This book is open access under a CC BY 4.0 license. The book presents the Proceedings of the 13th International Congress on Mathematical Education (ICME-13) and is based on the presentations given at the 13th International Congress on Mathematical Education (ICME-13). ICME-13 took place from 24th- 31st July 2016 at the University of Hamburg in Hamburg (Germany). The congress was hosted by the Society of Didactics of Mathematics (Gesellschaft fur Didaktik der Mathematik - GDM) and took place under the auspices of the International Commission on Mathematical Instruction (ICMI). ICME-13 brought together about 3.500 mathematics educators from 105 countries, additionally 250 teachers from German speaking countries met for specific activities. Directly before the congress activities were offered for 450 Early Career Researchers. The proceedings give a comprehensive overview on the current state-of-the-art of the discussions on mathematics education and display the breadth and deepness of current research on mathematical teaching-and-learning processes. The book introduces the major activities of ICME-13, namely articles from the four plenary lecturers and two plenary panels, articles from the five ICMI awardees, reports from six national presentations, three reports from the thematic afternoon devoted to specific features of ICME-13. Furthermore, the proceedings contain descriptions of the 54 Topic Study Groups, which formed the heart of the congress and reports from 29 Discussion Groups and 31 Workshops. The additional important activities of ICME-13, namely papers from the invited lecturers, will be presented in the second volume of the proceedings.

This booklet addresses Unit 2 (Mechanics) of the current CCEA GCSE Further Mathematics specification, and is one of a set of 4 revision resources. * Valuable revision questions with answers. * The questions are arranged into five distinct 'tests'. * NOT from past papers; commissioned specifically for this booklet. * Similar in style to the existing M1 to M8 revision booklets for GCSE Mathematics. * Two of the booklets address the content of Pure Mathematics, one covers Statistics and this one covers Mechanics.

Spectrum(R) Word Problems for grade 5, includes focused practice for essential math skills. Skills include: *Real world applications *Multi-step word problems *Fractions and decimals *Metric and customary measurement *Graphs and probability *Geometry *Preparing for algebra --Spectrum(R) Word Problems workbooks supplement classroom work and proficiency test preparation. The workbooks provide examples of how the math skills students learn in school apply to everyday life with challenging, multi-step word problems. It features practice with word problems that are an essential part of the Common Core State Standards, making it a perfect supplement at home or school.

Geometry: A Metric Approach with Models, imparts a real feeling for Euclidean and non-Euclidean (in particular, hyperbolic) geometry. Intended as a rigorous first course, the book introduces and develops the various axioms slowly, and then, in a departure from other texts, continually illustrates the major definitions and axioms with two or three models, enabling the reader to picture the idea more clearly. The second edition has been expanded to include a selection of expository exercises. Additionally, the authors have designed software with computational problems to accompany the text. This software may be obtained from George Parker.

This handbook connects the practice of statistics to the teaching and learning of the subject with contributions from experts in several disciplines. Chapters present current challenges and methods of statistics education in the changing world for statistics and mathematics educators. Issues addressed include current and future challenges in professional development of teachers, use of technology tools, design of learning environments and appropriate student assessments. This handbook presents challenging and inspiring international research perspectives on the history and nature, current issues, and future directions of statistics education and statistics education research.

This book adopts an interdisciplinary approach to investigate the development of mathematical reasoning in both children and adults and to show how understanding the learner's cognitive processes can help teachers develop better strategies to teach mathematics. This contributed volume departs from the interdisciplinary field of psychology of mathematics education and brings together contributions by researchers from different fields and disciplines, such as cognitive psychology, neuroscience and mathematics education. The chapters are presented in the light of the three instances that permeate the entire book: the learner, the teacher, and the teaching and learning process. Some of the chapters analyse the didactic challenges that teachers face in the classroom, such as how to interpret students' reasoning, the use of digital technologies, and their knowledge about mathematics. Other chapters examine students' opinions about mathematics, and others analyse the ways in which students solve situations that involve basic and complex mathematical concepts. The approaches adopted in the description and interpretation of the data obtained in the studies documented in this book point out the limits, the development, and the possibilities of students' thinking, and present didactic and cognitive perspectives to the learning scenarios in different school settings. Mathematical Reasoning of Children and Adults: Teaching and Learning from an Interdisciplinary Perspective will be a valuable resource for both mathematics teachers and researchers studying the development of mathematical reasoning in different fields, such as mathematics education, educational psychology, cognitive psychology, and developmental psychology.

