Conference Paper

  • In the recent years, statistics educators have been actively rethinking how students learn statistics and how to teach introductory statistics. Furthermore, the current technology continues to open new opportunities for developing innovative teaching strategies. This article presents a paradigm, the PACE approach, for teaching the introductory statistics. PACE stands for projects, activities, cooperative learning using computer and exercises. The approach begins with in-class hands-on activities and cooperative team work. The class lectures are organized to provide the basic concepts and guide students through the activities using team work and computer to help students understand the concepts and problem-solving strategies. Exercises are designed to reinforce the basic concepts and to practice solving real world problems. Projects are self-selected by students under some guidance provided by the instructor. Report writing and oral presentation are emphasized. It is believed that self-selected projects reflect student's interest, and hence better motivate them to be active learners. The paradigm of integrating these components together in a structured system motivates students to be actively involve with their learning.

  • In the past, K-12 mathematics students' exposure to statistical concepts has been rather impoverished, consisting primarily of measures of center-mean, median, mode-and perhaps some graphical representations of data. Both the Curriculum and Evaluation Standards (NCTM, 1989) and the Principles and Standards for School Mathematics (NCTM, 2000) advocate for a much wider and deeper role for statistics in school mathematics, including reasoning about data in context and making data-based decisions. An understanding of the role of variability in various contexts-e.g., in sampling, in data sets, and in probability experiments-is one of the critical components students need for statistical reasoning. The research reported here on students' conceptions of variability is part of a three-year NSF grant The Development of Secondary Students' Conceptions of Variability (Shaughnessy, 2003).

  • The difficulties that many students, particularly those in the social and behavioral sciences, encounter while taking an introductory statistics course have been widely reported in many parts of the world. Factors that have been purported as relating to performance in introductory statistics include a variety of cognitive and affective variables (Feinberg &amp; Halperin, 1978). Cognitive factors, such as mathematics ability and background, certainly play a major role in performance in an introductory statistics course; however, affective variables are also important. Gal and Ginsburg (1994) reported that "The body of research on students' attitudes, beliefs, and affect related directly to statistics education is very small and problematic." They further state that concerns for studying non-cognitive aspects of statistics education should not only be motivated by outcome (performance) but also by process considerations.<br><br>A major issue concerns the influence of attitudes on achievement. McLeod (1992) suggested that neither attitude nor achievement is dependent on the other, but they "interact with each other in complex and unpredictable ways. (p. 582)" The prospect of the reciprocal relationship of attitude and achievement has been proposed by others (Kulm, 1980) and negates the possibility of isolating the cognitive and affective domains. A number of studies have investigated the relationship between attitudes toward statistics and performance in an introductory course using a variety of correlational and regression techniques. Results generally indicate a small to moderate positive relationship. This relationship appears to be fairly consistent regardless of the instrument used, the time of administration of either the attitude or performance measure, or the level of the student.<br><br>Longitudinal studies of math attitudes and performance (Pajares &amp; Miller, 1994; Meece, Wigfield, &amp; Eccles, 1990; Eccles &amp; Jacobs, 1986) have provided path analyses of the relationship of these variables. In a study of undergraduates, Pajares and Miller (1994) determined that mathematics self-efficacy was highly related to mathematics performance with mathematics self-concept and high school mathematics experience making a small, but significant contribution. Perceived usefulness was not a contributor to mathematics performance. Eccles and Jacobs' (1986) path analysis indicated that mathematics grades were influenced by the students' self-concept of math ability and math anxiety, but were not influenced by the student's perception of the task difficulty or the perceived value of mathematics. Meece, Wigfield, and Eccles' (1990) path analysis found that students' prior grades and expectancies were predictors of grades, while importance and anxiety were not. In several other papers, the first two of the current authors have developed a model suggesting that some aspects of statistics attitude at the beginning of a course affect test performance during the course and that end of course attitudes were both directly and indirectly influenced by performance during the course. The research reported here extends that line of inquiry looking at data from English and Arabic speaking samples available in the U.S. and Israel.

  • In 1993 the new government of the Ukraine confirmed conception of the transition of the National Ukrainian Statistics to the International Standards. Now the Ukraine has transition from planned to market economy in the areas of productive forces, structure of economy, the integration of economy to international economy and the social role of the state institutions. The three stage planned realisation of the conception are:<br><br>1) Preparatory. It is determined of organisational, methodical, fundamental, essential principals of the transition of the Ukrainian statistics to international standards.<br>2) Transitional. Then these principles are introduced (take root) to practice of statistics.<br>3) Final. It is attainment integration of all the sphere of the statistical activity.<br>Now Ukrainian statistics have come to the second level.<br><br>The important task for Ukraine is the training of specialists of the Economic Statistics required for the market economy. Therefore the content of teaching Economic Statistics has transition to the International Standards. Knowledge about international statistics is need for specialists of economics, management, statistics, international economy and other. I have elaborated the course of International Economic Statistics for the students of Universities of Economics of Ukraine. In this paper only the problems of the statistics of population, labour, industry, agriculture, trade, prices and the Systems of National Accounts are considered.

