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| how to solve partitive proportion word problems: Discovering Math for Global Learners 6 Tm' 2003 Ed. , |
| how to solve partitive proportion word problems: Mathematize It! [Grades 6-8] Kimberly Morrow-Leong, Sara Delano Moore, Linda M. Gojak, 2020-08-21 Help students reveal the math behind the words I don’t get what I’m supposed to do! This is a common refrain from students when asked to solve word problems. Solving problems is about more than computation. Students must understand the mathematics of a situation to know what computation will lead to an appropriate solution. Many students often pluck numbers from the problem and plug them into an equation using the first operation they can think of (or the last one they practiced). Students also tend to choose an operation by solely relying on key words that they believe will help them arrive at an answer, without careful consideration of what the problem is actually asking of them. Mathematize It! Going Beyond Key Words to Make Sense of Word Problems, Grades 6–8 shares a reasoning approach that helps students dig into the problem to uncover the underlying mathematics, deeply consider the problem’s context, and employ strong operation sense to solve it. Through the process of mathematizing, the authors provide an explanation of a consistent method—and specific instructional strategies—to take the initial focus off specific numbers and computations and put it on the actions and relationships expressed in the problem. Sure to enhance teachers’ own operation sense, this user-friendly resource for Grades 6–8: · Offers a systematic mathematizing process for students to use when solving word problems · Gives practice opportunities and dozens of problems to leverage in the classroom · Provides specific examples of questions and explorations for multiplication and division, fractions and decimals, as well as operations with rational numbers · Demonstrates the use of visual representations to model problems with dozens of short videos · Includes end-of-chapter activities and reflection questions How can you help your students understand what is happening mathematically when solving word problems? Mathematize it! |
| how to solve partitive proportion word problems: Word Problems from Literature Denise Gaskins, 1900 You can help prevent math anxiety by giving your children the mental tools they need to conquer story problems. Young children expect to look at a word problem and instantly see the answer. But as they get older, their textbook math problems also grow in difficulty, so this solution-by-intuitive-leap becomes impossible. Too often the frustrated child concludes, “I’m just not good at math.” But with practice, any student can learn to master word problems. Word Problems from Literature features math puzzles for elementary and middle school students inspired by classic books such as Mr. Popper's Penguins and The Hobbit. Denise Gaskins demonstrates step by step how to solve these problems--and how to build a strong foundation of problem-solving skills that can handle any situation. And when you finish the puzzles in this book, Denise shows you how to create your own word problems from literature, using your child’s favorite story worlds. You'll love this book, because it prepares your children for mathematical success. Order your copy of Word Problems from Literature today. * * * If you’re using these word problems with your children, check out the companion Word Problems Student Workbook: Word Problems from Literature. |
| how to solve partitive proportion word problems: Mathematize It! [Grades 3-5] Sara Delano Moore, Kimberly Morrow-Leong, Linda M. Gojak, 2019-09-04 The list of math books to truly synthesize what we know so far and what we need to know is a very short and exclusive list. Well, you can confidently add Mathematize It to this collection. Written by three of the most respected math educators today, the book zeros in on that often poorly traveled journey between the question and answer in problem solving. Mathematize It will be your go-to resource to install the mathematical play revolution in elementary classes everywhere! Suni Singh Author of Pi of Life: the Hidden Happiness of Mathematics and Math Recess: Playful Learning in an Age of Disruption Help students reveal the math behind the words I don’t get what I’m supposed to do! This is a common refrain from students when asked to solve word problems. Solving problems is about more than computation. Students must understand the mathematics of a situation to know what computation will lead to an appropriate solution. Many students often pluck numbers from the problem and plug them into an equation using the first operation they can think of (or the last one they practiced). Students also tend to choose an operation by solely relying on key words that they believe will help them arrive at an answer, which without careful consideration of what the problem is actually asking of them. Mathematize It! Going Beyond Key Words to Make Sense of Word Problems, Grades 3-5 shares a reasoning approach that helps students dig into the problem to uncover the underlying mathematics, deeply consider the problem’s context, and employ strong operation sense to solve it. Through the process of mathematizing, the authors provide an explanation of a consistent method—and specific instructional strategies—to take the initial focus off specific numbers and computations and put it on the actions and relationships expressed in the problem. Sure to enhance teachers’ own operation sense, this user-friendly resource for Grades 3–5 • Offers a systematic mathematizing process for students to use when solving word problems • Gives practice opportunities and dozens of problems to leverage in the classroom • Provides specific examples of questions and explorations for all four operations (addition, subtraction, multiplication, and division) with whole numbers, fractions, and decimals • Demonstrates the use of concrete manipulatives to model problems with dozens of short videos • Includes end-of-chapter activities and reflection questions How can you help your students understand what is happening mathematically when solving word problems? Mathematize it! |
