What does it mean to have a visual representation of a mathematical object, concept, or process? What visualization strategies support growth in mathematical thinking, reasoning, generalization, and knowledge? Is mathematical seeing culture-free? How can information drawn from studies in blind subjects help us understand the significance of a multimodal approach to learning mathematics? Toward a Visually-Oriented School Mathematics Curriculum explores a unified theory of visualization in school mathematical learning via the notion of progressive modeling. Based on the author's longitudinal research investigations in elementary and middle school classrooms, the book provides a compelling empirical account of ways in which instruction can effectively orchestrate the transition from personally-constructed visuals, both externally-drawn and internally-derived, into more structured visual representations within the context of a socioculturally grounded mathematical activity. Both for teachers and researchers, a discussion of this topic is relevant in the history of the present. The ubiquity of technological tools and virtual spaces for learning and doing mathematics has aroused interest among concerned stakeholders about the role of mathematics in these contexts. The book begins with a prolegomenon on the author's reflections on past and present visual studies in mathematics education. In the remaining seven chapters, visualization is pursued in terms of its role in bringing about progressions in mathematical symbolization, abduction, pattern generalization, and diagrammatization. Toward a Visually-Oriented School Mathematics Curriculum views issues surrounding visualization through the eyes of a classroom teacher-researcher; it draws on findings within and outside of mathematics education that help practitioners and scholars gain a better understanding of what it means to pleasurably experience the symmetric visual/symbolic reversal phenomenon - that is, seeing the visual in the symbolic and the symbolic in the visual."

Why do some students achieve more than others? Do we have to wait until pupils are ready? Can children discover math for themselves? Does language interfere with the learning of math? This classic text, written from the viewpoint of the math teacher, provides answers to these and many more questions. Each chapter explores a particular issue that illustrates the interaction between theory and practice. New chapters have been included on cognition, pattern, and ICT.

The only textbook that completely covers the OxfordAQA International GCSE Mathematics Core Level specification (9260), for first teaching in September 2016. Written by experienced authors, the clear, international approach ensures strong mathematical understanding and provides exam-focused practice to build assessment confidence. This textbook helps students to develop the key mathematical, reasoning and problem solving skills needed for the Oxford AQA International GCSE Mathematics Core Level exam, with extensive opportunities for practice and model answers. The online textbook can be accessed on a wide range of devices and the licence is valid until 31st December 2026, for use by one student or teacher. Your first login will be sent to you in the mail on a printed access card.

New Wave Mental Maths workbooks will sit comfortably with your mathematics programme. It offers day-to-day activities that cover all mathematic strands and are developmental throughout each book and the series. It is written to provide comprehensive coverage of mental maths concepts in the Irish mathematics curriculum. It provides opportunities for consolidation of mathematical concepts to develop and maintain speed of recall. It includes opportunities for reinforcement of ongoing mathematical concepts. You can introduce, practice and understand a range of mathematical vocabulary. It also offers sequential development of mathematical concepts and vocabulary. You can develop and reinforce problem-solving strategies. It also provides a structured daily mental maths programme for the whole academic year. It also contains pictorial, graphic and written representation of problems. It features: simple weekly pupil and teacher assessment (1st and 2nd Class books); and an inbuilt review and assessment programme (3rd - 6th Class books). It offers wide curriculum coverage that aids identification of 'problem' areas of maths, to help planning and assessment. It also features clear two-colour presentation throughout. It provides record pages. It covers all mathematics strands and strand units applicable to mental activities. It also includes pages of useful 'maths facts'. It also provides weekly testing/review for books 3-6. Developmental books provide ideal opportunity for differentiation, with pupils working on a level appropriate to their ability rather than age. Comprehensive teachers guide is available.

This all-in-one Study & Question book is a brilliant way for Year Two pupils (ages 6-7) to get to grips with Key Stage One Maths. For every topic, there's a page of clear, colourful notes that summarises all the important skills. This is followed by a page of practice questions to test children on what they've just learned. The book also contains two objective tests - one to assess children's skills at the start of Year Two, and one to measure their progress at the end of the year. All the answers are included in a cut-out-and-keep section in the middle of the book, and there's an explanation of all the key maths terms at the back.

