Features: * key points * guided practice *'no-stabilisers' practice *'step into GCSE' stretch questions *'don't forget' - key reminders * exam-style practice questions * self-assessment record * complete practice paper.

Concept Mapping in Mathematics: Research into Practice is the first comprehensive book on concept mapping in mathematics. It provides the reader with an understanding of how the meta-cognitive tool, namely, hierarchical concept maps, and the process of concept mapping can be used innovatively and strategically to improve planning, teaching, learning, and assessment at different educational levels. This collection of research articles examines the usefulness of concept maps in the educational setting, with applications and examples ranging from primary grade classrooms through secondary mathematics to pre-service teacher education, undergraduate mathematics and post-graduate mathematics education. A second meta-cognitive tool, called vee diagrams, is also critically examined by two authors, particularly its value in improving mathematical problem solving.

Thematically, the book flows from a historical development overview of concept mapping in the sciences to applications of concept mapping in mathematics by teachers and pre-service teachers as a means of analyzing mathematics topics, planning for instruction and designing assessment tasks including applications by school and university students as learning and review tools. This book provides case studies and resources that have been field tested with school and university students alike. The findings presented have implications for enriching mathematics learning and making problem solving more accessible and meaningful for students.

The theoretical underpinnings of concept mapping and of the studies in the book include Ausubel s cognitive theory of meaningful learning, constructivist and Vygotskian psychology to name a few. There is evidence particularly from international studies such as PISA and TIMSS and mathematics education research, which suggest that students mathematical literacy and problem solving skills can be enhanced through students collaborating and interacting as they work, discuss and communicate mathematically. This book proposes the meta-cognitive strategy of concept mapping as one viable means of promoting, communicating and explicating students mathematical thinking and reasoning publicly in a social setting (e.g., mathematics classrooms) as they engage in mathematical dialogues and discussions.

Concept Mapping in Mathematics: Research into Practice is of interest to researchers, graduate students, teacher educators and professionals in mathematics education.

Constructing concise and correct proofs is one of the most challenging aspects of learning to work with advanced mathematics. Meeting this challenge is a defining moment for those considering a career in mathematics or related fields. Mathematical Thinking and Writing teaches readers to construct proofs and communicate with the precision necessary for working with abstraction. It is based on two premises: composing clear and accurate mathematical arguments is critical in abstract mathematics, and that this skill requires development and support. Abstraction is the destination, not the starting point.
Maddox methodically builds toward a thorough understanding of the proof process, demonstrating and encouraging mathematical thinking along the way. Skillful use of analogy clarifies abstract ideas. Clearly presented methods of mathematical precision provide an understanding of the nature of mathematics and its defining structure.
After mastering the art of the proof process, the reader may pursue two independent paths. The latter parts are purposefully designed to rest on the foundation of the first, and climb quickly into analysis or algebra. Maddox addresses fundamental principles in these two areas, so that readers can apply their mathematical thinking and writing skills to these new concepts. From this exposure, readers experience the beauty of the mathematical landscape and further develop their ability to work with abstract ideas.
* Covers the full range of techniques used in proofs, including contrapositive, induction, and proof by contradiction
* Explains identification of techniques and how they are applied in the specific problem
* Illustrates how to read written proofs with many step by step examples
* Includes 20% more exercises than the first edition that are integrated into the material instead of end of chapter
* The Instructors Guide and Solutions Manual points out which exercises simply must be either assigned or at least discussed because they undergird later results

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

This book develops the theoretical perspective on visuospatial reasoning in ecocultural contexts, granting insights on how the language, gestures, and representations of different cultures reflect visuospatial reasoning in context. For a number of years, two themes in the field of mathematics education have run parallel with each other with only a passing acquaintance. These two areas are the psychological perspective on visuospatial reasoning and ecocultural perspectives on mathematics education. This volume examines both areas of research and explores the intersection of these powerful ideas. In addition, there has been a growing interest in sociocultural aspects of education and in particular that of Indigenous education in the field of mathematics education. There has not, however, been a sound analysis of how environmental and cultural contexts impact visuospatial reasoning, although it was noted as far back as the 1980s when Alan Bishop developed his duality of visual processing and interpreting visual information. This book provides this analysis and in so doing not only articulates new and worthwhile lines of research, but also uncovers and makes real a variety of useful professional approaches in teaching school mathematics. With a renewed interest in visuospatial reasoning in the mathematics education community, this volume is extremely timely and adds significantly to current literature on the topic.

