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| Author | : Susan Carol Baker |
| Publisher | : |
| Total Pages | : 404 |
| Release | : 1994 |
| Genre | : |
| ISBN | : |
| Author | : Jessica Shumway |
| Publisher | : Taylor & Francis |
| Total Pages | : 193 |
| Release | : 2023-10-10 |
| Genre | : Education |
| ISBN | : 1003839789 |
In this groundbreaking and highly practical book,Number Sense Routines: Building Numerical Literacy Every Day in Grades K-3, author Jessica Shumway proposes that all children have innate number sense which can be developed through daily exercise. Shumway createda series of math routines designed to help young students strengthen and build their facility with numbers. These quick 5, 10, or 15 minute exercises are easy to implement as an add-on to any elementary math curriculum. Understanding Number Sense: Students with strong number sense understand numbers, how to subitize, relationships among numbers, and number systems. They make reasonable estimates, compute fluently, use reasoning strategies, and use visual models to solve problems. Number Sense Routines supports the early learner by instilling the importance of daily warm-ups and explains how they benefit developing math minds for long-term learning. Real Classroom Examples: Shumway compiled her classroom observations from around the country. She includes conversations among students who practice number sense routines to illustrate them in action, how children's number sense develops with daily use, and math strategies students learn as they develop their numerical literacy through self-paced practice. Assessment Strategies: Number Sense Routines demonstrates the importance of listening to your students and knowing what to look for. Teachers will gain a deeper understanding of the underlying math skills and strategies students learn as they develop numerical literacy. Shumway writes, As you read, you will step into various classrooms and listen in on students' conversations, which I hope will give you insight into the power of number sense routines and the impact they have on students' number sense development. My hope is that going into the classroom, into students' conversations, and into their thought processes, you will come away with new ideas and tools to use in your own classroom.
| Author | : Marjorie M. Petit |
| Publisher | : Routledge |
| Total Pages | : 208 |
| Release | : 2015-07-24 |
| Genre | : Education |
| ISBN | : 1317597303 |
A Focus on Fractions is a groundbreaking effort to make the mathematics education research on how students develop their understanding of fraction concepts readily accessible and understandable to pre- and in-service K– 8 mathematics educators. Using extensive annotated samples of student work, as well as vignettes characteristic of classroom teachers’ experiences, this book equips educators with the knowledge and tools to reveal students’ thinking so that they can modify their teaching and improve student learning of fraction concepts. A Focus on Fractions 2nd edition includes sections on the Common Core State Standards for Mathematics and the Ongoing Assessment Project (OGAP) Fraction Framework integrated into each chapter as well as a new chapter on the OGAP Fraction Progression and how it can be used for formative assessment purposes. This updated edition assists teachers in translating research findings into their classroom practice by conveying detailed information about how students develop fraction understandings. Additional images and examples serve to flesh out and supplement the newly-introduced concepts in this updated and expanded edition. Special Features: Looking Back Questions at the end of each chapter provide teachers the opportunity to analyze student thinking and consider instructional strategies for their own students. Instructional Links help teachers relate concepts from the chapter to their own instructional materials and programs. Big Ideas frame the chapters and provide a platform for meaningful exploration of the teaching of fractions. Answer Key posted online offers extensive explanations of in-chapter questions. New sections devoted to the CCSSM and OGAP Fraction Progression are woven throughout the book as well as a new stand alone chapter on the OGAP Fraction Progression. The OGAP Fraction Framework is an all-new eResource, now available as a free download from the book’s website: www.routledge.com/9781138816442.
