A Volume in The Montana Mathematics Enthusiast: Monograph Series in Mathematics EducationSeries Editor Bharath Sriraman, The University of MontanaInterdisciplinarity is increasingly viewed as a necessary ingredient in the training of future oriented 21st century disciplinesthat rely on both analytic and synthetic abilities across disciplines. Nearly every curricular document or vision statement ofschools and universities include a call for promoting creativity in students. Yet the construct of creativity and giftednessacross disciplines remains elusive in the sense that the prototypical examples of such work come from eminent scientists, artists and mathematicians, and little if any work has been conducted with non-eminent individuals. This monograph is anattempt to fill this gap by putting forth the view that interdisciplinarity and creativity are related constructs, and that thecultivation of domain general creativity is possible. Mathematics has historically been anchored to numerous disciplineslike theology, natural philosophy, culture and art, allowing for a flexibility of thought that is difficult to cultivate in otherdisciplines. In this monograph, the numerous chapters from Australia, U.S.A., Canada, Cyprus, Denmark and Japanprovide a compelling illustration of the intricate connection of mathematics with literature, paradoxes, history, technologyand modeling, thus serving as a conduit for interdisciplinarity, creativity and learning to occur.

If you were to peer into a primary school classroom somewhere across Australia and New Zealand, you would be forgiven for thinking that science, technology, engineering and mathematics (STEM) education is synonymous with coding and digital technologies. However, while these aspects are important, technology alone does not reflect the broad learning opportunities afforded by STEM. In countering this narrow approach, STEM Education in Primary Classrooms offers a platform for research that innovates, excites and challenges the status quo. It provides educators with innovative and up-to-date research into how to meaningfully and authentically embed STEM into existing classroom practices. It incorporates accurate explanations of STEM as an integrated approach to solving real-world problems, including social issues, along with case studies and stories to bring practice to life in evidence-informed ways. This book showcases the impact of a broader approach to STEM in the primary classroom through Australian-based and New Zealand-based research that will challenge current teaching practices. Thus, this book will be of interest to pre- and in-service primary school teachers, along with researchers and postgraduate students in the STEM education field.

What do children love? Minecraft! What will make them love Math? Learning it with Minecraft! This kid-friendly workbook features well-loved video game characters and concepts to reinforce the development of third and fourth grade math skills laid out in the national Common Core State Standards. Colorfully-illustrated and high-interest word problems use beloved items from the Overworld, the Nether, and the End to turn math into an exciting adventure. Whether they?re multiplying the number of mobs they spawn or dividing items in their inventory among their treasure chests, the problems in this workbook will grab the attention of even the most reluctant student. They'll practice all of the word problem skills they need in school, including: Grade 3: Use multiplication and division within 100 to solve word problems Multiplying and dividing three whole numbers Solve two-step word problems using addition, subtraction, multiplication, or division Grade 4: Solve word problems involving addition and subtraction of fractions Solve word problems involving multiplication of a fraction by a whole number Solving for area and perimeter Skip to the pages that suit your child's needs and learning style or start at the beginning and advance page by page-it's up to you! As the workbook progresses, the problems become more challenging so that learners of all levels can enjoy an exciting, skill-building math adventure. Perfect for Minecrafters who learn at all paces, Math for Minecrafters: Word Problems is as fun as it is educational-and is just what young learners need to get ahead academically! This educational series is created especially for readers who love the fight of good vs. evil, magical academies like Hogwarts in the Harry Potter saga, and games like Minecraft, Terraria, and Pokemon GO.

Discovering Mathematics is adapted from the leading Singapore course to fully match the English Key Stage 3 National Curriculum. This groundbreaking series harnesses authentic mastery principles through a Concrete-Pictorial-Abstract (CPA) approach, and use of precise mathematical language. Students learn by discovery, an approach pioneered by this course. Written by an experienced UK/Singapore team, this engaging book provides progression and practice for Middle tier students in Year 7 . Topics are introduced through inclusive whole-class activities. Worked examples give clear steps of how to present solutions, with hints and discussion points to encourage paired, group and whole-class working. Practice exercises are differentiated into three levels, progressing from basic fluency to application to problem solving, with consolidation through end-of-chapter exercises. Short answers in the back of the book help students quickly check their understanding, with fully-worked solutions containing GCSE grades in the Teacher Guide. Exercises incorporate 'intelligent practice', with careful variation of the numbers to reinforce and deepen learning. Problem-solving skills are identified throughout, with two dedicated problem-solving sections to support skills development. Students are also encouraged to reflect upon and embed their learning through a Write in Your Journal in every chapter. This Student Book will help students discover the underlying principles of mathematics and set them on the road to mastery.

