Research

  • We used a clinical methodology to explore elementary students' reasoning about data modeling and inference in the context of long-term design tasks. Design tasks provide a framework for student-centered inquiry (Perkins, 1986). In one context (Study 1), a class of fifth-grade students worked in six different design teams to develop hypermedia documents about Colonial America. In a second context (Study 2), a class of fifth-grade students designed science experiments to answer questions of personal interest. In the first, a hypermedia design context, students compared the lifestyles of colonists to their own lifestyles. To this end, ten "data analysts" developed a survey, collected and coded data, and used the dynamic notations of a computer-based tool, Tabletop (Hancock, Kaput, & Goldsmith, 1992), to develop and examine patterns of interest in their data. Tabletop's visual displays were an important cornerstone to students' reasoning about patterns and prediction. Analysis of student conversations, including their dialog with the teacher-researcher, indicated that the construction of data was an important preamble to description and inference, as suggested by Hancock et al. (1992). We probed students' ideas about the nature of chance and prediction, and noted close ties between forms of notation and reasoning about chance. In the second study involving the context of experimental design, we consulted with two children and their classroom teacher about the use of a simple randomization distribution to test hypotheses about the nature of extra-sensory perception (ESP). Here, experimentation afforded a framework for teaching about inference grounded by the creation of a randomization distribution of the students' data. We conclude that design contexts may provide fruitful grounds for meaningful data modeling.

  • In this work problem solving procedures about statistical association using microcomputers, are analyzed. The effect of several didactical variables on these procedures is also studied. The sample was formed by 18 trainee teachers who received previous training during a seven week period. The study of the arguments expressed by the students allows us to know the scope and meaning given by them to the concept of association and to infer criteria to design new didactical situations.

  • An experimental college level course, Functions and Statistics with Computers, was designed using the textbook Functions Statistics and Trigonometry with Computers developed by the University of Chicago School Mathematics Project. A case study of this course and its influence on a more traditional course is described. Students in the experimental course were compared with students in the traditional course based on attitude toward mathematics and achievement in mathematics. Experimental course students showed a significant gain in confidence about learning and performing well in mathematics. Final grade distributions for the experimental and traditional courses were similar, although experimental course students entered the course with somewhat weaker mathematical backgrounds. On a course evaluation document, students in the experimental course reported that computer laboratory activities helped them understand course material. Based on an analysis of the attitude, achievement and course evaluation data, the traditional course was modified to deemphasize algebraic manipulation, emphasize modeling and applications and to include computer laboratory activities.

  • Although the use of software has become widespread in elementary statistics courses, there has been little formal evaluation of its effectiveness. In this experiment with the use of software, primarily for simulations in an introductory statistics course, effectiveness was measured in two ways: whether students did better on examinations and whether they believed that the software was useful. Results showed that students did significantly better on the examinations and that about half of them considered the software to be useful. However, even among those who believed that the software was helpful, many objected to the extra time involved.

  • ChancePlus is a three-year project to research and develop effective methods for teaching introductory probability and statistics, especially at the high-school level. In this report, we summarize our activities during the second year of the project. Our efforts in this year were concentrated on developing and revising instructional units in probability and statistics and on the development of our statistical analysis program, DataScope. We also describe progress in our research of student understanding of probability and statistics and in the development of items to test for conceptual understanding.

  • A number of studies have reported that there is a strong tendency to ignore base-rate information in favor of individuating information, except when the former can readily be incorporated into a causal schema. In the present study, students in eight undergraduate classes were given problems in which the base-rate information was (1) either causal of noncausal and (2) either incongruent or congruent with the individuating information. In addition, twelve subjects were interviewed as they attempted to solve several versions of the one of the problems. We found (1) strong individual differences in the perceived importance of base-rate information and even in how the probability estimation task itself was interpreted, (2) little if any effect of the causality manipulations employed by Ajzen (1977) and Tversky and Kahneman (1980, and (3) greater use of base-rate information congruent with the individuating information than of base-rate information which is incongruent. The interview data indicate that it is difficult to determine from the answer alone whether or not the subject thought that the base-rate information was relevant. These data also suggest that subjects have different strategies for dealing with probability estimation problems. One of these we characterize as not only nonBayesian, but also nonprobabilistic.

  • The experimental literature on the calibration of assessors making probability judgments about discrete propositions is reviewed in the first section of this chapter. The second section looks at the calibration of probability density functions assessed for uncertain numerical quantities. Although calibration is essentially a property of individuals, most of the studies reviewed here have reported data grouped across assessors in order to secure the large quantities of data needed for stable estimates of calibration.

  • The purpose of the present study was to extent the evaluation of Wise's Attitudes Toward Statistics (ATS) Scale by examining scale responses in relation to (a) its factor structure and (b) the correlation of ATS subscale scores with students' grades in statistics courses at several levels of graduate study, students' sex (which was found to be a useful predictor by Woehlke & Leitner, 1980), and scores on measures of basic mathematics and comprehension of statistical terminology.

  • In the research reported in this paper, we address two major sets of questions about children's understanding of average. 1) When they are working with data sets, how do children construct and interpret indicators of center? It's important to examine how children learn to describe data sets in a meaningful, useful, and flexible manner. In particular, we are concerned with the development and use of the idea of "representativeness" in the context of real data sets. The second major question we are addressing deals with the use of the mean in a precise mathematical sense: 2) How do children develop their thinking about the mean as a mathematical relationship? This question moves into the important more general question of how children develop mathematical abstractions, and how they map (or fail to map) these abstractions onto their informal understanding of a concept.

  • This paper reports selected results from a larger study designed to investigate the stability of students' conceptions of probability. The "Reasoning About Chance Events" survey was administered to students both before and after the "Coin Toss" unit in order to identify consistent patterns of response as well as to capture changes in responses that might be caused by the instructional unit. Subjects in this study were first and second year college students from three sections of an introductory statistics courses.

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