Teaching Probability

Probability is vitally important but poorly understood, and therefore good teaching
is essential. It forms part of most secondary school mathematics curricula and is
also a component of many science curricula. However, the problems associated
 ...

Teaching Probability

Author: Jenny Gage

Publisher: Cambridge University Press

ISBN: 1316605892

Page: 206

View: 900

This title focuses on the approaches that can be taken in the classroom to develop skills and a conceptual understanding of probability. Written by leading subject specialists, Teaching Probability is designed to support teaching concepts in probability by providing a new approach to this difficult subject from a perspective not limited by a syllabus, giving teachers both theoretical and practical knowledge of an innovative way of teaching probability. This alternative approach to teaching probability focuses on the methods that teachers can apply to help their students engage with the topic using experiments and mathematical models to solve problems, considering how to overcome common misconceptions and the way in which probability can be communicated.

Examining an Operational Approach to Teaching Probability

This is where studying probability from an operational approach has gained much traction. The most interesting aspect is the use of a very artisanal approach, starting with objects that students can, in part, find in their daily lives.

Examining an Operational Approach to Teaching Probability

Author: Drivet, Alessio

Publisher: IGI Global

ISBN: 1799838722

Page: 369

View: 841

Several years ago, there began a consideration of the inadequacy of a traditional approach to teaching mathematics. Many teachers and perhaps a majority of the students often realize something is wrong with these methods and report a lack of enthusiasm in dealing with the discipline. Many teachers think that certain established habits have a serious pedagogical basis, and therefore, it is difficult to question them. In addition, perhaps, there is also a certain fear in imagining and experimenting with new ways. Unfortunately, the excessive use of examples and abstract formulations with exclusive reference to algebraic language distances the student from the pleasure of the discipline. Mathematics, on the other hand, requires attention and concentration, but the understanding of its meaning gives rise to interest, pleasure to discover, and promotes deep learning. This is where studying probability from an operational approach has gained much traction. The most interesting aspect is the use of a very artisanal approach, starting with objects that students can, in part, find in their daily lives. Trying to identify objects and situations that speak of "different mathematics," embodied in everyday life, may offer more possibilities to deal with the mathematical illiteracy that seems to afflict a large part of our society. Examining an Operational Approach to Teaching Probability focuses on probability examined from an educational point of view and the implementation of a very concrete operational approach in the classroom. Two main pillars are examined within this book: concrete objects and IT tools used to perform simulations for probability teaching. Each chapter is devoted to an essential concept related to probability and covers the operational approach all the way from its historical development to types of probability studies, different teaching methods within the approach, and the theories surrounding it. This book is ideal for pre-service and in-service teachers looking for nontraditional approaches in teaching along with instructional designers, curricula developers, practitioners, researchers, academicians, and students interested in learning more about operational research and the use of objects to introduce probabilistic concepts in a new method of teaching.

Research on Teaching and Learning Probability

2.3.1 Probability in Primary School At the beginning of this century, the Standards
of the National Council of Teachers of Mathematics (NCTM 2000) in the United
States included the following recommendations related to understanding and ...

Research on Teaching and Learning Probability

Author: Carmen Batanero

Publisher: Springer

ISBN: 3319316257

Page: 33

View: 230

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.

How to Work with Probability and Statistics Grades 6 8

A collection of lessons in probability and statistics for the teachers of students in grades six offers units and practice pages incorporating the math skills established by the National Council of Teachers of Mathematics.

How to Work with Probability and Statistics  Grades 6 8

Author: Tcr

Publisher: Teacher Created Resources

ISBN: 1576909689

Page: 48

View: 655

A collection of lessons in probability and statistics for the teachers of students in grades six offers units and practice pages incorporating the math skills established by the National Council of Teachers of Mathematics.

Exploring Probability in 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.

Exploring Probability in School

Author: Graham A. Jones

Publisher: Springer Science & Business Media

ISBN: 0387245308

Page: 390

View: 978

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.

Chances Are

This book can serve as an introduction for any beginner, from gifted and advanced students in upper elementary school, to high school students needing enrichment or preparation for Advanced Placement Statistics or future college courses.

Chances Are

Author: Nancy Pfenning

Publisher: PRUFROCK PRESS INC.

