# Chapter

• ### Principles of Instructional Design for Supporting the Development of Students' Statistical Reasoning

This chapter proposes design principles for developing statistical reasoning in elementary school. In doing so, we will draw on a classroom design experiment that we conducted several years ago in the United States with 12-year-old students that focused on the analysis of univariate data. Experiments of this type involve tightly integrated cycles of instructional design and the analysis of students' learning that feeds back to inform the revision of the design. To ground the proposed design principles, we first give a short overview of the classroom design experiment and then frame it as a paradigm case in which to tease out design principles that address five aspects of the classroom environment that proved critical in supporting the students' statistical learning:<br>o The focus on central statistical ideas<br>o The instructional activities<br>o The classroom activity structure<br>o The computer-based tools the students used<br>o The classroom discourse

• ### Research on Statistical Literacy, Reasoning, and Thinking: Issues, Challenges, and Implications

The collection of studies in this book represents cutting-edge research on statistical literacy, reasoning, and thinking in the emerging area of statistics education. This chapter describes some of the main issues and challenges, as well as implications for teaching and assessing students, raised by these studies. Because statistics education is a new field, taking on its own place in educational research, this chapter begins with some comments on statistics education as an emerging research area, and then concentrates on various issues related to research on statistical literacy, reasoning, and thinking. Some of the topics discussed are the need to focus research, instruction, and assessment on the big ideas of statistics; the role of technology in developing statistical reasoning; addressing the diversity of learners (e.g., students at different educational levels as well as their teachers); and research methodologies for studying statistical reasoning. Finally, we consider implications for teaching and assessing students and suggest future research directions.

• ### Navigating Data Analysis, Grades 9-12

The activities in this book introduce students to simple random sampling, sampling techniques, and simulation as a tool for analyzing both categorical and numerical data. Scenarios probe topics of interest to high school students, including possible workplace discrimination against women and links between vegetarian diets and blood cholesterol levels. As students work, they learn what makes a well-designed study; how to distinguish among observational studies, surveys, and experiments; and when statistical inference is permissible. The supplemental CD-ROM features interactive electronic activities, master copies of activity pages for students, and additional readings for teachers.

• ### The measurement of adult literacy

In December 1995, the Organisation for Economic Co-Operation and Development (OECD) and Statistics Canada jointly published the results of the first International Adult Literacy Survey (IALS). For this survey, representative samples of adults aged 16 to 65 were interviewed and tested in their homes in Canada, France, Germany, the Netherlands, Poland, Sweden, Switzerland, and the United States. This report describes how the survey was conducted in each country and presents all available evidence on the extent of bias in each country's data. Potential sources of bias, including sampling error, non-sampling error, and the cultural appropriateness and construct validity of the assessment instruments, are discussed. The chapters are; (1) "Introduction" (Irwin S. Kirsch and T. Scott Murray); (2) "Sample Design" (Nancy Darcovich); (3) "Survey Response and Weighting" (Nancy Darcovich); (4) "Non-Response Bias" (Nancy Darcovich, Marilyn Binkley, Jon Cohen, Mats Myrberg, and Stefan Persson); (5) "Data Collection and Processing" (Nancy Darcovich and T. Scott Murray); (6) "Incentives and the Motivation To Perform Well" (Stan Jones); (7) "The Measurement of Adult Literacy" (Irwin S. Kirsch, Ann Jungeblut, and Peter B. Mosenthal); (8) "Validity Generalization of the Assessment across Countries" (Don Rock); (9) "An Analysis of Items with Different Parameters across Countries" (Marilyn R. Binkley and Jean R. Pignal); (10) "Scaling and Scale Linking" (Kentaro Yamamoto); (11) "Proficiency Estimation" (Kentaro Yamamoto and Irwin S. Kirsch); (12) "Plausibility of Proficiency Estimates" (Richard Shillington); and (13) "Nested-Factor Models for the Swedish IALS Data" (Bo Palaszewski). Fourteen appendixes contain supplemental information, some survey questionnaires, and additional documentation for various chapters.

