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Functional Differential Geometry

Authors: ---
ISBN: 9780262315616 9780262019347 Year: Pages: 248 Language: English
Publisher: The MIT Press
Subject: Mathematics
Added to DOAB on : 2019-01-17 11:41:33
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An explanation of the mathematics needed as a foundation for a deep understanding of general relativity or quantum field theory.Physics is naturally expressed in mathematical language. Students new to the subject must simultaneously learn an idiomatic mathematical language and the content that is expressed in that language. It is as if they were asked to read Les Misérables while struggling with French grammar. This book offers an innovative way to learn the differential geometry needed as a foundation for a deep understanding of general relativity or quantum field theory as taught at the college level.The approach taken by the authors (and used in their classes at MIT for many years) differs from the conventional one in several ways, including an emphasis on the development of the covariant derivative and an avoidance of the use of traditional index notation for tensors in favor of a semantically richer language of vector fields and differential forms. But the biggest single difference is the authors' integration of computer programming into their explanations. By programming a computer to interpret a formula, the student soon learns whether or not a formula is correct. Students are led to improve their program, and as a result improve their understanding.

Keywords

geometry --- math

Fashion Figures

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ISBN: 9781484222737 9781484222744 Year: Pages: 109 DOI: https://doi.org/10.1007/978-1-4842-2274-4 Language: English
Publisher: Apress Grant: CA Technologies
Subject: Science (General) --- Education --- Mathematics
Added to DOAB on : 2018-07-27 15:02:02
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Missy Maker is a middle school girl who loves math and fashion. She sees math in everything she does. She tries to hide this from her friends, because she thinks it’s too geeky. Missy hears that the school math club needs more members, but she’s worried about what her friends will think if she joins, and she’s already committed to joining the fashion club.After an epic internal struggle and with the support of her peers and her quirky, loving family, Missy finds that she can be both a Mathlete and a Fashionista. Missy figures out how to bring the two clubs together to help both groups win. In the process, she discovers that she can openly excel in math and science and still be popular with her peers. She also learns how her math and science skills can help her artistic endeavors.Gain an inside perspective on what it’s like when you love math and science and happen to be a girl. Fashion Figures highlights the societal and internal pressures preteen and early-teen girls often face when they excel in these subjects, and it shows strategies for overcoming barriers to being themselves and doing what they love while still fitting in socially.

Keywords

STEM careers --- girls --- preteen --- YA --- mathlete --- fashionista --- math --- middle school

Educational Neuroscience, Constructivist Learning, and the Mediation of Learning and Creativity in the 21st Century

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Book Series: Frontiers Research Topics ISSN: 16648714 ISBN: 9782889195190 Year: Pages: 126 DOI: 10.3389/978-2-88919-519-0 Language: English
Publisher: Frontiers Media SA
Subject: Psychology --- Science (General)
Added to DOAB on : 2015-12-10 11:59:06
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The advent of educational neuroscience, a transdisciplinary exercise emerging from cognitive neuroscience and educational psychology, is the examination of physiological processes that undermine, support, and enhance the capacities to learn and create. The physiological underpinnings of learning and creativity each impact human ability and performance and mediate the processes of becoming educated, expert, and valued. Evidence of learning provides support to an ongoing canon, process, system, field or domain, while evidence of creativity results in an elaboration or departure from an ongoing canon, process, system, field, or domain. Educational neuroscience extends a challenge to scholars from multiple contexts to engage in the characterization and exploration of human ability and performance in these realms. The role of context, both environmental and interoceptive, is an integral part of efforts in educational neuroscience and in theories of constructivist learning to contribute ecologically valid insight to the pragmatic processes of learning and creativity. Examination at this level of specificity is vital to our ability to educate and support human potential in the 21st century. This Research Topic examines the neural basis of cognitive states and processes that influence knowledge and skill acquisition tied to the demonstration of human ability and performance across individual differences and in multiple contexts including STEM learning and the arts.

Building the Foundation: Whole Numbers in the Primary Grades: The 23rd ICMI Study

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Book Series: New ICMI Study Series ISSN: 1387-6872 ISBN: 9783319635545 9783319635552 Year: Pages: 536 DOI: https://doi.org/10.1007/978-3-319-63555-2 Language: English
Publisher: Springer Nature Grant: International Commission on Mathematical Instruction (ICMI); International Mathematical Union (IMU)
Subject: Education --- Mathematics
Added to DOAB on : 2018-06-22 15:48:51
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This twenty-third ICMI Study addresses for the first time mathematics teaching and learning in the primary school (and pre-school) setting, while also taking international perspectives, socio-cultural diversity and institutional constraints into account. One of the main challenges of designing the first ICMI primary school study of this kind is the complex nature of mathematics at the early level. Accordingly, a focus area that is central to the discussion was chosen, together with a number of related questions. The broad area of Whole Number Arithmetic (WNA), including operations and relations and arithmetic word problems, forms the core content of all primary mathematics curricula. The study of this core content area is often regarded as foundational for later mathematics learning. However, the principles and main goals of instruction on the foundational concepts and skills in WNA are far from universally agreed upon, and practice varies substantially from country to country. As such, this study presents a meta-level analysis and synthesis of what is currently known about WNA, providing a useful base from which to gauge gaps and shortcomings, as well as an opportunity to learn from the practices of different countries and contexts.

Empowering Teachers to Build a Better World

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Book Series: SpringerBriefs in Education ISBN: 9789811521379 Year: Pages: 135 DOI: 10.1007/978-981-15-2137-9 Language: English
Publisher: Springer Nature
Subject: Education --- Political Science --- Sociology
Added to DOAB on : 2020-05-14 09:27:58
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This open access book presents a comparative study on how large-scale professional development programs for teachers are designed and implemented. Around the world, governments and educators are recognizing the need to educate students in a broad range of higher order cognitive skills and socio-emotional competencies, and providing effective opportunities for teachers to develop the expertise needed to teach these skills is a crucial aspect of effective implementation of curricula which include those goals. This study examines how large-scale efforts to empower teachers for deeper instruction have been designed, how they have been implemented, and their outcomes. To do so, it investigates six programs from England, Colombia, Mexico, India, and the United States. Though all six are intended to broaden and deepen students’ curricular aspirations, each takes this expansion of curricular goals in a different direction. The ambitious education reforms studied here explicitly focus on building teachers’ capacity to teach on a broader set of goals. Through a discerning analysis of program documents, evaluations, and interviews with senior leaders and participants in the programs, the book identifies the various theories of action used in these programs, examines how they were implemented, and discusses what they achieved. As such, it offers an indispensable resource for education leaders interested in designing and implementing professional development programs for teachers that are aligned with ambitious instructional goals.

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