MasterClass in Mathematics Education provides accessible links between theory and practice and encourages readers to reflect on their own understanding of their teaching context. Each chapter, written by an internationally respected authority, explores the key concepts within the selected area of the field, drawing directly on published research to encourage readers to reflect on the content, ideas and ongoing debates. Using international case studies, each chapter will encourage readers to think about ways that the teaching and learning of mathematics reflect different cultural traditions and expectations and enable them to evaluate effective strategies for their own contexts.

Is the maths monster biting at your brain? Maths can be scary, but not with Monster Maths! Whether you're counting or measuring, sorting shapes or picking out patterns, these friendly maths monsters can help any young mathematician find the right answer.

Teacher Materials include: Presentation Books include a Guide section containing information for presenting exercises, correcting mistakes, and administering the pre-skill and placement tests. There is also a Presentation section that contains detailed lessons plans. Answer Key Booklets quickly and easily compare students' work with the actual calculations and word problem results.

The mathematics education community continues to contribute research-based ideas for developing and improving problem posing as an inquiry-based instructional strategy for enhancing students' learning. A large number of studies have been conducted which have covered many research topics and methodological aspects of teaching and learning mathematics through problem posing. The Authors' groundwork has shown that many of these studies predict positive outcomes from implementing problem posing on: student knowledge, problem solving and posing skills, creativity and disposition toward mathematics. This book examines, in-depth, the contribution of a problem posing approach to teaching mathematics and discusses the impact of adopting this approach on the development of theoretical frameworks, teaching practices and research on mathematical problem posing over the last 50 years.

Many in the mathematics community in the U.S. are involved in mathematics education in various capacities. This book highlights the breadth of the work in K-16 mathematics education done by members of US departments of mathematical sciences. It contains contributions by mathematicians and mathematics educators who do work in areas such as teacher education, quantitative literacy, informal education, writing and communication, social justice, outreach and mentoring, tactile learning, art and mathematics, ethnomathematics, scholarship of teaching and learning, and mathematics education research. Contributors describe their work, its impact, and how it is perceived and valued. In addition, there is a chapter, co-authored by two mathematicians who have become administrators, on the challenges of supporting, evaluating, and rewarding work in mathematics education in departments of mathematical sciences. This book is intended to inform the readership of the breadth of the work and to encourage discussion of its value in the mathematical community. The writing is expository, not technical, and should be accessible and informative to a diverse audience. The primary readership includes all those in departments of mathematical sciences in two or four year colleges and universities, and their administrators, as well as graduate students. Researchers in education may also find topics of interest. Other potential readers include those doing work in mathematics education in schools of education, and teachers of secondary or middle school mathematics as well as those involved in their professional development.

Level: KS2 Subject: Maths Learn the easy way with this multiplication & division activity book! Including helpful questions and answers, this Maths book provides reassurance whilst supporting your child's learning at home. Combining useful Maths practice with engaging, colourful illustrations, this Multiplication and Division practice book helps to boost your child's confidence and develop good learning habits for life. Each fun activity is designed to give your child a real sense of achievement. Included in this book: questions that allow children to practise the important skills learned at school colourful activities that make learning fun and motivate children to learn at home helpful tips and answers so that you can support your child's learning

This book presents a literature review of and a state-of-the-art glimpse into current research on affect-related aspects of teaching and learning in and beyond mathematics classrooms. Then, research presented at the MAVI 25 Conference, which took place in Intra (Italy) in June 2019, is grouped in thematic strands that capture cutting-edge issues related to affective components of learning and teaching mathematics. The concluding chapter summarises the main messages and sketches future directions for research on affect in mathematics education. The book is intended for researchers in mathematics education and especially graduate students and PhD candidates who are interested in emotions, attitudes, motivations, beliefs, needs and values in mathematics education.