This CGP Key Stage Two Mental Maths Workout Book is packed with essential practice exercises for Year 4 pupils (ages 7-8) - 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.

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.

This CGP Workbook (including answers) 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 and answers at the back. A matching KS3 Maths Study Guide is also available - see 9781841460307.

This CGP Study Guide explains everything students need to know for Key Stage Three Maths. It's ideal for students working at a higher level. Every topic is explained with clear, friendly notes and worked examples, and there's a range of practice questions to test the crucial skills.

The only textbook that completely covers the OxfordAQA International GCSE Mathematics Extended Level specification (9260), for first teaching in September 2016. Written by experienced authors, the clear, international approach strengthens mathematical understanding and provides exam-focused practice to build assessment confidence. This textbook helps students to develop the key mathematical, reasoning and problem solving skills needed for the Oxford AQA International GCSE Mathematiics Extended Level exam and provides an excellent grounding for further study at A Level . The online textbook license can be accessed on a wide range of devices and is valid until 31st December 2026, for use by one student or teacher. Your first login will be sent to you in the mail on a printed access card.

Power Maths is a leading primary maths mastery scheme that offers perfect alignment with the popular White Rose Maths Scheme of Learning. Written by a team of experts, led by Series Editor, Tony Staneff of White Rose Maths. For children who are following either the Power Maths or White Rose scheme, the textbooks provide lesson-by-lesson guidance throughout the curriculum. The textbooks include: Engaging contexts for problem solving help children to discover patterns and concepts for themselves in a meaningful way. Clear mathematical structures and representations ensure children make connections and grasp concepts. Lovable characters prompt and question children to promote reasoning skills and help to build a growth mindset.

Teacher education seeks to transform prospective and/or practicing teachers from neophyte possibly uncritical perspectives on teaching and learning to more knowledgeable, adaptable, analytic, insightful, observant, resourceful, reflective and confident professionals ready to address whatever challenges teaching secondary mathematics presents.

This transformation occurs optimally through constructive engagement in tasks that foster knowledge for teaching secondary mathematics. Ideally such tasks provide a bridge between theory and practice, and challenge, surprise, disturb, confront, extend, or provoke examination of alternatives, drawn from the context of teaching. We define tasks as the problems or activities that, having been developed, evaluated and refined over time, are posed to teacher education participants. Such participants are expected to engage in these tasks collaboratively, energetically, and intellectually with an open mind and an orientation to future practice. The tasks might be similar to those used by classroom teachers (e.g., the analysis of a graphing problem) or idiosyncratic to teacher education (e.g., critique of videotaped practice).

This edited volume includes chapters based around unifying themes of tasks used in secondary mathematics teacher education. These themes reflect goals for mathematics teacher education, and are closely related to various aspects of knowledge required for teaching secondary mathematics. They are not based on the conventional content topics of teacher education (e.g., decimals, grouping practices), but on broad goals such as adaptability, identifying similarities, productive disposition, overcoming barriers, micro simulations, choosing tools, and study of practice. This approach is innovative and appeals both to prominent authors and to our target audiences.

Do you want your child to attend an independent or grammar school? How do you give them the best chance at passing these exams? Practising test questions and extra help and coaching in preparation for the 11+ entrance exam can be the difference between passing and failing. The 11+ test or similar entrance exams must be passed for children to gain entrance to grammar and independent schools. And with limited places and high competition at each school it's vital to prepare your child so they have the best chance of gaining a place. Discover Maths is for beginners, introducing children to 11+ maths exam questions and tests so they can get the basics right first. Boasting expert coaching and guidance for both you and your child, Discover Maths explains how to tackle maths exam questions correctly and is filled with hundreds of brand new, authentic practise questions in the same multiple choice format the real maths exam is in. And when they've completed the Discover level make sure they move on to the next level, Develop, and lastly the Practise Test Papers so they receive a full programme of coaching needed to pass the 11+ maths exam. The Practise & Pass 11+ series has been developed in line with the current entrance exams so your children are practising identical format questions that they will answer in the test. Covering the four key subjects, verbal reasoning, non-verbal reasoning, maths and English, the series is split into three levels - Discover, Develop and Practise Test Papers. After working through the Practise & Pass 11+ series your child will be fully prepared for the tests, have the edge over other applicants and the best possible chance to get into the school of your choice. Give your child the skills and experience to pass the 11+ exam with flying colours.

