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.
In an age where the quality of teacher education programs has been called into question, it is more important than ever that teachers have a fundamental understanding of the principles of human learning, motivation, and development. Theory to Practice: Educational Psychology for Teachers and Teaching is a series for those who teach educational psychology in teacher education programs. At a time when educational psychology is at risk of becoming marginalized, it is imperative that we, as educators, “walk our talk” in serving as models of what effective instruction looks like. Each volume in the series draws upon the latest research to help instructors model fundamental principles of learning, motivation, and development to best prepare their students for the diverse, multidimensional, uncertain, and socially-embedded environments in which these future educators will teach. The inaugural volume, Teaching on Assessment, is centered on the role of assessment in teaching and learning. Each chapter translates current research on critical topics in assessment for educational psychology instructors and teacher educators to consider in their teaching of future teachers. Written for practitioners, the aim is to present contemporary issues and ideas that would help teachers engage in meaningful assessment practice. This volume is important not only because of the dwindling presence of assessment-related instructional content in teacher preparation programs, but also because the policy changes in the last two decades have transformed the meaning and use of assessment in K-12 classrooms. Praise for Teaching on Assessment "This thought-provoking book brings together perspectives from educational psychology and teacher education to examine how assessment can best support student motivation, engagement, and learning. In the volume, editors Nichols and Varier present a set of chapters written by leaders in the field to examine critical questions about how to best prepare teachers to make instructional decisions, understand assessment within the context of learning and motivation theory, and draw on assessment in ways which can meet the needs of diverse learners. Written in a highly accessible language and style, each chapter contains clear takeaway messages designed for educational psychologists, teacher educators, teachers, and pre-service teachers. This book is essential reading for anyone involved in teaching or developing our future teaching professionals." Lois R. Harris, Australian Catholic University "This impressive book provides a wealth of contemporary and engaging resources, ideas and perspectives that educational psychology instructors will find relevant for helping students understand the complexity of assessment decision-making as an essential component of instruction. Traditional assessment principles are integrated with contemporary educational psychology research that will enhance prospective teachers’ decision-making about classroom assessments that promote all students’ learning and motivation. It is unique in showing how to best leverage both formative and summative assessment to boost student engagement and achievement, enabling students to understand how to integrate practical classroom constraints and realities with current knowledge about self-regulation, intrinsic motivation, and other psychological constructs that assessment needs to consider. The chapters are written by established experts who are able to effectively balance presentation of research and theory with practical applications. Notably, the volume includes very important topics rarely emphasized in other assessment texts, including assessment literacy frameworks, diversity, equity, assessment strategies for students with special needs, and data-driven decision making. The book will be an excellent supplement for educational psychology classes or for assessment courses, introducing students to current thinking about how to effectively integrate assessment with instruction." James McMillan, Virginia Commonwealth University.
The purpose of this book is to collect, organize and disseminate collective wisdom with respect to designing, conducting, and publishing quality research in mathematics education. This wisdom will be gleaned from among those who, over the past several decades, have been instrumental in guiding the field in the pursuit of excellence in mathematics education research—insightful editors, educative reviewers, prolific writers, and caring mentors. Each chapter is written to the novice researcher with the intent of aiding them in avoiding common pitfalls, navigating difficult intellectual terrain, and understanding that they are not alone in experiencing rejection, frustration, confusion, and doubt. This book differs from existing literature in the sense that it is written about the enterprise of designing, conducting and publishing research in mathematics education as opposed to being reports of the results of such work. It also differs in the sense that it is written with the intent to mentor the rising generation as opposed to capture the state of the field (as would happen in a handbook, for example). It is written for the express purpose of helping the field work collectively to aid in the often isolated enterprise of mentoring new researchers. The primary audience is a potentially wide one: graduate students, novice researchers, graduate faculty, advisors, and mentors – or anyone seeking to improve their own abilities to design, conduct, and publish quality research in mathematics education.
This book provides prospective and practicing teachers with research insights into the mathematical difficulties of students with learning disabilities and classroom practices that address these difficulties. This linkage between research and practice celebrates teachers as learners of their own students’ mathematical thinking, thus contributing an alternative view of mathematical progression in which students are taught conceptually. The research-based volume presents a unique collaboration among researchers in special education, psychology, and mathematics education from around the world. It reflects an ongoing work by members of the International Group for the Psychology of Mathematics Education (PME) and the North American Chapter of the PME Working Groups. The authors of chapters in this book, who have been collaborating extensively over the past 7 years, are from Australia, Canada, the United Kingdom, and the United States.
With a focus on what mathematics and science educators need to know about academic language used in the STEM disciplines, this book critically synthesizes the current knowledge base on language challenges inherent to learning mathematics and science, with particular attention to the unique issues for English learners. These key questions are addressed: When and how do students develop mastery of the language registers unique to mathematics and to the sciences? How do teachers use assessment as evidence of student learning for both accountability and instructional purposes? Orienting each chapter with a research review and drawing out important Focus Points, chapter authors examine the obstacles to and latest ideas for improving STEM literacy, and discuss implications for future research and practice.
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.
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.
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.
Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts focuses on typical and atypical learning of complex arithmetic skills and higher-order math concepts. As part of the series Mathematical Cognition and Learning, this volume covers recent advances in the understanding of children's developing competencies with whole-number arithmetic, fractions, and rational numbers. Each chapter covers these topics from multiple perspectives, including genetic disorders, cognition, instruction, and neural networks. - Covers innovative measures and recent methodological advances in mathematical thinking and learning - Contains contributions that improve instruction and education in these domains - Informs policy aimed at increasing the level of mathematical proficiency in the general public
