Conference Paper

  • It is not discussed that the principles and Statistical methods are necessary not only for understanding, but also for the effective exercise in any profession, especially those that are related to the health, since the variability of the clinical, biological and laboratory data, either on individuals or communities, that to come to a decision goes always accompanied by a degree of uncertainty. This is due to the undeniable probabilistic nature of the Biomedical Sciences and it is in fact the Statistics the one that provides the appropriate tools to confront the differences and that uncertainty. (Leiva, Carrera, et al., 1999). The Statistics knowledge and of their procedures allow the student and the graduate to critically appreciate the phenomena that happen to their surroundings ; it allows him to understand scientific works and to produce his own ones, besides generating data of quality and knowing about the problems that affect the population under study.<br><br>Today, any citizen needs in his daily activity certain resources of the Statistics. In the last years this has taken to radically change the teaching of Statistics in many of the countries where it is part of the Mathematics curriculum. It is necessary that the citizen learns earlier to interpret the facts that happen to his surroundings and the data that he receives permanently through any means of diffusion. Learning Statistics is nowadays unquestionably based by the instrumental contribution that this science carries out. (Gal and Garfield, 1997). Besides through statistical education research, the Statistics has been shown as a "modern discipline," useful to develop in precise form the abilities required in the global world and the information society (Ottaviani, 1999).<br><br>That had motivated the next words of Susan Starkings (1996): Mathematical education has radically changed, in many countries, over the last decade The need for mathematically literate students who can function in today's technological society has instigated a change in the content of Mathematics curriculum. From the last educational reformation our country has recently begun to introduce emphasis in Statistic with emphasis in the pre-grade curricula. Some years before only charts were given, means and standard deviations and in some cases some other position measure.

  • This paper deals with the introduction of hypermedia technologies in statistical methods as well as their applications in the training of students. A hypermedia prototype to show statistical methods was developed and the toolkits are Toolbook and Kappa. Several screens were developed in a electronic book. The screens show the calculations modules. Some statistical graphs are shown through the screens. The electronic book shows about theoretical methods to calculate means, medians and variance for samples and it provides a deep knowledge about statistical methods. The consultation sessions are quite complete, allowing the student to learn the theory and practice to solve statistical problems. An hypertext system represents the information, in a different way from others usually employed because it is presented as a non-linear mode and, therefore, allowing to take advice with information in agreement with user interests.<br><br>Hypertext and hypermedia systems allow us to reach the following objectives:<br><br>* The structure of the classical text files;<br>* Non-Linear navigation on any selected order of the stored text;<br>* Cooperation, i. e., information with different formats, text, graphs, images, video and voice;<br>* Interaction, what means, sophisticate access tools, as graphical interfaces.<br><br>The paper debates about publications that suggest the benefits of hypermedia systems applications in personal training models.

  • Speaking of the teaching and learning of statistics at the undergraduate level, a moderate amount of training in small-scale data-handling seems to be an indispensable part of an introductory program in statistics. (See {1}.) In the Pakistani system of statistical education, however, there is very little emphasis on the conduct of practical projects involving collection and analysis of real data. ( See {2}.) Realizing the importance of such projects, the Department of Statistics at Kinnaird College for Women, Lahore initiated a series of small-scale statistical surveys back in 1985. ( See {3}, {4} and {5}) Each of these surveys has consisted of (a) identification of a topic of interest, (b) formulation of a questionnaire, (c) collection of data from a sample of individuals / a population of interest, (d) a fairly detailed analysis of the collected data, and (e) presentation of the survey findings in front of teachers and students in the form of an educational and entertaining program. Combining information with other items of interest, such a program provides an effective forum for increasing the popularity of a discipline that is generally considered to be a tough and "dry" subject.<br><br>The following section of this paper throws light on various segments of the most recent one of these programs. The one which was held in the college hall on November 12, 1999, and in which a group of students belonging to the FA Second Year Statistics Class (grade 12, ages 17-18) presented salient features of a survey that had been carried out in order to explore the plus points as well as the problems experienced by the female nurses of Lahore (the author acting as compere/moderator for the program).

  • If it is accepted that the concepts of probability are complicated, it should be also accepted that they are very near to the daily life of common people. Anyway, everybody has to face a variety of situations of uncertainty that can cause either anxiety or joy. As the idea is to teach these concepts to the students, the best way to do it is to have fun when carrying it out. This paper reports the experience with a group of students who are preparing to become high school teachers, in the world of probability by talking about soccer. With this sport as a reference a question is posed such that when students are asked about it, it not only allows an interesting probabilistic analysis, but also takes them, when solving it, to other mathematics concepts like limits and derivatives. The whole situation is presented: its position as conjecture, attempts of answering that include computer work and graphics up to its formal proof.

  • 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.

  • The most prominent characteristic of people's dealings with variability (that we are aware of to date) is their tendency to eliminate, or underestimate the dispersion of the data (e.g., Kareev, Arnon &amp; Horowitz-Zeliger, 2002), that is, the differences among individual observations and among means of samples from a population (Tversky &amp; Kahneman, 1971). One typically focuses on the average, and forgets about the individual differences in the material.<br><br>Shaughnessy and Pfannkuch (2002) report that when asked to analyze a set of data, many students just calculated a mean or a median. They claim that past teaching and textbooks concentrated heavily on such measures and neglected variation. Shaughnessy and Pfannkuch maintain, however, that variability is important. It exists in all processes. Understanding of variation is the central element of any definition of statistical thinking. They quote David Moore's slogan "variation matters" (p. 255).<br><br>In the history of statistics, the tendency to eliminate human variability was represented (in the first half of the 19th century) by Quetelet, who focused on regularities. According to Gigerenzer, et al. (1989), Quetelet understood variation within species as something akin to measurement- or replication-error: The average expressed the "essence" of humankind. "Variations from the average man were accidental - matters of chance - in the same sense that measurement errors were" (p. 142). Quetelet's conception of variation was diametrically different from Darwin's, who focused on variability itself and regarded variations from the mean as the crucial materials of evolution by natural selection.<br><br>One example of the tendency to ignore variability is obtained when assignment of probabilities (or weights) to a set of possible outcomes is called for. People often tend to distribute these probabilities equally over the available options (Falk, 1992; Lann &amp; Falk, 2002; Pollatsek, Lima &amp; Well, 1981; Zabell, 1988), employing what we call the uniformity heuristic. Equi-probability, or zero variability among the probabilities, is the simplest and easiest choice to fall back on.

  • 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.

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