Inferentialism has emerged as a valuable theoretical resource in mathematics education. As a theory of meaning about the use and content of concepts, it offers a fresh perspective on traditional epistemological and linguistic questions in the field. Despite its emergence, important inferentialist ideas still need to be operationalized. In this…

When planning a cluster randomized trial, evaluators often have access to an enumerated cohort representing the target population of clusters. Practicalities of conducting the trial, such as the need to oversample clusters with certain characteristics in order to improve trial economy or support inferences about subgroups of clusters, may preclude…

This paper reports on a study concerning the social nature of young students' informal inferential reasoning. Employing inferentialism as a background theory, we examine cognitive and sociocultural aspects of reasoning that arose during group discussions as well as trace relations between those aspects. Following a design experiment approach, we…

Teachers who engage primary school students in informal statistical inference (ISI) must themselves have good content knowledge of ISI (ISI-CK). However, little is known about how college education for pre-service teachers can contribute to the development of their ISI-CK. To address this shortcoming, we used a case study to investigate ISI-CK…

To identify the ways teachers and educational systems can improve learning, researchers need to make causal inferences. Analyses of existing datasets play an important role in detecting causal patterns, but conducting experiments also plays an indispensable role in this research. In this article, we advocate for experiments to be embedded in real…

Analysis of variance (ANOVA) is a test of "mean" differences, but the reference to "variances" in the name is often overlooked. Classroom activities are presented to illustrate how ANOVA works with emphasis on how to think critically about inferential reasoning.

Students recognise and analyse data and draw inferences. They represent, summarise and interpret data and undertake purposeful investigations involving the collection and interpretation of data… They develop an increasingly sophisticated ability to critically evaluate chance and data concepts and make reasoned judgments and decisions, as well as…

This theoretical paper relates recent interest in informal statistical inference (ISI) to the semantic theory termed inferentialism, a significant development in contemporary philosophy, which places inference at the heart of human knowing. This theory assists epistemological reflection on challenges in statistics education encountered when…

How can humans acquire relational representations that enable analogical inference and other forms of high-level reasoning? Using comparative relations as a model domain, we explore the possibility that bottom-up learning mechanisms applied to objects coded as feature vectors can yield representations of relations sufficient to solve analogy…

From the perspectives of the philosophy of science and statistical inference, we discuss the challenges of making prescriptive statements in quantitative research articles. We first consider the prescriptive nature of educational research and argue that prescriptive statements are a necessity in educational research. The logic of deduction,…

This article sets out some of the rationale and arguments for making major changes to the teaching and learning of statistical inference in introductory courses at our universities by changing from a norm-based, mathematical approach to more conceptually accessible computer-based approaches. The core problem of the inferential argument with its…

Sampling tasks and sampling distributions provide a fertile realm for investigating students' conceptions of variability. A project-designed teaching episode on samples and sampling distributions was team-taught in 6 research classrooms (2 middle school and 4 high school) by the investigators and regular classroom mathematics teachers. Data…

The purpose of the present paper is to critically examine causal inferences and internal validity as defined by Campbell and co-workers. Several arguments are given against their counterfactual effect definition, and this effect definition should be considered inadequate for causal research in general. Moreover, their defined independence between…

Causal inference is of central importance to developmental psychology. Many key questions in the field revolve around improving the lives of children and their families. These include identifying risk factors that if manipulated in some way would foster child development. Such a task inherently involves causal inference: One wants to know whether…

A recent study by Apperly et al. (2006) found evidence that adults do not automatically infer false beliefs while watching videos that afford such inferences. This method was extended to examine true beliefs, which are sometimes thought to be ascribed by "default" (e.g., Leslie & Thaiss, 1992). Sequences of pictures were presented in which the…