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…

In the last years special "ovals" appear increasingly often in diagrams and applets for discussing crucial items of statistical inference (when dealing with confidence intervals for an unknown probability p; approximation of the binomial distribution by the normal distribution; especially in German literature, see e.g. [Meyer,…

This note is concerned with the study of temporal development in several indices reflecting clustering effects in multilevel designs that are frequently utilized in educational and behavioral research. A latent variable method-based approach is outlined, which can be used to point and interval estimate the growth or decline in important functions…

This theoretical, methodological, and empirical networking study investigated the potential of inferentialism to contribute to the study of meaning and collective argumentation in mathematics. I carefully attended to my worldview and explicated my philosophical process for identifying inferentialism as my theory of choice. I then drew on Prediger…

Under the noisy-channel framework of language comprehension, comprehenders infer the speaker's intended meaning by integrating the perceived utterance with their knowledge of the language, the world, and the kinds of errors that can occur in communication. Previous research has shown that, when sentences are improbable under the meaning prior…

Given decision-makers often prioritize causal research that identifies the impact of treatments on the people they serve, a key question in education research is, "Does it work?". Today, however, researchers are paying increasing attention to successive questions that are equally important from a practical standpoint--not only does it…

The Gini index is probably the most commonly used indicator to measure inequality. For continuous distributions, the Gini index can be computed using several equivalent formulations. However, this is not the case with discrete distributions, where controversy remains regarding the expression to be used to estimate the Gini index. We attempt to…

The ability to predict upcoming events is essential in infancy because it enables babies to process information optimally and have successful goal-directed interactions with their environment. In this article, we examine how infants generate predictions in perception, cognition, and action, and address whether and how their predictions are…

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…

With the latest advances in conversational agents like Siri and Alexa, and Large Language Models (LLMs) like ChatGPT and PaLM, Question Answering (QA) systems have become more important. Users submit millions of queries per day and it is up to the system to provide reliable, to-the-point answers. In this dissertation, we explore various aspects to…

Sensitivity analysis, a statistical method crucial for validating inferences across disciplines, quantifies the conditions that could alter conclusions (Razavi et al., 2021). One line of work is rooted in linear models and foregrounds the sensitivity of inferences to the strength of omitted variables (Cinelli & Hazlett, 2019; Frank, 2000). A…

Differential equations (DEs) are a powerful tool for modeling real-world contexts. Most research in this area has examined students' understanding and reasoning with pre-packaged DEs, with little attention being given to setting up sophisticated DEs to model complicated real-world situations. This study contributes through a collective case study…

Causal inference is a central topic in education research, although oftentimes it relies on observational studies, which makes causal identification methodologically challenging. This manuscript introduces causal graphs as a powerful language for elucidating causal theories and an effective tool for causal identification analysis. It discusses…

Statistics education researchers have been challenged to consider the theory of inferentialism in understanding concept formation in students. A critique of inferentialism is that no comprehensive method has been formulated to use the theory in practice. In this paper an inferentialism-based framework is presented that appears to be capable of…