Some situations are presented with perplexing properties, which become clearer by looking at contingency tables. This in turn leads to problems that can be solved using conditional frequencies and thus leading to the Bayes formula with natural frequencies or probabilities.

This paper introduces AMMORE, a new dataset of 53,000 math open-response question-answer pairs from Rori, a mathematics learning platform used by middle and high school students in several African countries. Using this dataset, we conducted two experiments to evaluate the use of large language models (LLM) for grading particularly challenging…

This article is motivated by the importance of developing statistically literate students. The authors present a selection of problems that could be used to motivate student interest in probability as well as providing additional depth to the curriculum when used alongside traditional resources. The solutions presented utilise natural frequencies…

Investigators often rely on the proportion of correct responses in an assessment when describing the impact of early mathematics interventions on child outcomes. Here, we propose a shift in focus to the relative sophistication of problem-solving strategies and offer methodological guidance to researchers interested in working with strategies. We…

Students studying statistics often misunderstand what statistics represent. Some of the most well-known misunderstandings of statistics revolve around null hypothesis significance testing. One pervasive misunderstanding is that the calculated p-value represents the probability that the null hypothesis is true, and that if p < 0.05, there is…

Understanding a Bayesian perspective demands comfort with conditional probability and with probabilities that appear to change as we acquire additional information. This paper suggests a simple context in conditional probability that helps develop the understanding students would need for a successful introduction to Bayesian reasoning.

When researchers code behavior that is undetectable or falls outside of the validated ordinal scale, the resultant outcomes often suffer from informative missingness. Incorrect analysis of such data can lead to biased arguments around efficacy and effectiveness in the context of experimental and intervention research. Here, we detail a new…

We present an instructional approach to teaching causal inference using Bayesian networks and "do"-Calculus, which requires less prerequisite knowledge of statistics than existing approaches and can be consistently implemented in beginner to advanced levels courses. Moreover, this approach aims to address the central question in causal…

Modeling student learning processes is highly complex since it is influenced by many factors such as motivation and learning habits. The high volume of features and tools provided by computer-based learning environments confounds the task of tracking student knowledge even further. Deep Learning models such as Long-Short Term Memory (LSTMs) and…

Research Findings: Conversing abstract concepts boost children's language learning. Despite the numerous studies on the linguistic environment of early childhood education settings (ECE), most of this work disregards contextual factors that may influence abstract conversations and omits characteristics of children's verbal participation in these…

Current developments in the statistics community suggest that modern statistics education should be structured holistically, that is, by allowing students to work with real data and to answer concrete statistical questions, but also by educating them about alternative frameworks, such as Bayesian inference. In this article, we describe how we…

In "Maths for Business," a large first-year mathematics module, the continuous assessment component comprises 10 weekly quizzes which combine to contribute 40% of the final module mark. If students did not receive the full five marks on their weekly quiz, they were provided with the opportunity to resubmit their corrected weekly quiz…

In this article we discuss our attempt to incorporate research-informed learning and teaching activities into a final year undergraduate Statistics course. We make use of the Shiny web-based application framework for R to develop "Shiny apps" designed to help facilitate student interaction with methods from recently published papers in…

Achieving fluency in important mathematical procedures is fundamental to students' mathematical development. The usual way to develop procedural fluency is to practise repetitive exercises, but is this the only effective way? This paper reports three quasi-experimental studies carried out in a total of 11 secondary schools involving altogether 528…

This study explored a diagnostic assessment method that emphasized the cognitive process of algebra learning. The study utilized a design and a theory-driven model to examine the content knowledge. Using the theory driven model, the thinking skills of algebra learning was also examined. A Bayesian network model was applied to represent the theory…