Rigorous Mathematical Thinking

Author: James T. Kinard
Publisher: Cambridge University Press
ISBN: 0521876850
Release Date: 2008-06-02
Genre: Psychology

This book demonstrates how rigorous mathematical thinking can be fostered through the development of students' cognitive tools and operations. Though this approach can be applied in any classroom, it seems to be particularly effective with socially disadvantaged and culturally different students. The authors argue that children's cognitive functions cannot be viewed as following a natural maturational path: They should be actively constructed during the educational process. The Rigorous Mathematical Thinking (RMT) model is based on two major theoretical approaches allowing such an active construction - Vygotsky's theory of psychological tools and Feuerstein's concept of mediated learning experience. The book starts with general cognitive tools that are essential for all types of problem solving and then moves to mathematically specific cognitive tools and methods for utilizing these tools for mathematical conceptual formation. The application of the RMT model in various urban classrooms demonstrates how mathematics education standards can be reached even by the students with a history of educational failure who were considered hopeless underachievers.

Teaching Students Thinking Skills and Strategies

Author: Dorothy Howie
Publisher: Jessica Kingsley Publishers
ISBN: 0857005189
Release Date: 2011-08-15
Genre: Education

Developing the ability to think is a major part of education, which helps students become independent learners and participate fully in a learning environment. This book sets out the theory and outlines a model for implementing the teaching of thinking at whole-school, group and individual levels in inclusive settings. The model uses a three-tier approach to ensure that all learners are included: teaching thinking for all, which takes into account common needs; working with small groups, for those with exceptional needs such as learning difficulties or high ability; and addressing individualised learning needs, including those with a complex disability. The book covers key approaches to the teaching of thinking, giving examples of how each can best be used at each tier level. It also addresses the impact of different social contexts, cultures and environmental surroundings on learning. This book will be essential reading for all members of school communities, including education leaders and teachers. Educational psychologists, special educational needs co-ordinators, speech and language therapists, and those with particular interest in educating children who are vulnerable, from disadvantaged backgrounds, and from culturally different backgrounds, will find much of value in this book.

Individualisierte Diagnostik

Author: Aljoscha Jegodtka
Publisher: Lehmanns Media
ISBN: 9783865418913
Release Date:
Genre: Psychology

Ein gewisser Prozentsatz von Schüler*innen zeigt im Verlauf der Grundschulzeit trotz guter sonstiger schulischer Leistungen eine auffällige Minderleistung im Bereich der Mathematik. Die Diagnostik einer sogenannten Rechenschwäche bei einem Teil dieser Schüler*innen stellt in zwei Richtungen eine bisher nicht befriedigend gelöste Herausforderung dar: zum einen ist fraglich, ob der betreffende Personenkreis zutreffend identifiziert werden kann, zum anderen sind mit zutreffender Diagnose nicht automatisch die für die jeweiligen Schüler*innen sinnvollen pädagogischen Interventionen identifiziert. DerAutor stellt sich dieser Problematik über eineAuseinandersetzung mit verschiedenen Modellen des Lernens und einer entsprechend angelegten empirischen Untersuchung mit Schüler*innen der betreffenden Population. Ausgangspunkt der Studie ist die Auseinandersetzung mit der verbreiteten Diagnostik mittels der „Zareki-R“, die den neuropsychologischen Ansatz des 'Triple-Code-Modells' operationalisierbar zu machen verspricht. In der Auseinandersetzung mit diesem Vorgehen zeigen sich einerseits theoretische Inkohärenzen, andererseits Fehldiagnosen in der empirischen Überprüfung. Als Lösungsansatz greift der Autor auf den kulturhistorischen Ansatz von Vygotskij zurück und wendet diesen auf den Erwerb mathematischer Fähigkeiten und Fertigkeiten von Kindern bzw. Schüler*innen an. Hierbei zeigt sich die Tragfähigkeit dieses Konzepts der Entwicklung von Kindern auch in Bezug auf den Bereich der Mathematik. Es lassen sich allerdings auch Forschungsdesiderate aufzeigen, da die vorliegenden empirischen Erkenntnisse zur Entwicklung mathematischer Kompetenzen bei Kindern unter besonderer Beachtung von Schwierigkeiten bei ihrem Erwerb noch nicht ausreichend kulturhistorisch aufgearbeitet sind. Insbesondere methodische Überlegungen zur Erfassung von individuellen, lerngegenstandsbezogenen Zonen der nächsten Entwicklung stellen eine Herausforderung dar und wurden in dieser Untersuchung durch eine kulturhistorische Adaption des revidierten klinischen Interviews gelöst. Es kann gezeigt werden, dass es dieses Herangehen sowohl ermöglicht, Schüler*innen mit Schwierigkeiten im basalen mathematischen Bereich zu identifizieren, als auch ihre individuellen Zonen der nächsten Entwicklung zu ermitteln und damit für mögliche pädagogische Interventionen nutzbar zu machen.