ISBN: 1882664353

Page: 176

View: 903

Do you avoid teaching probability and statistics because the subjects seem confusing and complex? Are you less than sure about your knowledge of the topics? Let Chances Are take you and your students on a fun and exciting mathematical journey none of you will ever forget! Filled with easy-to-understand explanations and creative activities, this book offers teachers a simple method for teaching probability and statistics in an enjoyable way. This book can serve as an introduction for any beginner, from gifted and advanced students in upper elementary school, to high school students needing enrichment or preparation for Advanced Placement Statistics or future college courses. From helping to win a card game, to making life-or-death medical decisions, the uses of probability and statistics are virtually endless. For teachers of elementary students, the book offers simple, hands-on lessons and activities about probability and basic statistics. For teachers of older students, advanced statistical concepts are discussed and activities are provided. Reviewers have found the book's level to be appropriate for a wide range of ages, from fourth graders to postsecondary students.

Teaching and Learning Stochastics

This book presents a collection of selected papers that represent the current variety of research on the teaching and learning of probability.

Teaching and Learning Stochastics

Author: Carmen Batanero

Publisher: Springer

ISBN: 3319728717

Page: 384

View: 530

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.

Second Handbook of Research on Mathematics Teaching and Learning

need in teaching probability , research on teachers ' mathematical content
knowledge , pedagogical content knowledge , and knowledge of student learning
is limited . This dearth of research may be due to the fact that the introduction of ...

Second Handbook of Research on Mathematics Teaching and Learning

Author: Frank K. Lester

Publisher: Information Age Pub Incorporated

ISBN: 9781593115883

Page: 712

View: 496

An update to the original 1992 publication, this two-volume set unites current research to provide new conceptualizations of research problems, and to suggest possible research programs to move the field forward. In studying the existing research, the authors found that the community has maintained its focus on problems of learning, teaching, teacher education, assessment, technology, and social and cultural aspects of mathematics education, while some new areas of interest have emerged or been expanded. This set allows educators to step back and look at each of these areas to see where mathematics education research has been and where it should be going to enable the field to answer the questions about education that practitioners, policy makers, and politicians are asking.

Teaching Statistics at Its Best

Collaboration with the historian of probability is desirable but not always feasible
. To compensate for this there is a growing body of literature on the history of
probability which is easily accessible to non - specialists , whether teachers or ...

Teaching Statistics at Its Best

Author: David Green

Publisher:

ISBN:

Page: 166

View: 425

The Teaching of Statistics

Fischbein ( 1975 ) adds that , at an early age , teaching probability and statistics
can evolve from intuitive structures and fundamental mental operations .
According to Fischbein , this can be achieved by having children carry out all
sorts of ...

The Teaching of Statistics

Author: Robert Morris

Publisher: United Nations Educational

ISBN:

Page: 258

View: 869

Probability Combinatorics Teaching and Learning in Mathematics

Probability   Combinatorics   Teaching and Learning in Mathematics

Author: George Pólya

Publisher: Mit Press

ISBN:

Page: 642

View: 657

These two volumes complete the publication of the collected papers of George Pólya, one of the most influential mathematicians and teachers of our time. Volumes I (Singularities of Analytic Functions) and II (Location of Zeros) were published in 1974. Volume III contains 58 papers spanning Pólya's career (the earliest is from 1913, the latest from 1976) and covering a wide range of subjects in mathematical analysis and mathematical physics. The commentaries on these papers attest to the fertility and continued importance of Pólya's ideas in current mathematics. Volume IV presents 20 papers on probability, 17 on combinatorics, and 18 on the teaching and learning of mathematics. Pólya has made a number of fundamental contributions to the first two fields, including perhaps the first use of the term "central limit theorem," but his major influence on mathematics has clearly been his approach to pedagogy. Many of the papers throughout these volumes have a strongly pedagogical flavor, but the papers in the third section of this volume focus squarely on the real business of how to do mathematics - how to formulate a problem and then create a solution. George Pólya is professor emeritus at Stanford University. These volumes are the twenty-second and twenty-third in the series Mathematicians of Our Time, edited by Gian-Carlo Rota.

Teaching Children Mathematics

Data Analysis and Probability Resources from NCTM The world has entered an
age of instant access to larger and larger amounts of information , and the need
for methods to deal with this data is growing . In response to that need , data ...

Teaching Children Mathematics

Author:

Publisher:

ISBN:

Page:

View: 942