A volume in Research in Mathematics Education Series Editor Barbara J. Dougherty, University of Mississippi This volume investigates the evolution of the geometry curriculum in the United States over the past 150 years. A primary goal is to increase awareness of the nature of the current geometry curriculum by investigating the historical, mathematical and pedagogical influences that it has sustained since its inception. Given the limited access to first-hand accounts of the enacted geometry curriculum during the past 150 years, the book relies on textbooks to provide a record of the implemented curriculum at any given point in time and on policy documents and journal articles to provide insight into the prevalent issues and arguments of the day. The book is organized in a chronological sequence of ""notable events"" leading to discernable changes in thinking about the geometry curriculum over the past century and a half-roughly the extent of time during which geometry has been taught in American schools. Notable events include important reports or commissions, influential texts, new schools of thought, and developments in learning technologies.These events affected, among other things: content and aims of the geometry curriculum; the nature of mathematical activity as construed by both mathematicians and mathematics educators; and, the resources students are given for engaging in mathematical activity. Before embarking through the notable events, it is necessary to consider the ""big bang"" of geometry, namely the moment in time that shaped the future life of the geometry curriculum. This corresponds to the emergence of Euclidean geometry. Given its influence on the shape of the geometry curriculum, familiarity with the nature of the geometry articulated in Euclid's Elements is essential to understanding the many tensions that surround the school geometry curriculum. Several themes emerge over the course of the monograph, and include: the aims and means of the geometry curriculum, the importance of proof in geometry, the role of visualization and tactile experiences, the fusion between solid and plane geometry, the curricular connections between geometry and algebra, and the use of motion and continuity. The intended audience would include curriculum developers, researchers, teachers, and curriculum supervisors.

"PACTS: The Coalition for Change" offers a case study chronicling the efforts of one urban high school district in Northern California to change its curriculum. It quantifies surveyed responses solicited from parents, administrators, curriculum leaders, teachers, and students in the district. It also assesses their level of agreement on issues relating to mathematics reform.

These agents of change constitute the PACTS Coalition. As a group, they generally agree that mathematics is a tough subject and that it should be fun; however, their level of agreement vacillates when the investigation turns to issues such as ability level grouping, the incorporation of diversity, and the question of inclusion.

In general, members of the alliance believe that the effect of reform efforts has been deleterious to the overall quality of mathematics education at their school site and in the district. Many respondents cite poor communication, ineffectual leadership, and a lack of direction as chief deterrents to effective mathematics reform; additionally, most agree that cohesion, unity, and morale among the mathematics staff in the district have suffered as a result.

Author Bill Collins shows that the varying perspectives of the PACTS Coalition is key to recognizing the complexity of educational issues while revealing the vision needed for lasting education reform.

A Volume in The Montana Mathematics Enthusiast: Monograph Series in Mathematics Education Series Editor Bharath Sriraman, The University of Montana The name of Zoltan P. Dienes (1916-) stands with those of Jean Piaget and Jerome Bruner as a legendary figure whose theories of learning have left a lasting impression on the field of mathematics education. Dienes' name is synonymous with the Multi-base blocks (also known as Dienes blocks) which he invented for the teaching of place value. He also is the inventor of Algebraic materials and logic blocks, which sowed the seeds of contemporary uses of manipulative materials in mathematics instruction. Dienes' place is unique in the field of mathematics education because of his theories on how mathematical structures can be taught from the early grades onwards using multiple embodiments through manipulatives, games, stories and dance. Dienes' notion of embodied knowledge presaged other cognitive scientists who eventually came to recognize the importance of embodied knowledge and situated cognition - where knowledge and abilities are organized around experience as much as they are organized around abstractions. Dienes was an early pioneer in what was later to be called sociocultural perspectives and democratization of learning. This monograph compiled and edited by Bharath Sriraman honors the seminal contributions of Dienes to mathematics education and includes several recent unpublished articles written by Dienes himself. These articles exemplify his principles of guided discovery learning and reveal the non-trivial mathematical structures that can be made accessible to any student. The monograph also includes a rare interview with Dienes in which he reflects on his life, his work, the role of context, language and technology in mathematics teaching and learning today. The book finds an important place in any mathematics education library and is vital reading for mathematics education researchers, cognitive scientists, prospective teachers, graduate students and teachers of mathematics.

