Informal statistical inference (ISI) has been a frequent focus of recent research in statistics education. Considering the role that context plays in developing ISI calls into question the need to be more explicit about the reasoning that underpins ISI. This paper uses educational literature on informal statistical inference and philosophical literature on inference to argue that in order for students to generate informal statistical inferences, there are a number of interrelated key elements that are needed to support their informal inferential reasoning (IIR). In particular, we claim that ISI is nurtured by statistical knowledge, knowledge about the problem context, and useful norms and habits developed over time, and supported by an inquiry-based environment (tasks, tools, scaffolds). We adopt Peirce’s view that inquiry is a sense-making process driven by doubt and belief, leading to inferences and explanations. To illustrate the roles that these elements play in supporting students to generate informal statistical inferences, we provide an analysis of three sixth graders’ (aged 12) informal inferential reasoning—the reasoning processes leading to their informal statistical inferences.
This article describes a model for an interactive, introductory secondary- or tertiary-level statistics course that is designed to develop students’ statistical reasoning. This model is called a ‘Statistical Reasoning Learning Environment’ and is built on the constructivist theory of learning.test_363 72..77
Increasing attention has been given over the last decade by the statistics, mathematics and science education communities to the development of statistical literacy and numeracy skills of all citizens and the enhancement of statistics education at all levels. This paper introduces the emerging discipline of statistics education and considersits role in the development of these important skills.The paper begins with information on the growing importance of statistics in today’s society, schools and colleges, summarizes unique challenges students face as they learn statistics, and makes a case for the importance of collaboration between mathematicians and statisticians in preparing teachers to teach students how to understand and reason about data. We discussthe differences and interrelations between statistics and mathematics, recognizing that mathematics is the discipline that has traditionally included instruction in statistics. We conclude with an argument that statistics should be viewed as a bridge between mathematics and science and should be taught in both disciplines.
This paper provides practical examples of how statistics educators may apply a cooperative framework to classroom teaching and teacher collaboration. Building on the premise that statistics instruction ought to resemble statistical practice, an inherently cooperative enterprise, our purpose is to highlight specific ways in which cooperative methods may translate to statistics education. So doing, we hope to address the concerns of those statistics educators who are reluctant to adopt more student-centered teaching strategies, as well as those educators who have tried these methods but ultimately returned to more traditional, teacher-centered instruction.
This paper provides an overview of current research on teaching and learning statistics, summarizing studies that have been conducted by researchers from different disciplines and focused on students at all levels. The review is organized by general research questions addressed, and suggests what can be learned from the results of each of these questions. The implications of the research are describedintermsofeightprinciplesforlearningstatisticsfromGarfield(1995)whicharerevisited in the light of results from current studies.
This paper provides a broad overview of the role technological tools can play in helping students understand and reason about important statistical ideas. We summarize recent developments in the use of technology in teaching statistics in light of changes in course content, pedagogical methods, and instructional formats. Issues and practical challenges in selecting and implementing technological tools are presented discussed, and examples of exemplary tools are provided along with suggestions for their use.
This article is a discussion of and reaction to two collections of papers on research on Reasoning about Variation: Five papers appeared in November 2004 in a Special Issue 3(2) of the Statistics Education Research Journal (by Hammerman and Rubin, Ben-Zvi, Bakker, Reading, and Gould), and three papers appear in a Special Section on the same topic in the present issue (by Makar and Confrey, delMas and Liu, and Pfannkuch). These papers show that understanding of variability is much more complex and difficult to achieve than prior literature has led us to believe. Based on these papers and other pertinent literature, the present paper, written by the Guest Editors, outlines seven components that are part of a comprehensive epistemological model of the ideas that comprise a deep understanding of variability: Developing intuitive ideas of variability, describing and representing variability, using variability to make comparisons, recognizing variability in special types of distributions, identifying patterns of variability in fitting models, using variability to predict random samples or outcomes, and considering variability as part of statistical thinking. With regard to each component, possible instructional goals as well as types of assessment tasks that can be used in research and teaching contexts are illustrated. The conceptual model presented can inform the design and alignment of teaching and assessment, as well as help in planning research and in organizing results from prior and future research on reasoning about variability.
Variability stands in the heart of statistics theory and practice. 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. The focus in this paper is on the emergence of beginners’ reasoning about variation in a comparing distributions situation during their extended encounters with an Exploratory Data Analysis (EDA) curriculum in a technological environment. The current case 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 detailed 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 statistical representations. Learning statistics is conceived as cognitive development and socialization processes into the culture and values of “doing statistics” (enculturation). In the light of the analysis, a description of what it may mean to begin reasoning about variability in comparing distributions of equal size is proposed, and implications are drawn.