| Author | : Carolyn A. Maher |
| Publisher | : Springer |
| Total Pages | : 224 |
| Release | : 2017-06-10 |
| Genre | : Education |
| ISBN | : 9463510087 |
This book may be used for research, graduate and undergraduate teacher education, and teacher development. It presents an integrated set of studies of a heterogeneously grouped class of twenty-one nine-year olds, engaged in exploring fraction ideas prior to classroom instruction under conditions that supported investigation, collaboration and argumentation. It demonstrates with text and video narrative how young children can reason about mathematics in surprisingly sophisticated ways when provided the opportunity to do so in the proper classroom environment. In this volume, fourth grade students’ reasoning about fraction concepts is described through careful analysis and accompanying video excerpts showcasing the variety and originality of their thinking. These children will serve as an inspiration for educators to encourage the development of reasoning and argumentation in their students as part of a mathematics curriculum designed to produce critical thinkers.
| Author | : Leslie P. Steffe |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 379 |
| Release | : 2009-12-02 |
| Genre | : Education |
| ISBN | : 144190591X |
Children’s Fractional Knowledge elegantly tracks the construction of knowledge, both by children learning new methods of reasoning and by the researchers studying their methods. The book challenges the widely held belief that children’s whole number knowledge is a distraction from their learning of fractions by positing that their fractional learning involves reorganizing—not simply using or building upon—their whole number knowledge. This hypothesis is explained in detail using examples of actual grade-schoolers approaching problems in fractions including the schemes they construct to relate parts to a whole, to produce a fraction as a multiple of a unit part, to transform a fraction into a commensurate fraction, or to combine two fractions multiplicatively or additively. These case studies provide a singular journey into children’s mathematics experience, which often varies greatly from that of adults. Moreover, the authors’ descriptive terms reflect children’s quantitative operations, as opposed to adult mathematical phrases rooted in concepts that do not reflect—and which in the classroom may even suppress—youngsters’ learning experiences. Highlights of the coverage: Toward a formulation of a mathematics of living instead of being Operations that produce numerical counting schemes Case studies: children’s part-whole, partitive, iterative, and other fraction schemes Using the generalized number sequence to produce fraction schemes Redefining school mathematics This fresh perspective is of immediate importance to researchers in mathematics education. With the up-close lens onto mathematical development found in Children’s Fractional Knowledge, readers can work toward creating more effective methods for improving young learners’ quantitative reasoning skills.
| Author | : Susan B. Empson |
| Publisher | : Heinemann Educational Books |
| Total Pages | : 0 |
| Release | : 2011 |
| Genre | : Education |
| ISBN | : 9780325030531 |
"With the collaboration of a number of dedicated teachers and their students, Susan Empson and Linda Levi have produced a volume that is faithful to the basic principles of CGI while at the same time covering new ground with insight and innovation." -Thomas P. Carpenter This highly anticipated follow-up volume to the landmark Children's Mathematics: Cognitively Guided Instruction addresses the urgent need to help teachers understand and teach fraction concepts. Fractions remain one of the key stumbling blocks in math education, and here Empson and Levi lay a foundation for understanding fractions and decimals in ways that build conceptual learning. They show how the same kinds of intuitive knowledge and sense making that provides the basis for children's learning of whole number arithmetic can be extended to fractions and decimals. Just as they did in Children's Mathematics and Thinking Mathematically, Empson and Levi provide important insights into children's thinking and alternative approaches to solving problems. Three themes appear throughout the book: building meaning for fractions and decimals through discussing and solving word problems the progression of children's strategies for solving fraction word problems and equations from direct modeling through relational thinking designing instruction that capitalizes on students' relational thinking strategies to integrate algebra into teaching and learning fractions. With illuminating examples of student work, classroom vignettes, "Teacher Commentaries" from the field, sample problems and instructional guides provided in each chapter, you'll have all the tools you need to teach fractions and decimals with understanding and confidence.
