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This choices board assignment offers diverse options for all types of learners to show what they've learned. Written specifically for mathematics teachers, this lesson helps facilitate the understanding and process of writing choices board lessons.
Written specifically for K12 mathematics teachers, this resource provides the nuts and bolts of differentiation. Presented in an easy-to-implement format, this handy notebook is designed to facilitate the understanding and process of writing differenti
This volume is based on papers presented at the 30th Carnegie Mellon Symposium on Cognition. This particular symposium was conceived in reference to the 1974 symposium entitled Cognition and Instruction. In the 25 years since that symposium, reciprocal relationships have been forged between psychology and education, research and practice, and laboratory and classroom learning contexts. Synergistic advances in theories, empirical findings, and instructional practice have been facilitated by the establishment of new interdisciplinary journals, teacher education courses, funding initiatives, and research institutes. So, with all of this activity, where is the field of cognition and instruction? How much progress has been made in 25 years? What remains to be done? This volume proposes and illustrates some exciting and challenging answers to these questions. Chapters in this volume describe advances and challenges in four areas, including development and instruction, teachers and instructional strategies, tools for learning from instruction, and social contexts of instruction and learning. Detailed analyses of tasks, subjects' knowledge and processes, and the changes in performance over time have led to new understanding of learners' representations, their use of multiple strategies, and the important role of metacognitive processes. New methods for assessing and tracking the development and elaboration of knowledge structures and processing strategies have yielded new conceptualizations of the process of change. Detailed cognitive analysis of expert teachers, as well as a direct focus on enhancing teachers' cognitive models of learners and use of effective instructional strategies, are other areas that have seen tremendous growth and refinement in the past 25 years. Similarly, the strong impact of curriculum materials and activities based on a thorough cognitive analysis of the task has been extended to the use of technological tools for learning, such as intelligent tutors and complex computer based instructional interfaces. Both the shift to conducting a significant portion of the cognition and instruction research in real classrooms and the increased collaboration between academics and educators have brought the role of the social context to center stage.
Just as athletes stretch their muscles before every game and musicians play scales to keep their technique in tune, mathematical thinkers and problem solvers can benefit from daily warm-up exercises. Jessica Shumway has developed a series of routines designed to help young students internalize and deepen their facility with numbers. The daily use of these quick five-, ten-, or fifteen-minute experiences at the beginning of math class will help build students' number sense. Students with strong number sense understand numbers, ways to represent numbers, relationships among numbers, and number systems. They make reasonable estimates, compute fluently, use reasoning strategies (e.g., relate operations, such as addition and subtraction, to each other), and use visual models based on their number sense to solve problems. Students who never develop strong number sense will struggle with nearly all mathematical strands, from measurement and geometry to data and equations. In Number Sense Routines, Jessica shows that number sense can be taught to all students. Dozens of classroom examples -- including conversations among students engaging in number sense routines -- illustrate how the routines work, how children's number sense develops, and how to implement responsive routines. Additionally, teachers will gain a deeper understanding of the underlying math -- the big ideas, skills, and strategies children learn as they develop numerical literacy.
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Through a careful treatment of number theory and geometry, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofs. Classroom-tested, the book draws on the authors’ successful work with undergraduate students at the University of Chicago, seventh to tenth grade mathematically talented students in the University of Chicago’s Young Scholars Program, and elementary public school teachers in the Seminars for Endorsement in Science and Mathematics Education (SESAME). The first half of the book focuses on number theory, beginning with the rules of arithmetic (axioms for the integers). The authors then present all the basic ideas and applications of divisibility, primes, and modular arithmetic. They also introduce the abstract notion of a group and include numerous examples. The final topics on number theory consist of rational numbers, real numbers, and ideas about infinity. Moving on to geometry, the text covers polygons and polyhedra, including the construction of regular polygons and regular polyhedra. It studies tessellation by looking at patterns in the plane, especially those made by regular polygons or sets of regular polygons. The text also determines the symmetry groups of these figures and patterns, demonstrating how groups arise in both geometry and number theory. The book is suitable for pre-service or in-service training for elementary school teachers, general education mathematics or math for liberal arts undergraduate-level courses, and enrichment activities for high school students or math clubs.
Master the fundamentals of discrete mathematics with DISCRETE MATHEMATICS FOR COMPUTER SCIENCE with Student Solutions Manual CD-ROM! An increasing number of computer scientists from diverse areas are using discrete mathematical structures to explain concepts and problems and this mathematics text shows you how to express precise ideas in clear mathematical language. Through a wealth of exercises and examples, you will learn how mastering discrete mathematics will help you develop important reasoning skills that will continue to be useful throughout your career.
Islamic schools, or madrasas, have been accused of radicalizing Muslims and participating, either actively or passively, in terrorist networks since the events of 9/11. In Pakistan, the 2007 siege by government forces of Islamabad’s Red Mosque and its madrasa complex, whose imam and students staged an armed resistance against the state for its support of the "war on terror," reinforced concerns about madrasas’ role in regional and global jihad. By 2006 madrasas registered with Pakistan’s five regulatory boards for religious schools enrolled over one million male and 200,000 female students. In The Rational Believer, Masooda Bano draws on rich interview, ethnographic, and survey data, as well as fieldwork conducted in madrasas throughout the country to explore the network of Pakistani madrasas. She maps the choices and decisions confronted by students, teachers, parents, and clerics and explains why available choices make participation in jihad appear at times a viable course of action. Bano's work shows that beliefs are rational and that religious believers look to maximize utility in ways not captured by classical rational choice. She applies analytical tools from the New Institutional Economics to explain apparent contradictions in the madrasa system—for example, how thousands of young Pakistani women now demand the national adoption of traditional sharia law, despite its highly restrictive limits on female agency, and do so from their location in Islamic schools for girls that were founded only a generation ago.
