GSTAT is a software package for the didactical support of teaching statistics to beginners having no previous knowledge in statistics or EDP. The book and the programs (which are not included but separately available on 5 1/4'' - and 3 1/2'' - disks) are giving an intuitive approach to random processes by illustrating the concepts and theorems with graphics and simulations (like the central limit theorem and the law of big numbers).
From the content: Intuition and mathematics (didactical points of view, networks related to stochastics, intuitions and mathematics as key for understanding, history of ideas and their mathematization); intuitive ideas in classic statistics (interpretation of probability; random choice; expected value; variance); intuitive ideas in the Bayes approach (ratio of chances and degree of confidence, encouragement and thinking in informations, Bayes formula structures thinking, Bayes formula structures applications); intuitive ideas by persons (research framework; symmetry and basic space; relative frequencies and probability; causal relationships and stochastic dependency; statistical assessment; consequences for empirical research and education).
The changing role of mathematics in society may require a different mathematics curriculum in the schools. Curriculum builders work constructing pieces of the new mathematics curriculum. To last, this new curriculum must be based on a foundation of experience and research. This book provides access to that foundation for secondary schools and two-year colleges. Sections deal with curricular goals and instruction in algebra, geometry, precalculus, calculus, statistics and probability, and discrete mathematics. Concerns are expressed for the slow learner, gifted, and sex-related differences in mathematics. An opening chapter provides historical background. Other chapters deal with mathematical learning theory, the development of curriculum, evaluation, the use of computers, mathematics as recreation, and mathematical applications. Inservice teacher education and trends in secondary and two-year college education are discussed and a final chapter lists resources under the headings of organizations, newsletters, periodicals, National Council of Teachers of Mathematics yearbooks, films/videotapes, general references, and selected distributors and publishers. Annotated bibliographies are included throughout the book. (DC)
This manual designed for grade 3 is part of a series for a program to integrate the teaching and learning of mathematical and computer concepts and skills in the elementary school. The manual contains 20 lessons. Each lesson includes information on the topic, suggested grade level, mathematics concepts and skills, objective, prerequisite skills needed, and activities. Topics contained in the lessons include: (1) problem solving; (2) geometry; (3) numbers; (4) measurement; (5) number concepts; (6) addition; (7) time; (8) LOGO; (9) division; (10) fractions; and (11) probability, statistics, and graphing. Software programs used for the activities are specified for each lesson. (KR)
Reasons for poor performance in mathematics by students in the United States are discussed. According to the authors, too many students never experience arithmetic at a physical, concrete level. Students are drilled in arithmetic facts without any meaningful context and are given few opportunities to use numerical concepts in real-life applications. Described in this fastback in the form of a Decalogue, or ten commandments, are methods that can be used to teach mathematics successfully. These commandments hold for every grade level including postsecondary mathematics. Topics include: (1) the use of manipulatives and visuals; (2) cooperative learning models; (3) diagnosis of student development; (4) unit plan development; (5) problem solving; (6) algebra and geometry; (7) the use of computers and calculators; (8) mental computation, estimation, and measurement; (9) probability and statistics; (10) integration of skills and techniques from different branches of mathematics. (KR)
The book is for non-specialists visiting an introductory course in statistics. It does not only give a description of conventional statistical methods but discusses also limits and alternatives. It avoids mathematics without excessively simplifying basic concepts. Topics: mean values, variance measures, distribution functions, probabilities, random samples, correlation, regression, factor analysis, graphical representation, tables, remarks on empirical scientific working. Each chapter ends up with exercises.
Summarizes 19 papers presented at the Fourth International Conference on Teaching Statistics held in Morocco, July 1994. Papers presented were in five categories: (1) empirical studies on students' conceptions; (2) theoretical papers on teaching and learning; (3) assessment; (4) using computers in teaching probability and statistics; and (5) data analysis. (MKR)
One of the many difficulties facing a teacher of Statistics is to keep herself or himself informed about materials that are currently available, and requests have been made for an annotated bibliography of books that might prove useful to those teaching and using statistics in Schools. The ASA/NCTM Joint Committee has therefore started to compile such a bibliography, of which this is the first edition.
This book has been written to fill a substantial gap in the current literature in mathematical education. Throughout the world, school mathematical curricula have incorporated probability and statistics as new topics. There have been many research papers written on specific aspects of teaching, presenting novel and unusual approaches to introducing ideas in the classroom; however, there has been no book giving an overview. Here we have decided to focus on probability, making reference to inferential statistics where appropriate; we have deliberately avoided descriptive statistics as it is a separate area and would have made ideas less coherent and the book excessively long. The following chapters are included: - The educational perspective - Probabilistic perspective - Empirical research in understanding probability - Analysis of the probability curriculum - The theoretical nature of probability - Computers in probability education - Psychological Research in probabilistic understanding
This book proposes to set out the recent scientific discovery of an unconscious. Not the unconscious or subconscious explored by psychoanalysis, but one that always and unbeknownst to us involves the cognitive: that is, the world of reason, of judgment, of the choices to be made among different opportunities, of the difference between what we consider probably and what we consider unlikely. The material we deal with in this book derives from wherever we make decisions "under uncertainty." In short, our examples are based on phenomena found almost anywhere, in almost anyone, and just about at any moment. Chapters include: Probability Illusions, Calculating the Unknown, or Bayes' Law; The Fallacy of Near Certainty, and The Principle of Identity and the Psychology of Typicality.