The Routledge Handbook of Sociocultural Theory and Second Language Development

Author: James P. Lantolf
Publisher: Routledge
ISBN: 9781317229896
Release Date: 2018-06-14
Genre: Language Arts & Disciplines

The Routledge Handbook of Sociocultural Theory and Second Language Development is the first comprehensive overview of the field of sociocultural second language acquisition (SLA). In 35 chapters, each written by an expert in the area, this book offers perspectives on both the theoretical and practical sides of the field. This Handbook covers a broad range of topics, divided into several major sections, including: concepts and principles as related to second language development; concept-based instruction; dynamic assessment and other assessment based on sociocultural theory (SCT); literacy and content-based language teaching; bilingual/multilingual education; SCT and technology; and teacher education. This is the ideal resource for graduate students and researchers working in the areas of SLA and second language development.

Pre Service and In Service Teacher Education Concepts Methodologies Tools and Applications

Author: Management Association, Information Resources
Publisher: IGI Global
ISBN: 9781522573067
Release Date: 2018-11-02
Genre: Education

As with any industry, the education sector goes through frequent changes due to modern technological advancements. It is every educator’s duty to keep up with these shifting requirements and alter their teaching style to best fit the needs of their classroom. Pre-Service and In-Service Teacher Education: Concepts, Methodologies, Tools, and Applications explores the current state of pre-service teacher programs as well as continuing education initiatives for in-service educators. It also emphasizes the growing role of technology in teacher skill development and training as well as key pedagogical developments and methods. Highlighting a range of topics such as teacher preparation programs, teaching standards, and fieldwork and practicum experiences, this multi-volume book is designed for pre-service teachers, teacher educators, researchers, professionals, and academics in the education field.

The Routledge Handbook of Instructed Second Language Acquisition

Author: Shawn Loewen
Publisher: Routledge
ISBN: 9781317386742
Release Date: 2017-02-17
Genre: Language Arts & Disciplines

The Routledge Handbook of Instructed Second Language Acquisition is the first collection of state-of-the-art papers pertaining to Instructed Second Language Acquisition (ISLA). Written by 45 world-renowned experts, the entries are full-length articles detailing pertinent issues with up-to-date references. Each chapter serves three purposes: (1) provide a review of current literature and discussions of cutting edge issues; (2) share the authors’ understanding of, and approaches to, the issues; and (3) provide direct links between research and practice. In short, based on the chapters in this handbook, ISLA has attained a level of theoretical and methodological maturity that provides a solid foundation for future empirical and pedagogical discovery. This handbook is the ideal resource for researchers, graduate students, upper-level undergraduate students, teachers, and teacher-educators who are interested in second language learning and teaching. .

Advances in Multimedia Software Engineering and Computing Vol 1

Author: David Jin
Publisher: Springer Science & Business Media
ISBN: 9783642259890
Release Date: 2011-11-23
Genre: Computers

MSEC2011 is an integrated conference concentrating its focus upon Multimedia ,Software Engineering, Computing and Education. In the proceeding, you can learn much more knowledge about Multimedia, Software Engineering ,Computing and Education of researchers all around the world. The main role of the proceeding is to be used as an exchange pillar for researchers who are working in the mentioned field. In order to meet high standard of Springer, AISC series ,the organization committee has made their efforts to do the following things. Firstly, poor quality paper has been refused after reviewing course by anonymous referee experts. Secondly, periodically review meetings have been held around the reviewers about five times for exchanging reviewing suggestions. Finally, the conference organization had several preliminary sessions before the conference. Through efforts of different people and departments, the conference will be successful and fruitful.

