Combinatorics and Reasoning: Representing, Justifying and Building Isomorphisms is based on the accomplishments of a cohort group of learners from first grade through high school and beyond, concentrating on their work on a set of combinatorics tasks. By studying these students, the editors gain insight into the foundations of proof building, the tools and environments necessary to make connections, activities to extend and generalize combinatoric learning, and even explore implications of this learning on the undergraduate level. This volume underscores the power of attending to basic ideas in building arguments; it shows the importance of providing opportunities for the co-construction of knowledge by groups of learners; and it demonstrates the value of careful construction of appropriate tasks. Moreover, it documents how reasoning that takes the form of proof evolves with young children and discusses the conditions for supporting student reasoning.

Researchers examining children's mathematics acquisition are now questioning the belief that children learn mathematics principally through formalized, in-school mathematics education. There is increasing evidence that children gain mathematical understanding through their participation in out-of-school cultural practices and that their mathematics only occasionally resembles what they learn in the classroom. Culture and Cognitive Development presents the latest research by Dr. Geoffrey Saxe on this issue. In examinations of the mathematical understandings of child candy sellers in an urban center in northeastern Brazil, Dr. Saxe finds sharp contrasts between mathematics as practiced in school and in real-world settings. In this unique research project he presents a penetrating conceptual treatment of the interplay between culture and cognitive development, filling a void in current research literature. Subjects examined include: the interplay between sociocultural and cognitive developmental processes the differences between math knowledge learned in and out of the classroom the ways math learning in the classroom is modified by children's out-of-school mathematics and, correspondingly, how practical out-of-school mathematics use is modified by formal education

This is Book Three in CGP's range of three 10-Minute Tests books - it covers the most challenging material from KS3 Maths. Inside, you'll find over 30 bite-sized tests, each packed with questions on a mixture of topics. Complete answers and mark schemes are included at the back, so it's easy to find out how well students are progressing. For practice on the more straightforward parts of KS3 Maths, Book One (9781782944751) and Book Two (9781782944812) are also available.

This CGP Workout Book is packed with enjoyable practice exercises for Year 5 KS2 Maths (ages 9-10). Presented in a fun and friendly style, it's a great way to help make sure children have really got to grips with all the important topics. Answers are included in a removable section at the back of the book, 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 Workout Book is packed with enjoyable practice exercises for Year 4 KS2 Maths (ages 8-9). Presented in a fun and friendly style, it's a great way to help make sure children have really got to grips with all the important topics. Answers are included in a removable section at the back of the book, so it's simple to find out how well they're progressing.

Eminent scholars from around the globe gathered to discuss how educational systems would change if the prevailing principles of constructivism were applied to three major aspects of those systems -- knowledge and learning, communication, and environment. This volume provides documentation of the proceedings of this important meeting - - the Early Childhood Action Group of the Sixth International Congress on Mathematics Education.
This international assembly, representing such diverse disciplines as mathematics and math education, epistemology, philosophy, cognitive science, psycholinguistics, and science education, is the first to examine early childhood mathematics education from constructivist and international perspectives in addition to formulating recommendations for future work in the field.

Die reeks is volgens die Nasionale Kurrikulum- en Assesserings beleidsverklaring (“CAPS”) geskryf. ’n Moontlike werkskedule is ingesluit. Elke hoofstuk begin met ’n oorsig van wat onderrig word en die hulpbronne wat jy benodig. Daar is advies oor die voorgestelde pas wat jou sal help om die hele jaar se werk betyds af te handel. Ons gee by elke onderwerp raad oor hoe om konsepte bekend te stel en hoe om leerders met steierwerk voor te berei en te ondersteun. Al die antwoorde word gegee; jy bespaar dus tyd omdat jy nie die oefeninge self hoef uit te werk nie. ’n Volkleurplakkaat en ’n CD propvol hulpbronne is ook ingesluit om jou met onderrig en assessering te help. Addisionele voorbeeldvrae, toetse of assesserings take, wat jy kan kopieer, sal jou help om jou leerders effektief te assesseer.

