Research in mathematics teacher education as a distinctive field of inquiry has grown substantially over the past 10-15 years. Within this field there is emerging interest in how mathematics teacher educators (MTEs) themselves learn and develop. Until recently there were few published studies on this topic, and the processes by which mathematics teacher educators learn, and the forms of knowledge they require for effective practice, had not been systematically investigated. However, researchers in mathematics education are now beginning to investigate the development of MTE expertise and associated issues. This volume draws on the latest research and thinking in this area is therefore timely to stimulate future development and directions. It will survey the emerging field of inquiry in mathematics education, combining the work of established scholars with perspectives of newcomers to the field, with the aim of influencing development of the field, invite cross-cultural comparisons in becoming a mathematics teacher educator by highlighting issues in the development of MTEs in different countries, and examine the roles of both mathematics educators and mathematicians in preparing future teachers of mathematics. The primary audience will be university-based mathematics teacher educators and MTE researchers, and postgraduate research students who are seeking academic careers as MTEs. Additional interest may come from teacher educators in disciplines other than mathematics, and education policy makers responsible for accreditation and quality control of initial teacher education programs.

Strengthen your pupils' understanding The Exploring maths Class Books are organised into units to accompany the Teacher's Book and are designed to help strengthen pupils' understanding. Includes activities, games and investigations that put maths in a real world context. Worked examples at the beginning of each lesson help pupils work independently. 3 levels of differentiation in each exercise help you pitch work at the right level. Specific Functional Skills tasks focus on the important process skills. "How well are you doing?" levelled self-assessment tests help pupils see what they need to do to improve. Interesting facts inform pupils about the cultural and social roots of maths.

Consolidating pupils' learning The Exploring maths Home Books support and consolidate the work carried out in class. Each lesson has a homework task reinforcing what's been taught in class. Each homework task reminds pupils what they have learned in the lesson, so that they can apply it to the questions. Accessible language ensures that pupils can work without adult support.

Consolidating pupils' learning The Exploring maths Home Books support and consolidate the work carried out in class. Each lesson has a homework task reinforcing what's been taught in class. Each homework task reminds pupils what they have learned in the lesson, so that they can apply it to the questions. Accessible language ensures that pupils can work without adult support.

Edexcel's own teaching resources for the two-tier GCSE Maths specifications. Written by Edexcel themselves to provide complete coverage of the two-tier specifications as well as expert support with the assessment criteria. Gives students unparalleled support both in and out of the classroom with clearly structured and carefully differentiated content, accompanied by interactive ICT resources accessed directly from the digital pages of the ActiveBook provided FREE inside every Students' Book.

This book is designed for use throughout the year, whilst the topic is being studied. By working though the worked examples and advice from examiners, students learn how to avoid the common pitfalls and gain maximum marks in the exam. Plenty of questions are included for students to practice, and there is a link back to the Students' Books for further study. The Examiners' tips then reveal how to maximize marks.

Rapid Maths is the ideal way to help struggling learners catch up with their peers in maths. With lots of variety plus software and games, Rapid Maths makes catch-up fun and gives each child personalised support and repeated practice in the fundamentals of numeracy. Plus, it's proven to double children's progress in number skills. Helps children master basic number skills to enable them to access the curriculum. Clear layout and a concrete-pictorial-abstract approach helps to support struggling learners. Gradual spiral progression in number skills to aid confidence. Varied and engaging 'real life' maths activities. Time saving and accessible teacher and TA resources. Ideal for home learning. Textbook with questions for child to work through with adult support.

-Makes mathematics education research on fraction concepts accessible and understandable to pre-service and in-service teachers of grades K-8, allowing teachers to understand evidence in student work and make better instructional decisions. -Uses extensive annotated samples of student work, helping teachers improve their ability to recognize and assess student errors and misconceptions, as well as their understanding, learning, and fluency of fraction concepts. -Built off the wide-scale research gathered in the Ongoing Assessment Project (OGAP), drawn from hundreds of teachers and thousands of examples of student work. -Each chapter includes student work samples and vignettes to illuminate the research, guidance on CCSSM standards, end of chapter questions, professional development activities, and instructional links that help teachers relate concepts back to their own instructional materials and programs. -This edition has been updated throughout with the latest research, CCSSM standards, additional examples and vignettes, and more.

This Tutor Delivery Pack for AQA GCSE (9-1) Mathematics Higher has a curriculum that matches tutor packs for a whole academic year and contains everything needed for a whole academic year of private tutoring: 38 complete lessons, complete with plans, activities and homework Detailed explanation on the use of the pack Information for parents Specification guidance Needs analysis for the parents and the students Mapping guide to the Revise GCSE Series Progress and End-of-Lesson Report templates Differentiation and extension ideas Customisable certificates in the digital version of the pack

A volume in Research on Technology and the Teaching and Learning of Mathematics: Syntheses, Cases, and Perspectives According to NCTM's Principles and Standards for School Mathematics, ""Technology is essential in teaching and learning of mathematics; it influences the mathematics that is taught and it enhances students' learning."" How does research inform this clarion call for technology in mathematics teaching and learning? In response to the need to craft appropriate roles for technology in school mathematics new technological approaches have been applied to the teaching and learning of mathematics, and these approaches have been examined by researchers world-wide. The first volume provides insight into what research suggests about the nature of mathematics learning in technological environments. Included in this volume are syntheses of research on technology in the learning of rational number, algebra, elementary and secondary geometry, mathematical modeling, and calculus. Additional chapters synthesize research on technology in the practice of teaching and on equity issues in the use of technology in mathematics instruction.Instead of simply reporting achievement scores of students who use technology in their learning, authors provide thoughtful analyses of bodies of research with the goal of understanding the ways in which technology affects what and how students learn. Each of the chapters in this volume is written by a team of experts whose own research has provided important guidance to the field.