• ### Mathematical narratives, modeling, and algebra.

This book aims at understanding the functioning of algebraic reasoning, its characteristics, the difficulties students encounter in making the transition to algebra, and the situations conducive to its favorable development. Four different perspectives, each related to a corresponding conception of algebra, provide avenues for its introduction: generalization, problem solving, modeling, and functions. The analysis of research on these perspectives is illuminated by a dual focus on epistemological (via the history of the development of algebra) and didactic concerns. Series: Mathematics Education Library, Vol. 18

• ### Technology in college statistics courses

This paper examines the ways technology is being used in a variety of college-level statistics courses: introductory statistics, probability, mathematical statistics, and intermediate statistics. Although there is some overlap in the types of technological resources being used in these different courses, an attempt is made to isolate the particular types of technology or software that are most appropriate or most used in each type of course.

• ### Highlights of related research

Although there is considerable research on the reasoning of college students, there is<br>relatively little on how younger students reason and learn about data. Because data<br>analysis has only recently become an integral part of the pre-college curriculum in<br>the United States, we have limited practical experience with what works and what<br>doesn't. Accordingly, we draw heavily in this chapter on what we, as researchers,<br>have learned from the episodes in the Working with Data Casebook, connecting our observations when we can to published findings. In our opinion, the reflections of<br>these teachers and their descriptions of students' thinking is one of the richest source<br>of information to date on children's reasoning about data and on how children's<br>thinking evolves during instruction.

• ### Students analyzing data: Research of critical barriers

In describing the work of the nineteenth-century statistician Quetelet, Porter (1986)<br>suggested that his major contribution was in:<br><br>...persuading some illustrious successors of the advantage that could be gained in certain cases by turning attention away from the concrete causes of individual phenomena and concentrating instead on the statistical information presented by the larger whole (pg. 55).<br><br>This observation describes the essence of a statistical perspective - attending to features of aggregates as opposed to features of individuals. In attending to where a collection of values is entered and how those values are distributed, statistics deals for the most part with features belonging not to any of the individual elements, but to the aggregate which they comprise. While statistical assertions such as "50% of marriages in the U.S. result in divorce" or "the life expectancy of women born in the U.S. is 78.3 years" might be used to make individual forecasts, they are more typically interpreted as group tendencies or propensities. In this article, we raise the possibility that some of the difficulty people have in formulating and interpreting statistical arguments results from their not having adopted such a perspective, and that they make sense of statistics by interpreting them using more familiar, but inappropriate, comparison schemes.

• ### Students' difficulties in practicing computer supported data analysis

In this paper, I will report and summarize some preliminary results of two ongoing studies. The aim is to identify problem areas and difficulties of students in elementary data analysis based on preliminary results from the two ongoing studies. The general idea of the two projects is similar. Students took a course in data analysis where they learned to use a software tool, used the tool during the course, and worked on a data analysis project with this tool at the end of the course. The course covered elementary data analysis tools, such as variables and variable types, box plots, frequency tables and graphs, two-way frequency tables, summary measures (median, mean, quartiles, interquartile range, range), scatterplots, and line plots. The grouping of data and the comparison of distributions in the subgroups defined by a grouping variable was an important idea related to studying the dependence of two variables. The methods for analyzing dependencies differed according to the type of variables: for example, scatterplots were used in the case of two numerical variables, and two-way frequency tables and related visualizations were used in the case of two categorical variables.

• ### Subjective randomness

Early generalizations concerning conceptions of randomness were based on "probability-learning" experiments in which subjects predicted successive elements of random sequences, receiving trial-by-trial feedback. The conclusion was that humans are incapable of perceiving randomness. Convinced there was some pattern in the stimuli, most subjects believed the oncoming event depended on preceding ones (Lee [29]). The predicted sequenes that deviated systematically from randomness. However, evidence concerning people's notion of randonmness in these expereiments is indirect. The produced sequences, which are influenced by various feedback contingencies, may largely reflect subjects' hypotheses concerning the goal of the experiment and their problem-solving strategies.