Ken & Verstaan Wiskundige Geletterdheid Graad 12 is deur 'n ervare span skrywers geskryf, ooreenkomstig die vereistes van die Kurrikulum- en Assesseringsbeleidsverklaring (KABV).

Hierdie nuwe en toeganklike reeks sal leerders help om die inhoud van en vaardighede vir Wiskundige Geletterdheid maklik baas te raak.

Die omvattende Leerdersboek bevat 'n naslaan-afdeling oor basiese vaardighede om konsepte in Wiskundige Geletterdheid te hersien, aantekeninge in die kantlyn wat leerders met nuwe begrippe help, 'n verskeidenheid voorbeelde met sterk visuele inslag wat Wiskundige Geletterdheid met alledaagse situasies verbind, 'n opsommende kontrolelys en hersieningsoefeninge aan die einde van elke onderwerp.

Deck Ahoy! contains over 100 activities and games to teach primary maths skills with a deck of cards. Topics covered are not only the main operations - addition, subtraction, multiplication and division - but also fractions, statistics, time, ratios, squares and cubes and graphs. The ideas are great for homework as there are no worksheets needed (or marking to do!) and the whole family can get involved, any where any time.

An engaging math workbook to help your 6th grade student master the skills necessary to perform better in class and on standardized tests Colorful, dynamic, and filled with engaging activities, McGraw Hill Math Grade 6, Third Edition provides maximum educational value, giving your sixth grader a student-friendly learning experience to learn and practice the skills they need to do well in school and on standardized tests. Based on the curriculum standards followed by states across the U.S., McGraw Hill Math Grade 6 covers key topics with easy-to-follow instructions, helpful examples, and more than 1,000 practice problems with answers. End-of-chapter tests allow your child to see where mastery has been gained and what they need to focus on. As they master each concept, your child will sharpen their problem-solving skills and build the confidence they need to succeed in sixth grade math. Features include: New: Multi-step problems and word problems. A state-by-state guide shows you how to focus your child's lessons The guide shows which states have adopted Common Core State Standards, how each state has implemented the standards for math, and outlines the standards for non-Common Core states 1,000+ math problems with explanations for answers A 10-Week Summer Study Plan shows you how to create the best study schedule for your child A pretest helps your child determine which skills require more attention End-of-chapter tests helps your child assess if they've mastered the chapter's concepts Posttest at the end of the book shows your child how well they understand key concepts A glossary explains key terms that students will encounter in the book Topics covered: Place values and estimating Number properties and order of operations Negative numbers and absolute value Factors and multiples Solving problems with rational numbers Ratios and proportions Percent Exponents and scientific notation Solving equations and inequalities Customary and metric units of measure, including conversions Solving problems by graphing points on the coordinate plane Classifying polygons based on their properties Calculating perimeter, area, surface area, and volume Data presentation Statistical variability, including probability

The need to improve the mathematical proficiency of elementary teachers is well recognized, and it has long been of interest to educators and researchers in the U.S. and many other countries. But the specific proficiencies that elementary teachers need and the process of developing and improving them remain only partially conceptualized and not well validated empirically. To improve this situation, national workshops were organized at Texas A&M University to generate focused discussions about this important topic, with participation of mathematicians, mathematics educators and teachers. Developing Mathematical Proficiency for Elementary Instruction is a collection of articles that grew out of those exciting cross-disciplinary exchanges. Developing Mathematical Proficiency for Elementary Instruction is organized to probe the specifics of mathematical proficiency that are important to elementary teachers during two separate but inter-connected professional stages: as pre-service teachers in a preparation program, and as in-service teachers teaching mathematics in elementary classrooms. From this rich and inspiring collection, readers may better understand, and possibly rethink, their own practices and research in empowering elementary teachers mathematically and pedagogically, as educators or researchers.

