Researchers have documented many misconceptions students hold about sampling variability. This study takes a different approach--instead of identifying shortcomings, we consider the productive reasoning pieces students construct as they reason about sampling distributions. We interviewed eight undergraduate students newly enrolled in an…

Many studies have reported on the influence of teachers' conceptions of variability on different aspects of their professional knowledge for teaching statistics and their classroom practices. However, research on these kind of conceptions is still scarce, particularly in Latin American countries like Venezuela. In an effort to help fill this gap,…

Although hypothesis testing is ubiquitous in data analysis, research suggests it is commonly misunderstood. Simulation-based inference methods have potential to make student thinking visible, thus providing a valuable lens to analyze developing conceptions about inference. This paper identifies difficulties made visible through simulation-based…

This study examined a random stratified sample (n = 62) of teachers' work across eight institutions on three tasks that utilized dynamic statistical software. We considered how teachers may utilize and develop their statistical knowledge and technological statistical knowledge when investigating a statistical task. We examined how teachers engaged…

The study explores the development of 11-year-old students' informal inference about random bunny hops through student talk and use of computer simulation tools. Our aim in this paper is to draw on dialogic theory to explain how students make shifts in perspective, from intuition-based reasoning to more powerful, formal ways of using probabilistic…

Data distributions can be represented using different external representations, such as histograms and boxplots. Although the role of external representations has been extensively studied in mathematics, this is less the case in statistics. This study helps to fill this gap by systematically varying the representation that accompanies a task…

This study is an exploration of teachers' engagement with concepts embedded in the normal distribution. The participants were a group of 290 in-service teachers enrolled in a teacher development program. The research instrument was an assessment task that can be described as an "unknown percentage" problem, which required the application…

Information on the HIV/AIDS epidemic in Southern Africa is often interpreted through a veil of secrecy and shame and, I argue, with flawed understanding of basic statistics. This research determined the levels of statistical literacy evident in 316 future Mathematical Literacy teachers' explanations of the median in the context of HIV/AIDS…

This paper identifies key concepts and issues associated with the reasoning of informal statistical inference. I focus on key ideas of inference that I think all students should learn, including at secondary level as well as tertiary. I argue that a fundamental component of inference is to go beyond the data at hand, and I propose that statistical…

In this reflective paper, we explore students' local and global thinking about informal statistical inference through our observations of 10- to 11-year-olds, challenged to infer the unknown configuration of a virtual die, but able to use the die to generate as much data as they felt necessary. We report how they tended to focus on local changes…

This paper is a personal exploration of where the ideas of "distribution" that we are trying to develop in students come from and are leading to, how they fit together, and where they are important and why. We need to have such considerations in the back of our minds when designing learning experiences. The notion of "distribution" as a lens…

This exploratory study, a one group pretest-posttest design, investigated the development of elementary preservice teachers' understandings of distribution as expressed in the measures and representations used to compare data distributions. During a semester-long mathematics methods course, participants worked in small groups on two statistical…

Recent research into students' reasoning about variation refers specifically to notions of distribution that emerge. This paper reports on research where written responses, from tertiary introductory statistics students, were coded according to the level of consideration of variation. A hierarchy of reasoning about distribution is proposed, based…

Our primary goal is to design a micro world which aspires to research thinking-in-change about distribution. Our premise, in line with a constructivist approach and our prior research, is that thinking about distribution must develop from causal meanings already established. This study reports on a design research study of how students appear to…

Drawing conclusions from the comparison of datasets using informal statistical inference is a challenging task since the nature and type of reasoning expected is not fully understood. In this paper a secondary teacher's reasoning from the comparison of box plot distributions during the teaching of a Year 11 (15-year-old) class is analyzed. From…