# Book

• ### Used Numbers: Prediction and Sampling

A unit of study for greades 5-6 from "Used Numbers: Real Data in the Classroom."

• ### Research on students' understanding of probability

In this chapter, I provide a discussion of selected discoveries that have been made about students' conceptions of probability. I also include a discussion of some trends in student performace on probability items on the 1996 National Assessment of Educational Progress (NAEP). In light of what is known about student thinking and performance in probability, I present some suggestions for the teaching of probability, I point out that a separation of research discussions of probability and statistics is artificial, just as artificial as the separation of data and chance when teaching. Principles and Standards for School Mathematics (NCTM, 2000) aptly places probability and statistics under one shared heading. I believe the most interesting research questions for the future reside in the joint realm of the areas of probability and statistics, just as the most interesting teaching challenges for the future lie in making interconnections between these two areas.

• ### Statistics: The Shape of the Data. Used Numbers: Real Data in the Classroom. Grades 4-6

A unit of study that introduces collecting, representing, describing, and interpreting data is presented. Suitable for students in grades 4 through 6, it provides a foundation for further work in statistics and data analysis. The investigations may extend from one to four class sessions and are grouped into three parts: "Introduction to Data Analysis"; "Learning About Landmarks in the Data"; and "A Project in Data Analysis." An overview of the investigation, session activities, dialogue boxes, and teacher notes are included in each investigation. The major goals developed in each part of this guide are: (1) describing the shape of the data; (2) defining the way data will be collected; (3) summarizing what is typical of the data; (4) making quick sketches of the data; (5) inventing ways to compare two sets of data; (6) representing data first through sketches, then through a presentation graph or chart; (7) using the median as a landmark in the data; (8) understanding that the median is only one landmark in the data; and (9) experiencing all the stages of a data analysis investigation. Attached are 10 student sheets. (KR)

• ### Sorting: Groups and Graphs. Used Numbers. Grades 2-3

A unit of study that introduces sorting and classification as a way of organizing data is presented. Suitable for students in grades 2 and 3, it provides a foundation for further work in statistics and data analysis. The investigations may extend from one to five class sessions and are grouped into three parts: "Introduction to Sorting"; "Sorting and Classifying Data"; and "Projects in Data Analysis." An overview of the investigation, session activities, dialogue boxes, and teacher notes are included in each investigation. The major goals developed in each part of this guide are: (1) examining differences and similarities of objects or data; (2) decision making; (3) using negative information to clarify the definition of a category; (4) making sketches of data; (5) thinking flexibly about the characteristics of data; (6) articulating logical reasoning; (7) constructing categories to describe data; (8) inventing representations of data; (9) building theories about data; (10) collecting and recording survey data; (11) comparing two data sets; and (12) experiencing the phases of a data analysis investigation. Appended are reproducible student materials, including two sets of cards for developing sorting skills. (KR)

• ### Stochastic problems - analyses from the didactical and psychological perspective: Stochastische Problemaufgaben - Analysen aus didaktischer und psychologischer Perspektive

A selection of 19 problems analyzed from various points of view is presented. The problems are selected in a way that central issues in treating the problems are related with the concept of probability or the stochastic nature of information. The reader can observe many fallacies or false conclusions. Some of the problems introduced were used in experimental investigations in order to prove the limitedness of human power of judgment when processing stochastic information and estimating probabilities. On one hand, the results of the empirical findings are reported briefly in the discussion of the problems, on the other, the theoretical approaches which were developed in order to explain these findings are explained in detail.

• ### Subjective probability

During the last three decades the psychological exploration of subjective probability has produced a wide range of empirical findings and theoretical developments. In this book, prominent authorities from multiple disciplines analyse and document the human ability to deal with uncertainty. Contributions range from discussions of the philosophy of axiom systems through studies in the psychological laboratory to the real world of business decision making.

• ### Network science, a decade later: The internet and classroom learning

This book is the result of National Science Foundation-funded research that looked at the experiences of a set of science projects which use the Internet and offers an understanding of how the Internet can be used effectively by science teachers and students to support inquiry-based teaching and learning. The book emphasizes theoretical and critical perspectives, and is intended to raise questions about the goals of education and the ways that technology helps reach those goals and ways that it cannot. The theoretical perspective of inquiry-based teaching and learning in which the book is grounded is consistent with the current discipline-based curriculum standards and frameworks. The book begins by detailing the history and current practice of network science and extends the inquiry by examining discourse and data in depth. The second section examines the broader question of how the Internet should be used or not used to assist student learning. The author concludes that technology will not replace teachers; rather, the technology will provide teachers and students an overwhelming access to resources and an opportunity to pursue their own questions.

• ### Research design and statistical analysis

Intended both as a textbook for students and as a resource for researchers, this book emphasizes the statistical concepts and assumptions necessary to describe and make inferences about real data. Throughout the book the authors encourage the reader to plot and examine their data, find confidence intervals, use power analyses to determine sample size, and calculate effect sizes. The goal is to ensure the reader understands: the underlying logic and assumptions of the analysis and what it tells them; the limitations of the analysis; and the possible consequences of violating assumptions. The authors adopt a "bottom-up" approach--a simpler, less abstract discussion of analysis of variance is presented prior to developing the more general model. A concern for alternatives to standard analyses allows for the integration of non-parametric techniques into relevant design chapters, rather than in a single, isolated chapter. This organization allows for the comparison of the pros and cons of alternative procedures within the research context to which they apply. Basic concepts such as sampling distributions, expected mean squares, design efficiency and statistical models are emphasized throughout.

• ### The origin of the idea of chance in children

Translation of La gen&eacute;se de l'id&eacute;e de hasard chez l'enfant. Piaget and Inhelder study the development of the idea of chance in children. According to them, the concept of probability as a formal set of ideas develops only during the formal operational stage, which occurs about twelve years of age. By that age, children can reason probabilistically about a variety of randomising devices. In an experiment to demonstrate that children have an intuitive understanding of the law of large numbers and that intuitive thinking about chance events starts even before they are taught, they used a game with pointers which were stuck onto cards divided into various sectors and then spun. They found the children could predict that, in the long run, the pointer would fall onto every region marked on the card.