Journal Article

  • In the Connected Learning projects, we are studying students' learning of content through exploring and constructing computer-based models of that content. This paper present a case study of a high school physic teacher's design and exploration of a computer-based model of gas molecules in a box. We follow up the case study with shorter vignettes of students' exploration and elaboration of the Gas-in-a-Box model. The cases lead us to analyze and discuss the role of model-based inquiry in science and mathematics education as well as to draw some general conclusions with respect to the design of modeling languages and the design of pedagogies and activities appropriate for model-based inquiry in classroom settings.

  • Someone needs to bring reason and logic to this mass movement to solve all problems with data, and that task should fall to the statistician. Now, I realize that data sets are collected and analyzed by practitioners in many fields, but statisticians are the only professional group educated specifically to ask (and, hopefully, answer) the deep questions about data quality, reliability, and validity, and to seek optimal solutions to data production and analysis that can apply across a wide range of applications. At present, it may be true that statistics is more in demand than are statisticians, but there are plenty of opportunities for the latter. It is high time we expand our numbers so that we can meet the ever-increasing need for statisticians in the information age.

  • Advancing technology is inexorably shifting the demand for statisticians from being operators of mechanical procedures to being thinkers. Coupled with this is a perceived lack of development of statistical thinking in students. This chapter discusses the thought processes involved in statistical problem solving in the broad sense from problem formulation to conclusions. It draws on the literature and in-depth interviews, with statistics students and practising statisticians, which aimed at uncovering their statistical reasoning processes. From these interviews from all four exploratory studies, a four dimensional statistical thinking framework for empirical enquiry has been identified. It includes an investigative cycle, an interrogative cycle, types of thinking and dispositions. There are a number of associated elements such as techniques for thinking and constraints on thinking. The characterisation of these processes through models, that can be used as a basis for thinking tools or frameworks for the enhancement of problem-solving, is begun in this chapter. Tools of this form would complement the mathematical models used in analysis. The tools would also address areas of the process of statistical investigation that the mathematical models do not, particularly in areas requiring the synthesis of problem-contextual and statistical understanding. The central element of published definitions of statistical thinking is<br>"variation." The role of variation in the statistical conception of real-world problems, including the search for causes, is further discussed.

  • The tremendously popular movie Titanic has rejuvenated interest in the Titanic and its passengers. Students are particularly captivated by the story and by the people involved. Consequently, when I was preparing to explore categorical data and the chi square distribution with my class, I decided to use the available data about the Titanic's passengers to interest students in these topics. This article describes the activities that I incorporated into my statistics class and gives additional resources for collecting information about the Titanic.

  • New software tools for data analysis provide rich opportunities for representing and understanding data. However, little research has been done on how learners use thse tools to think about data, nor how that affects teaching. This paper describes several ways that learners use new software tools to deal with variability in analyzing data, specifically in the context of comparing groups. The two methods we discuss are 1) reducing the apparent variability in a data set by grouping the values usig numerical bins or cut points and 2) using proportions to interpret the relationship between bin size and group size. This work is based on our observations of middle- and high-school teachers in a professional development seminar, as well as of students in these teachers' classrooms, and in a 13-week sixth grade teaching experiment. We conclude with remarks on the implications of these uses of new software tools for research and teaching.

  • Although variability is of fundamental concern and interest to statisticians, often this does not get communicated to students who are taught instead to view variability as a nuisance parameter. A brief survey of a few case studies, as well as a recounting of some history, shows that variability is worthy of study in its own right, and examination of variability leads to insights that might have been missed had we focused all of our attention on the "trend" of the data. As on of the key components of statistical thinking, variability deserves more prominence in the classroom.

  • The research studies presented in this special issue have serveral common features. Their topics reflect the shift in emphasis in statistics instruction, from statistical techniques, formulas, and procedures to developing statistical reasoning and thinking. These studies employ various types of qualitative methodologies, which appear to have uncovered many interesting points about how students and teachers reason about variability. Most of them use extended teaching experiments, or represent cases where researchers collaborated with teachers in field settings or designed specialized learning episodes or environments, to be able to elicit detailed and deep data about students' actions and reasoning.

  • 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 anlaysis 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 anlaysis, a description of what it may mean to begin reasoning about variability in comparing distributions of equal size is proposed, and implications are drawn.

  • This paper examines ways in which coherent reasoning about key concepts such as variability, sampling, data, and distribution can be developed as part of statistics education. Instructional activities that could support such reasoning were developed through design research conducted with students in grades 7 and 8. Results are reported from a teaching experiments with grade 8 students that employed two instructional activities in order to learn more about their conceptual development. A "growing a sample" activity had students think about what happens to the graph when bigger samples are taken, followed by an activitiy requiring reasoning about shape of data. The results suggest that the instructional activities enable conceptual growth. Last, implications for teaching, assessment and research are discussed.

  • Variation is a key concept in the study of statistics and its understanding is a crucial aspect of most statistically related tasks. This study aimed to extend and apply a hierarchy for describing students' understanding of variation that was developed in a sampling context to the context of a natural event in which variation occurs. Students aged 13 to 17 engaged in an inference task that necessitated the description of both rainfall and temperature data. The SOLO Taxonomy was used as a framework for analyzing student responses. Two cycles of Unistructural-Multistructural-Relational levels, one for qualitative descriptions and the other for quantitative descriptions, were identified in responses. Implications of the extended hierarchy for describing understanding of variation for research, teaching and assessment are outlined.

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