Literature Index

Standard Microsoft Excel functions and the Excel Data Table facility are used in randomization applications using resampling with and without replacement.

This article shows how R can be used to perform resampling with and without replacement.

In the topic study group on probability at ICME 11 a variety of ideas on probability education<br>were presented. Some of the papers have been developed further by the driving ideas of interactivity and use<br>of the potential of electronic publishing. As often happens, the medium of research influences the results and<br>thus - not surprisingly - the research change its character during this process. This paper provides a summary<br>of the main threads of research in probability education across the world and the result of an experiment in<br>electronic communication. For convenience of international readers, abstracts in Spanish and German have<br>been supplied, as well as hints for navigation to linked electronic materials.

Probability and statistics (stochastics) are viewed as necessary for all students no matter their ambitions. However, there are barriers to the effective teaching of both stochastics and problem solving: 1) getting stochastics into the mainstream of the mathematical science school curriculum; 2) enhancing teachers' background and conceptions of probability and statistics; 3) confronting students' and teachers' beliefs about probability and statistics. Psychologists and mathematics educators should work collaboratively to diminish misconceptions. Doing so combines the roles of observer, describer, and intervener. Research in stochastics suggests that heuristics that are used intuitively by learners impede the conceptual understanding of concepts such as sampling. This paper reviews the research on judgemental heuristics and biases, conditional probability and independence (i.e., causal schemes), decision schema (i.e., outcome approach), and the mean. Learners have difficulties in these areas, however, evidence is contradictory as to whether training in stochastics improves performance and decreases misconceptions. The conclusion emerging from this research is that probability concepts can and should be introduced into the school at an early age. Instruction that is designed to confront misconceptions should encourage students to test whether their beliefs coincide with those of others, whether they are consistent with their own beliefs about other related things, and whether their beliefs are born out with empirical evidence. Computers can be used to provide both an exploratory and representational aspect of the discipline. The role of teachers in this type of environment and the issue of whether stu- dents should use artificial or real data sets should be considered.