| how to solve partitive proportion word problems: LET REVIEWER FOR GENERAL EDUCATION PNU, |
| how to solve partitive proportion word problems: Research Trends in Mathematics Teacher Education Jane-Jane Lo, Keith R. Leatham, Laura R. Van Zoest, 2014-05-28 Research on the preparation and continued development of mathematics teachers is becoming an increasingly important subset of mathematics education research. Such research explores the attributes, knowledge, skills and beliefs of mathematics teachers as well as methods for assessing and developing these critical aspects of teachers and influences on teaching. Research Trends in Mathematics Teacher Education focuses on three major themes in current mathematics teacher education research: mathematical knowledge for teaching, teacher beliefs and identities, and tools and techniques to support teacher learning. Through careful reports of individual research studies and cross-study syntheses of the state of research in these areas, the book provides insights into teachers’ learning processes and how these processes can be harnessed to develop effective teachers. Chapters investigate bedrock skills needed for working with primary and secondary learners (writing relevant problems, planning lessons, being attentive to student learning) and illustrate how knowledge can be accessed, assessed, and nurtured over the course of a teaching career. Commentaries provide context for current research while identifying areas deserving future study. Included among the topics: Teachers’ curricular knowledge Teachers’ personal and classroom mathematics Teachers’ learning journeys toward reasoning and sense-making Teachers’ transitions in noticing Teachers’ uses of a learning trajectory as a tool for mathematics lesson planning A unique and timely set of perspectives on the professional development of mathematics teachers at all stages of their careers, Research Trends in Mathematics Teacher Education brings clarity and practical advice to researchers as well as practitioners in this increasingly critical arena. |
| how to solve partitive proportion word problems: Handbook of Research on Mathematics Teaching and Learning Douglas Grouws, 2006-11-01 Sponsored by the National Council of Teachers of Mathematics and written by leading experts in the field of mathematics education, the Handbook is specifically designed to make important, vital scholarship accessible to mathematics education professors, graduate students, educational researchers, staff development directors, curriculum supervisors, and teachers. The Handbook provides a framework for understanding the evolution of the mathematics education research field against the backdrop of well-established conceptual, historical, theoretical, and methodological perspectives. It is an indispensable working tool for everyone interested in pursuing research in mathematics education as the references for each of the Handbook's twenty-nine chapters are complete resources for both current and past work in that particular area. |
| how to solve partitive proportion word problems: LET REVIEWER FOR GENERAL EDUCATION ( NEW CURRICULUM) , 2025-03-26 This LET Reviewer for General Education is designed to help aspiring teachers master essential concepts under the new curriculum. It covers key topics in English, Mathematics, Science, Filipino, and Social Studies, with practice questions and explanations to reinforce learning. Perfect for self-study, this reviewer enhances critical thinking and test-taking skills, ensuring confidence on exam day. Prepare effectively and pass the LET with ease! |
| how to solve partitive proportion word problems: The Ohio Teacher , 1906 |
| how to solve partitive proportion word problems: Grade 6 Word Problems Kumon Publishing, 2009-06 This workbook will introduce your child to word problems dealing with adding, subtracting, multiplying and dividing fractions with unlike denominators, as well as working with the concepts of ratio, average, speed and proportion.--Cover. |
| how to solve partitive proportion word problems: Mathematics Education Lyn D. English, Graeme S. Halford, 2012-12-06 To define better techniques of mathematics education, this book combines a knowledge of cognitive science with mathematics curriculum theory and research. The concept of the human reasoning process has been changed fundamentally by cognitive science in the last two decades. The role of memory retrieval, domain-specific and domain-general skills, analogy, and mental models is better understood now than previously. The authors believe that cognitive science provides the most accurate account thus far of the actual processes that people use in mathematics and offers the best potential for genuine increases in efficiency. As such, they suggest that a cognitive science approach enables constructivist ideas to be analyzed and further developed in the search for greater understanding