The methods for teaching mathematics usually follow the structure of mathematics. The problem with this is that the structure of mathematics took centuries of elaboration to develop and is not the same as how one originally experiences mathematics. Based on research of how mathematics is actually learned, this book presents an innovative approach for teaching mathematics that will engage pupils and can have lifelong benefits for how they take on board more advanced mathematical topics.Math Makes Sense! makes use of the realistic mathematics education (RME) philosophy, which bridges the gap between informal mathematics learning (such as in day-to-day life) and more formal teaching in school. Many real-life situations as examples for learning are included, as well as different mathematical and logic puzzles that will stimulate learning and foster understanding.The ideas presented are not confined to one national curriculum and so can be helpful worldwide to teachers/ instructors (both in practice and those still in training), private tutors, homeschooling parents, and educational researchers.

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.

The methods for teaching mathematics usually follow the structure of mathematics. The problem with this is that the structure of mathematics took centuries of elaboration to develop and is not the same as how one originally experiences mathematics. Based on research of how mathematics is actually learned, this book presents an innovative approach for teaching mathematics that will engage pupils and can have lifelong benefits for how they take on board more advanced mathematical topics.Math Makes Sense! makes use of the realistic mathematics education (RME) philosophy, which bridges the gap between informal mathematics learning (such as in day-to-day life) and more formal teaching in school. Many real-life situations as examples for learning are included, as well as different mathematical and logic puzzles that will stimulate learning and foster understanding.The ideas presented are not confined to one national curriculum and so can be helpful worldwide to teachers/ instructors (both in practice and those still in training), private tutors, homeschooling parents, and educational researchers.

Integrating Math and Science in Early Childhood Classrooms Through Big Ideas offers teachers a way to think about the future classroom and to meet the needs of children who come to into it with diverse experience, knowledge, and abilities. "Change how we think about math and science for young children," the authors say in their Preface. "Instead of separating the disciplines, planning lessons and topics and projects aimed at math OR science content, let's look at the world the way the child does. Children think in terms of big ideas." In this unique book, the authors focus on big ideas-like patterns, transformation, movement, balance, and relationships-as a way to think about content, and they integrate science and mathematics through these big ideas, rather than linking them topically. The book looks at why it is important to think about thinking, introduces assessment early to help the teacher plan for assessment before teaching even begins, and sets up an environment that will support the construction of the big ideas that integrate math and science. Real-life scenarios provide invaluable insights into the teacher's thinking and planning, and each chapter includes two modules to be used for in-depth exploration of different aspects of the big ideas. It's a unique exploration of thinking and learning.

Mathematics is a subject held in high esteem around the world, yet the teaching and learning of mathematics is rarely viewed as good enough and many find the subject difficult to comprehend, or engage with. In Manufacturing the Mathematical Child, Anna Llewellyn asks some difficult questions in order to determine why this is the case and to question who it is that we allow to succeed at mathematics, particularly within the context of neoliberalism, where education is a product of the market. By looking at the various sites of production, Llewellyn examines the ways that key discursive spaces produce very different expectations of what it means to do mathematics and demonstrates that these place various homogenised expectations upon children. Arguing that these are not natural, but instead a reproduction of discursive norms, the book demonstrates why some people fit these standardized ways of being and others do not. Using England as a case study and referring to other international contexts, Llewellyn argues that there is a functionality found within certain educational policy discourses, and a romantic attachment to the natural child found within educational research, neither of which can match what happens in the messy classroom. As a result, it becomes evident that exclusion from mathematics is inevitable for many children. Original and exciting, this book will be of great interest to academics, researchers and postgraduate students within the fields of mathematics education, childhood studies, policy studies, and Foucauldian or post-structural analysis.

