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Making Sense Of Mathematics For Teaching Grades 3 5

Author: Juli K. Dixon
Publisher: Solution Tree Press
ISBN: 1942496435
Size: 29.42 MB
Format: PDF, ePub, Mobi
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Develop a deep understanding of mathematics. This user-friendly resource presents grades 3–5 teachers with a logical progression of pedagogical actions, classroom norms, and collaborative teacher team efforts to increase their knowledge and improve mathematics instruction. Focus on an understanding of and procedural fluency with multiplication and division. Address how to learn and teach fraction concepts and operations with depth. Thoroughly teach plane and solid geometry. Explore strategies and techniques to effectively learn and teach significant mathematics concepts and provide all students with the precise, accurate information they need to achieve academic success. Benefits Dig deep into mathematical modeling and reasoning to improve as both a learner and teacher of mathematics. Explore how to develop, select, and modify mathematics tasks in order to balance cognitive demand and engage students. Discover the three important norms to uphold in all mathematics classrooms. Learn to apply the tasks, questioning, and evidence (TQE) process to ensure mathematics instruction is focused, coherent, and rigorous. Use charts and diagrams for classifying shapes, which can engage students in important mathematical practices. Access short videos that show what classrooms that are developing mathematical understanding should look like. Contents Introduction 1 Place Value, Addition, and Subtraction 2 Multiplication and Division 3 Fraction Concepts 4 Fraction Operations 5 Geometry 6 Measurement Epilogue Next Steps Appendix A Completed Classification of Triangles Chart Appendix B Completed Diagram for Classifying Quadrilaterals

Das Denken Von Kindern

Author: Robert S. Siegler
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3486806424
Size: 39.12 MB
Format: PDF, Kindle
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Bis in die jüngste Vergangenheit blieb uns der Zugang zu vielen der interessanten Aspekte des Denkens von Kindern verwehrt. Philosophen haben sich Jahrhunderte lang darum gestritten, ob Säuglinge die Welt als "strahlendes und dröhnendes Durcheinander" sehen oder ganz ähnlich wie ältere Kinder und Erwachsene. Erst mit der Entwicklung aufschlußreicher experimenteller Methoden in den vergangenen Jahren wurde die Antwort deutlich. Sogar Neugeborene sehen bestimmte Aspekte der Welt recht klar und mit 6 Monaten ähnelt die Wahrnehmung von Säuglingen der von Erwachsenen. Dies und andere Erkenntnisse über das Denken von Kindern sind Gegenstand dieses Buches.

Second Handbook Of Research On Mathematics Teaching And Learning

Author: Frank K. Lester
Publisher: IAP
ISBN: 160752709X
Size: 73.86 MB
Format: PDF, Mobi
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The audience remains much the same as for the 1992 Handbook, namely, mathematics education researchers and other scholars conducting work in mathematics education. This group includes college and university faculty, graduate students, investigators in research and development centers, and staff members at federal, state, and local agencies that conduct and use research within the discipline of mathematics. The intent of the authors of this volume is to provide useful perspectives as well as pertinent information for conducting investigations that are informed by previous work. The Handbook should also be a useful textbook for graduate research seminars. In addition to the audience mentioned above, the present Handbook contains chapters that should be relevant to four other groups: teacher educators, curriculum developers, state and national policy makers, and test developers and others involved with assessment. Taken as a whole, the chapters reflects the mathematics education research community's willingness to accept the challenge of helping the public understand what mathematics education research is all about and what the relevance of their research fi ndings might be for those outside their immediate community.

Der Zahlensinn Oder Warum Wir Rechnen K Nnen

Author: Stanislas Dehaene
Publisher: Springer-Verlag
ISBN: 3034878257
Size: 19.88 MB
Format: PDF, ePub
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Wir sind umgeben von Zahlen. Ob auf Kreditkarten gestanzt oder auf Münzen geprägt, ob auf Schecks gedruckt oder in den Spalten computerisierter Tabellen aufgelistet, überall beherrschen Zahlen unser Leben. Sie sind auch der Kern unserer Technologie. Ohne Zahlen könnten wir weder Raketen starten, die das Sonnensystem erkunden, noch Brücken bauen, Güter austauschen oder Rech nungen bezahlen. In gewissem Sinn sind Zahlen also kulturelle Erfindungen, die sich ihrer Bedeutung nach nur mit der Landwirtschaft oder mit dem Rad vergleichen lassen. Aber sie könnten sogar noch tiefere Wurzeln haben. Tausende von Jahren vor Christus benutzten babylonische Wissenschaftler Zahlzeichen, um erstaun lich genaueastronomische Tabellen zu berechnen. Zehntausende von Jahren zuvor hatten Menschen der Steinzeit die ersten geschriebenen Zahlenreihen geschaffen, indem sie Knochen einkerbten oder Punkte auf Höhlenwände malten. Und, wie ich später überzeugend darzustellen hoffe, schon vor weiteren Millionen von Jahren, lange bevor es Menschen gab, nahmen Tiere aller Arten Zahlen zur Kenntnis und stellten mit ihnen einfache Kopfrechnungen an. Sind Zahlen also fast so alt wie das Leben selbst? Sind sie in der Struktur unseres Gehirns verankert? Besitzen wir einen Zahlensinn, eine spezielle Intuition, die uns hilft, Zahlen und Mathematik mit Sinn zu erfüllen? Ich wurde vor fünfzehn Jahren, während meiner Ausbildung zum Mathema tiker, fasziniert von den abstrakten Objekten, mit denen ich umzugehen lernte, vor allem von den einfachsten von ihnen- den Zahlen.

Elementary And Middle School Mathematics

Author: John A. Van de Walle
Publisher: Allyn & Bacon
ISBN: 9780205386895
Size: 18.15 MB
Format: PDF, ePub, Docs
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New to the Fifth Edition *Inspired by one of the five process standards in the NCTM Principles and Standards', Content Connections is a new feature that highlights the connections between content areas in mathematics in various chapters. *NCTM icons appear in nearly every chapter and point explicitly to the alignment of this book with the NCTM Principles and Standards through excerpts and commentary. *Investigations in Number, Data, and Space and Connected Mathematics features spotlight examples of these two popular reform curricula for the K-5 and 6-8 grade levels, respectively. These excerpts occur in every chapter in Section 2, include an activity from the program along with a description of the surrounding content. The purpose is to acquaint students with materials reflecting the spirit of the NCTM Standards and the constructivist philosophy of the book. *Stop and Reflect features indicate places throughout the book to pause and become truly engaged with an idea. *Chapter 6, Planning in a Problem-Based Curriculum- includes a new step-by-step guide for planning student-centered lessons. A distinction between practice and drill provides a new perspective on the issue of drill. *