Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download A Study Of Proportional Reasoning As It Relates To The Development Of Multiplication Concepts PDF full book. Access full book title A Study Of Proportional Reasoning As It Relates To The Development Of Multiplication Concepts.
| Author | : Judith Flowers |
| Publisher | : |
| Total Pages | : 338 |
| Release | : 1998 |
| Genre | : |
| ISBN | : |
| Author | : Joanne Elizabeth Lobato |
| Publisher | : National Council of Teachers of English |
| Total Pages | : 0 |
| Release | : 2010 |
| Genre | : Curriculum planning |
| ISBN | : 9780873536226 |
"A series for teaching mathematics."--P. [1] of cover.
| Author | : Marjorie M. Petit |
| Publisher | : Routledge |
| Total Pages | : 242 |
| Release | : 2020-05-17 |
| Genre | : Education |
| ISBN | : 1000071448 |
This resource offers a groundbreaking effort to make mathematics education research on ratios and proportions readily accessible and understandable to preservice and in-service teachers of grades 6 to 8. Using extensive annotated samples of student work and based on research gathered in the Ongoing Assessment Project (OGAP), A Focus on Ratios and Proportions teaches readers how students develop understanding and fluency involving ratio and proportion concepts. Special features include: A close focus on student work, including 150+ annotated pieces of student work, to help teachers improve their ability to recognize, assess and monitor their students’ errors and misconceptions, as well as their developing conceptual understanding. A focus on the OGAP Ratios and Proportions Progression, based on research conducted with hundreds of teachers and thousands of pieces of student work. Sections on how Common Core State Standards for Math (CCSSM) are supported by math education research. Student work samples and vignettes to illuminate the research, as well as end of chapter Looking Back questions and Instructional Links, which allow teachers to analyze evidence of student thinking and strategies and consider instructional responses. An accompanying eResource, available online, offers an answer key as well as extensive explanation of the Looking Back questions. Like A Focus on Multiplication and Division and A Focus on Fractions, this book is designed to bridge the gap between what math education researchers know and what teachers need to know in order to better understand evidence in student work and make effective instructional decisions.
| Author | : Guershon Harel |
| Publisher | : SUNY Press |
| Total Pages | : 448 |
| Release | : 1994-01-01 |
| Genre | : Education |
| ISBN | : 9780791417638 |
Two of the most important concepts children develop progressively throughout their mathematics education years are additivity and multiplicativity. Additivity is associated with situations that involve adding, joining, affixing, subtracting, separating and removing. Multiplicativity is associated with situations that involve duplicating, shrinking, stressing, sharing equally, multiplying, dividing, and exponentiating. This book presents multiplicativity in terms of a multiplicative conceptual field (MCF), not as individual concepts. It is presented in terms of interrelations and dependencies within, between, and among multiplicative concepts. The authors share the view that research on the mathematical, cognitive, and instructional aspects of multiplicative concepts must be situated in an MCF framework.
| Author | : Sharon L. Senk |
| Publisher | : Taylor & Francis |
| Total Pages | : 536 |
| Release | : 2020-07-24 |
| Genre | : Education |
| ISBN | : 1000106152 |
The Curriculum and Evaluation Standards for School Mathematics published by the National Council of Teachers of Mathematics in 1989 set forth a broad vision of mathematical content and pedagogy for grades K-12 in the United States. These Standards prompted the development of Standards-based mathematics curricula. What features characterize Standards-based curricula? How well do such curricula work? To answer these questions, the editors invited researchers who had investigated the implementation of 12 different Standards-based mathematics curricula to describe the effects of these curricula on students' learning and achievement, and to provide evidence for any claims they made. In particular, authors were asked to identify content on which performance of students using Standards-based materials differed from that of students using more traditional materials, and content on which performance of these two groups of students was virtually identical. Additionally, four scholars not involved with the development of any of the materials were invited to write critical commentaries on the work reported in the other chapters. Section I of Standards-Based School Mathematics Curricula provides a historical background to place the current curriculum reform efforts in perspective, a summary of recent recommendations to reform school mathematics, and a discussion of issues that arise when conducting research on student outcomes. Sections II, III, and IV are devoted to research on mathematics curriculum projects for elementary, middle, and high schools, respectively. The final section is a commentary by Jeremy Kilpatrick, Regents Professor of Mathematics Education at the University of Georgia, on the research reported in this book. It provides a historical perspective on the use of research to guide mathematics curriculum reform in schools, and makes additional recommendations for further research. In addition to the references provided at the end of each chapter, other references about the Standards-based curriculum projects are provided at the end of the book. This volume is a valuable resource for all participants in discussions about school mathematics curricula--including professors and graduate students interested in mathematics education, curriculum development, program evaluation, or the history of education; educational policy makers; teachers; parents; principals and other school administrators. The editors hope that the large body of empirical evidence and the thoughtful discussion of educational values found in this book will enable readers to engage in informed civil discourse about the goals and methods of school mathematics curricula and related research.