Most education research is undertaken in western developed countries. While some research from developing countries does make it into research journals from time to time, but these articles only emphasize the rarity of research in developing countries. The proposed book is unique in that it will cover education in Papua New Guinea over the millennia. Papua New Guinea's multicultural society with relatively recent contact with Europe and the Middle East provides a cameo of the development of education in a country with both a colonial history and a coup-less transition to independence. Discussion will focus on specific areas of mathematics education that have been impacted by policies, research, circumstances and other influences, with particular emphasis on pressures on education in the last one and half centuries. This volume will be one of the few records of this kind in the education research literature as an in-depth record and critique of how school mathematics has been grown in Papua New Guinea from the late 1800s, and should be a useful addition to graduate programs mathematics education courses, history of mathematics, as well as the interdisciplinary fields of cross cultural studies, scholarship focusing on globalization and post / decolonialism, linguistics, educational administration and policy, technology education, teacher education, and gender studies.

This superb Revision Guide for Edexcel 9-1 GCSE Statistics is chock-full of game-changing study notes, helpful examples and essential exam advice. It contains all the topics from the new 9-1 specification in down-to-earth, crystal-clear language, plus we've thrown in plenty of realistic practice questions to get you well on your way to the top grades. Both Higher and Foundation tiers are covered, with the `Higher-only' material clearly labelled. Full answers are included at the back of the book. For even more brilliant practice check out our amazing 9-1 Statistics Exam Practice Workbook for Edexcel (9781782949527)

This friendly, colourful CGP favourite explains every Maths topic needed for the Key Stage Two! For each topic there are crystal-clear study notes covering all the important skills, plus handy markers to show which years pages are aimed at. We've also thrown in plenty of worked examples and practice questions to test what pupils are learning. Answers are included at the back. For the perfect combo, check out our matching Question Book (9781847621856)!

Fluid dynamics is an ancient science incredibly alive today. Modern technol ogy and new needs require a deeper knowledge of the behavior of real fluids, and new discoveries or steps forward pose, quite often, challenging and diffi cult new mathematical {:: oblems. In this framework, a special role is played by incompressible nonviscous (sometimes called perfect) flows. This is a mathematical model consisting essentially of an evolution equation (the Euler equation) for the velocity field of fluids. Such an equation, which is nothing other than the Newton laws plus some additional structural hypo theses, was discovered by Euler in 1755, and although it is more than two centuries old, many fundamental questions concerning its solutions are still open. In particular, it is not known whether the solutions, for reasonably general initial conditions, develop singularities in a finite time, and very little is known about the long-term behavior of smooth solutions. These and other basic problems are still open, and this is one of the reasons why the mathe matical theory of perfect flows is far from being completed. Incompressible flows have been attached, by many distinguished mathe maticians, with a large variety of mathematical techniques so that, today, this field constitutes a very rich and stimulating part of applied mathematics."

In this text the authors consider the Korteweg-de Vries (KdV) equation (ut = - uxxx + 6uux) with periodic boundary conditions. Derived to describe long surface waves in a narrow and shallow channel, this equation in fact models waves in homogeneous, weakly nonlinear and weakly dispersive media in general. Viewing the KdV equation as an infinite dimensional, and in fact integrable Hamiltonian system, we first construct action-angle coordinates which turn out to be globally defined. They make evident that all solutions of the periodic KdV equation are periodic, quasi-periodic or almost-periodic in time. Also, their construction leads to some new results along the way. Subsequently, these coordinates allow us to apply a general KAM theorem for a class of integrable Hamiltonian pde's, proving that large families of periodic and quasi-periodic solutions persist under sufficiently small Hamiltonian perturbations. The pertinent nondegeneracy conditions are verified by calculating the first few Birkhoff normal form terms -- an essentially elementary calculation.

Offering a proven, high-quality, step-by-step approach that builds students' confidence, these texts give your students the rigorous practice they need to get better results in the two-tier exams. Clearly organised, easy-to-use and carefully structured main texts provide thorough preparation for students on either a 1-year or 2-year course with clear, student-friendly language used throughout Fully worked examples with explanatory notes and commentary followed by carefully graded exercises offer gradual progression Exam and exam-style questions, presented in non-calculator and calculator section reviews, give further opportunities to consolidate skills acquired over a number of chapters Further compilations of exam and exam-style questions, which reflect how the examiners will assess the two-tier specifications are provided to give thorough preparation for the exams.

This pack from CGP contains two sets of complete practice exams, with detailed answers and mark schemes. They match the content and style of the Grade 9-1 Foundation Level Maths GCSE exams, with a separate booklet for each paper - just like the real thing. The mark scheme is straightforward to use, including hints and tips, making this the perfect way to prepare for the exams.