Reading Writing and Proving

Author: Ulrich Daepp
Publisher: Springer Science & Business Media
ISBN: 9781441994790
Release Date: 2011-06-23
Genre: Mathematics

This book, which is based on Pólya's method of problem solving, aids students in their transition from calculus (or precalculus) to higher-level mathematics. The book begins by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematics and ends with suggested projects for independent study. Students will follow Pólya's four step approach: analyzing the problem, devising a plan to solve the problem, carrying out that plan, and then determining the implication of the result. In addition to the Pólya approach to proofs, this book places special emphasis on reading proofs carefully and writing them well. The authors have included a wide variety of problems, examples, illustrations and exercises, some with hints and solutions, designed specifically to improve the student's ability to read and write proofs. Historical connections are made throughout the text, and students are encouraged to use the rather extensive bibliography to begin making connections of their own. While standard texts in this area prepare students for future courses in algebra, this book also includes chapters on sequences, convergence, and metric spaces for those wanting to bridge the gap between the standard course in calculus and one in analysis.

Mathematical Understanding 5 11

Author: Anne D Cockburn
Publisher: SAGE
ISBN: 9781848605282
Release Date: 2007-06-19
Genre: Education

Sam - a young and enthusiastic trainee teacher - asked the class, 'What is the difference between 7 and 6?'. Jo's hand shot up and he immediately responded, 'Well seven is all straight lines and sixes are all curly.' How can you help children to make progress in mathematical understanding? Children's mathematical misconceptions very often arise as a result of poor communication. This practical and innovative book presents a range of creative strategies to help teachers communicate effectively in the mathematics classroom, offering some new ways of presenting the fundamental concepts and principles of mathematics, and clearly demonstrating that the most effective form of communication is not always verbal. Each chapter focuses on a theme or concept central to the numeracy strategy, such as subtraction, shape and space, constructing and connecting 2D and 3D shapes, data-logging and graph interpretation, and mathematical reasoning. Each chapter supports teachers' subject knowledge as well as suggesting a range of communication strategies (e.g. speaking, listening, drawing, role play, and visual methods such as posters and ICT work) to help teachers and children to share and build on their understanding. All of the activities have been tried and tested in classrooms across Europe. Written by a team of highly experienced teachers, the book will be valuable reading for pre- and in-service teachers, teacher educators and anyone who has an interest in extending the ways children actively engage with mathematics. Teachers with EAL pupils in their class may find it of particular value in communicating mathematical concepts to those who find English difficult. The book is accompanied by a DVD which includes video clips of children at work in mathematics classrooms, software used in the project, copies of material from the book and additional activities.

Erfahrung Mathematik

Author: P.J. Davis
Publisher: Springer-Verlag
ISBN: 9783034850407
Release Date: 2013-09-03
Genre: Science

ie ältesten uns bekannten mathematischen Schriftta D feln stammen aus der Zeit um 2400 v. ehr. ; aber wir dürfen davon ausgehen, daß das Bedürfnis, Mathematik zu schaffen, ein Ausdruck der menschlichen Zivilisation an sich ist. In vier bis fünf Jahrtausenden hat sich ein gewalti ges System von Praktiken und Begriffen - die Mathematik herangebildet, die in vielfältiger Weise mit unserem Alltag verknüpft ist. Was ist Mathematik? Was bedeutet sie? Wo mit befaßt sie sich? Was sind ihre Methoden? Wie wird sie geschaffen und benützt? Wo ist ihr Platz in der Vielgestalt der menschlichen Erfahrung? Welchen Nutzen bringt sie? Was für Schaden richtet sie an? Welches Gewicht kommt ihr zu? Diese schwierigen Fragen werden noch zusätzlich kompliziert durch die Fülle des Materials und die weitver zweigten Querverbindungen, die es dem einzelnen verun möglichen, alles zu begreifen, geschweige denn, es in seiner Gesamtheit zu erfassen und zwischen den Deckeln eines normalen Buches unterzubringen. Um von dieser Material fülle nicht erdrückt zu werden, haben sich die Autoren für eine andere Betrachtungsweise entschieden. Die Mathema tik ist seit Tausenden von Jahren ein Feld menschlicher Ak tivität. In begrenztem Rahmen ist jeder von uns ein Mathe matiker und betreibt bewußt Mathematik, wenn er zum Beispiel auf dem Markt einkauft, Tapeten ausmißt oder ei nen Keramiktopf mit einem regelmäßigen Muster verziert. In bescheidenem Ausmaß versucht sich auch jeder von uns als mathematischer Denker. Schon mit dem Ausruf «Aber Zahlen lügen nicht!» befinden wir uns in der Gesellschaft von Plato oder Lakatos.