of children's mathematical learning. Not simply an application of cognitive science, however, this book provides a new perspective on mathematics education by examining the nature of mathematical concepts and processes, how and why they are taught, why certain approaches appear more effective than others, and how children might be assisted to become more mathematically powerful. The authors use recent theories of analogy and knowledge representation -- combined with research on teaching practice -- to find ways of helping children form links and correspondences between different concepts, so as to overcome problems associated with fragmented knowledge. In so doing, they have capitalized on new insights into the values and limitations of using concrete teaching aids which can be analyzed in terms of analogy theory. In addition to addressing the role of understanding, the authors have analyzed skill acquisition models in terms of their implications for the development of mathematical competence. They place strong emphasis on the development of students' mathematical reasoning and problem solving skills to promote flexible use of knowledge. The book further demonstrates how children have a number of general problem solving skills at their disposal which they can apply independently to the solution of novel problems, resulting in the enhancement of their mathematical knowledge. |
| how to solve partitive proportion word problems: Teaching Multiplication with Lesson Study Masami Isoda, Raimundo Olfos, 2020-11-23 This open access book is intended to assist teachers, teacher trainers, curriculum designers, editors and authors of textbooks in developing strategies to teach the multiplication of natural numbers based on the experience of the Lesson Study in Japan. This approach to mathematics education dates back to the 1870s and reconciles the emphasis on problem solving with the treatment of the curricular contents. It has gained international recognition since the 1990s and thanks to it mathematics education in Japan has been recognized as one of the most efficient and innovative in the world. This growing international awareness has led to an effort to apply the principles of Lesson Study to other parts of the world and this book shows how experienced authors from Brazil, Chile, Mexico, Spain and Portugal have worked to adapt some of these methods and techniques to the Portuguese and Spanish speaking countries of Ibero-America. Drawing on the impact of Lesson Study on government curriculum decisions and teacher behavior in Japanese classrooms; offering examples of lessons, lesson plans and suggestions for teaching; and presenting examples of the good reception of the principles of Lesson Study in Ibero-America, Teaching Multiplication with Lesson Study – Japanese and Ibero-American Theories for Mathematics Education shows how an efficient and cutting-edge experience in mathematics education can travel the world and help teachers in many different countries. |
| how to solve partitive proportion word problems: New Practical Arithmetic: for Grammar Departments James Bates Thomson, 1879 |
| how to solve partitive proportion word problems: Learning Mathematics in Elementary and Middle Schools W. George Cathcart, 2006 Brief Contents Chapter 1 Teaching Mathematics: Influences and DirectivesChapter 2 Learning and Teaching MathematicsChapter 3 Developing Mathematical Thinking and Problem-Solving AbilityChapter 4 Assessing Mathematics UnderstandingChapter 5 Developing Number ConceptsChapter 6 Developing Understanding of NumerationChapter 7. |
| how to solve partitive proportion word problems: The Arithmetic Teacher , 1991 |
| how to solve partitive proportion word problems: Ratio, Proportion, and Percent Instructional Fair, 2001-01-01 Your students will develop a greater understanding of the math concepts required for mastery of the new NCTM Standards. Easy-to-follow instructions, fun-to-solve puzzles and riddles, and many self-checking activities make these books a hit in any middle school math class. |
| how to solve partitive proportion word problems: A Study of Proportional Reasoning as it Relates to the Development of Multiplication Concepts Judith Flowers, 1998 |
| how to solve partitive proportion word problems: Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning for Teaching Mathematics in Grades 6-8 Joanne Elizabeth Lobato, Amy B. Ellis, Randall Inners Charles, 2010 A series for teaching mathematics.--P. [1] of cover. |
| how to solve partitive proportion word problems: Dissertation Abstracts International , 2004 Abstracts of dissertations available on microfilm or as xerographic reproductions. |
| how to solve partitive proportion word problems: Guiding Children to Mathematical Discovery Leonard M. Kennedy, 1970 This book reflects current thinking about the content of elementary school mathematics and the ways in which it should be presented to children. It is designed for preservice and inservice teachers, with a theoretical basis in the work of Piaget, Dienes, Gagne, and Skemp. Through carefully sequenced activities, children first develop their understanding of mathematical concepts, principles, and the operations to which they apply. Upon achieving this understanding, children then learn the skills they need to use mathematics effectively in a wide variety of situations. |
| how to solve partitive proportion word problems: Learning and Teaching Mathematics Peter Bryant, Terezinha Nunes, 2016-01-28 Newly available in paperback. Results of exciting new research. |
| how to solve partitive proportion word problems: Popular Educator , 1897 |
