The present work aims to investigate the educational value of statistics as perceived by teachers involved in the teaching of this subject in schools of every type and level in the city of Palermo. To achieve this aim a preliminary fact-finding investigation was performed.
The purpose of this research is to investigate the knowledge of the 1st grade High School students relating to the basic concepts of Statistics that are taught in Elementary School in Greece and to determine the effect that teaching through activities has on their performance. This research, which is part of a broader research conducted by the Department of Primary Education of Aristotle University of Thessaloniki, was realised at the prefectures of Imathia and Pieria. The research provided useful conclusions, such as that the majority of teachers use traditional approaches in their teaching of Statistics, that students have a fair knowledge of most of Statistics' concepts that are included in the Elementary School Curriculum, that major improvement of this knowledge is observed after a teaching approach through activities and that the performance of students who live in urban areas is better in comparison to the performance of those who live in rural areas.
In fulfilling their brief to build a digital university the Centre for IT in Higher Education (ITEd), presents academic modules in Digital Media to staff and students from technologically under-resourced backgrounds who have had limited opportunities for acquiring practical IT skills. In a core module on Research Data Analysis Theory and Tools, a component on Computer-based Quantitative Data Analysis develops competency in advanced software tools to assist implementation of research projects. A challenge of this course has been to build confidence in learners with limited statistical and quantitative backgrounds, who articulate anxiety and phobia about work of this nature. This paper reports on the design, implementation, assessment and outcomes of a predominantly Internet and web-based course that used the metaphor of a Big Bother/Survivor Challenge process to prepare largely 'quantophobic' post-graduate students and staff to conduct sound quantitative data analysis in research projects while reducing 'quantophobia' and building confidence. Initial results suggest that the use of the metaphor, together with other design features of the course, contributed to reduced 'quantophobia' and increased confidence with quantitative work.
Discussions of students' understandings of key course concepts typically investigate those understandings at one point in time. This paper reports results from a case study in which eighteen graduate students were interviewed throughout a fifteen-week introductory statistics course. Knowledge structures were assessed once every three weeks, and changes in these structures were discussed. One key finding was that students' understandings of certain course concepts change as the semester progresses, indicating that it may not be enough to assess these understandings at only one point in time. Two concepts in particular, mean and variance, are central to many ideas in the introductory course. Assessing how students "know" these concepts throughout the course may be beneficial to researchers and educators alike. Implications for both statistics education research and teaching introductory statistics are offered.
This paper reports on a preliminary study conducted for gaining better insight in the complexity of students' misconceptions of representativeness. Data from 156 students (112 high school graduates and 44 students with a university degree) are presented. The overall outcome indicates a lack of ability to refer problems about specific experiments to their correct context. Some results seem to contradict part of the representativeness heuristic described by Kahneman and Tversky (1972). They might also indicate that multiple-choice tests, even with two-part questions, are not able to fully capture the deep complexity of students' misunderstandings.
Many college students have difficulties in understanding and making connections among the main concepts of statistics. Compounding the difficulties is the misconception of a variety of statistical concepts that students hold even before taking any statistics course. It is, thus, crucial to investigate how the understanding of statistical concepts is constructed and at which stage students start to lose making connections among various concepts. This article reports some findings from our study of investigating the path of learning statistical concepts, specifically on how students learn the concept of variation. We focus on investigating the missing connections about their understanding of variation. The framework of statistical thinking, PPDAC investigative cycle, is used as our guideline for analyzing our interview data.
Compared kindergartners', third graders', and undergraduates' understanding and attribution of randomness. Found that kindergartners' interpretations were deterministic or outside the determinancy-indeterminancy frame. Most third graders had some grasp of randomness; their interpretations were less dominated by false attribution of determinism than kindergartners'. Undergraduates also showed performance deficiencies, suggesting that interpreting random phenomena constitutes a nontrivial challenge even for adults.
Recounts a study documenting the actual learning trajectory of the classroom community and the diversity in eighth-graders' reasoning as they participated in the classroom mathematical practices that constituted this trajectory. Describes the learning of the research team by documenting conjectures about students' statistical learning and the means of supporting it. Proposes a revised learning trajectory to inform design and instruction in other classrooms.
