Literature Index

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.

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).

As part of the Australian national online curriculum initiative, The Learning Federation is developing hundreds of multimedia learning objects for use in schools. Some of these learning objects are designed to allow children to explore some basic concepts of probability and statistics, such as the relationships between random generators, sample spaces, likelihood of outcomes and both short and long run data on frequency of outcomes. This paper reports on the initial design development of these learning objects and on plans to research their use with children aged 6 to 12 years.

New software tools for data analysis provide rich opportunities for representing and understanding data. However, little research has been done on how learners use thse tools to think about data, nor how that affects teaching. This paper describes several ways that learners use new software tools to deal with variability in analyzing data, specifically in the context of comparing groups. The two methods we discuss are 1) reducing the apparent variability in a data set by grouping the values usig numerical bins or cut points and 2) using proportions to interpret the relationship between bin size and group size. This work is based on our observations of middle- and high-school teachers in a professional development seminar, as well as of students in these teachers' classrooms, and in a 13-week sixth grade teaching experiment. We conclude with remarks on the implications of these uses of new software tools for research and teaching.