How tall would a pile of 1000 acorns be? And if those acorns grew into 1000 oak trees, how big would that forest be? As children learn about large numbers, counting becomes less practical and understanding these numbers becomes more and more important. In this playful and mathematically sound book, children will develop an understanding of how big, how small, how long and how tall 1000 really is!

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

A stimulating and rigorous approach to Mathematics that goes beyond the requirements of the National Curriculum for Year 5 pupils (aged 9 and above) and lays the foundation for success at Common Entrance and other independent entrance exams at 11+. - Plenty of worked examples to demonstrate method - Develops key skills with clear explanations and diagrams - Challenges pupils with exercises at various levels - Tests understanding with end-of-chapter activities Galore Park Mathematics Year 5 Answers is available to purchase, which includes photocopiable worksheets for selected exercises and activities. Also available from Galore Park www.galorepark.co.uk: - Mathematics Year 6 - 11+ Maths Practice Exercises - 11+ Maths Revision Guide - 10-Minute Maths Tests Workbook Age 8-10 - 10-Minute Maths Tests Workbook Age 9-11 - Mental Arithmetic Workbook Age 8-10 - Mental Arithmetic Workbook Age 9-11

Create confident and capable mathematicians with accessible explanations and engaging activities. This book gradually builds on prior knowledge to deepen understanding through clear explanations, worked examples and hundreds of differentiated questions, as well as class activities that you can choose from to build your lessons and teaching plans. Designed to be used flexibly, this scheme covers the four 'what matters' statements and follows the five principles of progression from the Curriculum for Wales. - Develop pupils' conceptual understanding and communication with symbols throughout using plenty of worked examples and banded questions that get progressively more difficult - Target fluency, logical reasoning and strategic competence by using the markers included in each exercise question - Improve outcomes by selecting from banded questions most suited to enable progression - Ease the transition between progression steps with skill-checker activities at the start of each topic and review questions after each chapter - Link topics to other areas of learning, such as Science and Technology, with cross-curricular activities and discussion points

We are working with Cambridge International to gain endorsement for this forthcoming title. Written by expert authors with an international focus, this book fully covers the Cambridge O Level Mathematics syllabus (4024/4029) for examination from 2025. It enables learners to effectively master and find connections between mathematical topics and their practical applications. - Chapters and topics are introduced through clear explanations and notes on prior knowledge needed, with worked examples that are accessible for students studying in a second language. - Key points at the end of each chapter provide opportunity for reflection to ensure that understanding and skills have been developed before students move on. - Formative exercises support active, engaged learning throughout, and aid retention of knowledge with questions that progress in difficulty to test understanding at all levels. - Regular review exercises, including past paper questions, consolidate learning and help students to prepare for assessment. - 'Non-calculator' questions are clearly flagged so students can feel confident when approaching this type of question in their final summative assessment. - Answers, including worked solutions for review exercises, are available free on www.hoddereducation.com/cambridgeextras

Teaching Mathematics: Foundation to Senior Phase is the second edition of the first South African text on mathematics methodology. It includes reference to the South African mathematics syllabus as contained in the Curriculum and Assessment Policy Statement (CAPS) and focuses on typical challenges faced in the mathematics classroom in South Africa and southern African countries. Teaching Mathematics also contributes to the Africanisation of the discipline of mathematics education by stimulating thought and research about African perspectives and indigenous knowledge, including the language of location and the importance of using place-based examples in the classroom. The text makes use of African contexts in the teaching of mathematics, using African examples to which learners can relate, such as local names, artefacts, and elements of cultural heritage. Teaching Mathematics has a unique structure that takes readers through the stages of how learners learn mathem at ics, and how to teach mathematics, before drilling down to specific themes. The book provides practical pedagogy that will connect student teachers to the bigger picture of mathematics. This textbook will encourage student teachers to feel positive about mathematics and their role in teaching it, and to enter the classroom confident that they are equipped with the practical knowledge, skills and strategies for teaching mathematics.