# Chapter

• ### Statistics and probability for the middle grades: Examples from Mathematics in Context

This chapter describes the Mathematics in Context (MiC) project. This project involves presenting students with activities, in the middle grades, which help them understand how to reason from and make conclusions based on data, judge the quality of other people's conclusions, recognize the degree of uncertainty in any endeavor, and quantify the uncertainty.

• ### Graphical representations: Helping students interpret data

The process of statistical investigation may be conceptualized as having four components: Posing the question, collecting the data, analyzing the data, and interpreting the data. Graphical representations of data are a critical part of the analysis phase, since the use of different representations communicates information in different ways. This chapter discusses instructional strategies for moving between three different pairs of representations: bar graphs showing ungrouped data and standard bar graphs, line plots and bar graphs, and stem-and-leaf plots and histograms. These strategies are designed to optimize the accuracy of interpretations and avoid common pitfalls in making sense of the data; the strategies focus on reading rather than on making the representations themselves. Students' attempts to make the translations between representations are discussed within the framework of the instructional suggestions.

• ### Teach-Stat: A model for professional development in data analysis and statistics for teachers K-6

What do elementary teachers need to know and be able to do in order to successfully integrate the teaching and learning of data analysis and statistics as part of their instruction? This chapter discusses the design and implementation of a professional development program to help teachers integrate teaching about statistics in their instruction. This project included: the design of professional development curricula for use with teachers and with teacher leaders (statistics educators), a large-scale implementation program to provide professional development for both teachers and statistics educators using the professional development curricula, and a program of research and evaluation to assess the impact of the project and to surface research questions related to the agenda of the project. The focus of the program is the statistical investigation process: posing questions, collecting and analyzing the data, and interpreting the results. Evidence from participating teachers demonstrates the success of this program in supporting work with students and in promoting inquiry-based pedagogy.

• ### Data and Data Analysis

Whereas data analysis was once considered synonymous with statistics, a broader view is emerging in educational psychology. In their presient work, Tukey and Wilk (1966/1986) articulated such a broad view, one we adopt for this chapter: "[T]he science and art of data analysis concerns the process of learning from ...records of experience" (p. 554). Although Tukey and Wilk wrote about their own quantitative analysis, the definition seems equally appropriate for qualitative work. Good data analysis, regardless of the approach, is a mixture of science and art. Data analysis employs creativity in search of meaning, intelligibility, and pattern while rooted in systematic methods that emphasize open-mindedness and public scrutiny. Regardless of the theoretical emphasis, data analysis seeks revelation --the unveiling of the world around us.

• ### Research in Statistics Education

The research reported in this chapter spans students in preparatory grades, undergraduate statistics students, preservice teachers, and practising statisticans. The chapter starts with theoretical frameworks that have been developed by Australasian researchers, then focuses on reserach involving students' reasoning and thinking within the statistics discipline, related to probability, variation, sampling, and data representation and interpretation, rounding off with a section on improving teaching and the curriculum. The conclusion addresses reserach areas for future development, as well as areas that should continue to receive attention.

• ### Action research as a research methodology for the study of the teaching and learning of science

This chapter addresses issues of action research from three perspectives. In the first section, what it means to engage in action research as a methodology for investigating teaching and learning in science education is overviewed and various conceptions of action research are explicitly made. The second perspective is that of an individual engaged in action research in the classroom to improve teaching, students' learning, and advance knowledge of the teaching and learning of physics. The third perspective is that of a facilitator of action research done by others. By providing views from these three perspectives, the concerns and issues of action research are addressed and helps readers develop their own understanding of what action research is and can be so that it can be used as a methodology for the study of teaching and learning in science.

• ### Children's Work with Data

This book looks at how teachers implement national math and science standards in their classrooms. Teacher-authored chapters provide insights into how children think and reason as they pose questions, collect data, and build data models to answer their questions. While the spotlight is primarily on student understanding and its development over time, the text also highlights teachers' professional development of a specific form of knowledge. Chapters include: (1) "Children's Work with Data" (Richard Lehrer, Nancy D. Giles, and Leona Schauble); (2) "How Children Organize and Understand Data" (Angie Putz); (3) "How Much Traffic? Beep! Beep! Get That Car Off the Number Line!" (Jean Gavin); (4) "What's Typical? A Study of the Distributions of Items in Recycling Bins" (Carmen Curtis); (5) "Shadows" (Susan Wainwright); (6) "Graphing" (Jennie Clement); (7) "Graphing Artistry: Data Displays as Tools for Understanding Literary Devices" (Deborah Lucas); (8) "Data Models of Ourselves: Body Self-Portrait Project" (Erin Diperna); and (9) "Classification Models Across the Grades" (Sally Hanner, Eric James, and Mark Rohlfing)

• ### The case for randomized experiments

This chapter seeks to show how randomized experiments can be productively used to learn about the effects of important aspects of educational technology and even about the effects of important aspects of educational technology and even about technology writ large. To achieve this, we first work through a hypothetical example and then later present an abstract analysis of the example. The point is to elucidate the conditions under which random assignment is desirable and feasible in studies of educational technology.