The Mathematics Learner’s Book has been developed according to the requirements of the Curriculum and Assessment Policy Statement (CAPS) for Grade 2. The book can be used year after year. It gives an opportunity for introducing and reinforcing learning content, with at least two pages of activities per week. It also provides learners with activities and assessments. The teaching plans in the Teacher's Guide describes in detail how, when and where every page in the Learner’s Book can be used. The book is in full colour and beautifully illustrated. The Learner’s Book has been written by experts in the Foundation Phase field. All the authors have years of experience and have been involved in series which are successfully used in schools. The series have been developed under the guidance of Mart Meij, whose various educational series, from Grade R to 3, are widely used. The New All-In-One series is nationally recognised and used in many schools. The Learner’s Books were written according to the themes for each term, specified in the CAPS, Foundation Phase. The Learner’s Books provide background information and activities on each page to ensure the effective use of the book by the teacher. The Learner’s Books contain innovative multisensory activities that promote active learning and accommodate different learning styles. Free worksheets on the CDs supplement the activities in the Learner’s Books so that workbooks do not have to be bought.

The Edexcel Entry Level Certificate in Mathematics provides awards at levels 1, 2 and 3 of the National Curriculum and prepares students for entry to GCSE and VNVQ/VGCE and NVQ courses. The Certificate can be taken as a pre-GCSE course to introduce students to maths examinations and to give them the confidence to progress to GCSE. It is also ideal for further education students who require a basic understanding of maths as part of their study programme.

Spesifiek geskryf om aan al die vereistes van die nasionale Kurrikulum- en Assessering beleidsverklaring (KABV) te voldoen. Sleutelterme word in rooi gedruk as dit vir die eerste keer verskyn. ’n Lys van hierdie terme word ook in rooi aan die begin van elke eenheid of hoofstuk gelys. Nuwe woorde is in blou en word in die kantlyn verduidelik. Aktiwiteite help leerders om te verstaan wat hulle geleer het. 'n Opsomming aan die einde van elke onderwerp help leerders studeer. Die Formele Assesserings taak (FAT) blokkie bevat take wat leerders voorberei vir die wat in die klas voltooi moet word. Vrae aan die einde van elke onderwerp help leerders met hersiening. ‘n Voorbeeld van ‘n eksamenvraestel aan die einde van die boek sal leerders ook help oefen en leer oor alles wat hulle nodig het om te weet.

Spesifiek geskryf om aan al die vereistes van die nasionale Kurrikulum- en Assessering beleidsverklaring (KABV) te voldoen. Sleutelterme word in rooi gedruk as dit vir die eerste keer verskyn. ’n Lys van hierdie terme word ook in rooi aan die begin van elke eenheid of hoofstuk gelys. Nuwe woorde is in blou en word in die kantlyn verduidelik. Aktiwiteite help leerders om te verstaan wat hulle geleer het. 'n Opsomming aan die einde van elke onderwerp help leerders studeer. Die Formele Assesserings taak (FAT) blokkie bevat take wat leerders voorberei vir die wat in die klas voltooi moet word. Vrae aan die einde van elke onderwerp help leerders met hersiening. ‘n Voorbeeld van ‘n eksamenvraestel aan die einde van die boek sal leerders ook help oefen en leer oor alles wat hulle nodig het om te weet.

Hierdie 3 in 1 studiegids bied ’n gegronde oorgang tussen die basiese konsepte wat in Graad 10 Wiskundige Geletterdheid behandel is en die vaardighede wat nodig is vir die Graad 12-eindeksamen. Dit bevat: Omvattende Notas en Uitgewerkte Voorbeelde in al 7 onderwerpe, Oefeninge en ‘Toets jou Begrippe’ vir elke onderwerp en Gedetailleerde Antwoorde met Verduidelikings & nuttige wenke. Hierdie boek is volgepak met inhoud, toepassings en assessering en sal tuis en in die klaskamer baie goed gebruik kan word. ’n Toeganklike, logiese benadering maak die leerervaring makliker. Die rangskikking en aanbieding van die materiaal gekombineer met verduidelikende notas, motiveer leerders om hul vaardigheid in hierdie kernvak te verbeter. Die uitgebreide reeks vrae fokus daarop om vaardighede te ontwikkel om wiskundige probleme in die werklike lewe, binne die raamwerk van die KABV-kurrikulum, aan te pak. Leerders word toegerus om uitdagende vrae met selfvertroue en insig te benader. Al verskil hul vermoens en leerstyle, sal alle Graad 11-leerders hierdie boek as ’n treffer ervaar.

