In this report, we analyze students' learning of compound probability by describing connections they generated while engaged with tasks involving two independent events. Several of their connections were compatible with the development of expertise, such as recognizing the need to determine sample spaces across a variety of situations and noting…

This paper reports the statistical and probabilistic reasoning of young children in terms of randomness, variability, and data representations in the context of informal inferential reasoning (IIR). Using the IIR approach, a task was designed and conducted one-on-one with 28 children aged 5 to 6 years old, in a case study setting. The researcher…

This paper reports on a study that investigated young children's responses to a range of probabilistic tasks. A central aspect of the study was our examination of the children's use of subjective thinking. Most research that has been conducted in relation to young children's probabilistic thinking has focused on the extent to which young children…

To promote the development of young children's probabilistic intuitions through experience, we focus on the dual nature of probability related to both belief (subjective notion) and frequency (objective notion). This paper reports on the responses of 7-8-year-olds on two tasks used to bridge subjective and objective notions of probability. We…

In Italy, parents are free to choose the primary school for their children without restrictions imposed by catchment areas. This freedom of choice, inspired by quasi-market mechanisms, aims to foster competition between schools and raise educational standards. Analysing the case of Milan using regression models and administrative data for the…

Due to shifts in society's attitudes toward special education and changes in U.S. federal policies, such as the Individuals with Disabilities Education Act and No Child Left Behind, more students with disabilities (SWDs) are beginning kindergarten in general education classrooms. As a result, schools and districts across the United States have…

The current study examined whether bystander behaviours in class were associated with being perpetrators of ethnic victimization and whether they moderated the association between disengagement from morality and perpetrating ethnic-based victimization. The sample included 1065 adolescents residing in Sweden (M[subscript age] = 13.12, SD=.42; 55%…

Many generalization studies in education are typically based on a sample of 30-70 schools while the inference population is at least twenty times larger. This small sample to population size ratio limits the precision of design-based estimators of the population average treatment effect. Prior work has shown the potential of small area estimation…

Findings on children's proportional reasoning abilities strongly vary across studies. This might be due to the different contexts that can be used in proportional problems: fair-sharing, mixtures, and probability. A review of the scientific literature suggests that the context of proportional problems may not only impact the difficulty of the…

Various sources suggest preparing teachers of early- or primary-age students to teach probability and statistics involves various challenges. Some of the approaches researchers take for resolving these challenges include developing preservice teacher content knowledge, pedagogical knowledge, as well as providing other opportunities to learn.…

This article deals with an introduction of probability at school through sensory modalities. This approach is based on sampling fluctuation with empirical observations of frequencies. Initially, we analyze how students from high school work on such a task by using dice, pencil, and paper. We then identify the use of schemas and data visualization…

Multiple factors influence a student's success in high school graduation. Individual factors such as disability, racial or ethnic identity, and gender may result in inequity in the school environment, interfering with learning and possibly leading to poorer educational outcomes. This secondary analysis of student educational records (N = 3,782)…

Causal inference involves determining whether a treatment (e.g., an education program) causes a change in outcomes (e.g., academic achievement). It is well-known that causal effects are more challenging to estimate than associations. Over the past 50 years, the potential outcomes framework has become one of the most widely used approaches for…

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 paper asks whether improving the quality of public schools can be an effective long-run crime-prevention strategy in the U.S. Specifically, we examine the effect of school quality improvements early in children's lives on the likelihood that they are arrested as adults. We exploit quasi-experimental variation in school quality due to…