Simulation studies are the basic tools of quantitative methodologists used to obtain empirical solutions to statistical problems that may be impossible to derive through direct mathematical computations. The successful execution of many simulation studies relies on the accurate generation of correlated multivariate data that adhere to a particular…

The practice of statistics has the power to motivate and support learning across the STEM (Science, Technology, Engineering, and Mathematics) disciplines. When connected with meaningful science contexts, statistical problem solving through the collection of data and subsequent data analysis, supported by contemporary graphing technology, presents…

Background/purpose: This study aims to examine the inferential statistical literacy of mathematics education students based on their cognitive styles--field-dependent (FD) and field-independent (FI). Inferential statistical literacy involves not only understanding statistical concepts such as hypothesis testing and parameter estimation but also…

Background: A single-case design focuses on individual performance and measures the causal relationships between variables (Kazdin, 2019). This experimental design enables researchers to measure the learning behaviors of individual participants over time across phases and assess the effectiveness of an instructional strategy in improving or…

Instructors traditionally lecture on new content before providing practice problems, but learning is often superficial. Exploratory learning before instruction deepens conceptual understanding by giving students a novel activity to explore before direct instruction. We examined how increasing the salience of contrasting cases in exploration versus…

As is rapidly becoming clear, data science increasingly permeates many aspects of life. Educational research recognizes the importance and complexity of learning data science. In line with this imperative, there is a growing need to investigate the factors that influence student performance in data science tasks. In this paper, we aimed to apply…

It has been established that, in Bayesian tasks, performance and typical errors in reading information from filled visualizations depend both on the type of the provided visualization and information format. However, apart from reading visualizations, students should also be able to create visualizations on their own and successfully use them as…

Background: Metacognitive processes have been linked to the development of conceptual knowledge in STEM courses, but previous work has centered on the regulatory aspects of metacognition. Purpose: We interrogated the relationship between epistemic metacognition and conceptual knowledge in engineering statics courses across six universities by…

Bayesian Knowledge Tracing (BKT) is a well-established model for formative assessment, with optimization typically using expectation maximization, conjugate gradient descent, or brute force search. However, one of the flaws of existing optimization techniques for BKT models is convergence to undesirable local minima that negatively impact…

Computational Thinking (CT) skills are increasingly recognized as essential for junior high school students, especially in addressing the demands of the digital era. This study explores how CT skills--decomposition, pattern recognition, abstraction, and algorithmic thinking--manifest in learning statistics based on students' cognitive abilities. A…

Preparing the new generation to be data-literate citizens is a pressing challenge, and some explorations have been made to cultivate K-12 students' data science skills and attitudes. However, there is a lack of instructional models to guide the design of data science programs in K-12 due to its complex and interdisciplinary nature as well as the…

A hallmark of effective teaching is that it grants learners not just a collection of facts about the world, but also a toolkit of abstractions that can be applied to solve new problems. How do humans teach abstractions from examples? Here, we applied Bayesian models of pedagogy to a necklace-building task where teachers create necklaces to teach a…

This article details an exploratory data analysis project using the Common Online Data Analysis Platform (CODAP) based on the "Guidelines for Assessment and Instruction in Statistics Education" (GAISE) four-part statistical problem-solving model. The project goal was to answer what similarities and differences exist within the school…

The ability to properly evaluate one's own academic progress has long been considered a predictor of academic success. However, its distinctive role in the context of computational mathematics remains underexplored. Grounded in social cognitive theory, this study investigates the critical role of self-regulated learning (SRL) strategies in…

Algebra has been identified as a gatekeeper to careers in STEM, but little research exists on how algebra appears for practitioners in the workplace. Surveys and interviews were conducted with 77 STEM practitioners from a variety of fields, examining how they reported using algebraic functions in their work. Survey and interview reports suggest…