Teaching mathematics is one of the most difficult and important jobs that anyone can do. Mathematics is a critical part of education and an essential building block for problem solving skills that are needed in the real world. However, many students struggle to learn and understand mathematical concepts and educators need to do everything possible to help our students learn. This book focuses on four areas necessary to be an impactful teacher of mathematics: Planning, Pedagogy, Assessment, and Relationships. For each of the ideas presented in the book, a brief introduction will be shared and then two different perspectives will be detailed with examples. The first is Not like This which is often the traditional way of teaching mathematics or the less effective approach. The second perspective is Teach Like This which is my recommended approach based upon research and my own experience as a teacher, math coordinator, and graduate instructor of math education.

This book examines the mathematical difficulties in typical and atypical populations. It discusses the behavioural, educational and neuropsychological characteristics of people with mathematical difficulties, and educational interventions to prevent, diagnose, treat or ameliorate such difficulties. The book brings together studies from different disciplines, including developmental psychology, neuroscience and education, and includes perspectives from practicing teachers.
The book is divided into three major sections. The first includes chapters about the nature and characteristics of mathematical difficulties in the population as a whole, in relation to both psychology and education. The second deals with mathematical difficulties in children with other problems such as specific language impairment and dyslexia. The third discusses methods of interventions aimed at preventing, treating or ameliorating mathematical difficulties, and will include discussions of assessment and diagnosis.

Algebra in the Middle Grades addresses topics that are formalized in the first half of an Algebra 1 course, focusing on linear equations, their graphs and their applications to problem solving. The book is intended to be used by students in the middle school in preparation for the formal study of Algebra 1. In this, it is a truly Pre-Algebra program. Algebra in the Middle Grades is an approach that brings Algebra to the students. It is written to have the essential elements of Algebra be understood on an inductive level so that when students later address the topic formally, there will be an informal background to create deep understanding. The approach is extremely visual using both algebra tile-type diagrams along with graphs for equations and grids for ratio. In this way, the text gives students 3 aspects of a topic, the Numerical, the Geometric and the Algebraic. The text places the Numerical and Geometric first having understanding in these contexts leading to understanding in an Algebraic, symbolic context.

Teaching mathematics is one of the most difficult and important jobs that anyone can do. Mathematics is a critical part of education and an essential building block for problem solving skills that are needed in the real world. However, many students struggle to learn and understand mathematical concepts and educators need to do everything possible to help our students learn. This book focuses on four areas necessary to be an impactful teacher of mathematics: Planning, Pedagogy, Assessment, and Relationships. For each of the ideas presented in the book, a brief introduction will be shared and then two different perspectives will be detailed with examples. The first is Not like This which is often the traditional way of teaching mathematics or the less effective approach. The second perspective is Teach Like This which is my recommended approach based upon research and my own experience as a teacher, math coordinator, and graduate instructor of math education.

Curriculum materials are among the most pervasive and powerful influences on school mathematics. In many mathematics classes, student assignments, the questions the teacher asks, the ways students are grouped, the forms of assessment, and much more originate in curriculum materials. At the same time, teachers have considerable latitude in how they use their curriculum materials. Two classes making use of the same materials may differ markedly in what mathematics content is emphasized and how students are engaged in learning that content. This volume considers a variety of research tools for investigating the enactment of mathematics curriculum materials, describing the conceptualization, development, and uses of seven sets of tools. Mathematics education researchers, curriculum developers, teacher educators, district supervisors, teacher leaders, and math coaches will find insights that can improve their work, and guidance for selecting, adapting, and using tools for understanding the complex relationship between curriculum materials and their enactment in classroom instruction.

