This paper presents a cognitive analysis of subjective probability judgments and proposes that these are assessments of belief-processing activities. The analysis is motivated by an investigation of the concepts of belief, knowledge, and uncertainty.
Tversky and Kahneman showed that when subjects are asked to rate the likelihood of several alternatives, including single and joint events, they often make a "conjunction fallacy." That is, they rate the conjunction of two events as being more likely than one of the constituent events. We argue that in some contexts, an alternative that contains the conjunction of two events can be more probable than an alternative that contains only one of the conjunction constituent events. We carried out four experiments in which we manipulated this context.
A method that enables people to obtain the benefits of statistics and probability theory without the shortcomings of conventional methods because it is free of mathematical formulas and is easy to understand and use is described. A resampling technique called the "bootstrap" is discussed in terms of application and development. (KR)
This article discusses how intensional heuristics can be suppressed when alternative strategies are taught.
The statistics course given as part of Psychology I in 1976 is described.
When analyzing episodes of mathematics instruction from an epistemological perspective, it is seen that the disparity between teacher and student knowledge is not simply due to their knowing more or their knowing less. The independent and frequently incompatible levels of understanding knowledge which are peculiar to teachers and to students show how essential it is to make allowance for conceptual as opposed to material aspects, and how the condition of classroom processes nevertheless always tend to regress to a form of mathematical knowledge strongly determined by subject matter and method.
This article discusses some of the past, present and future events of the Probability and Statistics Study Group.
This article discusses the misconceptions of probability based on an experiment with college students.
This article describes a lesson that exemplifies an alternative approach to teaching introductory probability. In this approach, students learn to apply probability models to real-life situations and estimate probabilities through conducting simulations. (See NCTM [1981] for several articles on using simulations in teaching probability.) The particular activity described in this article has been used in high school and introductory college courses for which Macintosh laboratories and the simulation tool Pro Sim (1992) were available. However, it could be done using other software, or without computers, by having students model the problem by flipping coins and pooling the class's data.
We are beginning to identify problems that children and adults have in constructing the notion of average. In addition, we are examining the mathematical and organizational concepts that are needed to successfully solve averaging problems. Even though we are in the midst of this research, we know enough at this point to question the methods usually used to teach averaging in the 4th grade. Children no doubt can be taught to do the appropriate calculation, but our research shows that understanding of central tendency is far more complex. Given a good deal of experience in working with data sets, children do show a deeper, although by no means a complete, understanding of average. Experiences in which children are given more opportunities to connect their informal strategies with their formal mathematical knowledge seem to facilitate this deeper understanding.