If our goal is to broaden and deepen students' awareness and understanding of mathematics, we advance the idea that engaging students with what we metaphorically call the personality of math. That is, we think that students who engage with the math's (1) human champions, (2) with its history and philosophy, and (3) with the nature of its problems and inferential challenges, are more likely to have a positive attitude toward math that will encourage greater learning.

The combined impact of linguistic, cultural, educational and cognitive factors on mathematics learning is considered in this unique book. By uniting the diverse research models and perspectives of these fields, the contributors describe how language and cognitive factors can influence mathematical learning, thinking and problem solving. The authors contend that cognitive skills are heavily dependent upon linguistic skills and both are critical to the representational knowledge intimately linked to school achievement in mathematics.

This work is a complete, comprehensive and progressive teaching and learning programme. It is for children sitting 11+, SATs, common entrance and scholarship examinations. Arranged in a topic by topic format, it adopts a more traditional approach. A unique code is used covering Information, Technique and Exercises. Clear methodologies, with examples, are given for each technique. Plenty of practice exercises are also included. All books are rigorously classroom tested. Methodologies have been used in AE Tuition classes for over 20 years. There is over 85 per cent success rate in 11+ and selection tests. These books are designed to be used in sequence from Workbook 1 onwards and are frequently revised and updated. Answers, Progress Charts and a Certificate of Achievement are included at the end of every book.

This book offers fresh insight and understanding of the many ways in which children, youth and adults may find their paths to mathematics. The chapters of the volume offer and analyse promising new ways into mathematics. The focus is on spaces and modalities of learning, dialogue and inquiry, embodiment and aesthetic experience, information and communication technology and on the use of mathematics in public communication. The chapters present new mathematical activities and conceptions enriching the repertoire of mathematics education practices. Critical commentaries discuss the innovative potential of the new approaches to the teaching and learning of mathematics. As a consequence, the commentaries point to requirements and open issues in the field of research in mathematics education.The volume is remarkably international. Teachers and researchers from 14 countries authored 21 chapters and 7 commentaries. The reader is invited to reflect on the particular effect of presenting avenues to mathematics contrived in diverse national settings in which the praxis of mathematics education might look different compared to what happens in the reader's place. The book starts a series of sourcebooks edited by CIEAEM, the Commission Internationale pour l'Etude et l'Amelioration de l'Enseignement des Mathematiques / International Commission for the Study and Improvement of Mathematics Education.

This book contributes to both mathematical problem solving and the communication of mathematics by students, and the role of personal and home technologies in learning beyond school. It does this by reporting on major results and implications of the Problem@Web project that investigated youngsters' mathematical problem solving and, in particular, their use of digital technologies in tackling, and communicating the results of their problem solving, in environments beyond school. The book has two focuses: Mathematical problem solving skills and strategies, forms of representing and expressing mathematical thinking, technological-based solutions; and students and teachers perspectives on mathematics learning, especially school compared to beyond-school mathematics.

Level: KS1 Subject: Maths Motivating maths practice for Year 2 Including helpful questions and answers, this Maths book provides reassurance whilst supporting your child's learning at home. Combining useful practice with engaging, colourful illustrations, this Maths practice book helps to boost your child's confidence and develop good learning habits for life. Each fun activity is designed to give your child a real sense of achievement. Included in this book: questions that allow children to practise the important numeracy skills learned at school colourful activities that make learning fun and motivate children to learn at home helpful tips and answers so that you can support your child's learning

This series has been endorsed by Cambridge Assessment International Education. Practise and consolidate knowledge gained from the Student's Book with this write-in workbook full of corresponding learning activities. - Save time when planning with ready-made homework or extension exercises. - Reinforce student's understanding of key mathematical concepts with varied question types, knowledge quizzes and the use of ICT. - Challenge learners with extra practice activities to encourage regular self-assessment.

