The value of patterns to the teaching and learning of mathematics is well understood, both in terms of research and application. When we involve or appeal to pattern in teaching mathematics, it is usually because we are trying to help students to extract greater meaning, or enjoyment, or both, from the experience of learning environments within which they are occupied, and perhaps also to facilitate remembering. As a general skill it is thought that the ability to discern a pattern is a precursor to the ability to generalize and abstract, a skill essential in the early years of learning and beyond. Research indicates that the larger problem in teaching mathematics does not lie primarily with students; rather it is with the teachers themselves. In order to make changes for students there first needs to be a process of change for teachers. Understanding the place of patterns in learning mathematics is a predicate to understanding how to teach mathematics and how to use pedagogical reasoning necessary in teaching mathematics. Importantly, the lack of distinction created by the pedagogical use of patterns is not immediately problematic to the student or the teacher. The deep -seated cognitive patterns that both teachers and students bring to the classroom require change. Chapter 1 opens the book with a focus on mathematics as the science of patterns and the importance of patterns in mathematical problem solving, providing the reader with an introduction. The authors of Chapter 2 revisit the work of Po lya and the development and implementation of problem solving in mathematics. In Chapter 3, the authors present an argument for core pedagogical content knowledge in mathematics teacher preparation. The authors of Chapter 4 focus on preservice teachers' patterns of conception as related to understanding number and operation. In Chapter 5 the authors examine the role of visual representation in exploring proportional reasoning, denoting the importance of helping learners make their thinking visible. The authors of Chapter 6 examine patterns and relationships, and the importance of each in assisting students' learning and development in mathematical understanding. The authors of Chapter 7 examine the use of worked examples as a scalable practice, with emphasis on the importance of worked examples in teaching fraction magnitude and computation is discussed. In Chapter 8, the authors expand on the zone of proximal development to investigate the potential of Zankov's Lesson in terms of students analyzing numerical equalities. The authors of Chapter 9 focus on high leverage mathematical practices in elementary pre-service teacher preparation, drawing into specific relief the APEX cycle to develop deep thinking. In Chapter 10, the author focuses on number talks and the engagement of students in mathematical reasoning, which provides opportunities for students to be sensemakers of mathematics. Chapter 11 presents an epilogue, focusing on the importance of recognizing the special nature of mathematics knowledge for teaching.

Unbeatable practice for the latest SATS tests! This splendid Mixed Practice Paper Pack 2 contains 6 full sets of realistic tests - two Maths SATS papers, and two English SATS papers, plus two Science papers! All this, plus detailed answers and full exam-style mark scheme. What's more, this pack comes with a whole host of online extras, including: Pupil-Friendly Answers - Crystal-clear worked answers, perfect for pupils marking their own work; SATS Parents' Guide - Everything parents need to know about the SATS; Mini Quizzes - Mini quizzes to print or view online. Perfect as warm-up activities or extra practice; Online Edition - Digital versions of the Practice Papers to view on your PC or tablet! Just use the unique code included in the pack to gain access to all these free online goodies.

The series is edited by the head coaches of China's IMO National Team. Each volume, catering to different grades, is contributed by the senior coaches of the IMO National Team. The Chinese edition has won the award of Top 50 Most Influential Educational Brands in China.The series is created in line with the mathematics cognition and intellectual development levels of the students in the corresponding grades. All hot mathematics topics of the competition are included in the volumes and are organized into chapters where concepts and methods are gradually introduced to equip the students with necessary knowledge until they can finally reach the competition level.In each chapter, well-designed problems including those collected from real competitions are provided so that the students can apply the skills and strategies they have learned to solve these problems. Detailed solutions are provided selectively. As a feature of the series, we also include some solutions generously offered by the members of Chinese national team and national training team.

Packed to the rafters with helpful practice questions for Key Stage Two Maths, this CGP classic is fully up-to-date for the latest curriculum! It contains a huge range of questions for all the essential KS2 Maths topics - with hints and tips for the trickiest parts. We've also thrown in complete answers for easy marking. Matching study notes are available in our KS2 Maths Study Book (9781847621849).

You can never have too much practice - that's why we've loaded this Question Book to the hilt with challenging KS2 Maths questions. It's been carefully written for pupils working above the expected standard in KS2 Maths - it'll test them on everything they need for a top mark in the SATS. It contains a wide range of realistic SATS-style practice questions for every topic, covering all the essential skills pupils will need on the big day. Matching study notes are available in our SATS Stretch Revision Book (9781782944188). Pupils working at or towards the expected standard should try our other Targeted SATS Question Book (9781782944218).

