# Research

• ### Probability tests report

This report presents results of tests undertaken with English school pupils aged from 7 to 14 years during 1986 and 1990. This first edition of the report concentrates on presenting basic statistical analyses of the various tests carried out. A future edition will include more detailed results for those questions concerning spatial distribution which are not yet fully analysed, together with more sophisticated analyses.

• ### The conjunction fallacy?

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.

• ### An Investigation of Factors Influencing Student Attainment of Statistical Competence

This doctoral dissertation describes a study that attempted to isolate factors which influence attainment of statistical competence in an introductory college statistics course. The study defined a broad goal of an introductory course: to enable students to solve basic, applied statistical problems. A ten-stage model of the problem solving process was used to develop a framework for evaluating achievement of this goal. A problem-oriented statistics course was developed and taught to four classes that included two different experimental treatments. These treatments involved different types of supplementary statistics problems given to students for each instructional unit. Dependent variables included scores on unit tests and a final exam. Independent variables included scores on a pretest of basic mathematics skills and scores on the Mathematics Anxiety Rating Scale. Students also completed an end-of-course attitude questionnaire. Although the treatments did not appear to be related to significant differences in student learning, several relationships were observed between the variables measured and students reported a high level of satisfaction with the problem-oriented course.

• ### Encoding difficulty: A psychological basis for 'misperceptions' of randomness

Subjects' ratings of the apparent randomness of ten binary sequences were compared to the time required to memorize those same sequences. Memorization time proved a better predictor of the subjective randomness ratings than measures of the "objective" randomness of the sequences. This result is interpreted as supporting the hypothesis that randomness judgments are mediated by subjective assessments of encoding difficult. Such assessments are seen as compatible with the information theorists' interpretation of randomness as complexity.

• ### Suppressing natural heuristics by formal instruction: The case of the conjunction fallacy

This article discusses how intensional heuristics can be suppressed when alternative strategies are taught.

• ### Learning and Testing Mathematics in Context; The case: Data visualization

This monograph describes a teaching experiment related to the NCTM Curriculum and evaluation Standards (1989).

• ### Initial considerations concerning the understanding of probabilistic and statistical concepts in Australian students

Following the questions raised by Watson (1992) concerning research in probability and statistics education in Australia in the 1990's, this paper reports on the initial trailing of items with 64 Grade 9 and 10 Grade 6 students. The analysis supports the belief that misconceptions observed in other countries also are present in Australia. Further, the application of a developmental cognitive model offers promise for classifying responses to items and structuring remediation procedures. Suggestions are made for the next stage of research in the area.

• ### Misconceptions of probability: An experiment with a small-group, activity-based, model building approach to introductory probability at the college level

This article discusses the misconceptions of probability based on an experiment with college students.

• ### Results of visualization testing in introductory statistics courses

The present study utilized tests selected from the Kit of Factor-Referenced Cognitive Tests to measure spatial ability.

• ### Evaluating the teaching of statistics in grades 9-12

This report discusses the results of a project to evaluate the teaching of statistics.