A volume in Research in Mathematics Education Series Editor Barbara J. Dougherty, University of Mississippi This monograph reports on an analysis of a small part of the mathematics curriculum, the definitions given to quadrilaterals. This kind of research, which we call micro-curricular analysis, is often undertaken by those who create curriculum, but it is not usually done systematically and it is rarely published. Many terms in mathematics education can be found to have different definitions in mathematics books. Among these are ""natural number,"" ""parallel lines"" and ""congruent triangles,"" ""trapezoid"" and ""isosceles trapezoid,"" the formal definitions of the trigonometric functions and absolute value, and implicit definitions of the arithmetic operations addition, subtraction, multiplication, and division. Yet many teachers and students do not realize there is a choice of definitions for mathematical terms. And even those who realize there is a choice may not know who decides which definition of any mathematical term is better, and under what criteria. Finally, rarely are the mathematical implications of various choices discussed.As a result, many students misuse and otherwise do not understand the role of definition in mathematics. We have chosen in this monograph to examine a bit of mathematics for its definitions: the quadrilaterals. We do so because there is some disagreement in the definitions and, consequently, in the ways in which quadrilaterals are classified and relate to each other. The issues underlying these differences have engaged students, teachers, mathematics educators, and mathematicians. There have been several articles and a number of essays on the definitions and classification of quadrilaterals. But primarily we chose this specific area of definition in mathematics because it demonstrates how broad mathematical issues revolving around definitions become reflected in curricular materials. While we were undertaking this research, we found that the area of quadrilaterals supplied grist for broader and richer discussions than we had first anticipated. The intended audience includes curriculum developers, researchers, teachers, teacher trainers, and anyone interested in language and its use.

Perfect for children aged 10-11 preparing for 11+ Maths and other selective entrance exams, this book contains a huge range of questions at the level of the final tests. The first section of the book focuses on one topic at a time to help children gain understanding and confidence. This is followed by four realistic Assessment Tests to improve their speed and accuracy across a wide range of questions. And if they get stuck or go wrong, the detailed pull-out answers make it easy to understand the reasoning behind the questions. Multiple-choice answer sheets for the Assessment Tests are available to download from the CGP website. This book is ideal for the 11+ tests set by GL Assessment and other test providers, and provides excellent practice for the Kent Test. A separate edition for the CEM tests is also available. Great news - a free Online Edition of the whole book is included - just use the unique access code printed inside the cover to access it on a PC, Mac or tablet!

Goue reeks is een van die heel bekendste en gewildste inheemse leesreekse met beproefde sukses oor dekades. Derduisende onderwysers en ouers het self daarmee leer lees – en dit werk steeds! Op publieke aanvraag is die volledige reeks nou weer beskikbaar. Dit volg ’n basiese benadering tot leesonderrig deur klank- en woordbouvaardighede en is gebaseer op herhaling, herkenning en inoefening. Goue reeks se hersiene uitgawe (2009) bied alles wat nodig is om jong leerders te ontwikkel in jong lesers.

The goal of this series is to use teachers' accounts of classroom inquiry to make public and explicit the processes of doing research in classrooms. Teaching is a complex, multi-faceted task, and this complexity often is not captured in research articles. Our goal is to illuminate this complexity. Research that is done in classrooms by and with teachers is necessarily messy, and our stance is that the ways in which this is so should be articulated, not hidden. Through the chapters in this volume we learn about the questions that capture the attention of teachers, the methodologies they use to gather data, and the ways in which they make sense of what they find. Some of the research findings could be considered preliminary, others confirmatory, and some may be groundbreaking. In all cases, they provide fodder for further thinking and discussion about critical aspects of mathematics education.

During the past few years, groups like the President's Council of Advisors on Science and Technology, Center for Education have been placing great emphasis on the significance of STEM (science, technology, engineering, and math) education. In brief, the US is seen as falling behind the rest of the world in science and technology education. In response, the curricula have been revised in many educational institutions and school districts across the country. It is clear that for STEM to be successful, other community organizations, most particularly libraries, need to be closely involved in the process. Library staff realize the importance of getting involved in STEM education, but many have difficulty finding comprehensive information that will help them plan and successfully implement STEM direction in their organization. This book is designed to meet that need. It is timely and relevant. How to STEM: Science, Technology, Engineering, and Math Education in Libraries is by and for libraries who are involved in contributing efforts into advancing these subjects. It is organized in 9 parts including funding, grant writing, community partnerships, outreach, research, and examples of specific programming activities. Authors are drawn from the professional staffs of educational institutions, libraries, and non-profit organizations such as science museums. The book contains eight parts, each emphasizing a different aspect of how to succeed with STEM. Part 1 emphasizes how hands-on activities that are both fun and educational can be used to further STEM awareness. Parts 2 and 3 contain chapters on the uniting of STEM with Information Literacy. Innovative collection development ideas are discussed in Part 4 and Part 5 focuses on research and publishing. Outreach is the theme of Part 6 and the programs described in these chapters offer an array of ways to connect with students of all ages. The final section of How to STEM: Science, Technology, Engineering, and Math Education in Libraries addresses the funding of these programs. Librarians of all types will be pleased to discover easy-to-implement suggestions for collaborative efforts, many rich and diverse programming ideas, strategies for improving reference services and library instruction to speakers of English as a second language, marketing and promotional tips designed to welcome multicultural patrons into the library, and much more.

