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In diesem Open-Access-Buch führt Valentin Katter eine umfassende didaktisch orientierte Sachanalyse unter historisch-, logisch-, und individualgenetischen Gesichtspunkten durch, mit der es ihm möglich ist, systematisch sechs Grundvorstellungen zum Sinusbegriff zu identifizieren. Anhand detaillierter Videoanalysen zeigt der Autor anschließend, wie diese Grundvorstellungen genutzt werden können, um Denkprozesse von Lehramtsstudierenden in kooperativen Problemlösesituationen zu rekonstruieren. Diese Rekonstruktionen gewähren einen Einblick in das komplexe individuelle Netz von Vorstellungen und ermöglichen es, das Potential und mögliche Hindernisse, die in ihm stecken, auszuloten. Der Autor Valentin Katter arbeitet als Wissenschaftler und Dozent am Institut für Didaktik der Mathematik (IDM) der Universität Bielefeld und promovierte dort bei Prof. Dr. Rudolf vom Hofe. Seine Arbeit ist am Übergang von der Schule zur Hochschule anzusiedeln, wo er sich mit stoffdidaktischen Fragestellungen in den Bereichen der Analysis und der Trigonometrie beschäftigt.

Mathematics. --- History. --- History of Mathematical Sciences. --- General Mathematics and Education. --- Math --- Science

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This open access book provides an overview of Felix Klein’s ideas, highlighting developments in university teaching and school mathematics related to Klein’s thoughts, stemming from the last century. It discusses the meaning, importance and the legacy of Klein’s ideas today and in the future, within an international, global context. Presenting extended versions of the talks at the Thematic Afternoon at ICME-13, the book shows that many of Klein’s ideas can be reinterpreted in the context of the current situation, and offers tips and advice for dealing with current problems in teacher education and teaching mathematics in secondary schools. It proves that old ideas are timeless, but that it takes competent, committed and assertive individuals to bring these ideas to life. Throughout his professional life, Felix Klein emphasised the importance of reflecting upon mathematics teaching and learning from both a mathematical and a psychological or educational point of view. He also strongly promoted the modernisation of mathematics in the classroom, and developed ideas on university lectures for student teachers, which he later consolidated at the beginning of the last century in the three books on elementary mathematics from a higher standpoint.

Mathematics. --- Mathematics Education. --- History of Mathematical Sciences. --- Teaching and Teacher Education. --- Math --- Science --- Mathematics—Study and teaching . --- History. --- Teaching. --- Didactics --- Instruction --- Pedagogy --- School teaching --- Schoolteaching --- Education --- Instructional systems --- Pedagogical content knowledge --- Training --- Annals --- Auxiliary sciences of history --- Mathematics—Study and teaching  --- Mathematics --- History --- Teaching

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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 open access book explores commentaries on an influential text of pre-Copernican astronomy in Europe. It features essays that take a close look at key intellectuals and how they engaged with the main ideas of this qualitative introduction to geocentric cosmology. Johannes de Sacrobosco compiled his Tractatus de sphaera during the thirteenth century in the frame of his teaching activities at the then recently founded University of Paris. It soon became a mandatory text all over Europe. As a result, a tradition of commentaries to the text was soon established and flourished until the second half of the 17th century. Here, readers will find an informative overview of these commentaries complete with a rich context. The essays explore the educational and social backgrounds of the writers. They also detail how their careers developed after the publication of their commentaries, the institutions and patrons they were affiliated with, what their agenda was, and whether and how they actually accomplished it. The editor of this collection considers these scientific commentaries as genuine scientific works. The contributors investigate them here not only in reference to the work on which it comments but also, and especially, as independent scientific contributions that are socially, institutionally, and intellectually contextualized around their authors.

Literature: history & criticism --- Interdisciplinary studies --- European history --- History of mathematics --- History of science --- History. --- Europe—History. --- Mathematics. --- Books—History. --- History of Science. --- European History. --- History of Mathematical Sciences. --- History of the Book. --- Humanities and Social Sciences, multidisciplinary. --- Math --- Science --- Annals --- Auxiliary sciences of history --- History --- Europe—History --- Mathematics --- Books—History --- Astronomy --- Sacro Bosco, Joannes de, --- Bosco, Joannes de Sacro, --- De Sacro Bosco, Joannes, --- Giovanni di Sacrobosco, --- Halifax, John, --- Holybush, Joannes, --- Holywood, Jean de, --- Holywood, Joannes, --- Holywood, John, --- Ioannes de Sacrobusco, --- Iohannes de Sacro Busto, --- Joannes de Sacro Bosco, --- Joannes de Sacro Busco, --- Joannes de Sacro Busto, --- Joannes de Sacrobusco, --- Joannes de Sacrobusto, --- Sacro Bosco, Johannes de, --- Sacro Busco, Joannes de, --- Sacro Busto, Ioannes de, --- Sacro Busto, Iohannes de, --- Sacro Busto, Joannes de, --- Sacro Busto, Johannes de, --- Sacrobosco, Giovanni di --- Sacrobosco, Johannes de, --- Sacrobuschus, Joannes, --- Sacrobusco, Joannes de, --- Sacrobusto, Giovanni di, --- Sacrobusto, Joannes de,