The present knowledge society requires statistical literacy-the ability to interpret, critically evaluate, and communicate about statistical information and messages (Gal, 2002). However, research shows that students generally do not gain satisfactory statistical understanding. The research presented in this thesis is a sequel to design research carried out by Cobb, McClain, and Gravemeijer (2003) and aims at contributing to an empirically grounded instruction theory for early statistics education in which educational computer tools are used. Computer software allows users to dynamically interact with large data sets and to explore different representations in ways that are impossible by hand. The computer tools used were the Statistical Minitools (Cobb et al., 1997), which have been designed for middle school students. One important end goal of instruction was that students would gain understanding of sampling and learn to use 'shape' to reason about distributions. In line with the theory of Realistic Mathematics Education, a central tenet was that learning mathematics should be a meaningful activity. The research questions were: 1. How can students with little statistical background develop a notion of distribution? 2. How does the process of symbolizing evolve when students learn to reason about distribution? In the latter question, 'symbolizing' refers to the reflexive process of making symbols and mentally constructing the objects which they represent. The design research consisted of five cycles of three phases: a design phase, a teaching experiment, and a retrospective analysis. Prior to these cycles, historical and didactical phenomenological analyses (Freudenthal, 1991) were carried out as well as exploratory interviews. The historical study gave rise to hypotheses that were partially tested in the teaching experiments carried out in grades 7 and 8 (12 to 14 years old). In the design phase, a so-called hypothetical learning trajectory (Simon, 1995) was formulated, which was tested and revised in the subsequent cycles of design research. The recurring activity of discussing growing samples proved useful to support reasoning about distribution and sampling. For the analyses of students' learning, a method was used similar to the constant comparative method (Strauss & Corbin, 1998). It turned out that students conceived distributions as 'bumps' consisting of a small group of low values, a large group of 'average' values, and a small group of high values. Peirce's semiotics proved useful for analyzing students' process of symbolizing, in particular, his notions of hypostatic abstraction and diagrammatic reasoning. Hypostatic abstraction refers to the transition from a predicate to a new abstract object ("the dots are spread out" to "the spread is large"). Diagrammatic reasoning consists of three steps: making a diagram, experimenting with it, and reflecting on the results. The research shows the importance of letting students make their own diagrams and discussing these. The computer tools seemed most useful during the experimentation phase. Remarkably, the best diagrammatic reasoning occurred only during class discussions without computers around. One recommendation is: only invest in using computer tools if all educational factors such as teaching, end goals, instructional activities, tools, and assessment are tuned to each other.
Concerns about equity in the ways that schools are using the data from the results of their students' state-mandated exams (Confrey & Makar, in press) prompted this mixed-method study, based on the model of Design Research (Cobb et al., 2003). The study was conducted to provide insight into the ways that understanding of the statistical concepts of variation and distribution, developed in the context of learning about equity and assessment, can allow prospective teachers to broaden their understanding of equity and gain experience with conducting an inquiry of an ill-structured problem through the use of data generated by high-stakes tests to investigate equity and fairness in the accountability system. The study took place in an innovative one-semester course for preservice teachers designed to support and develop understanding of equity and fairness in accountability through data-based statistical inquiry (Confrey, Makar, and Kazak, 2004). The prospective teachers' investigations were conducted using Fathom Dynamic Statistics (Finzer, 2001), a learning software built for novice data analysts which emphasizes visualization and building inferential thinking through highlighting relationships between multiple variable displays. Semi-structured investigations during the course led up to a three-week self-designed inquiry project in which the prospective teachers used data to investigate an area of interest to them about equity in accountability, communicating their findings both orally and as a written paper. Results from the study provide insight into prospective teachers' experiences of conducting inquiry of ill-structured problems and their struggle with articulating beliefs of equity. The study also reports how statistical concepts documented in structured settings showed that the subjects developed rich conceptions of variation and distribution, but that the application of these concepts as evidence in their inquiry of an ill-structured problem was more challenging for them. No correlation was found between the level of statistical evidence in the structured and open-ended inquiry settings, however there was a significant correlation between prospective teachers degree of engagement with their topic of inquiry and the depth of statistical evidence they used, particularly for minority students. Implications and suggestions for improving the preparation of teachers in the areas of statistical reasoning, inquiry, equity, and interpreting assessment data are provided.