The Intuitive Sources of Probabilistic Thinking in Children

The Intuitive Sources of Probabilistic Thinking in Children
Author: H. Fischbein
Publisher: Springer Science & Business Media
Total Pages: 221
Release: 2012-12-06
Genre: Psychology
ISBN: 9401018588

About a year ago I promised my friend Fischbein a preface to his book of which I knew the French manuscript. Now with the printer's proofs under my eyes I like the book even better than I did then, because of, and influenced by, new experiences in the meantime, and fresh thoughts that crossed my mind. Have I been influenced by what I remembered from the manuscript? If so, it must have happened unconsciously. But of course, what struck me in this work a year ago, struck a responsive chord in my own mind. In the past, mathematics teaching theory has strongly been influenced by a view on mathematics as a heap of concepts, and on learning mathematics as concepts attainment. Mathematics teaching practice has been jeopardised by this theoretical approach, which in its most dangerous form expresses itself as a radical atomism. To concepts attainment Fischbein opposes acquisition of intuitions. In my own publications I avoided the word "intuition" because of the variety of its meanings across languages. For some time I have used the term "constitution of mathematical objects", which I think means the same as Fischbein's "acquisition of intuitions" - indeed as I view it, constituting a mental object precedes its conceptualising, and under this viewpoint I tried to observe mathematical activities of young children.

Probabilistic Thinking

Probabilistic Thinking
Author: Egan J. Chernoff
Publisher: Springer Science & Business Media
Total Pages: 746
Release: 2013-12-05
Genre: Education
ISBN: 940077155X

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.

Thinking With Data

Thinking With Data
Author: Marsha C. Lovett
Publisher: Psychology Press
Total Pages: 488
Release: 2012-08-21
Genre: Psychology
ISBN: 1136679421

The chapters in Thinking With Data are based on presentations given at the 33rd Carnegie Symposium on Cognition. The Symposium was motivated by the confluence of three emerging trends: (1) the increasing need for people to think effectively with data at work, at school, and in everyday life, (2) the expanding technologies available to support people as they think with data, and (3) the growing scientific interest in understanding how people think with data. What is thinking with data? It is the set of cognitive processes used to identify, integrate, and communicate the information present in complex numerical, categorical, and graphical data. This book offers a multidisciplinary presentation of recent research on the topic. Contributors represent a variety of disciplines: cognitive and developmental psychology; math, science, and statistics education; and decision science. The methods applied in various chapters similarly reflect a scientific diversity, including qualitative and quantitative analysis, experimentation and classroom observation, computational modeling, and neuroimaging. Throughout the book, research results are presented in a way that connects with both learning theory and instructional application. The book is organized in three sections: Part I focuses on the concepts of uncertainty and variation and on how people understand these ideas in a variety of contexts. Part II focuses on how people work with data to understand its structure and draw conclusions from data either in terms of formal statistical analyses or informal assessments of evidence. Part III focuses on how people learn from data and how they use data to make decisions in daily and professional life.

Concept Development in the Secondary School

Concept Development in the Secondary School
Author: Peter Langford
Publisher: Routledge
Total Pages: 181
Release: 2016-03-10
Genre: Psychology
ISBN: 1317226909

Originally published in 1987, this book introduces the reader to work on the intellectual development of adolescents relevant to the secondary school teacher. It covers the teaching of English, history, geography, economics, politics, legal studies, physics, chemistry, biology and mathematics. Although it emphasises the continuing importance of Piaget’s thought, the book aims to introduce readers to the non-Piagetian research that had taken place in recent years.

Exploring Probability in School

Exploring Probability in School
Author: Graham A. Jones
Publisher: Springer Science & Business Media
Total Pages: 394
Release: 2006-03-30
Genre: Education
ISBN: 0387245308

Exploring Probability in School provides a new perspective into research on the teaching and learning of probability. It creates this perspective by recognizing and analysing the special challenges faced by teachers and learners in contemporary classrooms where probability has recently become a mainstream part of the curriculum from early childhood through high school. The authors of the book discuss the nature of probability, look at the meaning of probabilistic literacy, and examine student access to powerful ideas in probability during the elementary, middle, and high school years. Moreover, they assemble and analyse research-based pedagogical knowledge for teachers that can enhance the learning of probability throughout these school years. With the book’s rich application of probability research to classroom practice, it will not only be essential reading for researchers and graduate students involved in probability education; it will also capture the interest of educational policy makers, curriculum personnel, teacher educators, and teachers.

Teaching and Learning Stochastics

Teaching and Learning Stochastics
Author: Carmen Batanero
Publisher: Springer
Total Pages: 381
Release: 2018-03-01
Genre: Education
ISBN: 3319728717

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.

Understanding and Teaching the Intuitive Mind

Understanding and Teaching the Intuitive Mind
Author: Bruce Torff
Publisher: Routledge
Total Pages: 288
Release: 2001
Genre: Education
ISBN: 1135673845

Pulls together diverse theoretical & methodological approaches to the origin, structure, function, & development of intuitive conceptions; explores these in a diversity of academic disciplines; explicitly links theory & research to educ. implications.

Stepping Stones for the 21st Century

Stepping Stones for the 21st Century
Author:
Publisher: BRILL
Total Pages: 264
Release: 2007-01-01
Genre: Education
ISBN: 908790150X

Over the years a number of "must read" articles and book chapters have appeared—work that has formed the foundational stepping stones of mathematics education research for the 21st century. Twelve such seminal articles have been reproduced in this book. Each is accompanied by two independent appraisals of the longer term impact of the work within and beyond the mathematics education research community. Collectively these writings cover a wide range of topics and provide a broad overview of the outstanding contributions of Australasian mathematics education research prior to 2000.

The Science of Conjecture

The Science of Conjecture
Author: James Franklin
Publisher: Johns Hopkins University Press
Total Pages: 520
Release: 2001-07-27
Genre: Science
ISBN: 0801865697

How did we make reliable predictions before Pascal and Fermat's discovery of the mathematics of probability in 1654? What methods in law, science, commerce, philosophy, and logic helped us to get at the truth in cases where certainty was not attainable? In The Science of Conjecture, James Franklin examines how judges, witch inquisitors, and juries evaluated evidence; how scientists weighed reasons for and against scientific theories; and how merchants counted shipwrecks to determine insurance rates. The Science of Conjecture provides a history of rational methods of dealing with uncertainty and explores the coming to consciousness of the human understanding of risk.