| Author | : Jo Boaler |
| Publisher | : Penguin |
| Total Pages | : 296 |
| Release | : 2008-07-17 |
| Genre | : Education |
| ISBN | : 1440639353 |
“Highly accessible and enjoyable for readers who love and loathe math.” —Booklist A critical read for teachers and parents who want to improve children’s mathematics learning, What’s Math Got to Do with It? is “an inspiring resource” (Publishers Weekly). Featuring all the important advice and suggestions in the original edition of What’s Math Got to Do with It?, this revised edition is now updated with new research on the brain and mathematics that is revolutionizing scientists’ understanding of learning and potential. As always Jo Boaler presents research findings through practical ideas that can be used in classrooms and homes. The new What’s Math Got to Do with It? prepares teachers and parents for the Common Core, shares Boaler’s work on ways to teach mathematics for a “growth mindset,” and includes a range of advice to inspire teachers and parents to give their students the best mathematical experience possible.
| Author | : National Research Council |
| Publisher | : National Academies Press |
| Total Pages | : 289 |
| Release | : 2004-11-12 |
| Genre | : Education |
| ISBN | : 0309092426 |
This book reviews the evaluation research literature that has accumulated around 19 K-12 mathematics curricula and breaks new ground in framing an ambitious and rigorous approach to curriculum evaluation that has relevance beyond mathematics. The committee that produced this book consisted of mathematicians, mathematics educators, and methodologists who began with the following charge: Evaluate the quality of the evaluations of the thirteen National Science Foundation (NSF)-supported and six commercially generated mathematics curriculum materials; Determine whether the available data are sufficient for evaluating the efficacy of these materials, and if not; Develop recommendations about the design of a project that could result in the generation of more reliable and valid data for evaluating such materials. The committee collected, reviewed, and classified almost 700 studies, solicited expert testimony during two workshops, developed an evaluation framework, established dimensions/criteria for three methodologies (content analyses, comparative studies, and case studies), drew conclusions on the corpus of studies, and made recommendations for future research.
| Author | : National Research Council |
| Publisher | : National Academies Press |
| Total Pages | : 53 |
| Release | : 2002-07-31 |
| Genre | : Education |
| ISBN | : 0309131987 |
Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.
| Author | : David Ben-Chaim |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 264 |
| Release | : 2012-07-30 |
| Genre | : Education |
| ISBN | : 9460917844 |
Ratio and Proportion—Research and Teaching in Mathematics Teachers’ Education offers its readers an intellectual adventure where they can acquire invaluable tools to turn teaching ratio and proportion to professionals and school children into an enjoyable experience. Based on in-depth research, it presents a deep, comprehensive view of the topic, focusing on both the mathematical and psychological-didactical aspects of teaching it. The unique teaching model incorporates both theoretical and practical knowledge, allowing instructors to custom-design teacher courses according to their speci?c needs. The book reports on hands-on experience in the college classes plus teachers’ experience in the actual classroom setting. An important feature is the extensive variety of interesting, meaningful authentic activities. While these activities are on a level that will engage pre- and in-service mathematics teachers in training, most can also be utilized in upper elementary and middle school classes. Accompanying the majority of these activities are detailed remarks, explanations, and solutions, along with creative ideas on how to conduct and expand the learning adventure. While primarily written for educators of mathematics teachers, this book can be an invaluable source of information for mathematics teachers of elementary and middle school classes, pre-service teachers, and mathematics education researchers.
| Author | : Susan J. Lamon |
| Publisher | : Routledge |
| Total Pages | : 254 |
| Release | : 2006-08-15 |
| Genre | : Education |
| ISBN | : 1135606781 |
This popular text addresses the urgent need for curriculum materials that cross traditional boundaries to include many of the elements that are integrated in the teaching/learning enterprise: mathematics content, teacher understanding, student thinking, teaching methods, instructional activities, and assessment. The book pushes readers beyond the limits of their current understanding of rational numbers, challenging them to refine and explain their thinking--without falling back on rules and procedures they have relied on throughout their lives. Written in a conversational and easy to understand style, this is not a textbook as much as it is a resource book. An underlying assumption is that facilitating teacher understanding using the same questions and activities that may be used with children is one way to help teachers build the comfort and confidence they need to begin talking to children about complex ideas. Unlike a textbook that is used to study formal theory and then discarded when it comes to putting ideas into practice, the many problems and activities included to facilitate teacher learning are valuable resources for use in elementary and middle school classrooms. Changes in the second edition include: *even more student work incorporated in every chapter; *discussion of the connectivity between the topics addressed in the book and the elementary and middle school mathematics curricula; *an increased emphasis on measurement; *expansion of some topics, including number sense, percent, scale factors, similarity, and linear graphs; *clarification of the characteristics of ratio and proportions and how to use these to generate discussion with children; and *content-related interview questions for exploring children's thinking. This book is a valuable resource for researchers and curriculum developers in mathematics education, pre-service and in-service teachers of mathematics, those involved in the mathematical and pedagogical preparation of mathematics teachers, and graduate students in mathematics education. The methods and activities it includes have been tested with students in grades 3-8 and with pre-service and in-service teachers and other adults. This text is accompanied by MORE--a supplement that is not merely an answer key but a resource that includes in-depth discussions of all the problems in the text; develops and extends discussion of the issues, teaching problems, and other considerations raised in the chapters; and contains additional problems--with and without solutions--that instructors may find helpful for assessment purposes.
