The driving forces behind mathematics learning trajectories is the need to understand how children actually learn and make sense of mathematics-how they progress from prior knowledge, through intermediate understandings, to the mathematics target understandings-and how to use these insights to improve instruction and student learning. In this book, readers will come to understand what learning trajectories are, the research and methodology that are necessary for developing them, and gain insight into potential applications of learning trajectories. A synthesis and research outcome in their own right, learning trajectories provide detailed description of instructionally-grounded development of mathematical concepts and reasoning from the perspective of student learning, and, overall, building on decades of accumulated experience in mathematics education research. However, their greater importance may lie in their potential as frameworks that contribute an unprecedented coherence across classroom instruction, professional development, standards, and assessment, by focusing squarely on conceptual understanding and reasoning instead of assessment-driven procedural knowledge. This potential was sufficiently compelling as an organizing framework to have been cited as a basis for the Common Core mathematics standards, the new mathematics learning expectations that are now consistent across most of the United States. (Among the conference attendees were the writers of the Common Core State Standards for Mathematics, at the beginning of the Standards drafting process.) This book is an outgrowth of a conference on learning trajectories, hosted in 2009 at North Carolina State University, which examined research on learning trajectories. An overarching message of the chapters in this volume is that learning trajectories, by focusing on how children's mathematical reasoning develops, are coming into their own as a rigorous underpinning for both instruction and accountability. Some of the learning scientists featured in this volume have played major roles learning trajectories' evolution--from small-scale day-to-day conjectures by individual teachers, to systematic research endeavors that teachers and scientists alike can use to interpret standards, plan instruction, and formatively assess student work. The work in this volume will be of interest to mathematics educators, teachers, and professional development specialists.

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.

My Desktop Dictionary is designed, written and illustrated for young children in their first years of learning. It is a student dictionary for children who are developing a written vocabulary and contains a wide range of commonly used words.

Ample space is provided for recording new words that students may add to the dictionary.

Features:

• designed, written and illustrated for young children
• contains a wide range of commonly used words, plus space for recording new words
• a blank square at the top right-hand corner of each double page allows children to write letters of the alphabet in their school script
• a popular, high-interest theme for each letter of the alphabet
• lists of commonly used topics and themes

This CGP Exam Practice Workbook is fully up-to-date for Edexcel's latest 'Grade 9-1' International GCSE Maths course (specification A). It contains a huge range of realistic exam-style questions targeted at the Higher Tier of the specification (with step-by-step answers at the back), along with grade stamps indicating the difficulty level of each question. The questions are arranged by topic, making it easy for students to focus their practice on the areas they find the most challenging. The book is rounded off with two full practice papers for even more exam preparation - the answers to these are available to download from the CGP website. For even more help with this course, don't miss CGP's matching Revision Guide (9781782946694) and Workbook (9781782946724).

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 5 Mastery Checkpoints 40 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 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?

Travel to an ancient realm of magic where the powerful Grand Wizard Koeus set in motion events that would lead to a cataclysmic end. In his arrogance, he believed he could train ten apprentices in the ways of magic. He created magical stones controlling the powers of earth, wind, fire, and water. Using these stones, the apprentices became powerful wizards, but their hearts became corrupt and turned against Koeus when they learned of the life limitations the stones imposed on them. The Grand Wizard was forced to destroy his apprentices, but destroyed himself in the process.

Centuries later, after the great wizards have long vanished, apprentices Kale and Masan are awarded the titles of wizard and earn their first magical stones at the School of Hundir. They embark upon a journey in search of other stones, and along the way, learn the true power of friendship. Their quest takes them through dangerous lands, where unlikely alliances are formed with Corsair, a great warrior, Megaera, an omniscient elf, and Lasca a beautiful and captivating thief. Through their quest the group discovers a bond that unites them as they battle the powerful Darklocks, an ancient evil threatening the peace of the lands.

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 Workbook page has three levels of challenge which allow learners to practise and consolidate their newly acquired knowledge, skills and understanding of the mathematics they are learning. Questions throughout the course develops learners' Thinking and Working Mathematically skills, and each lesson offers an opportunity for personal reflection on progress. 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.

180 Days of Math is an effective workbook designed to help students improve their math skills. This easy-to-use second grade workbook is great for at-home learning or in the classroom. The engaging standards-based activities cover grade-level skills with easy to follow instructions and an answer key to quickly assess student understanding. Each daily practice page includes 8 math problems covering algebraic thinking, numbers and operations, measurement and data, and geometry. Watch as student s math confidence grows with these quick independent learning activities.Parents appreciate the teacher-approved activity books that keep their child engaged and learning. Great for homeschooling, to reinforce learning at school, or prevent learning loss over summer.Teachers rely on the daily practice workbooks to save them valuable time. The ready to implement activities are perfect for daily morning review or homework. The activities can also be used for intervention skill building to address learning gaps.

