The purpose of this article is to illustrate the dynamic process involved in developing and utilizing a theoretical model in a mixed methods study. Specifically, I illustrate how the theoretical model can serve as the starting point in framing the study, as a lens for guiding the data collection and analysis, and as the end point in explaining the…

Research questions regarding how, for whom, and where a treatment achieves its effect on an outcome have become increasingly valued in substantive research. Such questions can be answered by causal moderated mediation analysis, which assesses the heterogeneity of the mediation mechanism underlying the treatment effect across individual and…

Statistical association is a key facet of statistical literacy: claims based on relationships between variables or ideas rooted in data are found everywhere in media and discourse. A key development in introductory statistics curricula is the use of simulation-based inference, which has shown positive outcomes for students, especially in regards…

The study reported in this article investigated the appropriateness of Mathematical Knowledge in Teaching of three pre-service primary school teachers (PSTs), teaching an informal statistical inference (ISI) lesson to primary school students. Using an ISI framework and the Knowledge Quartet framework, the presence and appropriateness of the PSTs'…

We consider two-level models where a continuous response R and continuous covariates C are assumed missing at random. Inferences based on maximum likelihood or Bayes are routinely made by estimating their joint normal distribution from observed data R[subscript obs] and C[subscript obs]. However, if the model for R given C includes random…

A growing body of research has examined the relationship between family socioeconomic status (SES) and educational outcomes. Meta-analyses of raw correlations generally indicate moderate associations, typically between 0.12 and 0.3 for academic achievement and around 0.18 to 0.4 for educational attainment. Causal inference studies, aimed at…

This paper discusses the place of precision in mathematics education by exploring its role in curricular guidelines and in classroom life. By means of a joke on precision delivered by a school student in South Sweden, our study focuses on student participation in mathematical tasks that require precision in processes of measuring and reasoning.…

Inferential comprehension is necessary to connect ideas in a text together in a meaningful manner. There have been multiple studies on inferential comprehension involving texts of different genres (narrative and expository), but not a coherent overview of the findings of inferential comprehension by genre. The purpose of this study is to provide a…

Collaboration is an increasingly popular topic in mathematics education due to its potential to foster students' learning. The purpose of this article is to draw attention to the semantic philosophical theory of inferentialism and its value for investigating students' collaboration. We suggest that Brandom's inferentialism can serve as a valuable…

In this study, researchers compared the concordance of teacher-level effectiveness ratings derived via six common generalized value-added model (VAM) approaches including a (1) student growth percentile (SGP) model, (2) value-added linear regression model (VALRM), (3) value-added hierarchical linear model (VAHLM), (4) simple difference (gain)…

With the widespread use of computers in modern assessment, online calibration has become increasingly popular as a way of replenishing an item pool. The present study discusses online calibration strategies for a joint model of responses and response times. The study proposes likelihood inference methods for item paramter estimation and evaluates…

Inferential comprehension is necessary to connect ideas in a text together in a meaningful manner. There have been multiple studies on inferential comprehension involving texts of different genres (narrative and expository), but not a coherent overview of the findings of inferential comprehension by genre. The purpose of this study is to provide a…

Beliefs about the controllability of positive or negative events in the environment can shape learning throughout the lifespan. Previous research has shown that adults' learning is modulated by beliefs about the causal structure of the environment such that they update their value estimates to a lesser extent when the outcomes can be attributed to…

Interpreting statistical graphs and making inferences based on the graphs are a precursor for formal statistical inferences. To support student inferences, both teachers and future teachers should have adequate knowledge regarding students' thinking on graphs as well as their potential misinterpretations and difficulties in interpreting graphs. In…

We examined the extent to which the timing of inferential questioning influenced kindergartners' inferencing performance in a non-reading context, while also taking into account individual differences in language comprehension and executive function. Students completed the eight-week Early Language Comprehension Individualized Instruction (ELCII)…