# Research

• ### Readiness of teachers on Northern Ireland to teach data handling

Data handling has recently been introduced on the United Kingdom as a major component of the mainstream school mathematics curriculum. A survey of teachers in Northern Ireland showed that they are generally not well prepared to teach the new material, particularly probability.

• ### Primary and secondary intuitions in the introduction of probability

The main objective of our research has been to study the intuitive biases corresponding to certain fundamental concepts and methods of the theory of probability. This is not simply a question of the general concepts of chance, or randomness, on which there are data already available. Research which has already been done by psychologists indicates the existence of a natural intuition of chance, or even of probability (cf. Fischbein et al., 1967, 1970a, b). However, A. Engel, a mathematician, has written: "...we have a natural geometric intuition but no probabilistic intuition". In order to elucidate this problem, we decided to go beyond the notion of chance, and try to follow the course of what, in fact, happens during the systematic teaching of certain concepts in the theory of probability. We therefore decided to study the intuitive responses of subjects to certain concepts and calculational precedures which were introduced during some experimental lessons on probability, viz. chance, and probability as a metric of chance; the multiplication of probabilities in the case of an intersection of independent events, and the addition of probabilities in the case of mutually exclusive events. Reprinted from Educational Studies in Mathematics 4 (1971), 264 - 280.

• ### Interplay of the number concept and statistics using attitudes and techniques of EDA

A report on work that has been undertaken with stem-and-leaf plots and box plots. The report was supported with the representation of childrens' work. This presentation provides an excellent model of what could be achieved in statistical education. It shows how statistical concepts could be utilised to develop other significant mathematical ideas and, particularly through the childrens' work, indicates the high level of understanding and graphical comprehension that can be achieved.

• ### Students' concepts of bar graphs - Some preliminary findings

This paper will report some of the findings of a study of grade four and grade six students' understanding of the information conveyed by bar graphs. The total study examined the effects of various characteristics of graphical displays on students' ability to read, interpret, and predict from such displays, and discusses the results within Davis's Frame Theory.

• ### Research report about reasons, development, and evaluation of a curriculum in probability for 10-12 year old pupils

This curriculum was so designed that it could be integrated into the effective mathematical curriculum for this age group at all secondary schools in West Germany. A report was given on the pedagogical and psychological rationales for why this age group must be instructed in probability and statistics. Furthermore, the presentation reported on the different empirical research methods used during the development and evaluation phase. Finally, information was given on how this curriculum was integrated into mathematics instruction in this age group.

• ### Some apparent violations of the representativeness heuristic in human judgment

According to the representativeness heuristic, the probability that an element is an exemplar of a given class is judged to be high to the extent that the element is representative of the class with respect to its salient features. In three experiments involving situations previously called upon in support of representativeness theory, questionnaire responses from 265 university students demonstrated systematic biases that deviated sharply from the obvious predictions of the theory. One such bias, the students' misinterpretation of proportion information as absolute-number information, is comparable to Piaget's concrete operations. The implications for representativeness theory are discussed in terms of the theory's relationship to concrete thinking, the importance of task characteristics, and the difficulty of a priori specification of the salient features with respect to which representativeness is assessed.

• ### The effect of context on the teaching of statistics at first year university level

In 1993 a sample of 102 class members participated in an exploratory study which consisted of ten pairs of statistical questions. For each pair students were asked to specify which of the two options they felt that they would prefer to answer if they were required to or if they had no preference. They were also asked if they could say why they chose particular options. This study clearly indicated that in some ares the students had very definite preferences (70% or more of the group) for particular contexts over others.

• ### Designing curricular software for conceptualizing statistics

ConStatS is used in almost all the discipline-specific introductory statistics courses taught at Tufts. Even though most students seem able to use the software for an extended period of time without a great deal of direction, most of the instructors provide assignments that provoke open-ended use of the software. These assignments usually contain short essay questions that address the kinds of conceptual issues captured in ConStatS experiments. During the past year, ConStatS has been at the center of a large scale, FIPSE funded project for evaluating the effectiveness of curricular software. The goal of the evaluation was to assess if ConStatS in particular, and curricular software in general, could help students to develop a deeper conceptual understanding of statistics. The evaluation tool place in the fall 1992 and the spring 1993 semesters. Classes at three universities participated. In total, seven classes with 303 students participated as control groups.

• ### A comparison of the statistics curriculum for children aged 5-11 in Britain, Canada and the U.S.A.

This paper will concentrate on the role of statistics in the curriculum for the 5-11 age group. It is in the early years of schooling that the conceptual foundation is laid on which the secondary and tersary phases of a student's education are built. A brief overview of what and when certain topics are currently taught in the elementary schools in Britain, Canada, and the USA is presented.

• ### Elementary schools students' use of strategy in playing microcomputer probability games

Games are often used in teaching as a means of introducing and exploring probability concepts, since they provide familiar and practical instances of the notions in question. This paper describes a study in which two versions of a game are used as the setting in which students' understanding of probability is assessed. The subjects involved had received no formal instruction in probability prior to the experiment, but during it some of them used intuitions about chance as they developed their strategies for playing. There is also evidence that as they responded to the interviewer's questions and explained their strategies, subjects sometimes attended to previously unnoticed features of the situations and developed new strategies as a result.