Creativity of an Aha! Moment and Mathematics Education introduces bisociation, the theory of Aha! moment creativity into mathematics education. It establishes relationships between Koestler's bisociation theory and constructivist learning theories. It lays down the basis for a new theory integrating creativity with learning to describe moments of insight at different levels of student development. The collection illuminates the creativity of the eureka experience in mathematics through different lenses of affect, cognition and conation, theory of attention and constructivist theories of learning, neuroscience and computer creativity. Since Aha! is a common human experience, the book proposes bisociation as the basis of creativity for all. It discusses how to facilitate and assess Aha! creativity in mathematics classrooms. Contributors are: William Baker, Stephen Campbell, Bronislaw Czarnocha, Olen Dias, Gerald Goldin, Peter Liljedahl, John Mason, Benjamin Rott, Edme Soho, Hector Soto, Hannes Stoppel, David Tall, Ron Tzur and Laurel Wolf.

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.

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.

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.

First Mental Arithmetic provides carefully graded questions that develop children's essential mathematics skills. A downwards extension of the Schofield & Sims bestseller Mental Arithmetic, the series comprises three workbooks for Year 1 (Books 1 to 3) and three for Year 2 (Books 4 to 6). The term 'mental arithmetic' is usually associated with spoken questions. However, children using all the Schofield and Sims Mental Arithmetic materials read the questions themselves and write down their answers. A Language of Maths glossary helps to develop children's number vocabulary and three Check-ups assess children's understanding. The separate First Mental Arithmetic Answers provides answers to all questions contained in this book, plus additional resources for teachers. Book 1 includes: counting, adding and subtracting, 2D and 3D shapes, days of the week, word problems.

Children love learning with Smart-kids. Bright illustrations, stickers, creative activities and fun-loving characters bring the South African Maths curriculum to life. This Smart-kids workbook is specially written for Grade R learners by experienced South African teachers and contains valuable notes, tips and answers for parents.

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.

Exam Board: Edexcel Level: GCSE Subject: Maths First teaching: September 2015 First exams: June 2017 Problem-solving and reasoning questions included throughout. Exam-style questions give students exposure to the sort of questions they will need to answer in their exam. Problem-solving lessons build up strategies from the Student Book so that students need to choose the most appropriate strategy. Mixed problem-solving questions drawing on knowledge from this and previous chapters in the book give students the opportunity to practice using this strategy.

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.

Rapid Maths is the ideal way to help struggling learners catch up with their peers in maths. With lots of variety plus software and games, Rapid Maths makes catch-up fun and gives each child personalised support and repeated practice in the fundamentals of numeracy. Plus, it's proven to double children's progress in number skills. Helps children master basic number skills to enable them to access the curriculum. Clear layout and a concrete-pictorial-abstract approach helps to support struggling learners. Gradual spiral progression in number skills to aid confidence. Varied and engaging 'real life' maths activities. Time saving and accessible teacher and TA resources. Ideal for home learning. Textbook with questions for child to work through with adult support.

Increase students' skills, confidence and chance of success in their National 5 Maths exam, with full course coverage delivered through the trusted TeeJay approach. This book provides hundreds of practice questions, with progression and consolidation - the core TeeJay philosophy - underpinning every exercise and chapter. - Use Book 4+, followed by Book N5, to cover the entire National 5 course - Chapter Zero revises all of the strands from Third Level - Every chapter ends with 'Remember Remember' exercises for revision and assessment - Every third chapter ends with 'Practice Makes Perfect' exercises that consolidate learning across those 3 chapters, plus cumulative exercises based on all chapters up to that point - Plenty of non-calculator exercises are included to enhance numeracy skills - Answers for all questions are in the back of the book; answers for the 'Practice Makes Perfect' home exercises are available on the TeeJay Maths website

Did you know there's a single spot on your brain that recognizes numbers? Or that the first computer bugs were actual insects and that most of the internet is under water? This fascinating book is filled with 100 fascinating facts, bright, infographic illustrations, a glossary and index and links to specially selected websites to find out more.

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.

Die Nuwe Alles-In-Een reeks is volledig hersien en aangepas volgens die Kurrikulum-en asesseringsbeleidsverklaring. Is beskikbaar vir die vakke Huistaal, Wiskunde en Lewensvaardighede. Kan per vak of as pakket gebruik word. Is beskikbaar vir Gr R-3. Word gebruik saam met die gratis werkvelle op die CD in die Onderwysersgids.

Primary Maths for Scotland Textbook 2C is the third of 3 second level textbooks. These engaging and pedagogically rigorous books are the first maths textbooks for Scotland completely aligned to the benchmarks and written specifically to support Scottish children in mastering mathematics at their own pace. Primary Maths for Scotland Textbook 2C is the third of 3 second level textbooks. The books are clear and simple with a focus on developing conceptual understanding alongside procedural fluency. They cover the entire second level mathematics Curriculum for Excellence in an easy-to-use set of textbooks which can fit in with teacher's existing planning, resources and scheme of work. - Packed with problem-solving, investigations and challenging problems - Diagnostic check lists at the start of each unit ensure that pupils possess the required pre-requisite knowledge to engage on the unit of work - Worked examples and non-examples help pupils fully understand mathematical concepts - Includes intelligent practice that reinforces pupils' procedural fluency