Studies have embraced a range of issues, some central, such as the teaching of algebra, some closely related, such as the impact of history and psychology, and some looking at mathematics education from a particular perspective, such as cultural differences between East and West. These studies have been commissioned at the rate of about one per year. Once the ICMI Executive decides on the topic, one or two chairs are selected and then, in consultation with them, an International Program Committee (IPC) of about 12 experts is formed. The IPC then meets and prepares a Discussion Document that sets forth the issues and invites interested parties to submit papers. These papers are the basis for invitations to a Study Conference, at which the various dimensions of the topic are explored and a book, the Study Volume, is sketched out. The book is then put together in collaboration, mainly using electronic communication. The entire process typically takes about six years.
This volume is a case study of education reform and innovation using technology that examines the issue from a wide variety of perspectives. It brings together the views and experiences of software designers, curriculum writers, teachers and students, researchers and administrators. Thus, it stands in contrast to other analyses of innovation that tend to look through the particular prisms of research, classroom practice, or software design. The Geometric Supposer encourages a belief in a better tomorrow for schools. On its surface, the Geometric Supposer provides the means for radically altering the way in which geometry is taught and the quality of learning that can be achieved. At a deeper level, however, it suggests a powerful metaphor for improving education that can be played out in many different instructional contexts.
Volume 3 of Research in Collegiate Mathematics Education (RCME) presents state-of-the-art research on understanding, teaching and learning mathematics at the post-secondary level. This volume contains information on methodology and research concentrating on these areas of student learning: Problem Solving; Understanding Concepts; and Understanding Proofs.
This second edition of Classroom Discourse Analysis continues to make techniques widely used in the field of discourse analysis accessible to a broad audience and illustrates their practical application in the study of classroom talk, ideal for upper-level undergraduate and graduate students in discourse analysis, applied linguistics, and anthropology and education. Grounded in a unique tripartite "dimensional approach," individual chapters investigate interactional resources that model forms of discourse analysis teachers may practice in their own classrooms while other chapters provide students with a thorough understanding of how to actually collect and analyse data. The presence of a number of pedagogical features, including activities and exercises and a comprehensive glossary help to enhance students‘ understanding of these key tools in classroom discourse analysis research. Features new to this edition reflect current developments in the field, including: increased coverage of peer interaction in the classroom greater connecting analysis to curricular and policy mandates and standards-based reform movements sample excerpts from actual student classroom discourse analysis assignments a new chapter on the repertoire approach, an increasingly popular method of analysis of particular relevance to today’s multilingual classrooms