Literature Index

Simulations can make complex ideas easier for students to visualize and understand. It has been shown that guidance in the use of these simulations enhances students’ learning. This paper describes the implementation and evaluation of the Independent Interactive Inquiry-based (I3) Learning Modules, which use existing open-source Java applets, combined with audio-visual instruction. Students are guided to discover and visualize important concepts in post-calculus and algebra-based courses in probability and statistics. Topics include the binomial distribution, confidence intervals, significance testing, and randomization. We show that this format can be used independently by students at the introductory and advanced levels. The percentage of students answering correctly on posttests was larger than that for pretests for three of the four modules described.

This report focuses on a research project concerning individual curricula regarding the instruction of statistics and of probability theory. Individual curricula will be described as belief systems which contain teachers' subjective knowledge and conceptions about mathematics, about learning and teaching mathematics, and particularly about statistics and probability. This report stresses two aspects: the theoretical settings, and the methodological settings of the research. The theoretical settings concern central assumptions and theoretical constructs. The discussion of the methodological settings which will be illustrated by research results, includes the description of a five-step-methodology used for investigating individual curricula.

Examined individual differences in procedures for learning to use a statistical computing package among 36 students who were computer novices. Ss provided think aloud protocols over sessions of learning to use the package. Success in learning depended on use of particular learning procedures. In Exp 1, 5 faster learners tackled problems in a goal-directed, structured manner, abandoning one approach when appropriate and trying alternative approaches. The 5 slower learners engaged in unsystematic trial and error search, were repetitive in their approaches to problem solving, gave up more frequently, and paid less attention to prompts and error messages. In Exp 2, instructing Ss to use the effective procedures identified in Exp 1 enhanced their performance on statistical computing problems. (PsycLIT Database Copyright 1990 American Psychological Assn, all rights reserved)

Evolutionary approaches to judgment under uncertainty have led to new data showing that untutored subjects reliably produce judgments that conform to many principles of probability theory when (a) they are asked to compute a frequency instead of the probability of a single event and (b) the relevant information is expressed as frequencies. But are the frequency-computation systems implicated in these experiments better at operating over some kinds of input than others? Principles of object perception and principles of adaptive design led us to propose the individuation hypothesis: that these systems are designed to produce well-calibrated statistical inferences when they operate over representations of "whole" objects, events, and locations. In a series of experiments on Bayesian reasoning, we show that human performance can be systematically improved or degraded by varying whether a correct solution requires one to compute hit and false-alarm rates over "natural" units, such as whole objects, as opposed to inseparable aspects, views, and other parsings that violate evolved principles of object construal.