A design experiment where students in Grade 5 (11-12 years old) play the Color Run game constitutes the context for investigating how students can be introduced to informal hypothesis testing. The result outlines a three-step hypothetical learning trajectory on informal hypothesis testing. In the first step, students came to favor sample space…

This article reports on a study in which third-grade students (8-9 years) were given a degree of agency in conducting chance experiments and representing the outcomes. Students chose their own samples of 12 coloured counters, ensuring all colours were represented. They predicted the outcomes of item selection, tested their predictions, explained…

The internal validity of observational study is often subject to debate. In this study, we define the counterfactuals as the unobserved sample and intend to quantify its relationship with the null hypothesis statistical testing (NHST). We propose the probability of a robust inference for internal validity, that is, the PIV, as a robustness index…

This study examines informal hypothesis testing in the context of drawing inferences of underlying probability distributions. Through a small-scale teaching experiment of three lessons, the study explores how fifth-grade students distinguish a non-uniform probability distribution from uniform probability distributions in a data-rich learning…

A fundamental aspect of statistical inference is representation of real-world data using statistical models. This article analyzes students' articulations of statistical models and modeling during their first steps in making informal statistical inferences. An integrated modeling approach (IMA) was designed and implemented to help students…

Latent transition analysis (LTA) was initially developed to provide a means of measuring change in dynamic latent variables. In this article, we illustrate the use of a cognitive diagnostic model, the DINA model, as the measurement model in a LTA, thereby demonstrating a means of analyzing change in cognitive skills over time. An example is…

Differential bundle functioning (DBF) analyses were conducted to determine whether seventh and eighth grade second language learners (SLLs) had lower probabilities of answering bundles of math word problems correctly that had heavy language demands, when compared to non-SLLs of equal math proficiency. Math word problems on each of four test forms…

Children's decisions regarding the allocation of societal resources in the context of preexisting inequalities were investigated. African American and European American children ages 5 to 6 years (n = 91) and 10 to 11 years (n = 94) judged the acceptability of a medical resource inequality on the basis of race, allocated medical supplies,…

The purpose of this case study was to determine the effectiveness of a combined intervention in remediating the social skills in a first-grader with a disorder from the autism spectrum disorders (ASDs). The researcher also aimed to identify the changes observed during the intervention period. The combined intervention consisted of reading…

Behavioral, psychophysiological, and neuropsychological studies have revealed large developmental differences in various learning paradigms where learning from positive and negative feedback is essential. The differences are possibly due to the use of distinct strategies that may be related to spatial working memory and attentional control. In…

In an effort to improve academic performance for students receiving special education services, a large urban school district in Tennessee has implemented Integrated Service Delivery Model. The purpose of this study was to compare the performance of students receiving instruction in self-contained classrooms to the performance of students…

Two experiments explored whether children's correct answers to counter factual and future hypothetical questions were based on an understanding of possibilities. Children played a game in which a toy mouse could run down either 1 of 2 slides. Children found it difficult to mark physically both possible outcomes, compared to reporting a single…