Research

  • 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.

  • 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.

  • 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.

  • 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.

  • Although statistical variation does not receive detailed attention in mathematics curriculum documents, students actually experience variation every day of their lives. Among other varying phenomena, the weather provides a topic of discussion for young and old. From early childhood, teachers are known to put up weather calendar charts recording the weather for weeks at a time. This study uses the weather context to explore students' development of intuitive ideas of variation from the third to the ninth grade.<br><br>Three aspects of understanding these intuitions associated with variation are explored in individual video taped interviews with 66 students: explanations, suggestions of data, and graphing. The development of these three aspects across grades is explored, as well as the associations among them. Fifty-eight of the students also answered a general question on the definition of variation and variable and these responses are discussed and compared with responses to the weather task. The interview protocol may prove useful for teachers, particularly with younger children, to appreciate students' developing understanding of variation and provide starting points for classroom work of a more specific nature, either with respect to weather or other contextual topics.

  • This study investigated students' understanding of the concept of the standard deviation. In particular, students' understanding of the factors that affect, and how they affect, the size of the standard deviation were investigated. Thirteen students enrolled in an introductory statistics course participated in the study. Students engaged in two activities during a one-hour interview. In the first activity, they arranged a number of bars on a number line to produce the largest and smallest standard deviation. The second activity asked students to judge the relative sizes of the standard deviation of two distributions. Initial analysis identified rules/strategies that students used to construct their arrangements and make comparisons. A discussion of these distinctive rules and the conceptions they represent is presented.

  • Variability and comparing data sets stand in the heart of statistics theory and practice. "Variation is the reason why people have had to develop sophisticated statistical methods to filter out any messages in data from the surrounding noise" (Wild &amp; Pfannkuch, 1999, p. 236). Concepts and judgments involved in comparing groups have been found to be a productive vehicle for motivating learners to reason statistically and are critical for building the intuitive foundation for inferential reasoning (Watson &amp; Moritz, 1999; Konold and Higgins, 2003). Thus, both variation and comparing groups deserve attention from the statistics education community.<br><br>The focus in this paper is on the emergence of beginners' reasoning about variation in a comparing groups situation during their encounters with Exploratory Data Analysis (EDA) curriculum in a technological environment. The current study is offered as a contribution to understanding the process of constructing meanings and appreciation for variability within a distribution and between distributions and the mechanisms involved therein. It concentrates on the qualitative analysis of the ways by which two seventh grade students started to develop views (and tools to support them) of variability in comparing groups using various numerical, tabular and graphical statistical representations. In the light of the analysis, a description of what it may mean to begin reasoning about variability in comparing distributions is proposed, and implications are drawn.

  • Current reforms in mathematics education place increasing emphasis on statistics and data analysis in the school curriculum. The statistics education community has pushed for school instruction in statistics to go beyond measures of center, and to emphasize variation in data. Little is known about the way that teachers "see variation". The study reported here was conducted with 22 prospective secondary math and science teachers enrolled in a preservice teacher education course at a large university in the U.S. which emphasized assessment, equity, inquiry, and analysis of testing data. Interviews conducted at the beginning and end of the course asked the teachers to make comparisons of data distributions in a context that many U.S. teachers are increasingly faced with: results from their students' performance on high-stakes state exams. The results of these interviews revealed that although the prospective teachers in the study did not rely on traditional statistical terminology and measures as much as anticipated, the words they did use illustrate that through more informal descriptions of distributions, they were able to express rich views of variation and distribution. This paper details these descriptions, categorizing them into three major areas: traditional notions, clumps &amp; chunks (distribution subsets), and notions of spread. The benefits of informal language in statistics is outlined.

  • The paper describes how the transformative and conjecture-driven research design, a research model that utilizes both theory and common core classroom conditions, was employed in a study examining introductory statistics students' understanding of the concept of variation. It describes how the approach was linked to classroom practice and was employed in terms of research design, data collection, and data analysis. The rich insights into the evolution of students' thinking about variation that have originated from this research are then discussed. Implications for research and instruction follow.

Pages

register