The only official Minecraft maths book for children aged 8-9! Children embark on a Minecraft adventure in each maths topic, using their maths skills and knowledge to complete the tasks and earn rewards. This is a write-in maths practice workbook which uses the Minecraft game as a mechanism for practising the key maths skills covered in Year 4. Accomplish maths activities to help Minecraft characters on their missions Explore different biomes in each topic Earn emeralds as you work through the book, and choose how you spend them Go hardcore with challenging questions

The driving forces behind mathematics learning trajectories is the need to understand how children actually learn and make sense of mathematics-how they progress from prior knowledge, through intermediate understandings, to the mathematics target understandings-and how to use these insights to improve instruction and student learning. In this book, readers will come to understand what learning trajectories are, the research and methodology that are necessary for developing them, and gain insight into potential applications of learning trajectories. A synthesis and research outcome in their own right, learning trajectories provide detailed description of instructionally-grounded development of mathematical concepts and reasoning from the perspective of student learning, and, overall, building on decades of accumulated experience in mathematics education research. However, their greater importance may lie in their potential as frameworks that contribute an unprecedented coherence across classroom instruction, professional development, standards, and assessment, by focusing squarely on conceptual understanding and reasoning instead of assessment-driven procedural knowledge. This potential was sufficiently compelling as an organizing framework to have been cited as a basis for the Common Core mathematics standards, the new mathematics learning expectations that are now consistent across most of the United States. (Among the conference attendees were the writers of the Common Core State Standards for Mathematics, at the beginning of the Standards drafting process.) This book is an outgrowth of a conference on learning trajectories, hosted in 2009 at North Carolina State University, which examined research on learning trajectories. An overarching message of the chapters in this volume is that learning trajectories, by focusing on how children's mathematical reasoning develops, are coming into their own as a rigorous underpinning for both instruction and accountability. Some of the learning scientists featured in this volume have played major roles learning trajectories' evolution--from small-scale day-to-day conjectures by individual teachers, to systematic research endeavors that teachers and scientists alike can use to interpret standards, plan instruction, and formatively assess student work. The work in this volume will be of interest to mathematics educators, teachers, and professional development specialists.

This volume was written primarily for teachers who have developed (or who are being encouraged to develop) an awareness of and commitment to teaching mathematics for understanding. The research findings presented in these chapters suggest instructional implications worthy of these teachers' consideration. Often, the authors in this volume describe instructional practices or raise issues that have the potential to broaden views of teaching and learning mathematics. These chapters provide interesting problems and tasks used in the authors' work that readers can use in their own classrooms. The volume can also be used with courses for preservice and inservice teachers, collaborative teacher study groups, and other professional activities. A hallmark of good research is its connection to the relevant literature in the field, and the authors of this volume have themselves drawn from the research literature to inform their work. The reference lists accompanying these chapters can be useful resources and should not be overlooked. Most importantly for teacher education, this volume showcases the variety of ways teachers can become engaged in research, and we hope that readers will recognize that teacher research can be both accessible and beneficial in the preparation and professional development of teachers. This is not to suggest, however, that this volume is intended only for teachers and teacher educators. It is also intended to be an interesting, informative resource for other researchers, school administrators, and policy makers. The research presented in this volume is intended to provide an opportunity for those outside the classroom to gain insight into the kinds of issues that matter to teachers, the ways in which those issues might be researched, and the contributions that classroom research makes to mathematics education.