-Offers an innovative introduction to the psychology of mathematics and the nature of mathematical thinking and learning, using an approach that empowers students by fostering their own construction of mathematical structures. - In clear, engaging writing, award-winning mathematician and educator Norton Anderson explores the psychological basis for mathematics at every level, relevant for pre-service and in-service secondary and elementary math teachers, math teacher educators, and anyone interested in the nature of mathematics. -Reflections and exercises are included in each chapter, as well as footnotes for those interested in building off their understanding with related research.

-Offers an innovative introduction to the psychology of mathematics and the nature of mathematical thinking and learning, using an approach that empowers students by fostering their own construction of mathematical structures. - In clear, engaging writing, award-winning mathematician and educator Norton Anderson explores the psychological basis for mathematics at every level, relevant for pre-service and in-service secondary and elementary math teachers, math teacher educators, and anyone interested in the nature of mathematics. -Reflections and exercises are included in each chapter, as well as footnotes for those interested in building off their understanding with related research.

-Offers a theory of secondary mathematics teacher learning in schools to achieve ambitious and equitable mathematics in their classroom, drawing on sociocultural learning theory. -Explores teacher learning as well as the role of context in teacher learning, using closely-documented case studies from across the US. -Offers researchers and scholars new theoretical and methodological tools for the elusive phenomenon of teacher learning, and instructional leaders and coaches practical examples of how teachers shift their thinking and practice.

-Offers a theory of secondary mathematics teacher learning in schools to achieve ambitious and equitable mathematics in their classroom, drawing on sociocultural learning theory. -Explores teacher learning as well as the role of context in teacher learning, using closely-documented case studies from across the US. -Offers researchers and scholars new theoretical and methodological tools for the elusive phenomenon of teacher learning, and instructional leaders and coaches practical examples of how teachers shift their thinking and practice.

The series is edited by the head coaches of China's IMO National Team. Each volume, catering to different grades, is contributed by the senior coaches of the IMO National Team. The Chinese edition has won the award of Top 50 Most Influential Educational Brands in China.The series is created in line with the mathematics cognition and intellectual development levels of the students in the corresponding grades. All hot mathematics topics of the competition are included in the volumes and are organized into chapters where concepts and methods are gradually introduced to equip the students with necessary knowledge until they can finally reach the competition level.In each chapter, well-designed problems including those collected from real competitions are provided so that the students can apply the skills and strategies they have learned to solve these problems. Detailed solutions are provided selectively. As a feature of the series, we also include some solutions generously offered by the members of Chinese national team and national training team.

remove remove This book was developed with the caring and concerned adult in mind and is a one-stop for anyone who would like to help a child develop problem solving thinking. They will become adept at the use of problem solving strategies over the course of their development from birth. For each age range, this book provides developmental information, relevant mathematical concepts, sample problems with multiple solutions, and finally activities to engage with as a family in order to develop mathematical thinking and problem solving skill.

Daily practice is the best way to improve children's Mental Maths skills - that's why we've written this fantastic Daily Practice workbook for the Year 5 Summer Term! Packed with colourful characters and engaging activities, there's a page of Mental Maths practice for every school day of the term. It's all matched to the National Curriculum and perfect for use in class or at home! For each day, there's a short explanation of what to do, followed by a selection of Mental Maths questions. New topics are introduced gradually, then revisited throughout the book - the questions increase in difficulty through each week, and also through the term. Score boxes at the end of each page make it easy to track children's progress and there are answers to every question at the back. For complete coverage of Year 5, check out our books for the Autumn (9781789087697) and Spring (9781789087710) terms too!

This book covers the elementary school mathematics curriculum common in most parts of the world. Its aim is to serve educators (teachers and parents) as a guide for teaching mathematics at elementary school level. The book focuses both on content knowledge and on pedagogical content knowledge. It bridges the gap between fundamental mathematical principles and good teaching practices. It also offers the reader a glimpse on how mathematicians perceive elementary mathematics and presents ideas for specific mathematical activities.The author is also a co-founder of Matific, an adaptive game-based teaching and learning tool for primary school mathematics. Independent studies have shown Matific to improve test scores, reduce maths anxiety, and increase motivation. Matific is available in 26 languages and aligned to mathematics curricula in 46 countries. Awards include Best Mathematics Instructional Solution, Best Game-Based Curriculum Solution and Best Educational App. For a trial, visit https://www.matific.com.

This book contains the answers to every question in our Year 3 Maths Textbook for KS2 Maths (978178294967). We've also included plenty of helpful features for teachers, such as a suggested Scheme of Work and a guide to how the Textbook matches the Y3 Programme of Study!

