Abacus is a unique maths toolkit for inspiring a love of maths and ensuring progression for every child. Written by an expert author team, it has been carefully crafted on a robust approach to creating inspired and confident young mathematicians. Year 3 Mastery Checkpoints 34 short activities, to be used throughout the school year Designed to help you check mastery of key concepts straight after teaching, enabling quick intervention for those children who need it 'Have you mastered...?' questions aim to assess mastery of the relevant outcome 'Champions' Challenge' questions aim to assess whether some children have achieved mastery with greater depth 'My Learning' pages provide opportunities for children to reflect on their learning

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by Bharath Sriraman honors the seminal contributions of Dienes to mathematics education and includes several recent unpublished articles written by Dienes himself.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.

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.

Category Description for Kumon Math Workbooks (1-6):

A math program based on the Kumon method. Basically, the earmarks of this system are:

• Concepts introduced in small, incremental steps, allowing children to master them without confusion
• Single topic books rather than mixed strands. Children concentrate just on addition, for example, before moving to subtraction
• Concepts are taught by discovery method than being spelled out

The series is meant to be self-directed. Students take charge of their own learning on every level. They complete pages, check their work, record their scores, and determine whether to move on or review. The pace almost guarantees success. Children should work a "few" pages a day; assignments should take about 20 minutes to complete. Pages are marked with the skill level required at top and the points each question is valued at (a very young child will need some help totaling points). Very short instruction (or an example) is given on a few pages. For example, there is a short explanation when children begin to subtract a 2-digit number from a 3-digit number where borrowing is needed. However, the child is given every opportunity to intuit this beforehand. By the time he reaches this page, he has already been subtracting double-digit numbers for many pages. Some of these would require borrowing, but, since they are able to subtract, say, 7 from 12, the Kumon method wants the child to see a pattern when increasing to 7 from 22, 7 from 32, etc. This does remind me of the approach used in Miquon as well. Besides these very infrequent helps there are just some small prompts for children to look for patterns in their answers, and words of encouragement. Pages are pleasing to the eye; they are colored, clean, and problems are well-spaced. The Kumon method has been used successfully with children around the world for over 50 years. It does seem like it would help a child to take charge of his own learning and help himself to understanding rather than being spoon-fed each bite. For Kumon math earlier than Grade 1, see the Kumon section in Early Learning.

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.

"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.

Written in a user-friendly, conversational style, the fourth edition of this groundbreaking text helps pre-service and in-service mathematics teachers build the comfort and confidence they need to begin talking to children about fractions and ratios, distilling complex ideas and translating research into usable ideas for the classroom. For two decades, 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. Each chapter includes children's strategies and samples of student work for teacher analysis, as well as activities for practicing each thinking strategy, designed to be solved without rules or algorithms, using reasoning alone. The fourth edition of this popular text has been updated throughout and includes new examples of student work, updated artwork, and more. As with previous editions, an equally valuable component of this text is the companion book MORE! Teaching Fractions and Ratios for Understanding (2012), a supplement that is not merely an answer key but a resource that provides the scaffolding for the groundbreaking approach to fraction and ratio instruction explored here. 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.

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.

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.

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.

We are working with Cambridge International to gain endorsement for this forthcoming title. Confidently deliver and ensure full coverage of the core content of the latest Cambridge IGCSE (TM) Mathematics syllabuses (0580/0980) using a tried-and-tested approach to improve mathematical skills with an emphasis on problem solving and interrogating findings in new topics. - Trust an experienced team of authors offering advice on how to put theory into practice with plenty of exercises, worked examples and solutions with scaffolding for the appropriate levels - Encourage full understanding of mathematical principles with commentaries and additional explanations - Develop problem-solving skills with guidance on techniques to help complete open-ended investigations and justify reasoning for solutions - Check understanding with end of chapter student assessments to consolidate learning and test skills

NHM Reception Activity Books: Use language at an appropriate reading level. Place maths in a variety of contexts. Lead more able children through a range of problem-solving activities.

The Check-up Workbook includes: Check-ups - which assess specific pieces of work Round-ups - provide assessment of the range of mathematics covered according to the 5-14 Attainment targets. They include an end of level test.

This pack from CGP contains two sets of complete practice exams, with detailed answers and mark schemes. They match the content and style of the AQA Grade 9-1 Higher Level Maths GCSE exams, with a separate booklet for each paper - just like the real thing. The mark scheme is straightforward to use, including hints and tips, making this the perfect way to prepare for the exams.

These practice papers are designed to be completed after our 11+ Maths workbooks and short testbooks. They should be used as learning reinforcement and are essential for exam preparation. Each practice paper simulates the format and content of the 11+ exam and may be completed as a standard or multiple-choice test. Each test should take about 50 minutes, however it is more important that a child completes the test accurately and does not rush. Children will speed up naturally with practice.

A Volume in The Montana Mathematics Enthusiast: Monograph Series in Mathematics EducationSeries Editor Bharath Sriraman, The University of MontanaThe intent of this monograph is to showcase successful implementation ofmathematical discourse in the classroom. Some questions that might beaddressed are: * How does a teacher begin to learn about using discourse purposefully toimprove mathematics teaching and learning?* How is discourse interwoven into professional development content courses toprovide teachers with the tools necessary to begin using discourse in their ownclassrooms?* What does a discourse-rich classroom look like and how is it different from other classrooms, from both theteacher's and the students' perspectives?* How can teachers of pre-service teachers integrate discourse into their content and methods courses?* How can we use discourse research to inform work with teachers, both pre- and in-service, for example, to helpthem know how to respond to elicited knowledge from students in their classrooms?* What are the discourse challenges in on-line mathematics courses offered for professional development? Canon-line classrooms also be discourse-rich? What would that look like?* In what ways does mathematical discourse differ from discourse in general?