This paper reports on an exploratory study about probabilistic intuition in learning mathematics for decision-making. The analysis was carried out on a group of high school students in relation to their probabilistic intuition in problem-solving, after performing playful learning activities on a simulation platform specifically designed for this…

This paper delves into statistical disparities between human-written and ChatGPT-generated texts, utilizing an analysis of Shannon's equitability values, and token frequency. Our findings indicate that Shannon's equitability can potentially be a differentiating factor between texts produced by humans and those generated by ChatGPT. Additionally,…

Propensity score matching and weighting methods are often used in observational effectiveness studies to reduce imbalance between treated and untreated groups on a set of potential confounders. However, much of the prior methodological literature on matching and weighting has yet to examine performance for scenarios with a majority of treated…

Although possible to recall in both forward and backward order, recall proceeds most naturally in the order of encoding. Prior studies ask whether and how forward and backward recall differ. We reexamine this classic question by studying recall dynamics while varying the predictability and timing of forward and backward cues. Although overall…

The current literature on test equating generally defines it as the process necessary to obtain score comparability between different test forms. The definition is in contrast with Lord's foundational paper which viewed equating as the process required to obtain comparability of measurement scale between forms. The distinction between the notions…

The extraction of cooccurrences between two events, A and B, is a central learning mechanism shared by all species capable of associative learning. Formally, the cooccurrence of events A and B appearing in a sequence is measured by the transitional probability (TP) between these events, and it corresponds to the probability of the second stimulus…

In pursuing goals, people seek favorable odds. We investigated whether young children use this fact to infer goals from people's actions across two experiments on Canadian 3- to 7-year-old children (N = 316; 167 girls, 149 boys). Participants' demographic information was not formally collected, but the region is predominantly middle-class and…

Many challenges are identified when students solve mathematic problems especially in solving probability word problems. This study was conducted to identify the major challenges faced by matriculation college students while solving the probability of an event word problem. Seven matriculation college students were the sample for this case study.…

This work reports the results of an investigation that aimed to know the informal reasoning of high school students with and about the frequency approach of probability and the law of large numbers when they were faced with a problem about random intervals. The research question was as follows: What features of students' reasoning about the…

This paper examines coin-toss comparison questions from two recent studies involving undergraduate students and high school teachers and connects to findings from two prior studies in the literature. Considering possible sample spaces employed by participants, this is a reflection on whether one sequence could be more likely depending on the…

The Premack principle states that any Response A can reinforce any other Response B if the independent rate of A is greater than the independent rate of B (Premack, 1959). Applying the Premack principle involves arranging the environment to restrict access to certain responses based on relative probabilities of a set of given responses (Timberlake…

The ability to relate physical concepts and phenomena to multiple mathematical representations--and to move fluidly between these representations--is a critical outcome expected of physics instruction. In upper-division quantum mechanics, students must work with multiple symbolic notations, including some that they have not previously encountered.…

Background: Adverse childhood experiences (ACEs) have been associated with poor health outcomes in the general population. However, their impact on autistic youth remains unclear. Objective: The primary objective was to understand how childhood adversity is related to the general health, mental health, and physical health of transition-age…

This article proposes a fully nonparametric model to investigate the dynamics of intergenerational income mobility for discrete outcomes. In our model, an individual's income class probabilities depend on parental income in a manner that accommodates nonlinearities and interactions among various individual and parental characteristics, including…

The aim of this article is to buid a Guide to the Analysis of Probability Textbook Lessons for secondary education (students aged 12-14), using the framework of Didactic Suitability. The facets, components and indicators of the didactic suitability construct are applied to categorize and organize didactic-mathematical knowledge on teaching and…