- Prof Dev
The goal of this article is to introduce the topic of learning to reason from samples, which is the focus of this special issue of Educational Studies in Mathematics on statistical reasoning. Samples are data sets, taken from some wider universe (e.g., a population or a process) using a particular procedure (e.g., random sampling) in order to be able to make generalizations about this wider universe with a particular level of confidence. Sampling is henceakeyfactorinmakingreliablestatisticalinferences.Wefirstintroducethethemeandthe key questions this special issue addresses. Then, we provide a brief literature review on reasoning about samples and sampling. This review sets the grounds for the introduction of thefivearticlesandtheconcludingreflectivediscussion.Weclosebycommentingontheways to support the development of students’ statistical reasoning on samples and sampling.
This paper describes the importance of developing students’ reasoning about samples and sampling variability as a foundation for statistical thinking. Research on expert–novice thinking as well as statistical thinking is reviewed and compared. A case is made thatstatisticalthinkingisatypeofexpertthinking,andassuch,researchcomparingnoviceand expert thinking can inform the research on developing statistical thinking in students. It is also posited that developing students’ informal inferential reasoning, akin to novice thinking, can help build the foundations of experts’ statistical thinking.
Research on informal statistical inference has so far paid little attention to the development of students’ expressions of uncertainty in reasoning from samples. This paper studies students’ articulations of uncertainty when engaged in informal inferential reasoning. Using data from a design experiment in Israeli Grade 5 (aged 10–11) inquiry-based classrooms, we focus on two groups of students working with TinkerPlots on investigations with growing sample size. From our analysis, it appears that this design, especially prediction tasks, helped in promoting the students’ probabilistic language. Initially, the students oscillated between certainty-only (deterministic) and uncertainty-only (relativistic) statements. As they engaged further in their inquiries, they came to talk in more sophisticated ways with increasing awareness of what is at stake, using what can be seen as buds of probabilistic language. Attending to students’ emerging articulations of uncertainty in making judgments about patterns and trends in data may provide an opportunity to develop more sophisticated understandings of statistical inference.
This article describes a model for an interactive inquiry-based statistics learning environment that is designed to develop students’ statistical reasoning. This model is called a “Statistical Reasoning Learning Environment” (SRLE) and is built on the socio-constructivist theory of learning and teaching. This model is based on six principles of instructional design: fundamental statistical ideas, motivating real data sets, inquiry- and data-based classroom activities, innovative technological tools, classroom norms, and alternative assessment. Two examples of SRLEs are briefly discussed.
Informal statistical inference (ISI) has been a frequent focus of recent research in statistics education. Considering the role that context plays in developing ISI calls into question the need to be more explicit about the reasoning that underpins ISI. This paper uses educational literature on informal statistical inference and philosophical literature on inference to argue that in order for students to generate informal statistical inferences, there are a number of interrelated key elements that are needed to support their informal inferential reasoning (IIR). In particular, we claim that ISI is nurtured by statistical knowledge, knowledge about the problem context, and useful norms and habits developed over time, and supported by an inquiry-based environment (tasks, tools, scaffolds). We adopt Peirce’s view that inquiry is a sense-making process driven by doubt and belief, leading to inferences and explanations. To illustrate the roles that these elements play in supporting students to generate informal statistical inferences, we provide an analysis of three sixth graders’ (aged 12) informal inferential reasoning—the reasoning processes leading to their informal statistical inferences.