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Statistics and probability are fascinating fields, tightly interwoven with the context of the problems which have to be modelled. The authors demonstrate how investigations and experiments provide promising teaching strategies to help high-school students acquire statistical and probabilistic literacy. In the first chapter the authors put into practice the following educational principles, reflecting their views of how these subjects should be taught: a focus on the most relevant ideas and postpone extensions to later stages; illustrating the complementary/dual nature of statistical and probabilistic reasoning; utilising the potential of technology and show its limits; and reflecting on the different levels of formalisation to meet the wide variety of students’ previous knowledge, abilities, and learning types. The remaining chapters deal with exploratory data analysis, modelling information by probabilities, exploring and modelling association, and with sampling and inference. Throughout the book, a modelling view of the concepts guides the presentation. In each chapter, the development of a cluster of fundamental ideas is centred around a statistical study or a real-world problem that leads to statistical questions requiring data in order to be answered. The concepts developed are designed to lead to meaningful solutions rather than remain abstract entities. For each cluster of ideas, the authors review the relevant research on misconceptions and synthesise the results of research in order to support teaching of statistics and probability in high school. What makes this book unique is its rich source of worked-through tasks and its focus on the interrelations between teaching and empirical research on understanding statistics and probability.
Statistics --- Probabilities --- Study and teaching (Secondary) --- Probability --- Statistical inference --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Education. --- Education, general. --- Children --- Education, Primitive --- Education of children --- Human resource development --- Instruction --- Pedagogy --- Schooling --- Students --- Youth --- Civilization --- Learning and scholarship --- Mental discipline --- Schools --- Teaching --- Training --- Education --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Econometrics
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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. .
Probabilities --- Study and teaching. --- Education. --- Probabilities. --- Mathematics --- Teaching. --- Mathematics Education. --- Probability Theory and Stochastic Processes. --- Teaching and Teacher Education. --- Learning & Instruction. --- Didactics --- Instruction --- Pedagogy --- School teaching --- Schoolteaching --- Education --- Instructional systems --- Pedagogical content knowledge --- Training --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Children --- Education, Primitive --- Education of children --- Human resource development --- Schooling --- Students --- Youth --- Civilization --- Learning and scholarship --- Mental discipline --- Schools --- Teaching --- Mathematics. --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Math --- Science --- Mathematics—Study and teaching . --- Learning. --- Instruction. --- Learning process --- Comprehension
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This book summarizes the vast amount of research related to teaching and learning probability that has been conducted for more than 50 years in a variety of disciplines. It begins with a synthesis of the most important probability interpretations throughout history: intuitive, classical, frequentist, subjective, logical propensity and axiomatic views. It discusses their possible applications, philosophical problems, as well as their potential and the level of interest they enjoy at different educational levels. Next, the book describes the main features of probabilistic thinking and reasoning, including the contrast to classical logic, probability language features, the role of intuitions, as well as paradoxes and the relevance of modeling. It presents an analysis of the differences between conditioning and causation, the variability expression in data as a sum of random and causal variations, as well as those of probabilistic versus statistical thinking. This is followed by an analysis of probability’s role and main presence in school curricula and an outline of the central expectations in recent curricular guidelines at the primary, secondary and high school level in several countries. This book classifies and discusses in detail the three different research periods on students’ and people’s intuitions and difficulties concerning probability: early research focused on cognitive development, a period of heuristics and biases programs, and the current period marked by a multitude of foci, approaches and theoretical frameworks.
Education. --- Mathematics --- Teaching. --- Mathematics Education. --- Teaching and Teacher Education. --- Learning & Instruction. --- 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 --- Mathematics Education --- Teaching and Teacher Education --- Learning and Instruction
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In recent years, there have been an expansion and renewal of the statistics content in the mathematics curricula in many countries through all school grade levels from primary to secondary levels. However, no similar attention has been paid to the preparation of mathematics teacher to teach statistics at these levels. This book presents the results from the Joint ICMI/IASE Study, Teaching Statistics in School Mathematics. Challenges for Teaching and Teacher Education that was intended to address the lack of attention to teaching statistics by promoting international collaborative research specifically focussed on the education and professional development of teachers to teach statistics.The volume covers a very wide field, including examples of statistics curricula and teacher education programmes around the world; analysis of the fundamentals to teaching statistics; survey chapters of research related to teachers’ attitudes, beliefs and knowledge related to fundamental statistics ideas and its teaching; and analyses of challenges and experiences related to training teachers to teach statistics. The book is designed to be useful to researchers in mathematics education and statistics education teacher educators, and people involved in curricular development in statistics with the hope that it will foster further research in the problems related to educating teachers to teach statistics at different school levels. It could be of interest to teachers themselves, since the basic ideas for teaching statistics and the research summarised in the book both in learning difficulties or teaching strategies is applicable in both the training of students and teachers. .
Research -- Mathematical models. --- Statistics -- Research. --- Statistics -- Study and teaching. --- Statistics. --- Statistics --- Mathematics --- Education --- Physical Sciences & Mathematics --- Social Sciences --- Education, Special Topics --- Mathematical Statistics --- Study and teaching --- Study and teaching. --- Education. --- Mathematics Education. --- Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law. --- Statistics for Social Science, Behavioral Science, Education, Public Policy, and Law. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Children --- Education, Primitive --- Education of children --- Human resource development --- Instruction --- Pedagogy --- Schooling --- Students --- Youth --- Civilization --- Learning and scholarship --- Mental discipline --- Schools --- Teaching --- Training --- Mathematics. --- Statistics for Social Sciences, Humanities, Law. --- Math --- Science --- Mathematics—Study and teaching . --- Statistics .
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