Literature Index

Since the introduction of the first iPod portable music player (MP3 player) by Apple, Inc., users have questioned the randomness of the shuffle feature. Most evidence cited by users claiming to show nonrandom behavior in the shuffle feature is anecdotal in nature and not based on any systematic analysis of its randomness. This article reports on our attempt to investigate the shuffle feature on the iPod and to test its randomness through the use of probability and statistical modeling. We begin by reviewing the research on people's inability to perceive and understand both random and nonrandom behavior. Probability models are then developed, under the assumption of a random shuffle, for several of the most common types of events cited as evidence of a nonrandom shuffle. Under this null hypothesis of a random shuffle, several goodness-of-fit tests of one of the probability models are conducted using data collected from real iPods. No evidence to support user claims of a nonrandom shuffle was found. Finally, we conclude with some reflections on and ideas for incorporating these examples into undergraduate probability and statistics courses.

In this article I discuss the fundamental relation between people's ability to do induction and their beliefs about randomness or noise, and I illustrate the special difficulties that psychologists face when they try to evaluate the rationality of these beliefs. The presentation is divided into four sections. The first describes the traditional experimental approach to evaluating people's conceptions of randomness and summarizes the data that have been taken to support the conclusion that people have a very poor conception of randomness. The second contrasts the relatively narrow conception of randomness that one finds in philosophical and mathematical treatments of the topic. The third outlines some benefits for psychologists to be gained from thinking about induction as a problem in signal detection., and the fourth presents the argument that any adequate evaluation of ordinary people's conceptions of randomness must consider the role that these conceptions play an inductive inference, that is, in distinguishing between random and nonrandom events. Originally appeared in the Journal of Experimental Psychology; Learning, Memory, and Cognition, 1982, 8 (6), 626 - 636

In epistemological studies, two main interpretations of probabilities are the frequentist and the Bayesian. In this paper we first show that both interpretations are present in French Secondary schools, albeit the official curriculum only supports the frequentist approach. We then suggest a possible teaching situation to introduce teachers and students to the subjective-objective duality with some statistics training situations via the use of problem solving. We also give some characteristics and conditions useful to build situations fitted to this goal.

Bakker (2002) identified two categories of learning software in mathematics: landscape-type software and route-type software. Route type software was designed to guide learners through a hypothetical learning trajectory with a fairly fixed destination. Alternatively, landscape-type software is designed to support learners in conducting open-ended investigations. The use of these dynamic software tools for the learning of mathematics and statistics has gained increasing prominence in schools because of its ability to support multiple purposes defined by the user rather than the software. Little is known, however, about the diversity of approaches in which learners use these software packages to conduct investigations. This paper reports on a study of eighteen prospective secondary mathematics and science teachers' approaches to conducting a statistical investigation using the hynamic data analysis software FathomTM (Finzer, 2001). Three distinct approaches were identified by the research-- Wonderers, Wanderers, and Answerers--each with measurable and quantitative differences in these approaches as well as their potential epistemological roots.