The Mathematics Teacher's Guide contains a year plan, the four term plans, possible time schedules for a full week and daily step-by-step teaching plans for 40 weeks for the subject. The teaching plans include the following: the weekly teaching plan, hints and essential information as background knowledge before the lessons are tackled, the rhymes and songs mentioned in the teaching plan, complete step-by-step lessons for each day and guidance on how to complete the prescribed assessment tasks. The CD in the Teacher's Guide contains the year and term plans for the subject, so that the teacher can print it out and keep it at hand, free resources for teacher and learner, free prescribed worksheets, the theme-oriented stories mentioned in the teaching plans, the sheet music for the songs in the teaching plans and the assessment forms and rubrics. The Teacher's Guide is written by experts in the field of the Foundation Phase. All the authors have years of experience and have been involved in series which has been successfully used in schools. The series has been developed under the guidance of Mart Meij whose various educational series, from Grade R to 3, are widely used by schools. The New All-In-One series is nationally recognised and used in many schools. The Teacher's Guides not only provide lessons for the teacher that describe exactly what to do, but also background information so that the teacher knows why certain instructions are included in the lesson. The teaching plans include innovative, multisensory activities that promote active learning and accommodate different learning styles. The guides contain a CD with full colour free resources which can be used over and over by the teacher and the learner. Free worksheets on the CD can be downloaded and printed so that it is not necessary to buy workbooks.

This book brings together international research on school teachers', and university lecturers' uses of digital technology to enhance teaching and learning in mathematics. It includes contributions that address theoretical, methodological, and practical challenges for the field with the research lens trained on the perspectives of teachers and teaching. As countries around the world move to integrate digital technologies in classrooms, this book collates research perspectives and experiences that offer valuable insights, in particular concerning the trajectories of development of teachers' digital skills, knowledge and classroom practices.

Board: AQA Examination: Maths Foundation Specification: GCSE 9-1 Type: Revision (includes answers) (Please note this title is also available for Edexcel and All Boards) "The Scholastic resources go into far more detail than some of the other revision guides we have used and I've not seen any other resources that have an app linked to them. We would definitely recommend the resources to other schools. Everything you need to revise is in one place to enable students to work independently." Dave Richardson, Deputy Head [in reference to the GCSE English Language & Literature and Mathematics revision guides and exam practice books] Aim for the highest pass with Scholastic's GCSE Grades 9-1 series of Practice and Revision books. Our revision guides cover GCSE exam topics at greater depth, with clear and focused explanations of tricky topics and questions that offer additional challenge. Taking an active, stepped approach, our guides include popular 'It!' features giving students opportunities to self-test their understanding and apply their knowledge as they study. Snap it! Read it, snap it on your phone, revise it...helps you retain key facts Nail it! Examiner tips to help you get better grades Stretch it! Support for the really tough stuff that will get you higher grades "What they thought was especially clever is the resources 'knowing' the day of their exam, and then highlighting what they needed to do and when in the days and weeks leading up to it. That captured them there and then." Dave Richardson, Deputy Head [Read the full case study from Brentwood County High School] The accompanying app helps you revise on-the-go: Use the free, personalised digital revision planner and get stuck into the quick tests to check your understanding Download our free revision cards which you can save to your phone to help you revise on the go Implement 'active' revision techniques - giving you lots of tips and tricks to help the knowledge sink in Other subjects covered by Scholastic's Practice and Revision series: Maths Foundation, Maths Higher, SPAG, English Language and Literature, Biology, Chemistry, Physics, Combined Science and Geography

Level: KS2 Subject: Maths Suitable for 2023 SATs Targeted SATs practice for every topic taught at school! When it comes to getting the best results, practice really does make perfect! Matched the National Curriculum, this Collins Maths Year 6 workbook is designed to target every Maths Year 6 topic in depth. Using a repeated practice method that is proven to work, this book improves performance in tests and assessments. Questions for each topic are organised into three levels of increasing difficulty while progress tests throughout check pupil's understanding along the way. Children can record their own results too, supporting awareness and boosting confidence. A handy pull-out answer section is also included to ensure every pupil is prepared ahead of their Maths SATs Year 6 curriculum tests. For Year 6 English SATs, we've got another Collins KS2 Targeted Practice Workbook (9780008125189) available as well.