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Places Ellis at the heart of early-Victorian Cambridge with in-depth descriptions on his scientific work and tragic life Provides a unique glimpse into Victorian intellectual culture, based on previously unpublished archival materials This open access book brings together for the first time all aspects of the tragic life and fascinating work of the polymath Robert Leslie Ellis (1817–1859), placing him at the heart of early-Victorian intellectual culture. Written by a diverse team of experts, the chapters in the book’s first part contain in-depth examinations of, among other things, Ellis’s family, education, Bacon scholarship and mathematical contributions. The second part consists of annotated transcriptions of a selection of Ellis’s diaries and correspondence. Taken together, A Prodigy of Universal Genius: Robert Leslie Ellis, 1817–1859 is a rich resource for historians of science, historians of mathematics and Victorian scholars alike. Robert Leslie Ellis was one of the most intriguing and wide-ranging intellectual figures of early Victorian Britain, his contributions ranging from advanced mathematical analysis to profound commentaries on philosophy and classics and a decisive role in the orientation of mid-nineteenth century scholarship. This very welcome collection offers both new and authoritative commentaries on the work, setting it in the context of the mathematical, philosophical and cultural milieux of the period, together with fascinating passages from the wealth of unpublished papers Ellis composed during his brief and brilliant career. - Simon Schaffer, Department of History and Philosophy of Science, University of Cambridge

History of Western philosophy --- History of science --- Interdisciplinary studies --- History of mathematics --- Cultural studies --- Robert Leslie Ellis --- the Cambridge network --- mathematical education --- William Whewell --- history of science in Britain --- the history of ideas --- early-Victorian Cambridge --- history of mathematical sciences --- Victorian intellectual culture --- life of Robert Leslie Ellis

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This book is Open Access under a CC BY 4.0 license. The book presents the Invited Lectures given at 13th International Congress on Mathematical Education (ICME-13). ICME-13 took place from 24th- 31st July 2016 at the University of Hamburg in Hamburg (Germany). The congress was hosted by the Society of Didactics of Mathematics (Gesellschaft für Didaktik der Mathematik - GDM) and took place under the auspices of the International Commission on Mathematical Instruction (ICMI). ICME-13 – the biggest ICME so far - brought together about 3500 mathematics educators from 105 countries, additionally 250 teachers from German speaking countries met for specific activities. The scholars came together to share their work on the improvement of mathematics education at all educational levels.. The papers present the work of prominent mathematics educators from all over the globe and give insight into the current discussion in mathematics education. The Invited Lectures cover a wide spectrum of topics, themes and issues and aim to give direction to future research towards educational improvement in the teaching and learning of mathematics education. This book is of particular interest to researchers, teachers and curriculum developers in mathematics education.

Education. --- Mathematics --- Teaching. --- Mathematics Education. --- Learning & Instruction. --- Teaching and Teacher Education. --- Study and teaching. --- Didactics --- Instruction --- Pedagogy --- School teaching --- Schoolteaching --- Education --- Instructional systems --- Pedagogical content knowledge --- Training --- Children --- Education, Primitive --- Education of children --- Human resource development --- Schooling --- Students --- Youth --- Civilization --- Learning and scholarship --- Mental discipline --- Schools --- Teaching --- Mathematics. --- Math --- Science --- Mathematics—Study and teaching . --- Learning. --- Instruction. --- Learning process --- Comprehension --- Tertiary Mathematics Education --- Mathematics Teaching --- 13th Congress on Mathematical Education --- Mathematics Educators --- Primary Mathematics Education --- ICME-13 --- Theoretical Reflections on Mathematics Education --- Mathematics Learning --- Mathematics Teachers --- Global Mathematics Trends --- Society of Didactics of Mathematics --- Mathematics Education --- Empirical Studies in Mathematics Education --- Secondary Mathematics Education --- Improvement of Mathematics Education

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In recent years, the methodologies of teaching have been in a process of transition. Multiple active methodologies have proliferated, with the aim of changing the concept we have had of teaching so far. These advocate for a student who plays a leading role in the process of building learning, while the teacher acts as a figure who facilitates and glimpses the paths to learning. In order to be able to carry out this type of teaching in an optimal way, it is necessary for the teaching and research community to be correctly trained in its pedagogical principles and in the tools that boost its implementation. Among these principles and tools, it is of vital importance that information and communication technologies (ICT) be adequately handled. The use of active methodologies (project-based learning, problem-based learning, service learning, flipped classroom, mobile learning, etc.) or innovative pedagogical approaches (simulation, role-playing, gamification, etc.) promotes an improvement in the motivation of students as well as their skills. This aspect is especially important in the area of mathematics, whose contents are characterized by their abstraction, thus highlighting the need for its dynamization in classrooms of different educational stages.