  • This study sought to investigate perceptions of students' conceptual challenges among A-Level statistics teachers and examiners. The nature and extent of participants' insights were assessed using a questionnaire administered in either written form or via a semi-structured interview. The questionnaire comprised two sections: (i) free-response questions in which participants were asked to list the three most significant conceptual challenges faced by students; and (ii) an attitude scale designed to assess agreement with specific statements regarding possible conceptual challenges. Each section addressed five topic areas: regression and correlation, estimation, sampling methods, distribution modelling, and general statistical thinking. Forty-nine participants completed the questionnaire, though not all teachers were familiar with all of the topic areas. Results revealed interesting patterns of agreement and disagreement among participants with regard to students' conceptual difficulties and concomitant factors.

  • In Japan, many students in women's junior college dislike statistics. In order to arouse students' interest in statistics, we had tried to develop teaching materials for many years and succeeded in arousing their interest in statistics.

  • Teaching factor analysis to non scientific audience is not easy. These methods should be taught with rigor so that students develop the capacity of interpreting correctly the results of the statistical analysis. But it can not be taught in a too theoretical way because it would be rejected by students who often have a difficult relationship with mathematics (Dassonville et Hahn, 1999). Development of technology, especially multimedia, allowed to consider conception of new pedagogical tools that could improve learning (Legros, 1997). But we know that human mediation is an essential part of the process of knowledge construction (Tall, 1994; Linard, 1998). So, the question of the position of such tools in a pedagogical programme is still fundamental. It is why the Paris Chamber of Commerce and Industry supported a research project on learning Principal Components Analysis (PCA). The first step of this project was to create a multimedia tool (Dassonville, 1997). The second step was to evaluate the efficiency of the tool.<br><br>In our presentation, we will first say a few words about teaching of statistics in French Business schools. Then describe shortly the pedagogical programme we experimented at Ecole Sup&Egrave;rieure de Commerce de Paris (ESCP), integrating the multimedia tool. Then we will present the main results of the evaluation of this tool's efficiency we conducted in 1998/99.

  • In response to the critical role that information plays in our technological society, there have been international calls for reform in statistical education at all grade levels (e.g., National Council of Teachers of Mathematics, 1989; School Curriculum and Assessment Authority &amp; Curriculum and Assessment Authority for Wales, 1996). These calls for reform have advocated a more pervasive approach to the study of statistics, one that includes describing, organizing, representing, and interpreting data. This broadened perspective has created the need for further research on the learning and teaching of statistics, especially in the elementary grades, where instruction has tended to focus narrowly on graphing rather than on broader topics of data handing (Shaughnessy, Garfield, &amp; Greer, 1996).<br><br>Notwithstanding these calls for reform, there has been relatively little research on children's statistical thinking and even less research on the efficacy of instructional programs in data exploration. Although some elements of children's statistical thinking and learning have been investigated (Cobb, 1999; Curcio, 1987; Curcio &amp; Artz, 1997; De Lange et al., 1993; Gal &amp; Garfield, 1997; Mokros &amp; Russell, 1995), research on students' statistical thinking is emergent rather than well established. Existing research on children's statistical thinking has certainly not developed the kind of cognitive models of students' thinking that researchers like Fennema et al. (1996) deem necessary to guide the design and implementation of curriculum and instruction.<br><br>In this paper, we will discuss how our research has built and used a cognitive model to support instruction in data exploration. More specifically, the paper will: (a) examine the formulation and validation of a framework that describes students' statistical thinking on four processes; and (b) describe and analyze teaching experiments with grades 1 and 2 children that used the framework to inform instruction.

  • The breakneck advance of multimedia capabilities and internet technologies offers an unprecedented opportunity to improve the quality of teaching and learning. Nowadays the use of multimedia resources and WWW-supported learning environments is a crucial issue in education and further education. Integrating visualization, animation, interactive experiments, sound and hotlinks to relevant internet sites opens completely new dimensions of learning. Modern multimedia may also incorporate new communication channels and could be part of emerging virtual educational networks.<br><br>Statistics seems to be particularily suitable for illustrating the benefits of multimedia-based teaching. On the one hand, Statistics connects quite different fields of application. This interdisciplinary character of the science can be well demonstrated by suitable videos and motivating examples closely related to people's life. On the other hand, multimedia represents an ideal platform for visualizing statistical concepts and for discovering basic statistical principles by self-driven experiments. Multimedia software for Statistics can go beyond closed instructional microworlds by offering properly maintained subject-specific gateways to recent statistical data and supplementary information from the rapidly growing internet.

  • In the literature means, modes and medians are referred as measures of central tendency and they are important concepts in data handling and analysis. Some authors (Batanero et al., 1994; Carvalho, 1996, 1998; Cudmore, 1996; Hawkins, Jolliffe and Glickman, 1991) also stress that students have difficulty with these basic concepts and to some of them these concepts can be reduced to a computation formula. The main goal of this study was to analyse peer interactions in order to understand their role in pupils' performances when they were solving statistical tasks. A deep analysis of their discourse makes clear the way they construct an intersubjectivity (Wertsch, 1991) that facilitates the choice of the solving strategies and helps pupils to undertake their mistakes.

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