Become a super spy, crack codes and train your brain! By using maths and logic to solve and navigate the codes, kids will build great skills to help them with problem solving and reasoning. Developed by Dr Gareth Moore, an expert in the field, this book will have your kids cracking codes in no time! Reveal secret messages with codes used by real-life spies Use maths to crack into mysterious safes Become a master tech-decoder using logic, and more Discover cryptic co-ordinates to hunt down hidden treasure ...and much more! Including amazing alphabet and number codes, grids, and picture puzzles. Don't worry, if kids get stuck, there are tips and subtle clues to help improve code-breaking skills. With full-colour graphics and illustrations throughout, this book is as eye-catching as it is entertaining.

Learn all about fractions with Mo the Monster and his friends in these fun first maths books for children aged 5 and up. Mo and his mum are going shopping today! Mo is very distracted by all the lovely things to buy (especially the cake), but manages to learn about sets, halves, thirds and quarters, and how fractions work, during his day out. But when he's busy eating pizza with Slippery Sid, his mum disappears. Help! How can you find her Mo? If a monster can understand maths, anyone can! Join Mo the Monster as he discovers the basic principles of maths, from what a fraction is, to what 3D shapes are to how to multiply BIG numbers. Along the way, Mo is kept focused (monsters are notoriously easily distracted) with the help of simple, clearly presented information, plenty of questions to answer and lots of maths puzzles and activities. The funny, colourful illustrations offer lots of scope for humour and interest to keep children engaged while they learn. Aimed at readers aged 5+. Titles in the series: Addition & Subtraction/Geometry/Division/Fractions/Measuring/Multiplication Contents: One half Find half of a set Mixed numbers One quarter Quarter turns Halves and quarters Thirds Fractions that make wholes Greater than or less than Fractions of small numbers Equivalence Tenths Twelfths Glossary Answers

Underpinned by the most effective teaching practices, and created by a team of mastery experts led by Series Editor Tony Staneff, Power Maths is designed to make the whole-class mastery teaching approach work for you, your children and your school. The Power Maths Teacher Guides provide expert support for your day-to-day teaching, and offer opportunities for reflection and continual professional development. Provides guidance on using the Textbooks and Practice Books, explaining how they support a mastery approach. Support with key strategies such as modelling a growth mindset, assessing mastery, speedy same-day intervention, C-P-A approaches and using key mathematical structures and representations. Focused unit-level support for each mathematical concept within the Power Maths progression, including important structures and representations, key language, common misconceptions and intervention strategies. Specific advice and commentary for each pupil book page - including insight into why tasks and exercises have been selected, and how to strengthen and deepen learning. Templates for teacher reflection, lesson study, and tracking pupil progress.

This book discusses a significant area of mathematics education research in the last two decades and presents the types of semiotic theories that are employed in mathematics education. Following on the summary of significant issues presented in the Topical Survey, Semiotics in Mathematics Education, this book not only introduces readers to semiotics as the science of signs, but it also elaborates on issues that were highlighted in the Topical Survey. In addition to an introduction and a closing chapter, it presents 17 chapters based on presentations from Topic Study Group 54 at the ICME-13 (13th International Congress on Mathematical Education). The chapters are divided into four major sections, each of which has a distinct focus. After a brief introduction, each section starts with a chapter or chapters of a theoretical nature, followed by others that highlight the significance and usefulness of the relevant theory in empirical research.

This book offers a detailed look into the how and what of mathematics instruction in Singapore. It presents multiple aspects of mathematics instruction in schools, ranging from the unique instructional core, practices that promote mastery, development of conceptual knowledge through learning experiences, nurturing of positive attitudes, self-regulation of learning and development and use of instructional materials for making connections across mathematical ideas, developing mathematical reasoning, and developing fluency in applying mathematical knowledge in problem solving.The book presents a methodology that is successful in documenting classroom instruction in a comprehensive manner. The research findings illuminate instruction methods that are culturally situated, robust and proven to impact student learning. It demonstrates how a unique data source can be analysed through multiple lenses and provides readers with a rich portrait of how the school mathematics instruction is enacted in Singapore secondary schools.

