With the Seeing and Thinking Mathematically materials, students learn mathematics by doing mathematics, by using and connecting mathematical ideas, and by actively constructing their own understandings. In this unit students learn to see probability through a mathematical lens by exploring and creating games and simulations and by applying the…

This is a collection of articles dealing with mathematical applications for use by high school teachers and students. The articles are intended to illustrate several themes: (1) how mathematics is applied via construction of mathematical models; (2) the various types of activities in applied mathematics; (3) the role of pure mathematics in applied…

This book is intended as a demonstration that a variety of interesting problems suitable for use in the school mathematics experience of everyperson can be fabricated from available sources. It is intended to be illustrative rather than exhaustive. The problems in the book are intended to be accessible to children by the middle school years. The…

The sixteen chapters of this book provide the core material for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…

This volume, a part of the Elements of Mathematics Program (EM), provides the student with an experience in developing a mathematical model for a "real-life" situation. After discussing the process of mathematization by reference to geometry, and presenting a flow-chart diagram describing the relationship of mathematical models to real…

Using Ehrenberg's application of mathematical models to the analysis and prediction of repeated buying patterns of consumers, this study focuses on the concept of library use as a form of consumer behavior. The following hypotheses were tested: designated library user groups will tend to exhibit stable behavioral patterns with respect to the…

This volume and its companion, "Part 2," bring together transactions of the Rasch measurement special interest group of the American Educational Research Association. This volume opens with a discussion of the early years in Rasch measurement and then presents the "transactions" in chronological order, from a 1987 discussion…

This volume and its companion, "Part 1," bring together transactions of the Rasch measurement special interest group of the American Educational Research Association. It presents "transactions" in chronological order, from a 1992 discussion through the winter 1995 volume. Four issues of the "Transactions" are…

This book represents a compilation of the views and ideas of the late Hans Freudenthal, representing his last major contribution to the field of mathematics education. Rather than a presentation of new views, Freudenthal selected and streamlined old ideas, many gathered from his lectures in China, and formed a review of questions and issues in…

This yearbook provides the mathematics education community with specific perceptions about discrete mathematics concerning its importance, its composition at various grade levels, and ideas about how to teach it. Many practical suggestions with respect to the implementation of a discrete mathematics school program are included. A unifying thread…

This Study Guide on Contemporary Problems, Number 8, is one of a series prepared by the American Association for the Advancement of Science representing part of the 1974-75 National Science Foundation Chautauqua-Type Short Courses for College Teachers Program. This is a test edition and contains evaluation forms to be completed by the users and to…

This second edition explains the historical background and techniques for constructing various types of polyhedra. Seven center-fold sheets are included, containing full-scale drawings from which nets or templates may be made to construct the models shown and described in the text. Details are provided for construction of the five Platonic solids,…

Expertise in the technical aspects of planning and a keen appreciation of the social factors involved are not, in themselves, sufficient for satisfactory educational planning. The plan will still not be feasible unless there is attention to a third group of factors called "practical issues", "organizational features", or…

This book discusses constructing variables and making measures. It begins by outlining the qualities a number must meet before it qualifies as a measure of something. The basis is the measurement philosophy of G. Rasch. The first requirement for making good measures is good raw material. To achieve the possibility of comparisons, the data must…

The psychometric research done by G. Rasch between 1951 and 1959, which is explained and illustrated in this book, takes psychometrics from being purely descriptive to being a science of objective measurement. Individual centered statistics require models in which each individual is characterized separately and from which, given adequate data,…