This book uses meta-analysis to synthesize research on scaffolding and scaffolding-related interventions in STEM (science, technology, engineering, and mathematics) education. Specifically, the volume examines the extent to which study quality, assessment type, and scaffolding characteristics (strategy, intended outcome, fading schedule, scaffolding intervention, and paired intervention) influence cognitive student outcomes. It includes detailed descriptions of the theoretical foundations of scaffolding, scaffolding strategies that have been proposed to meet different intended learning outcomes in STEM, and associated efficacy information. Furthermore, the book describes assessment strategies and study designs which can be used to evaluate the influence of scaffolding, and suggests new fields in which scaffolding strategies that have proven efficacious may be used.

Unearthing Culturally Responsive Mathematics Teaching: The Legacy of Gloria Jean Merriex focuses on the theory and practices of a highly successful mathematics teacher of African American children in a high-poverty school. The book aims to contribute to the limited literature base in this area in mathematics education. The discussions in the book center on the ideals of culturally responsive teaching (CRT), and seek to build understanding of this concept in the context of mathematics. Further, the story of Gloria Jean Merriex speaks to the importance of historical influences on teaching practice. Her story is couched in sociopolitical realities of the American educational system, and is discussed as such. Cultural incongruities that exist in classrooms and contribute to the black-white achievement gap, particularly in mathematics, are also discussed.

This book covers the elementary school mathematics curriculum common in most parts of the world. Its aim is to serve educators (teachers and parents) as a guide for teaching mathematics at elementary school level. The book focuses both on content knowledge and on pedagogical content knowledge. It bridges the gap between fundamental mathematical principles and good teaching practices. It also offers the reader a glimpse on how mathematicians perceive elementary mathematics and presents ideas for specific mathematical activities.The author is also a co-founder of Matific, an adaptive game-based teaching and learning tool for primary school mathematics. Independent studies have shown Matific to improve test scores, reduce maths anxiety, and increase motivation. Matific is available in 26 languages and aligned to mathematics curricula in 46 countries. Awards include Best Mathematics Instructional Solution, Best Game-Based Curriculum Solution and Best Educational App. For a trial, visit https://www.matific.com.

Math educator Kate Snow gives parents the tools they need to teach Math with Confidence. This scripted, open-and-go program leads parents step-by-step through teaching all the concepts second-graders need to master: reading, writing, and comparing numbers to 1000 adding and subtracting two- and three-digit numbers solving addition and subtraction word problems telling time, counting money, measuring length reading graphs, identifying shapes, and understanding simple fractions Short, lively lessons will hold a child's attention by incorporating hands-on activities, games, and real-life situations. Straightforward, colorful worksheets give students practice with new concepts and review previously-learned material. Snow makes math fun by including optional enrichment lessons, with suggestions for wonderful math picture books to enjoy together and application activities to make math come alive. Beyond just telling parents what to do, Second Grade Math with Confidence also helps them understand why the lessons are designed the way they are, giving them the knowledge and confidence to help their children learn. Using Second Grade Math with Confidence will allow parents to build a strong math foundation for their children. Age Range: 7 to 8 Grade: Second Grade

The Teaching File: Provides true variety and interactivity for your oral and mental starters. Suggests a wide choice of practical and oral teaching activities and suggestions for clearly focused review sessions. Activities enable you to adjust the pace of teaching to suit your class and offer options for consolidation, reinforcement, extension and differentiation.

This fantastic Functional Skills book has everything students need to prepare for the Level 2 Maths test! It covers every exam board and every topic, including all the calculator and non-calculator skills needed for the latest L2 Functional Skills specifications. Everything's explained in CGP's easy-to-understand style, with examples and notes galore. Each topic is followed by a page of practice questions, so students can learn then test themselves as they go. We've also included exam-style practice papers with full answers so you'll know what to expect on the big day. Nice!

First Published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.

CGP's KS2 Maths Question Cards are spot-on for practising the important skills pupils will need in the tough Maths SATS. This pack contains over 60 cards of fun, informal questions covering all the key Maths SATS topics, plus plenty of helpful notes to aid pupils and parents with tricky or less familiar topics. Challenge sections throughout the pack stretch pupils and deepen their understanding of Mathematics. Answers can be found on back of each card. For more pocketable SATS practice, try our great KS2 Spelling, Punctuation and Grammar cards (9781789084047).

remove remove This book was developed with the caring and concerned adult in mind and is a one-stop for anyone who would like to help a child develop problem solving thinking. They will become adept at the use of problem solving strategies over the course of their development from birth. For each age range, this book provides developmental information, relevant mathematical concepts, sample problems with multiple solutions, and finally activities to engage with as a family in order to develop mathematical thinking and problem solving skill.