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 knowledgeTeachers' personal and classroom mathematicsTeachers' learning journeys toward reasoning and sense-makingTeachers' transitions in noticingTeachers' 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."

This volume presents a set of studies that explore significant questions about mathematics teaching and learning, and illustrate new methodologies for the analysis of new questions about mathematics education. The data from the "Second International Mathematical Study" (SIMS) is the starting point for all of the material in this work. SIMS was one of the largest and most comprehensive data-collection effort on mathematics teaching and learning ever undertaken. Because of its scale, comparative cross-cultural perspective, conceptualization and design, its data offer an indispensable beginning point for the exploration of many of the fundamental questions that circle around mathematics teaching and learning, not only internationally, but in the United States as well.

The series Mental Maths develops children's ability to understand number problems and to use their knowledge to resolve these problems confidently and logically. Mental Maths Book 2 covers: counting and ordering numbers to 100, patterns and sequences, counting money and calculating change, 2-D and 3-D shapes, tens and units; addition/subtraction of 2-digit numbers, time problems, estimating and measuring and multiples of 2/5/10.

A Volume in The Montana Mathematics Enthusiast: Monograph Series in Mathematics EducationSeries Editor Bharath Sriraman, The University of MontanaPaul Ernest's name is synonymous with social constructivism as a philosophy ofmathematics. His contributions to mathematics education have occurred at a veryfundamental level and to an extent shaped theory development in this field. Hisresearch addresses fundamental questions about the nature of mathematics and how itrelates to teaching, learning and society. For the last three decades Paul has been aprolific scholar who has published in a wide array of topics such as the relationshipbetween the philosophy of mathematics and mathematics education, and moregenerally the philosophy of mathematics education, ethics and values in mathematics education, and the philosophy ofresearch methodology.The title of this Festschrift is meant to be a pun to convey the sometimes relativistic dimension to mathematical certaintythat Paul argued for in developing his philosophy, and also a play on words for the fact that absolute "earnestness" mayperhaps be a Platonic construct, and not possible in the realm of language and human discourse Paul Ernest's scholarlyevolution and life can best be summarized in the words of Walt Whitman "Do I contradict myself? Very well then Icontradict myself" (I am large, I contain multitudes). Indeed his presence has beenlarge and multitudinous and this Festschrift celebrates his 65th Birthday withnumerous contributions coming from the mathematics, philosophy and mathematicseducation communities around the world.

Packed with realistic exam-style questions for every topic, this newly updated Exam Practice Workbook is perfectly matched to the Higher Level Edexcel GCSE Maths course. Handy grade stamps indicate the difficulty level of each question, and problem-solving stamps highlight those that require a bit of extra thought. There are also plenty of helpful exam tips throughout the book. Plus, it comes with complete step-by-step solutions (with a full mark scheme) at the back of the book, so it's simple for students to check and correct their work - and there are even QR codes to access brilliant new worked video solutions! And finally, the book is rounded off with a full set of mock exam papers - the answers to these are available to download from the CGP website. CGP's range for Higher Level Edexcel GCSE Maths also includes a matching Revision Guide (9781782944041), Workbook (9781782944072) and Grade 8-9 Targeted Exam Practice Workbook (9781782944157).

With a huge range of Maths practice for ages 7 to 8, plus fully explained answers to every question, this book is ideal for building up the skills children need for the 11+ and other selective entrance exams. The first section of the book focuses on one topic at a time to help children gain understanding and confidence. This is followed by six 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!