A collection of 150 unique games and activities to help support teaching of maths in the primary classroom. Designed with busy teachers in mind, the Classroom Gems series draws together an extensive selection of practical, tried-and-tested, off-the-shelf ideas, games and activities guaranteed to transform any lesson or classroom in an instant. Easily navigable, allowing you to choose the right activity quickly and easily, these invaluable resources are guaranteed to save you time and are a must-have tool to plan, prepare and deliver first-rate lessons.

Nisa Qamar is 10 years old, living in Johannesburg, South Africa with her single mum, Zainab, her little sister Aisha and their 3-year-old twin brothers, Ali and Isa. Nisa loves books, ice cream, bicycles and hanging out with her bestie. She also has a special bond with her grandmother who tells her wonderful stories from the past. Gran teaches her the importance of prayer and The Verse of the Throne ie aayat ul qursi.

Written as an adventure with the thematic elements of good triumphing over evil, Nisa uncovers a plot to take over her school by the evil TroubleMaker. In a race against time she has to figure out who she can trust on this quest or lose the game to the Master of Jinniaville.

This story is the first in the series and actively promotes the idea that even a young child can make a difference by keeping the heart clean and making the choice to do good over evil.

Abacus is a popular Maths scheme used by thousands of schools all over the world. It fully aligns to the UK National Curriculum. Written by a team of experts, led by Series Editor, Professor Ruth Merttens. For children who are following a UK National Curriculum-based maths scheme, the pupil book provides guidance for each strand the national curriculum. Each Pupil Book includes: the right balance of practice and problem-solving for each area of maths pictorial representations to support children's conceptual understanding clearly laid out questions with instructions that are easy to follow a self-assessment opportunity on every page

This title combines easily decodable words with a few essential high-frequency words. It is great for guided or shared reading and independent practice of initial and final phonemes and short medial vowels.

The book is based on the recently held Symposium on mathematics and its connections to the arts and sciences, namely the second Mathematics and its Connections to the Arts and Sciences (MACAS2)Symposium in Odense, Denmark (May 29-31, 2007). The chapters are an eclectic collection of interdisciplinary research initiatives undertaken by mathematics educators with implications for practitioners concerned with teaching and learning processes. The papers cover a wide genre of research domains within mathematics education (cognition, modelling, problem solving, teacher education, ethnomathematics, mathematical/statistical literacy, curricular and technological initiatives and research related to science education). The major interdisciplinary themes of the papers in this book are: 1. How can modelling activities be used to foster interdisciplinary projects in the school and university setting? 2. How can the intricate connections between mathematics and physics be used to design and research interdisciplinary activities in schools and the university? 3. How can research within the ethnomathematics domain of mathematics education be linked to critical mathematics education and interdisciplinary projects involving mathematics, art and culture? 4. How can the push for mathematical and statistical literacy be connected to other subjects in the school curricula and emphasized via interdisciplinary activities? 5. What are concrete examples of classroom experiments with empirical data that demonstrate new and unusual connections/relations between mathematics, arts and the sciences with implications for pedagogy? 6. What is the role of technology and new ICT interfaces in linking communities of learners in interdisciplinary activities involving problem solving? The book is an important contribution to the literature on educational initiatives in interdisciplinary education increasing vital for emerging professions of the 21st century.

A brand-new kind of maths practice book developed with UK teachers and based on cutting-edge approaches to help students make the most of practice. Our unique Purposeful Practice Books use minimal variation to bolster students' Key Stage 3 studies in and out of the classroom. Each book encourages progression for all with over 3,750 concise and varied questions that: build in small steps to consolidate knowledge and boost confidence deepen understanding by helping students connect, reason and reflect on what they're learning focus on strengthening skills and strategies, such as problem-solving help every student put their learning into practice in different ways give students a strong preparation for progressing to GCSE study. They can be used flexibly alongside current resources: in class, for homework, or independent study. Supports the new Maths Progress (Second Edition) that builds students' confidence at KS3 and gives the best preparation for progressing to GCSE.

Answers are printed in a separate book (9781841464848) - or you can buy a version including answers all in one workbook (9781841460383). This CGP Workbook is packed with practice questions for Key Stage Three Maths. It's ideal for students working at a higher level, with a huge range of skill-building questions for every topic.

This edited volume explores key areas of interests in Singapore math and science education including issues on teacher education, pedagogy, curriculum, assessment, teaching practices, applied learning, ecology of learning, talent grooming, culture of science and math, vocational education and STEM. It presents to policymakers and educators a clear picture of the education scene in Singapore and insights into the role of math and science education in helping the country excel beyond international studies such as PISA, the pedagogical and curricula advancements in math and science learning, and the research and practices that give Singaporean students the competitive edge in facing the uncertain and challenging landscape of the future.