| how to solve partitive proportion word problems: Teaching and Learning About Whole Numbers in Primary School Terezinha Nunes, Beatriz Vargas Dorneles, Pi-Jen Lin, Elisabeth Rathgeb-Schnierer, 2016-08-29 This book offers a theory for the analysis of how children learn and are taught about whole numbers. Two meanings of numbers are distinguished – the analytical meaning, defined by the number system, and the representational meaning, identified by the use of numbers as conventional signs that stand for quantities. This framework makes it possible to compare different approaches to making numbers meaningful in the classroom and contrast the outcomes of these diverse aspects of teaching. The book identifies themes and trends in empirical research on the teaching and learning of whole numbers since the launch of the major journals in mathematics education research in the 1970s. It documents a shift in focus in the teaching of arithmetic from research about teaching written algorithms to teaching arithmetic in ways that result in flexible approaches to calculation. The analysis of studies on quantitative reasoning reveals classifications of problem types that are related to different cognitive demands and rates of success in both additive and multiplicative reasoning. Three different approaches to quantitative reasoning education illustrate current thinking on teaching problem solving: teaching reasoning before arithmetic, schema-based instruction, and the use of pre-designed diagrams. The book also includes a summary of contemporary approaches to the description of the knowledge of numbers and arithmetic that teachers need to be effective teachers of these aspects of mathematics in primary school. The concluding section includes a brief summary of the major themes addressed and the challenges for the future. The new theoretical framework presented offers researchers in mathematics education novel insights into the differences between empirical studies in this domain. At the same time the description of the two meanings of numbers helps teachers distinguish between the different aims of teaching about numbers supported by diverse methods used in primary school. The framework is a valuable tool for comparing the different methods and identifying the various assumptions about teaching and learning. |
| how to solve partitive proportion word problems: Let's Play Math Denise Gaskins, 2012-09-04 |
| how to solve partitive proportion word problems: Math Word Problems 2nd Grade Rainbow Bridge Publishing, 2002-05 |
| how to solve partitive proportion word problems: Math Matters Suzanne H. Chapin, Art Johnson, 2000 Written to help teachers deepen their understanding of the mathematics they teach, the authors present a concise description of the mathematical ideas encountered in the elementary grades. Each of the book's 13 chapters focuses on an important math topic, and interspersed throughout each chapter are many activities that bring to life the mathematical information presented. |
| how to solve partitive proportion word problems: Understanding Morphology Martin Haspelmath, Andrea Sims, 2013-10-28 This new edition of Understanding Morphology has been fully revised in line with the latest research. It now includes 'big picture' questions to highlight central themes in morphology, as well as research exercises for each chapter. Understanding Morphology presents an introduction to the study of word structure that starts at the very beginning. Assuming no knowledge of the field of morphology on the part of the reader, the book presents a broad range of morphological phenomena from a wide variety of languages. Starting with the core areas of inflection and derivation, the book presents the interfaces between morphology and syntax and between morphology and phonology. The synchronic study of word structure is covered, as are the phenomena of diachronic change, such as analogy and grammaticalization. Theories are presented clearly in accessible language with the main purpose of shedding light on the data, rather than as a goal in themselves. The authors consistently draw on the best research available, thus utilizing and discussing both functionalist and generative theoretical approaches. Each chapter includes a summary, suggestions for further reading, and exercises. As such this is the ideal book for both beginning students of linguistics, or anyone in a related discipline looking for a first introduction to morphology. |
| how to solve partitive proportion word problems: Unpacking Fractions Monica Neagoy, 2017-03-10 For years, the teaching and learning of fractions has been associated with rote memorization. But this mechanical approach to instruction—which strips students of an ability to reason or make sense of math—has resulted in a failure of understanding. Author Monica Neagoy, drawing on decades of research studies, evidence from teacher practice, and 25 years of experience working around the world with teachers, students, and parents, addresses seven big ideas in the teaching and learning of fractions in grades 2–6. Each idea is supported by a vignette from a real classroom, common misconceptions, a thorough unpacking of productive mathematical thinking, and several multistep and thought-provoking problems for teachers to explore. She offers three fundamental reasons why it's imperative for us to take a closer look at how we teach fractions: Fractions play a key role in students' feelings about mathematics. Fractions are fundamental to school math and daily life. Fractions are foundational to success in algebra. While a solid grounding in algebra is necessary for a STEM career, the worthy goal of algebra for all will not be possible until fractions for all is a reality. Unpacking Fractions provides teachers with concrete strategies for achieving that reality—in short, helping all students gain the knowledge they need to feel at ease with fractions. |
