Download or read book Proportional Reasoning written by Sheldon Erickson and published by Aims Educational Foundation. This book was released on 2000 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Developing Essential Understanding of Ratios Proportions and Proportional Reasoning for Teaching Mathematics in Grades 6 8 written by Joanne Elizabeth Lobato and published by National Council of Teachers of English. This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A series for teaching mathematics."--P. [1] of cover.
Download or read book Building Proportional Reasoning Across Grades and Math Strands K 8 written by Marian Small and published by Teachers College Press. This book was released on 2015-04-10 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although proportional reasoning is not formally introduced as a topic in the Common Core and other mathematics curricula until 6th grade, introducing its fundamental ideas in the early grades helps students develop essential skills in ratios, percentages, and other proportional representations when they reach the upper grades. The author takes this complex subject and crafts examples and questions that help teachers see the larger purpose in teaching concepts, such as unitizing, and how that understanding is essential for more complex ideas, such as ratios. Teachers and vertical teams can see how the concepts can build year after year. This new resource by well-known professional developer Marian Small suggests questions that are both interesting for students and useful for providing diagnostic information to teachers. Chapters are organized by grade level (K-8) around the Common Core State Standards for Mathematics to help teachers use the resource more easily.
Download or read book It s All Connected written by Carmen Whitman and published by Math Solutions. This book was released on 2010-09-01 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Presents 18 proportional reasoning lessons for middle-school students; each lesson contains standards correlations, vocabulary, teacher notes, student connections, and reproducible pages, with the goal of seeing inclusive proportionality as the big idea that helps educators to make a unifying connection across all mathematics strands"--Provided by publisher.
Download or read book Building Proportional Reasoning Across Grades and Math Strands K 8 written by Marian Small and published by Teachers College Press. This book was released on 2014-04-15 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although proportional reasoning is not formally introduced as a topic in the Common Core and other mathematics curricula until 6th grade, introducing its fundamental ideas in the early grades helps students develop essential skills in ratios, percentages, and other proportional representations when they reach the upper grades. The author takes this complex subject and crafts examples and questions that help teachers see the larger purpose in teaching concepts, such as unitizing, and how that understanding is essential for more complex ideas, such as ratios. Teachers and vertical teams can see how the concepts can build year after year. This new resource by well-known professional developer Marian Small suggests questions that are both interesting for students and useful for providing diagnostic information to teachers. Chapters are organized by grade level (K–8) around the Common Core State Standards for Mathematics to help teachers use the resource more easily. Math teachers can use this resource to help students develop a solid foundation for more proficient and more confident work with multiplicative thinking and proportionality. It will also help math coaches as they assist teachers in their transition to teaching mathematics within the more demanding framework of the CCSS. This book will also help preservice teachers and their instructors as they prepare themselves and their students to understand and teach math with a deep level of understanding. “Once again, Marian Small has created an outstanding resource for anyone working with elementary or middle grades mathematics students. With her trademark ‘good questions to ask,’ clear explanations of underlying ideas, and rich activities, Dr. Small gets at the heart of ways to correct often misunderstood and poorly taught concepts of proportional reasoning, starting with the rarely mentioned primary level.” —Linda Sheffield, Regents Professor Emerita, Northern Kentucky University
Download or read book Teaching Fractions and Ratios for Understanding written by Susan J. Lamon and published by Routledge. This book was released on 2006-08-15 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Study of Proportional Reasoning as it Relates to the Development of Multiplication Concepts written by Judith Flowers and published by . This book was released on 1998 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ratio and Proportion written by David Ben-Chaim and published by Springer Science & Business Media. This book was released on 2012-07-30 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book If You Hopped Like A Frog written by David M. Schwartz and published by Scholastic Inc.. This book was released on 2017-03-28 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: How far could you hop?If you hopped like a frog...you could jump from home plate to first base in one mighty leap!Did you know that a frog can jump 20 times its body length? Or that an ant can lift an object 50 times its own weight?Read this book and find out what you could do -- if you had the amazing abilities of animals! And there are endless possibilities for making more hilarious comparisons of your own. Get ready for ratio and proportion like you've never seen them before!
Download or read book A Focus on Ratios and Proportions written by Marjorie M. Petit and published by Routledge. This book was released on 2020-05-17 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Development of Multiplicative Reasoning in the Learning of Mathematics written by Guershon Harel and published by SUNY Press. This book was released on 1994-01-01 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Proportional Reasoning by Young Children written by Alan Christopher Schorn and published by . This book was released on 1989 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Illusion of Linearity written by Dirk de Bock and published by Springer Science & Business Media. This book was released on 2007-09-30 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the reader with a comprehensive overview of the major findings of the recent research on the illusion of linearity. It discusses: how the illusion of linearity appears in diverse domains of mathematics and science; what are the crucial psychological, mathematical, and educational factors being responsible for the occurrence and persistence of the phenomenon; and how the illusion of linearity can be remedied.
Download or read book Proportional Reasoning Unit written by and published by . This book was released on 1996 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops and enhances students' abilities to reason with proportional relationships in their daily living.
Download or read book Acquisition of Mathematics Concepts and Processes written by Richard A. Lesh and published by . This book was released on 1983 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book EMPower Math Keeping Things in Proportion Reasoning with Ratios Student Edition written by Contemporary and published by McGraw-Hill Education. This book was released on 2011-06-06 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students use various tools—objects, diagrams, tables, graphs, and equations—to understand proportional and non-proportional relationships.
Download or read book Teaching Fractions and Ratios for Understanding written by Susan J. Lamon and published by Routledge. This book was released on 2012-03-22 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: For over a decade, Teaching Fractions and Ratios for Understanding has pushed readers beyond the limits of their current understanding of fractions and rational numbers, challenging them to refine and explain their thinking without falling back on rules and procedures they have relied on throughout their lives. All of the material offered in the book has been used with students, and is presented so that readers can see the brilliance of their insights as well as the issues that challenge their understanding. Written in a user-friendly, conversational style, this text helps teachers build the comfort and confidence they need to begin talking to children about fractions and ratios. The clear distillation of complex ideas and the translation of research into usable ideas for the classroom make this text a valuable resource for all pre- and in-service mathematics teachers. The highly anticipated third edition of this popular text has been heavily expanded and reorganized to make the connectivity of topics even more transparent, including more mathematics content, teaching/reasoning techniques, classroom activities, connections to other content, and applications to everyday life. In addition, the most effective features from previous editions have been retained. Special Features: Children’s Strategies and samples of student work are provided in each chapter for teacher analysis. Activities for practicing the thinking strategies explained in each chapter, designed to be solved without rules or algorithms, using reasoning alone. Online Resources for Instructors including a sample syllabus, chapter overviews and relevant Big Content ideas for each chapter, and graphics that can be copied and resized for use in instruction and in constructing exams. An equally valuable component of this text is MORE! Teaching Fractions and Ratios for Understanding, Third Edition---a supplement that is not merely an answer key but a resource that provides the scaffolding for this groundbreaking approach to fraction and ratio instruction. Also heavily expanded, MORE! includes in-depth discussions of selected problems in the main text, supplementary activities, Praxis preparation questions, more student work, and templates for key manipulatives.