How can early years practitioners help young children to become not only numerate but aspiring mathematicians who love numbers, shapes and mathematical comparisons? The introduction of the Foundation Stage has led to practitioners seeking ways to teach maths which are more in line with the creative and playful ways young children learn other subjects. Linda Pound draws on current thinking about children's mathematical development to show how you can encourage and enhance the numeracy skills of any child in the early years by linking maths to every-day life situations and making it a playful and enjoyable cross-curricular activity.This highly practical and engaging text includes chapters on: why maths is often seen as 'hard' and what practitioners can do to help young children be more successful; exploring shapes, space, measures and patterns; how to make maths more fun and playful, using games, humour, stories and rhymes; using music and dance to enhance mathematical understanding; encouraging children to see the connection between maths and everyday experiences through, for example sorting, matching and guessing; and, creating an environment for mathematical development, indoors and out. Concluding with a chapter on how practitioners and parents can become more confident in their use of maths, this user-friendly text, packed full of ideas, is essential reading for practitioners in any early years setting. Students on Early Education courses will also find much here to inspire them.

This CGP Key Stage Two Mental Maths Workout Book is packed with essential practice exercises for Year 6 pupils (ages 10-11) - including a section of 'Time Yourself' tests. Presented in a fun and friendly style, it's a great way to help make sure children have really got to grips with working out maths problems in their heads. Answers are included in a removable section, so it's simple to find out how well they're progressing.

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.

The primary aim of this book is to provide teachers of mathematics with all the tools they would need to conduct most effective mathematics instruction. The book guides teachers through the all-important planning process, which includes short and long-term planning as well as constructing most effective lessons, with an emphasis on motivation, classroom management, emphasizing problem-solving techniques, assessment, enriching instruction for students at all levels, and introducing relevant extracurricular mathematics activities. Technology applications are woven throughout the text.A unique feature of this book is the second half, which provides 125 highly motivating enrichment units for all levels of secondary school mathematics. Many years of proven success makes this book essential for both pre-service and in-service mathematics teachers.

AMTE, in the Standards for Preparing Teachers of Mathematics (SPTM), puts forward a national vision of initial preparation for all Pre-K-12 teachers who teach mathematics. SPTM contains critical messages for all who teach mathematics, including elementary school teachers teaching all disciplines, middle and high school mathematics teachers who may teach mathematics exclusively, special education teachers, teachers of emergent multilingual students, and other teaching professionals and administrators who have responsibility for students' mathematical learning. SPTM has broad implications for teacher preparation programs, in which stakeholders include faculty and administrators in both education and mathematics at the university level; teachers, principals, and district leaders in the schools with which preparation programs partner; and the communities in which preparation programs and their school partners are situated. SPTM is intended as a national guide that articulates a vision for mathematics teacher preparation and supports the continuous improvement of teacher preparation programs. Such continuous improvement includes changes to preparation program courses and structures, partnerships involving schools and universities and their leaders, the ongoing accreditation of such programs regionally and nationally, and the shaping of state and national mathematics teacher preparation policy. SPTM is also designed to inform assessment practices for mathematics teacher preparation programs, to influence policies related to preparation of teachers of mathematics, and to promote national dialogue around preparing teachers of mathematics. The vision articulated in SPTM is aspirational in that it describes a set of high expectations for developing a well-prepared beginning teacher of mathematics who can support meaningful student learning. The vision is research-based and establishes a set of goals for the continued development and refinement of a mathematics teacher preparation program and a research agenda for the study of the effects of such a program. SPTM contains detailed depictions of what a well-prepared beginning teacher knows and is able to do related to content, pedagogy, and disposition, and what a strong preparation program entails with respect to learning experiences, assessments, and partnerships. Stakeholders in mathematics teacher preparation will find messages related to their roles. Standards for Preparing Teachers of Mathematics includes standards and indicators for teacher candidates and for the design of teacher preparation programs. SPTM outlines assessment practices related to overall quality, program effectiveness, and candidate performance. SPTM describes specific focal practices by grade band and provides guidance to stakeholders regarding processes for productive change.

