Author: Ernst Schuberth Publisher: ISBN: 9781888365795 Category : Geometry Languages : en Pages : 134
Book Description
This practical book is a valuable teacher resource for teaching geometry in Year 6 in the Steiner-Waldorf curriculum.Comprehensively illustrated, it covers angles in regular polygons, triangles, right-angled triangles, and platonic solids. It concludes with a chapter on teaching shadow drawing and projection.This is the third volume in Ernst Schuberth's series on Geometry Lessons for Waldorf Schools.
Author: Ernst Schuberth Publisher: ISBN: 9781888365375 Category : Mathematics Languages : en Pages : 155
Book Description
An experienced Waldorf teacher and mathematician sets out a comprehensive curriculum for teaching mathematics in the Year 6 (age 11-12) in the Steiner-Waldorf curriculum.The book includes guidance on teaching banking formulae, interest calculation and gives an introduction to basic economics.It includes weekly lesson plans, with plenty of maths exercises and solutions.
Author: Andrew McInerney Publisher: Springer Science & Business Media ISBN: 1461477328 Category : Mathematics Languages : en Pages : 420
Book Description
Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view. This book, unlike other introductory texts in differential geometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduate student who already has a solid foundation in the standard mathematics curriculum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful use of examples and constructions in order to explore those consequences.
Author: Nick Thomas Publisher: Temple Lodge Publishing ISBN: 1902636023 Category : Astronomy Languages : en Pages : 193
Book Description
Rudolf Steiner discovered that, in addition to "ordinary" space, negative space, or "counterspace," also exists, leading to a more holistic worldview. Steiner suggested that it was important to understand counterspace as a necessary supplement to the conventional approach. Science between Space and Counterspace relates the phenomena of our world to both space and counterspace, which leads to a new scientific understanding. If counterspace actually exists, then the resulting interplay between counterspace and "ordinary" space must be significant. This concept is applied to gravity, liquids, gases, heat, light, chemistry, and life. Each aspect involves a separate investigation, whereas the various threads begin to interweave and become a unified whole. A new concept of time, and indications for a new approach to relativity and quantum physics begin to emerge. Note: Science between Space and Counterspace contains advanced mathematical and scientific proofs that the nonspecialist, general reader may find overly difficult.
Author: National Research Council Publisher: National Academies Press ISBN: 0309324882 Category : Social Science Languages : en Pages : 587
Book Description
Children are already learning at birth, and they develop and learn at a rapid pace in their early years. This provides a critical foundation for lifelong progress, and the adults who provide for the care and the education of young children bear a great responsibility for their health, development, and learning. Despite the fact that they share the same objective - to nurture young children and secure their future success - the various practitioners who contribute to the care and the education of children from birth through age 8 are not acknowledged as a workforce unified by the common knowledge and competencies needed to do their jobs well. Transforming the Workforce for Children Birth Through Age 8 explores the science of child development, particularly looking at implications for the professionals who work with children. This report examines the current capacities and practices of the workforce, the settings in which they work, the policies and infrastructure that set qualifications and provide professional learning, and the government agencies and other funders who support and oversee these systems. This book then makes recommendations to improve the quality of professional practice and the practice environment for care and education professionals. These detailed recommendations create a blueprint for action that builds on a unifying foundation of child development and early learning, shared knowledge and competencies for care and education professionals, and principles for effective professional learning. Young children thrive and learn best when they have secure, positive relationships with adults who are knowledgeable about how to support their development and learning and are responsive to their individual progress. Transforming the Workforce for Children Birth Through Age 8 offers guidance on system changes to improve the quality of professional practice, specific actions to improve professional learning systems and workforce development, and research to continue to build the knowledge base in ways that will directly advance and inform future actions. The recommendations of this book provide an opportunity to improve the quality of the care and the education that children receive, and ultimately improve outcomes for children.
Author: Daniel J. Velleman Publisher: Cambridge University Press ISBN: 0521861241 Category : Mathematics Languages : en Pages : 401
Book Description
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
Author: Serge Lang Publisher: Springer Science & Business Media ISBN: 147572022X Category : Science Languages : en Pages : 405
Book Description
At last: geometry in an exemplary, accessible and attractive form! The authors emphasise both the intellectually stimulating parts of geometry and routine arguments or computations in concrete or classical cases, as well as practical and physical applications. They also show students the fundamental concepts and the difference between important results and minor technical routines. Altogether, the text presents a coherent high school curriculum for the geometry course, naturally backed by numerous examples and exercises.
Author: Ernst Schuberth
Author: Ernst Schuberth
Author: Ernst Schuberth
Author: 
Author: Andrew McInerney
Author: Nick Thomas
Author: National Research Council
Author: Daniel J. Velleman
Author: Serge Lang
Author: Daniel C. Alexander