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Research on teaching and learning proof and proving has expanded in recent decades. This reflects the growth of mathematics education research in general, but also an increased emphasis on proof in mathematics education. This development is a welcome one for those interested in the topic, but also poses a challenge, especially to teachers and new scholars. It has become more and more difficult to get an overview of the field and to identify the key concepts used in research on proof and proving.

Proof theory --- Study and teaching.

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Industrial marketing - Research. --- Commerce --- Business & Economics --- Marketing & Sales --- Industrial marketing --- Research. --- B2B marketing (Business to business marketing) --- Business to business marketing --- Business-to-business selling --- Industrial equipment --- Marketing

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This book presents chapters exploring the most recent developments in the role of technology in proving. The full range of topics related to this theme are explored, including computer proving, digital collaboration among mathematicians, mathematics teaching in schools and universities, and the use of the internet as a site of proof learning. Proving is sometimes thought to be the aspect of mathematical activity most resistant to the influence of technological change. While computational methods are well known to have a huge importance in applied mathematics, there is a perception that mathematicians seeking to derive new mathematical results are unaffected by the digital era. The reality is quite different. Digital technologies have transformed how mathematicians work together, how proof is taught in schools and universities, and even the nature of proof itself. Checking billions of cases in extremely large but finite sets, impossible a few decades ago, has now become a standard method of proof. Distributed proving, by teams of mathematicians working independently on sections of a problem, has become very much easier as digital communication facilitates the sharing and comparison of results. Proof assistants and dynamic proof environments have influenced the verification or refutation of conjectures, and ultimately how and why proof is taught in schools. And techniques from computer science for checking the validity of programs are being used to verify mathematical proofs. Chapters in this book include not only research reports and case studies, but also theoretical essays, reviews of the state of the art in selected areas, and historical studies. The authors are experts in the field. .

Mathematics. --- Educational technology. --- Proof theory. --- Critical Thinking. --- Mathematics Education. --- Technology and Digital Education. --- Structures and Proofs. --- Teaching and Teacher Education. --- Critical reflection --- Reflection (Critical thinking) --- Reflection process --- Reflective thinking --- Thinking, Critical --- Thinking, Reflective --- Thought and thinking --- Reflective learning --- Logic, Symbolic and mathematical --- Instructional technology --- Technology in education --- Technology --- Educational innovations --- Instructional systems --- Teaching --- Math --- Science --- Aids and devices --- Proof theory --- Study and teaching. --- Mathematics—Study and teaching . --- Teaching. --- Didactics --- Instruction --- Pedagogy --- School teaching --- Schoolteaching --- Education --- Pedagogical content knowledge --- Training --- Evaluative thinking --- Mathematics --- Teachers --- Digital Education and Educational Technology. --- Proof Theory and Constructive Mathematics. --- Teacher education --- Teacher training --- Teachers, Training of --- Study and teaching . --- Training of.

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1650-1850 publishes essays and reviews from and about a wide range of academic disciplines-literature (both in English and other languages), philosophy, art history, history, religion, and science. Interdisciplinary in scope and approach, 1650-1850 emphasizes aesthetic manifestations and applications of ideas, and encourages studies that move between the arts and the sciences-between the "hard" and the "humane" disciplines. The editors encourage proposals for "special features" that bring together five to seven essays on focused themes within its historical range, from the Interregnum to the end of the first generation of Romantic writers. While also being open to more specialized or particular studies that match up with the general themes and goals of the journal, 1650-1850 is in the first instance a journal about the artful presentation of ideas that welcomes good writing from its contributors. First published in 1994, 1650-1850 is currently in its 24th volume. ISSN 1065-3112. Published by Bucknell University Press. Distributed worldwide by Rutgers University Press.

Aesthetics. --- Beautiful, The --- Beauty --- Esthetics --- Taste (Aesthetics) --- Philosophy --- Art --- Criticism --- Literature --- Proportion --- Symmetry --- Psychology --- Radio broadcasting Aesthetics --- Aesthetics