Collins International Primary Maths supports best practice in primary maths teaching, whilst encouraging teacher professionalism and autonomy. A wealth of supporting digital assets are provided for every lesson, including slideshows, tools and games to ensure they are rich, lively and engaging. Each lesson is based on a 'big idea', providing an engaging, exciting theme which is anchored in a real-life international context. Activities, exercises and investigations provide opportunities for learners to apply their knowledge, skills and understanding of the mathematics they are learning. The course develops learners' Thinking and Working Mathematically skills and offers opportunities for group and individual learning. The series also supports Cambridge Global Perspectives (TM) with activities that develop and practise key skills. Provides learner support as part of a set of resources for the Cambridge Primary curriculum framework (0096) from 2020. This series is endorsed by Cambridge Assessment International Education to support the new curriculum framework 0096 from 2020.

This volume provides new insights on creativity while focusing on innovative methodological approaches in research and practice of integrating technological tools and environments in mathematics teaching and learning. This work is being built on the discussions at the mini-symposium on Creativity and Technology at the International Conference on Mathematical Creativity and Giftedness (ICMCG) in Denver, USA (2014), and other contributions to the topic. The book emphasizes a diversity of views, a variety of contexts, angles and cultures of thought, as well as mathematical and educational practices. The authors of each chapter explore the potential of technology to foster creative and divergent mathematical thinking, problem solving and problem posing, creative use of dynamic, multimodal and interactive software by teachers and learners, as well as other digital media and tools while widening and enriching transdisciplinary and interdisciplinary connections in mathematics classroom. Along with ground-breaking innovative approaches, the book aims to provide researchers and practitioners with new paths for diversification of opportunities for all students to become more creative and innovative mathematics learners. A framework for dynamic learning conditions of leveraging mathematical creativity with technology is an outcome of the book as well.

Practitioner and teacher confidence in their own mathematical understanding is often low - the book helps the reader to recognise the mathematics taking place in children's play. Provides guidance on building on children's existing knowledge to introduce new concepts and address misconceptions linking mathematical development to other key aspects of early years pedagogy Explores the meaning of Mastery in depth and shows clearly what this looks like in children's play and continuous provision It is a practice based book - includes full colour photographs, case studies, links to practice and reflective questions It includes examples from the TFMM exemplification which show how to build on and extend children's mathematical development and learning - giving ideas for the adults role, the enabling environment and home learning

Year 6 pupils (ages 10-11) will love this friendly, colourful Study Book - and it's perfectly matched to the latest curriculum! For each topic, there are straightforward study notes and plenty of clear examples explaining all the important skills, with objectives tick-boxes at the bottom of each page so that pupils can mark off their progress. Practice questions are included at the end of each section - these progress in difficulty to give pupils' understanding a thorough workout. On top of that, you'll also find Greater Depth Questions, so pupils can really test their knowledge, plus answers to every question at the back. For even more practice, don't miss our Year 6 Maths Targeted Question Book (9781847622143) - it's bursting with test-style practice for every topic!

The book is made up of 21 chapters from 25 presentations at the 23rd MAVI conference in Essen, which featured Alan Schoenfeld as keynote speaker. Of major interest to MAVI participants is the relationship between teachers' professed beliefs and classroom practice. The first section is dedicated to classroom practices and beliefs regarding those practices, taking a look at prospective or practicing teachers' views of different practices such as decision-making, the roles of explanations, problem-solving, patterning, and the use of play. The focus of the second section in this book deals with teacher change, which is notoriously difficult, even when the teachers themselves are interested in changing their practice. The third section of this book centers on the undercurrents of teaching and learning mathematics, what rises in various situations, causing tensions and inconsistencies. The last section of this book takes a look at emerging themes in affect-related research. In this section, papers discuss attitudes towards assessment.