| how to solve partitive proportion word problems: Algebra, Grades 7 - 9 , 2014-02-03 The 100+ Series, Algebra, offers in-depth practice and review for challenging middle school math topics such as radicals and exponents; factoring; and solving and graphing equations. Common Core State Standards have raised expectations for math learning, and many students in grades 6–8 are studying more accelerated math at younger ages. As a result, parents and students today have an increased need for at-home math support. The 100+ Series provides the solution with titles that include over 100 targeted practice activities for learning algebra, geometry, and other advanced math topics. It also features over 100 reproducible, subject specific, practice pages to support standards-based instruction. |
| how to solve partitive proportion word problems: Word Problems, Grade 6 Spectrum Spectrum, 2013-12-02 Math Word Problems Grade 6 for kids ages 11+ Support your child’s educational journey with Spectrum’s 6th grade math workbook that teaches essential math skills to sixth graders. 6th grade math workbooks are a great way for children to learn math skills through word problems that cover geometry, fractions, decimals, algebra 1 prep, and more through a variety of learning activities that are both fun AND educational! Why You’ll Love This 6th Grade Math Word Problems Book Engaging and educational math activities. “Using a number line”, “Graphing”, and “Finding percentages” are a few of the fun math activities that incorporate word problems to help inspire learning into your child’s classroom or homeschool curriculum. Tracking progress along the way. Pretests, posttests, a mid-test and final test are included to test student knowledge along the way. Use the scoring record and answer key in the back of the Spectrum math pre algebra workbook to track student progress before moving on to new and exciting activities. Practically sized for every activity. The 128-page math workbook is sized at about 8 1⁄4 inches x 10 1⁄2 inches—giving your child plenty of space to complete each exercise. About Spectrum For more than 20 years, Spectrum has provided solutions for parents who want to help their children get ahead, and for teachers who want their students to meet and exceed set learning goals—providing workbooks that are a great resource for both homeschooling and classroom curriculum. The 6th Grade Math Workbook Contains: 13 chapters of versatile math activities Pretests, posttests, a mid-test, and final test Scoring record sheets and answer key |
| how to solve partitive proportion word problems: The Ohio Educational Monthly , 1907 |
| how to solve partitive proportion word problems: A grammar of Gyeli Nadine Grimm , 2021 This grammar offers a grammatical description of the Ngòló variety of Gyeli, an endangered Bantu (A80) language spoken by 4,000-5,000 Pygmy hunter-gatherers in southern Cameroon. It represents one of the most comprehensive descriptions of a northwestern Bantu language. The grammatical description, which is couched in a form-to-function approach, covers all levels of language, ranging from Gyeli phonology to its information structure and complex clauses. It draws on nineteen months of fieldwork carried out as part of the Bagyeli/Bakola DoBeS (Documentation of Endangered Languages) project between 2010 and 2014. The resulting multimodal corpus from that project, which includes texts of diverse genres such as traditional stories, narratives, multi-party conversations and dialogues, procedural texts, and songs, provides the empirical basis for the grammatical description. The documentary text collection, supplemented by data from elicitation work, questionnaires, and experiments, are accessible in the Bagyeli/Bakola collection of The Language Archive. With additional ethnographic, sociolinguistic, diachronic, and comparative remarks, the grammar may appeal to a wider audience in general linguistics, typology, Bantu studies, and anthropology. In 2019, the grammar received the Pāṇini Award by the Association for Linguistic Typology. |
| how to solve partitive proportion word problems: Individualism, Collectivism, and Political Power Érvíń Lásźló, 2013-11-09 |
| how to solve partitive proportion word problems: Didactics of Mathematics as a Scientific Discipline Rolf Biehler, Roland W. Scholz, Rudolf Sträßer, Bernard Winkelmann, 1993-11-30 Didactics of Mathematics as a Scientific Discipline describes the state of the art in a new branch of science. Starting from a general perspective on the didactics of mathematics, the 30 original contributions to the book, drawn from 10 different countries, go on to identify certain subdisciplines and suggest an overall structure or `topology' of the field. The book is divided into eight sections: (1) Preparing Mathematics for Students; (2) Teacher Education and Research on Teaching; (3) Interaction in the Classroom; (4) Technology and Mathematics Education; (5) Psychology of Mathematical Thinking; (6) Differential Didactics; (7) History and Epistemology of Mathematics and Mathematics Education; (8) Cultural Framing of Teaching and Learning Mathematics. Didactics of Mathematics as a Scientific Discipline is required reading for all researchers into the didactics of mathematics, and contains surveys and a variety of stimulating reflections which make it extremely useful for mathematics educators and teacher trainers interested in the theory of their practice. Future and practising teachers of mathematics will find much to interest them in relation to their daily work, especially as it relates to the teaching of different age groups and ability ranges. The book is also recommended to researchers in neighbouring disciplines, such as mathematics itself, general education, educational psychology and cognitive science. |