| Author | : Gary D. Phye |
| Publisher | : Elsevier |
| Total Pages | : 633 |
| Release | : 1997-01-08 |
| Genre | : Psychology |
| ISBN | : 0080532934 |
The Handbook of Academic Learning provides a comprehensive resource for educational and cognitive psychologists, as well as educators themselves, on the mechanisms and processes of academic learning. Beginning with general themes that cross subject and age level, the book discusses what motivates students to learn and how knowledge can be made personal for better learning and remembering. Individual chapters identify proven effective teaching methods for the specific domains of math, reading, writing, science, and critical problem solving, how students learn within those domains, and how learning can be accurately assessed for given domains and age levels. The Handbook takes a constructivist perspective to academic learning, emphasizing the construction of personal knowledge of an academic nature. Constructivism within the context of learning theory is viewed as involving an active learner that constructs an academic knowledge base through the development of cognitive strategies and metacognition. The book discusses the development of basic literacy skills that provide the foundation for higher order thinking and problem solving. Constructivism recognizes the social dimension of classroom learning and emphasizes the motivational elements of self-regulation and volition as essential learner characteristics. Written by authors who have first-hand experience with both theory development and the development of authentic classroom instructional techniques, the Handbook empowers educators to develop, implement, and field-test authentic instructional practices at their school site. The book provides a review of the literature, theory, research, and skill techniques for effective teaching and learning. Identifies effective teaching with specific techniques Covers elementary school through high school Discusses teaching methods for all main subject areas: reading, writing, math, science, and critical thinking Identifies how students learn to learn Reviews theory, research, techniques, and assessment Contains field tested examples for the educational professional at the school site Provides a resource for staff development
| Author | : John Dunlosky |
| Publisher | : Cambridge University Press |
| Total Pages | : 1130 |
| Release | : 2019-02-07 |
| Genre | : Psychology |
| ISBN | : 1108245102 |
This Handbook reviews a wealth of research in cognitive and educational psychology that investigates how to enhance learning and instruction to aid students struggling to learn and to advise teachers on how best to support student learning. The Handbook includes features that inform readers about how to improve instruction and student achievement based on scientific evidence across different domains, including science, mathematics, reading and writing. Each chapter supplies a description of the learning goal, a balanced presentation of the current evidence about the efficacy of various approaches to obtaining that learning goal, and a discussion of important future directions for research in this area. It is the ideal resource for researchers continuing their study of this field or for those only now beginning to explore how to improve student achievement.
| Author | : Peter J. Rich |
| Publisher | : Springer |
| Total Pages | : 423 |
| Release | : 2017-04-24 |
| Genre | : Education |
| ISBN | : 331952691X |
This book reports on research and practice on computational thinking and the effect it is having on education worldwide, both inside and outside of formal schooling. With coding becoming a required skill in an increasing number of national curricula (e.g., the United Kingdom, Israel, Estonia, Finland), the ability to think computationally is quickly becoming a primary 21st century “basic” domain of knowledge. The authors of this book investigate how this skill can be taught and its resultant effects on learning throughout a student's education, from elementary school to adult learning.
| Author | : Marjorie M. Petit |
| Publisher | : Routledge |
| Total Pages | : 264 |
| Release | : 2010-06-10 |
| Genre | : Education |
| ISBN | : 1136998098 |
A Focus on Fractions is the first book to make cognitive research on how students develop their understanding of fraction concepts readily accessible and understandable to pre- and in-service K– 8 mathematics educators. This important resource assists teachers in translating research findings into their classroom practice by conveying detailed information about how students develop fraction understandings as well as common student misconceptions, errors, preconceptions, and partial understandings that may interfere with students learning. Using extensive annotated samples of student work, as well as vignettes characteristic of classroom teachers’ experiences, this book equips educators with knowledge and tools to reveal students’ thinking so that they can modify their teaching to improve student learning of fractions concepts. Special Features: End of Chapter Questions provide teachers the opportunity to analyze student thinking and consider instructional strategies for their own students. Instructional Links help teachers relate concepts from the chapter to their own instructional materials and programs. Big Ideas and Research Reviews frame the chapters and provide a platform for meaningful exploration of the teaching of fractions. Answer Key posted online offers extensive explanations of in-chapter questions. A Focus on Fractions bridges the gap between what mathematics education researchers have discovered about the learning of fraction concepts and what teachers need to know to make effective instructional decisions.
