probabilistic thinking presenting plural perspectives advances in mathematics education

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Probabilistic Thinking

Author : Egan J Chernoff
ISBN : 9789400771550
Genre : Education
File Size : 65. 77 MB
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This volume provides a necessary, current and extensive analysis of probabilistic thinking from a number of mathematicians, mathematics educators, and psychologists. The work of 58 contributing authors, investigating probabilistic thinking across the globe, is encapsulated in 6 prefaces, 29 chapters and 6 commentaries. Ultimately, the four main perspectives presented in this volume (Mathematics and Philosophy, Psychology, Stochastics and Mathematics Education) are designed to represent probabilistic thinking in a greater context.

Teaching And Learning Stochastics

Author : Carmen Batanero
ISBN : 9783319728711
Genre : Education
File Size : 63. 16 MB
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This book presents a collection of selected papers that represent the current variety of research on the teaching and learning of probability. The respective chapters address a diverse range of theoretical, empirical and practical aspects underpinning the teaching and learning of probability, curricular issues, probabilistic reasoning, misconceptions and biases, as well as their pedagogical implications. These chapters are divided into THREE main sections, dealing with: TEACHING PROBABILITY, STUDENTS' REASONING AND LEARNING AND EDUCATION OF TEACHERS. In brief, the papers presented here include research dealing with teachers and students at different levels and ages (from primary school to university) and address epistemological and curricular analysis, as well as the role of technology, simulations, language and visualisation in teaching and learning probability. As such, it offers essential information for teachers, researchers and curricular designers alike.

Good Thinking

Author : Irving J. Good
ISBN : 9780486474380
Genre : Mathematics
File Size : 88. 52 MB
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These sparkling essays by a gifted thinker offer philosophical views on the roots of statistical interference. A pioneer in the early development of computing, Irving J. Good made fundamental contributions to the theory of Bayesian inference and was a key member of the team that broke the German Enigma code during World War II. Good maintains that a grasp of probability is essential to answering both practical and philosophical questions. This compilation of his most accessible works concentrates on philosophical rather than mathematical subjects, ranging from rational decisions, randomness, and the nature of probability to operational research, artificial intelligence, cognitive psychology, and chess. These twenty-three self-contained articles represent the author's work in a variety of fields but are unified by a consistently rational approach. Five closely related sections explore Bayesian rationality; probability; corroboration, hypothesis testing, and simplicity; information and surprise; and causality and explanation. A comprehensive index, abundant references, and a bibliography refer readers to classic and modern literature. Good's thought-provoking observations and memorable examples provide scientists, mathematicians, and historians of science with a coherent view of probability and its applications.

The Mathematics Enthusiast Issue

Author : Bharath Sriraman
ISBN : 9781681232584
Genre : Education
File Size : 50. 68 MB
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The Mathematics Enthusiast (TME) is an eclectic internationally circulated peer reviewed journal which focuses on mathematics content, mathematics education research, innovation, interdisciplinary issues and pedagogy. The journal exists as an independent entity. It is published on a print?on?demand basis by Information Age Publishing and the electronic version is hosted by the Department of Mathematical Sciences? University of Montana. The journal is not affiliated to nor subsidized by any professional organizations but supports PMENA [Psychology of Mathematics Education? North America] through special issues on various research topics.

The Routledge International Handbook Of Research On Teaching Thinking

Author : Rupert Wegerif
ISBN : 9781317752301
Genre : Education
File Size : 77. 41 MB
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The Routledge International Handbook of Research on Teaching Thinking is a comprehensive guide to research on teaching thinking. Teaching thinking is key to growing a more successful economy, is needed for increased democratic engagement and is vital for the well-being of individuals faced with the complexity of a globalised world. However, there are questions about what we mean by ‘thinking’, how best to teach it and how best to assess it, and it is these questions that this handbook explores and addresses. Containing surveys and summaries of international, cutting-edge research on every aspect of teaching thinking in a range of contexts, the handbook is thorough in its delivery, examining many different approaches and methods to help readers understand what teaching thinking is and how we can best take this movement forward. Key topics include: • Theoretical perspectives on teaching thinking • Approaches for teaching thinking • Developing creative thinking • Developing critical thinking and metacognition • The assessment of thinking • Teaching thinking in the context of STEM • Collaborative thinking and new technology • Neuro-educational research on teaching thinking This book is an essential guide for policy-makers, teachers and researchers who are interested in teaching thinking