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

Note that the Floris Books editions of Jamie York's books have been completely revised for UK and European notation, language and metric systems. They are also suitable for use in South Africa, Australia and New Zealand. Experienced maths teacher and consultant Jamie York believes that a love of learning comes through the teacher, so his books are committed to supporting teachers in developing their classroom skills and to fostering a love of maths in their students. Unlike conventional maths textbooks, his books are not full of fancy graphics and contrived ways to make maths fun. Rather, they: -- focus on the essentials, so teachers aren't overwhelmed by endless lists of required materials -- are genuinely interesting and challenging, sparking students' enthusiasm for learning maths -- are developmentally appropriate to the age of the child, thereby encouraging inner mathemetical awareness and thinking -- favour depth over superficiality, to avoid teaching blind procedures to solve meaningless problems. This student's workbook for Class 7 contains practice questions, with room for working, on all the topics a student needs to cover in Steiner-Waldorf Class 7 (age 13-14). The book includes: Arithmetic review topics from previous years. New topics for Class 7: measurement, percents, ratios, rates, geometry, algebra, the square root algorithm. Mental maths: it is as important as ever for children to develop the ability to do calculations in their head. Each worksheet therefore begins with a secion on mental maths, focusing on one of our areas described in the Teacher's Source Book (available separately). Note that this workbook is also available in a pack of ten with a teacher's answer booklet.

The 20th anniversary edition of this groundbreaking and bestselling volume offers powerful examples of the mathematics that can develop the thinking of elementary school children. Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts. Along with the original studies of U.S. and Chinese teachers' mathematical understanding, this 20th anniversary edition includes a new preface and a 2013 journal article by Ma, "A Critique of the Structure of U.S. Elementary School Mathematics" that describe differences in U.S. and Chinese elementary mathematics. These are augmented by a new series editor's introduction and two key journal articles that frame and contextualize this seminal work.

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.

This three-in-one book provides an extremely thorough treatment of the CAPS curriculum. It offers a ‘fresh start’ to learners with gaps in their understanding from previous years. It contains: Comprehensive Notes and Worked Examples per topic, Exercises that are graded to promote logic and develop techniques in each topic and Detailed Solutions for all exercises plus a fully explained comprehensive exam (paper 1 and paper 2) for thorough consolidation and final exam preparation. This 3 in 1 study guide will equip a learner to achieve their full potential in Grade 10 and put all the building blocks in place for success in Grade 11 and 12 Mathematics, notably in Algebra, Euclidean and Analytical Geometry and Trigonometry. Extensive practice through the carefully selected examples and exercises will build a thorough understanding and mastery of each topic as the learner grows in confidence and expertise. The learner will GET IT, learn to overcome misconceptions and understand all concepts from first principles.

This Grade 8 Mathematics study guide provides a thorough introduction to critical mathematical concepts such as algebra and geometry. This foundation is essential for the development of logical thinking and the growth of knowledge and confidence in this extremely important subject. This 2 in 1 publication includes: Topic-based Questions & Answers – to build an understanding of theory, techniques & concepts in each topic and Exam Papers & Memos – to put theory into practice and reinforce concepts in an integrated way. The first section introduces and builds understanding of each concept through graded questions on each topic. Comprehensive answers to all questions are provided with many extra tips and advice boxes for guidance. The second section consists of a range of exam papers. Detailed solutions with additional explanations, notes and hints are provided to develop the learner’s skills in examination technique. This study guide is beneficial for learners at all levels of competence in this challenging subject.

This Grade 9 publication offers extremely thorough and plentiful practice in mastering the essential techniques and concepts as required by the Grade 9 CAPS curriculum and includes several useful summaries of facts and formulae. This 2 in 1 publication includes: Topic-based Questions & Answers – for an understanding of theory, techniques & concepts and Exam Papers & Memos that put theory into practice. The first section covers questions per topic. The questions within each topic are graded with the purpose of developing concepts step-by-step and in so doing growing the understanding, knowledge and confidence of the learner. The second section consists of a set of exam papers that reflects the standard and the weighting per topic as required by CAPS. Detailed solutions with additional explanations, notes and hints develop the learner’s skills in examination technique. A most comprehensive study guide which will benefit learners of all levels of competence reached in this challenging subject.