| how to solve partitive proportion word problems: Common Core Math For Parents For Dummies with Videos Online Christopher Danielson, 2015-04-06 Help your child succeed with a better understanding of Common Core Math Common Core Math For Parents For Dummies is packed with tools and information to help you promote your child's success in math. The grade-by-grade walk-through brings you up to speed on what your child is learning, and the sample problems and video lessons help you become more involved as you study together. You'll learn how to effectively collaborate with teachers and keep tabs on your child's progress, so minor missteps can be corrected quickly, before your child falls behind. The Common Core was designed to improve college- and career-readiness, and to prepare U.S. students to be more competitive on an international stage when it's time to enter the workforce. This guide shows you how the standards were created, and how they've evolved over time to help ensure your child's future success. The Common Core Math Standards prepare students to do real math in the real world. Many new teaching methods are very different from the way most parents learned math, leading to frustration and confusion as parents find themselves unable to help with homework or explain difficult concepts. This book cuts the confusion and shows you everything you need to know to help your child succeed in math. Understand the key concepts being taught in your child's grade Utilize the homework tools that help you help your child Communicate more effectively with your child's teacher Guide your child through sample problems to foster understanding The Common Core was designed to ensure that every student, regardless of location or background, receives the education they need. Math skills are critical to real-world success, and the new standards reflect that reality in scope and rigorousness. Common Core Math For Parents For Dummies helps you help your child succeed. |
| how to solve partitive proportion word problems: Subatomic quantification Marcin Wągiel , 2021 The goal of this book is to explore the relationship between the cognitive notion of parthood and various grammatical devices expressing this concept in natural language. The monograph aims to investigate syntactic constructions and lexical categories, e.g., partitives, whole-adjectives, and multipliers, encoding different kinds of part-whole structures both in Slavic and non-Slavic languages. It is envisioned to inspire radical rethinking of the ontology of models accounting for nominal semantics. Specifically, it provides novel evidence for a mereotopological approach to meaning, i.e., a theory of wholes that captures not only parthood but also topological relations holding between parts. This evidence comes from the phenomenon of subatomic quantification, i.e., quantification over parts of referents of concrete count nouns. |
| how to solve partitive proportion word problems: Space Word Problems Starring Ratios and Proportions Rebecca Wingard-Nelson, 2009-01-01 Make ratios and proportions word problems easy and fun using facts about space. This fully-illustrated book provides readers with all the tools needed to start solving ratios and proportions word problems, including clue words, four simple steps for solving any word problem, and more. Readers will conquer word problems and make math fun. |
| how to solve partitive proportion word problems: Children's Fractional Knowledge Leslie P. Steffe, John Olive, 2009-12-02 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. |
| how to solve partitive proportion word problems: Anaphora Resolution and Text Retrieval Helene Schmolz, 2015-03-30 This book covers anaphora resolution for the English language from a linguistic and computational point of view. First, a definition of anaphors that applies to linguistics as well as information technology is given. On this foundation, all types of anaphors and their characteristics for English are outlined. To examine how frequent each type of anaphor is, a corpus of different hypertexts has been established and analysed with regard to anaphors. The most frequent type are non-finite clause anaphors - a type which has never been investigated so far. Therefore, the potential of non-finite clause anaphors are further explored with respect to anaphora resolution. After presenting the fundamentals of computational anaphora resolution and its application in text retrieval, rules for resolving non-finite clause anaphors are established. Therefore, this book shows that a truly interdisciplinary approach can achieve results which would not have been possible otherwise. Open Access: In July 2019, this volume was retroactively turned into an Open Access publication thanks to the support of the Fachinformationsdienst Linguistik. https://www.linguistik.de/ |
| how to solve partitive proportion word problems: Catalogue ... Announcements ... College of William and Mary, 1903 |
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