Mathematical Literacy On Statistical Measures

Author : Christian Büscher
ISBN : 9783658230692
Genre : Education
File Size : 60. 8 MB
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In most countries, only very limited time resources are available for statistics education within mathematics education. Thus, statistics education research needs to develop teaching-learning arrangements that are compact and applicable to classrooms. Christian Büscher designs and investigates a compact teaching-learning arrangement which aims at mathematical and reflective knowledge about statistics. Central results include the specification of the learning content of statistical measures, an empirical reconstruction of students’ learning processes towards statistical measures, and the identification of students’ situated reflections about mathematics within their learning processes.

Mathematik Im Unterricht Ausgabe 8

Author : Guenter Maresch
ISBN : 9780244351564
Genre : Education
File Size : 69. 90 MB
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Die Reihe Mathematik im Unterricht stellt verschiedenartigste Aspekte fYr einen modernen und sinnstiftenden Mathematikunterricht in den Mittelpunkt. Dabei werden aktuelle bildungspolitische Themen ebenso diskutiert wie innermathematische und fachdidaktische Fragestellungen. In den BSnden der Reihe werden zudem BeitrSge aus den verwandten UnterrichtsfSchern Geometrisches Zeichnen, Darstellende Geometrie oder Informatik sowie fYr BeitrSge aus den primSren Bezugswissenschaften PSdagogik, Psychologie oder Soziologie publiziert. Die Zielgruppe der Reihe Mathematik im Unterricht sind interessierte LehrerInnen aller Schultypen in den Sekundarstufen I und II sowie Lehrende und ForscherInnen an den PSdagogischen Hochschulen und UniversitSten. Die Ausgabe 8 umfasst insgesamt sechszehn BeitrSge, welche von AutorInnen aus ...sterreich, Deutschland und England verfasst wurden.

Advanced Problems In Mathematics

Author : Stephen Siklos
ISBN : 9781783741441
Genre : Mathematics
File Size : 75. 60 MB
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This book is intended to help students prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Papers). STEP examinations are used by Cambridge colleges as the basis for conditional offers in mathematics and sometimes in other mathematics-related subjects. They are also used by Warwick University, and many other mathematics departments recommend that their applicants practice on past papers to become accustomed to university-style mathematics. Advanced Problems in Mathematics is recommended as preparation for any undergraduate mathematics course, even for students who do not plan to take the Sixth Term Examination Paper. The questions analysed in this book are all based on recent STEP questions selected to address the syllabus for Papers I and II, which is the A-level core (i.e. C1 to C4) with a few additions. Each question is followed by a comment and a full solution. The comments direct the reader’s attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anybody interested in advanced mathematics.

Reconceptualizing Early Mathematics Learning

Author : Lyn D. English
ISBN : 9789400764408
Genre : Education
File Size : 49. 92 MB
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This book emanated primarily from concerns that the mathematical capabilities of young children continue to receive inadequate attention in both the research and instructional arenas. Research over many years has revealed that young children have sophisticated mathematical minds and a natural eagerness to engage in a range of mathematical activities. As the chapters in this book attest, current research is showing that young children are developing complex mathematical knowledge and abstract reasoning a good deal earlier than previously thought. A range of studies in prior to school and early school settings indicate that young learners do possess cognitive capacities which, with appropriately designed and implemented learning experiences, can enable forms of reasoning not typically seen in the early years. Although there is a large and coherent body of research on individual content domains such as counting and arithmetic, there have been remarkably few studies that have attempted to describe characteristics of structural development in young students’ mathematics. Collectively, the chapters highlight the importance of providing more exciting, relevant, and challenging 21st century mathematics learning for our young students. The chapters provide a broad scope in their topics and approaches to advancing young children’s mathematical learning. They incorporate studies that highlight the importance of pattern and structure across the curriculum, studies that target particular content such as statistics, early algebra, and beginning number, and studies that consider how technology and other tools can facilitate early mathematical development. Reconceptualising the professional learning of teachers in promoting young children’s mathematics, including a consideration of the role of play, is also addressed.

What Is Mathematics Really

Author : Reuben Hersh
ISBN : 0195130871
Genre : Medical
File Size : 26. 2 MB
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Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.

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