Research & information: general --- emerging methodology --- educational innovation --- e-learning --- educational experimentation --- adults --- students --- b-learning --- ICT --- vocational training --- constructivism --- mathematics learning --- MOOC --- new teaching techniques --- students’ access to MOOC --- learning --- reading comprehension --- complexity --- problem-solving --- arithmetic word problems --- fraction operator --- technological environment --- active methodology --- escape room --- gamification --- methodological contrast --- mathematics --- secondary education --- musical activities --- learning-teaching --- preschool --- mathematical modeling --- modeling projects --- elementary school --- learning opportunities --- computational thinking --- STEAM education --- leisure-time education --- mathematical education --- good practices in mathematics education --- mathematics achievement --- influencing factors --- university --- social sciences --- structural equation modelling (SEM) --- Flipped Classroom --- flipped learning --- higher education --- educational robotics --- active learning --- case studies --- videogame --- early childhood education --- education --- learning environments --- educational games --- engineering students --- augmented reality --- spatial intelligence --- STEM --- Geogebra AR --- teaching differential equations --- teaching mathematics --- solving problem --- formative assessment --- teacher education --- teachers’ knowledge --- game-based learning --- affective domain --- mathematics education --- systematic review --- EXPLORIA --- STEAM --- active methodologies --- university level --- afective domain --- mathematical teaching methodologies --- educative innovation --- learning through video games --- real-valued functions

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In recent years, the methodologies of teaching have been in a process of transition. Multiple active methodologies have proliferated, with the aim of changing the concept we have had of teaching so far. These advocate for a student who plays a leading role in the process of building learning, while the teacher acts as a figure who facilitates and glimpses the paths to learning. In order to be able to carry out this type of teaching in an optimal way, it is necessary for the teaching and research community to be correctly trained in its pedagogical principles and in the tools that boost its implementation. Among these principles and tools, it is of vital importance that information and communication technologies (ICT) be adequately handled. The use of active methodologies (project-based learning, problem-based learning, service learning, flipped classroom, mobile learning, etc.) or innovative pedagogical approaches (simulation, role-playing, gamification, etc.) promotes an improvement in the motivation of students as well as their skills. This aspect is especially important in the area of mathematics, whose contents are characterized by their abstraction, thus highlighting the need for its dynamization in classrooms of different educational stages.

Research & information: general --- emerging methodology --- educational innovation --- e-learning --- educational experimentation --- adults --- students --- b-learning --- ICT --- vocational training --- constructivism --- mathematics learning --- MOOC --- new teaching techniques --- students’ access to MOOC --- learning --- reading comprehension --- complexity --- problem-solving --- arithmetic word problems --- fraction operator --- technological environment --- active methodology --- escape room --- gamification --- methodological contrast --- mathematics --- secondary education --- musical activities --- learning-teaching --- preschool --- mathematical modeling --- modeling projects --- elementary school --- learning opportunities --- computational thinking --- STEAM education --- leisure-time education --- mathematical education --- good practices in mathematics education --- mathematics achievement --- influencing factors --- university --- social sciences --- structural equation modelling (SEM) --- Flipped Classroom --- flipped learning --- higher education --- educational robotics --- active learning --- case studies --- videogame --- early childhood education --- education --- learning environments --- educational games --- engineering students --- augmented reality --- spatial intelligence --- STEM --- Geogebra AR --- teaching differential equations --- teaching mathematics --- solving problem --- formative assessment --- teacher education --- teachers’ knowledge --- game-based learning --- affective domain --- mathematics education --- systematic review --- EXPLORIA --- STEAM --- active methodologies --- university level --- afective domain --- mathematical teaching methodologies --- educative innovation --- learning through video games --- real-valued functions