Our research in statistical cognition uses both qualitative and quantitative methods. A mixed method approach makes our research more comprehensive, and provides us with new directions, unexpected insights, and alternative explanations for previously established concepts. In this paper, we review four statistical cognition studies that used mixed…

This study examined students' development of reasoning about quantitative bivariate data during a one-semester university-level introductory statistics course. There were three research questions of interest: (1) What is the nature, or pattern of change in students' development in reasoning throughout the course?; (2) Is the sequencing of…

Practitioners and teachers should be able to justify their chosen techniques by taking into account research results: This is evidence-based practice (EBP). We argue that, specifically, statistical practice and statistics education should be guided by evidence, and we propose statistical cognition (SC) as an integration of theory, research, and…

Informal inferential reasoning is a relatively recent concept in the research literature. Several research studies have defined this type of cognitive process in slightly different ways. In this paper, a working definition of informal inferential reasoning based on an analysis of the key aspects of statistical inference, and on research from…

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…

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…

Little is known about the way that teachers articulate notions of variation in their own words. The study reported here was conducted with 17 prospective secondary math and science teachers enrolled in a preservice teacher education course which engaged them in statistical inquiry of testing data. This qualitative study examines how these…

This article discusses five papers focused on "Research on Reasoning about Variation and Variability", by Hammerman and Rubin, Ben-Zvi, Bakker, Reading, and Gould, which appeared in a special issue of the "Statistics Education Research Journal" (No. 3(2) November 2004). Three issues emerged from these papers. First, there is a link between the…

The study describes the nature of pre-service teachers' idiosyncratic metaphors for the concept of statistical sample. These metaphors were investigated because of their potential to provide insight about individuals' content knowledge and how that content knowledge is enacted during teaching. Personal metaphors were elicited from 54 pre-service…

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'…

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…