Katie Makar

Technology for enhancing statistical reasoning at the school level

The purpose of this chapter is to provide an updated overview of digital technologies relevant to statistics education, and to summarize what is currently known about how these new technologies can support the development of students’ statistical reasoning at the school level. A brief literature review of trends in statistics education is followed by a section on the history of technologies in statistics and statistics education. Next, an overview of various types of technological tools highlights their benefits, purposes and limitations for developing students’ statistical reasoning. We further discuss different learning environments that capitalize on these tools with examples from research and practice. Dynamic data analysis software applications for secondary students such as Fathom and TinkerPlots are discussed in detail. Examples are provided to illustrate innovative uses of technology. In the future, these uses may also be supported by a wider range of new tools still to be developed. To summarize some of the findings, the role of digital technologies in statistical reasoning is metaphorically compared with travelling between data and conclusions, where these tools represent fast modes of transport. Finally, we suggest future directions for technology in research and practice of developing students’ statistical reasoning in technology-enhanced learning environments.

Secondary Teachers’ Statistical Reasoning in Comparing Two Groups

The importance of distributions in understanding statistics has been well articulated in this book by other researchers (for example, Bakker & Gravemeijer, Chapter 7; Ben-Zvi, Chapter 6). The task of comparing two distributions provides further insight into this area of research, in particular that of variation, as well as to motivate other aspects of statistical reasoning. The research study described here was conducted at the end of a 6-month professional development sequence designed to assist secondary teachers in making sense of their students’ results on a statemandated academic test. In the United States, schools are currently under tremendous pressure to increase student test scores on state-developed academic tests. This paper focuses on the statistical reasoning of four secondary teachers during interviews conducted at the end of the professional development sequence. The teachers conducted investigations using the software FathomTM in addressing the research question: “How do you decide whether two groups are different?” Qualitative analysis examines the responses during these interviews, in which the teachers were asked to describe the relative performance of two groups of students in a school on their statewide mathematics test. Preand posttest quantitative analysis of statistical content knowledge provides triangulation (Stake, 1994), giving further insight into the teachers’ understanding.

Teaching Teachers to Teach Statistical Investigations

Despite its importance for the discipline, the statistical investigation cycle is given little attention in schools. Teachers face unique challenges in teaching statistical inquiry, with elements unfamiliar to many mathematics classrooms: Coping with uncertainty, encouraging debate and competing interpretations, and supporting student collaboration. This chapter highlights ways for teacher educators to support teachers’ learning to teach statistical inquiry. Results of two longitudinal studies are used to formulate recommendations to develop teachers’ proficiency in this area.

The Role of Context in Developing Reasoning about Informal Statistical Inference

Statistics education research is emerging as an important area of inquiry with multiple implications in school and tertiary curriculum design, instructional activities, technological tools that aid teaching and learning statistics, and teachers’ professional development. Over the past decade there has been an increasingly strong call for statistics education to focus more on statistical literacy, reasoning, and thinking. One of the main arguments presented is that traditional approaches to teaching statistics focus mainly on skills, procedures, and computations, which do not lead students to reason or think statistically. The papers in this Special Issue of Mathematical Thinking and Learning came out of discussions and presentations from the Sixth International Research Forum on Statistical Reasoning, Thinking, and Literacy (SRTL) in Brisbane, Australia in July 2009. SRTL is part of an international collaboration for research in statistics education that focuses on examining the nature and development of statistical literacy, reasoning, and thinking. SRTL organizes a series of biannual research forums since 1999 as an alternative to large conferences. The small size of these gatherings allows plenty of time for interaction and discussion of research data on a different clear thematic focus for each meeting with emphasis on qualitative analysis of classroom videos or interviews.

Undertaking data analysis of student outcomes as professional development for teachers

The study reports on collaborations with practitioners to examine the results of students’ performances on high stakes tests as a means to strengthen practitioners’ knowledge of probability and statistics and to empower their conduct of investigations on student performance. Four issues are summarized: the development of their statistical reasoning, their understanding of the meaning of and relationships among the concepts of validity, reliability and fairness as applied to testing, their introduction to the history of testing and its relationship to science, society and cultural inequality, and their reports of independent inquiries. Data on performance on pre- and post-tests demonstrate growth in teacher reasoning and in their professionalism in raising important issues about testing

Developing Young Children's Emergent Inferential Practices in Statistics.

ABSTRACT Informal statistical inference has now been researched at all levels of schooling and initial tertiary study. Work in informal statistical inference is least understood in the early years, where children have had little if any exposure to data handling. A qualitative study in Australia was carried out through a series of teaching experiments with a class of five- to six-year-old children in two phases over six months. The aim of the exploratory study was to understand and support the emergence of informal statistical inference in the early years of schooling. Through activities that initially built on children’s experiences with prediction and key characteristics of informal statistical inference, the children’s actions were observed in a data-based inquiry involving prediction to identify critical relationships that then supported children in making informal statistical inferences. Implications are discussed.

Moving the context of modelling to the forefront: Preservice teachers’ investigations of equity in testing

Prospective math and science teachers were engaged in interpretation and analysis of testing data with the innovative statistical software Fathom™. Armed with a few basic statistical concepts, their ability to model complex issues was correlated with their personal engagement in the process and context at the forefront of the modelling activity.

Learning About Statistical Inference

This chapter reviews research on the learning of statistical inference, focusing in particular on recent research on informal statistical inference. The chapter begins by arguing for the importance of broader access to the power of statistical inference—which, until recently, has been accessible only to those with extensive knowledge of mathematics—and then traces the philosophical roots of inference. We outline the challenges that students have encountered in learning statistical inference and strategies to facilitate its learning that have capitalized on technological advances. We describe the emergence of informal statistical inference and how researchers have framed the idea over the past decade. Rather than consider formal and informal statistical inference dichotomously, we highlight a number of dimensions along which approaches to statistical inference may differ, providing a richer perspective on how formal and informal statistical inference are related. Cases from classroom research aimed at primary, secondary, and tertiary levels are used to illustrate how informal statistical inference has shaped new ways to approach the teaching and learning of statistical inference. Finally, we outline gaps in research on statistical inference and present our speculations on its future in light of new research on statistical modeling and big data.

The teaching and learning of statistics: international perspectives

This book presents the breadth and diversity of empirical and practical work done on statistics education around the world. A wide range of methods are used to respond to the research questions that form its base. Case studies of single students or teachers aimed at understanding reasoning processes, large-scale experimental studies attempting to generalize trends in the teaching and learning of statistics are both employed. Various epistemological stances are described and utilized. The teaching and learning of statistics is presented in multiple contexts in the book. These include designed settings for young children, students in formal schooling, tertiary level students, vocational schools, and teacher professional development. A diversity is evident also in the choices of what to teach (curriculum), when to teach (learning trajectory), how to teach (pedagogy), how to demonstrate evidence of learning (assessment) and what challenges teachers and students face when they solve statistical problems (reasoning and thinking).

Teaching and Learning of Statistics

Being able to provide sound evidence-based arguments and critically evaluate data-based claims are important skills that all citizens should have. It is not surprising therefore that the study of statistics at all educational levels is gaining more students and drawing more attention than it has in the past. The study of statistics provides students with tools, ideas and dispositions to use in order to react intelligently to information in the world around them. Reflecting this need to improve students’ ability to think statistically, statistical literacy and reasoning are becoming part of the mainstream school and university curriculum in many countries.