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An Invitation to Fractal Geometry : Fractal Dimensions, Self-Similarity and Fractal Curves
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An Invitation to Fractal Geometry : Fractal Dimensions, Self-Similarity and Fractal Curves
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Pragmatist Philosophy for Critical Knowledge, Learning and Consciousness : A New Epistemological Framework for Education
Emerging from the confusion and chaos of neoliberal economic systems around the world, this book brings together a collection of major philosophical ideas from previous centuries and applies them to the practice of education.The book argues that pragmatist philosophy is the most appropriate to guide the organisation of curriculum, pedagogy and assessment.It outlines a number of philosophical dilemmas, exploring these in relation to particular philosophers and offers philosophical insights for educational practice.Further, the book proposes Critical Praxis Bricolage, an epistemological framework articulating a view that education practices are embedded in a social context.This reshapes formal education from being dominated by the market forces of neoliberalism, into a way of ethical life that respects the dignity and knowledgeability of each person and community regardless of background.Written in a narrative style, Pragmatist Philosophy for Critical Knowledge, Learning and Consciousness provides a philosophical paradigm of experience, culture and inquiry that actively connects with human interests of the everyday and with the distinctiveness of being human.This work will be of interest to researchers and higher degree students of education and philosophy of education.
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Constructing Pragmatist Knowledge : Education, Philosophy and Social Emancipation
Constructing Pragmatist Knowledge reintroduces an explicit and systematic philosophical approach to education through American Pragmatism, expanding and detailing the practice of pragmatism itself for practitioners across various fields of social action.While a number of theorists are referenced, it focuses on the work of the original pragmatists Charles Sanders Peirce, William James, John Dewey, George Herbert Mead and Jane Addams.It is written in a narrative style and connects personal and professional experience of the author with philosophical description, analysis and explanation.Major themes of pragmatism are encountered throughout involving knowledge, experience, inquiry, social acts, dialectic and contradiction, giving rise to human constructs of values, moral conduct and bricolage.Reintroducing pragmatism and epistemology as the focus of teaching and learning heralds revolutionary and democratic change for education systems worldwide and corrects neoliberal tendencies that impose anti-educational ideological, economic and political distortions.This book will be of interest to academics, graduate students, teachers and pre-service teachers, policy makers and researchers in education, philosophy, sociology and epistemology.
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What are similarity ratios?
Similarity ratios are ratios that compare the corresponding sides of two similar figures. They help us understand the relationship between the sides of similar shapes. The ratio of corresponding sides in similar figures is always the same, which means that if you know the ratio of one pair of sides, you can use it to find the ratio of other pairs of sides. Similarity ratios are important in geometry and are used to solve problems involving similar figures.
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What is the difference between similarity theorem 1 and similarity theorem 2?
Similarity theorem 1, also known as the Angle-Angle (AA) similarity theorem, states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. On the other hand, similarity theorem 2, also known as the Side-Angle-Side (SAS) similarity theorem, states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the triangles are similar. The main difference between the two theorems is the criteria for establishing similarity - AA theorem focuses on angle congruence, while SAS theorem focuses on both side proportionality and angle congruence.
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How can one calculate the similarity factor to determine the similarity of triangles?
The similarity factor can be calculated by comparing the corresponding sides of two triangles. To do this, one can divide the length of one side of the first triangle by the length of the corresponding side of the second triangle. This process is repeated for all three pairs of corresponding sides. If the ratios of the corresponding sides are equal, then the triangles are similar, and the similarity factor will be 1. If the ratios are not equal, the similarity factor will be the ratio of the two triangles' areas.
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How can the similarity factor for determining the similarity of triangles be calculated?
The similarity factor for determining the similarity of triangles can be calculated by comparing the corresponding sides of the two triangles. If the ratio of the lengths of the corresponding sides of the two triangles is the same, then the triangles are similar. This ratio can be calculated by dividing the length of one side of a triangle by the length of the corresponding side of the other triangle. If all three ratios of corresponding sides are equal, then the triangles are similar. This is known as the similarity factor and is used to determine the similarity of triangles.
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Reflective Teaching and Learning in Further Education
This book looks at critical reflection as a key skill for all teachers in further education (FE) and an important part of the new Professional Standards.In particular the text explores the key themes of self-awareness, planning, managing behaviour and CPD in relation to reflective practice to demonstrate how it can support those areas of teaching that most often cause concern.The limitations and benefits of reflection are analysed and action research is identified as an important facet in developing professional reflective practice which can in turn enhance both the personal and professional life of FE teachers. Â
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Understanding Teaching and Learning in Primary Education
This textbook gives you guidance and insights into the knowledge, values and commitments necessary to succeed in the primary classroom, supported by links to theory and research literature and realistic scenarios you may encounter as a new teacher. Fully updated throughout, key features of this second edition include:· A new chapter on inclusive education· Newly expanded coverage of digital learning, engaging with educational research and the role of the primary teacher· New ‘View from Practice’ examples· Cross-referenced links to the Teachers’ Standards in England and the GTCS Professional Standards in Scotland and where they are covered within the bookThis is essential reading for professional studies modules on primary initial teacher education courses, including university-based (PGCE, PGDE, BA QTS, BEd), school-based (SCITT, School Direct) and employment-based routes into teaching.
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Higher Education Teaching & Learning Space Design Guide
This book is essential reading for teaching staff and librarians to assist them in briefing the project design teams.It should also be a reference book for architects and interior designers.Student's need for social learning, collaborative and interactive facilities have had the greatest impact on the design of new teaching and learning spaces.The author, Brian Griffin, Architect researched this subject over many years and has included a large number of international Case Studies of successful designs.He is also the author of 'Laboratory Design Guide' 3rd Ed 2012 Routledge.
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Do you see the similarity?
Yes, I see the similarity between the two concepts. Both share common characteristics and features that make them comparable. The similarities can be observed in their structure, function, and behavior. These similarities help in understanding and drawing parallels between the two concepts.
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'How do you prove similarity?'
Similarity between two objects can be proven using various methods. One common method is to show that the corresponding angles of the two objects are congruent, and that the corresponding sides are in proportion to each other. Another method is to use transformations such as dilation, where one object can be scaled up or down to match the other object. Additionally, if the ratio of the lengths of corresponding sides is equal, then the two objects are similar. These methods can be used to prove similarity in geometric figures such as triangles or other polygons.
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What is similarity in mathematics?
In mathematics, similarity refers to the relationship between two objects or shapes that have the same shape but are not necessarily the same size. This means that the objects are proportional to each other, with corresponding angles being equal and corresponding sides being in the same ratio. Similarity is often used in geometry to compare and analyze shapes, allowing for the transfer of properties and measurements from one shape to another.
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What is the similarity ratio?
The similarity ratio is a comparison of the corresponding sides of two similar figures. It is used to determine how the dimensions of one figure compare to the dimensions of another figure when they are similar. The ratio is calculated by dividing the length of a side of one figure by the length of the corresponding side of the other figure. This ratio remains constant for all pairs of corresponding sides in similar figures.
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