The multiplication principle (MP) is foundational for combinatorial problem-solving. From a units-coordination perspective, applying the MP with justification entails establishing unit relationships between the number of options at each independent stage of a counting process and the total number of combinatorial outcomes. Existing research…

Many scientific concepts and theorems are often abstract and challenging to relate to real-life problems, making it difficult for students to grasp them. Therefore, some researchers have attempted to enhance students' understanding by employing a contextual learning approach, which allows students to apply scientific knowledge to real situations…

A quantitative literacy course titled "Computational Geology" has been taught at the University of South Florida for over 20 years at the undergraduate level, largely by the same professor. Due to the extended course tenure, a unique opportunity presented itself to qualitatively study what the perceived broader impacts of the course were…

The contents of calculus, known for their complexity, present significant challenges for students, particularly in mastering multiple integrals and effectively visualizing related concepts. The transition to distance learning prompted by the COVID-19 pandemic has further complicated the learning process in multiple integrals. In line with this and…

Due to their mostly normative and legitimatory nature, public policies at large and education policies in particular are liable to frame perceived problems in the social domain as seen through the policy-making elite's perspective and seek to advance solutions to them. On the surface, the staged process of policy design, implementation, and…

Graded Troubleshooting (GTS) is a powerful routine that teachers can use easily to engender students' metacognitive thinking and boost their understanding of mathematics concepts and procedures. This article describes a new GTS activity designed to prompt students to efficiently exploit worked examples when asked to diagnose erroneous examples…

The ability to reason with representations is pivotal for successful learning in Organic Chemistry and is closely linked to representational competence. Given the visual nature of this discipline, this comprises competency in extracting and processing relevant visual information. With regard to the resonance concept, proficiency in identifying…

The problem solving performed by students in solving mathematical literacy problems shows that at the developmental stage of proportional reasoning students have different strategies, especially at the developmental stage of functional and scalar relationships. The purpose of this study is to identify and explore the developmental stages of…

This paper presents the findings of a study involving 16 undergraduate students enrolled in a basic financial mathematics course. The study aimed to examine the nature of the students' problem-posing and problem-solving products and processes, as well as the interactions between the two. The findings revealed that the majority of the posed…

In this study, temporal speech cues were integrated into online curriculum to solve non-routine problems in curricular multimedia. Teachers-in-training (n=56) were randomly assigned to one of three treatment conditions. It was expected that participants in the temporal speech cues condition would be more likely to solve problems than those in the…

In this cross-national study, we explore the different ways of reasoning-and-proving (RP) presented in three 8th grade textbooks, one from each country: Turkey, Norway, and Slovakia. While the analysis revealed that all three textbooks contain similar numbers of problems involving some form of RP, differences exist in terms of the dominating ways…

Over the past few years, the author and her colleagues have been engaged in a teaching and research project that explores what it means to "connect math to the real world" and how to effectively design and implement mathematics lessons that integrate real-world, sociopolitical issues with mathematics in elementary classrooms.…

Background/purpose: The application of learning models is expected to significantly promote the enhancement of students' problem-solving abilities through the development of interactive learning models. This study aims to (1) determine whether the Development of the Component Display Theory (CDT) Model is categorized as valid, practical, and…

Background: Self-regulation is identified in the literature as an early predictor of later in life success and an important skill that develops over the course of a lifetime but begins in early childhood. Objective: The purpose of this research study was to assess whether direct instruction of Mindfulness Practices, such as guided meditation and…

One expected outcome of physics instruction is that students develop quantitative reasoning skills, including strategies for evaluating solutions to problems. Examples of well-known "canonical" evaluation strategies include special case analysis, unit analysis, and checking for reasonable numbers. We report on responses from three tasks…