Various features have been found hidden in the Pascal triangle. In this paper, some very well-known properties of the Pascal triangle will be presented, as well as the properties related to different extensions of the triangle, namely the Pascal pyramid. Given that in the textbooks of the tenth grade, respectively in the school, where we realised…

The most common challenges students face in solving first-order ordinary differential equations (ODEs) can be overcome by identifying the types of errors, understanding the factors that cause difficulties, and finding appropriate solutions. Therefore, this research aimed to adopt a descriptive qualitative approach, including nine sixth-semester…

This study aims to give chemistry students a deeper understanding of electron shielding and quantum transitions by interpreting the characteristic X-ray lines. There is a popular misunderstanding among learners and even teachers in which an outer-shell electron fills a vacancy in the inner shell, releasing some of its energy as an X-ray photon.…

While research on the opportunity to learn about mathematics concepts provided by textbooks at the secondary level is well documented, there is still a paucity of similar research at the undergraduate level. Contributing towards addressing this knowledge gap, the present study examined opportunities to engage in quantitative and covariational…

The present study seeks to explore the mathematical connections that 13-14-year-old secondary school students establish when solving area tasks. Emphasis is placed on different mathematical objects, and the connections between them, that allow students to successfully solve the tasks. The study follows a mixed methodology using qualitative and…

We are all fascinated by loops and their formation in space. When a line cuts itself, it forms an intersection point and creates a space. This is an experimental study done by analyzing several loops, forming a concrete formulation by visualizing the patterns observed, and then proving the formulations proposed using the known standard…

Solving math word problems (MWPs) involves uncovering logical relationships among quantities in natural language descriptions of math problems. Recent studies have demonstrated that the contrastive learning framework can assist models in identifying semantically similar examples while distinguishing between different mathematical logics. This…

In recent decades, there has been considerable research that explores the teaching and learning of combinatorics. Such work has highlighted the fact that understanding and justifying combinatorial formulas can be challenging for students, and there is a need to identify ways to support students' combinatorial reasoning. In this paper, we…

Proportional reasoning has been greatly influencing the development of students' mathematical abilities. Along with the area conservation ability, it helps elementary students comprehend area measurement. This exploratory study aimed to produce qualitative-descriptive data on elementary students' proportional reasoning in solving the conservation…

This study investigates the problem-solving strategies employed by ninth-grade students when addressing symbolic and real-world contextual problems involving trigonometric ratios. Conducted with 46 ninth-grade students from a Turkish public high school, this research employed a worksheet consisting of six problems aligned with the Turkish…

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…

This article proposes an in-depth mathematics analysis of simple and compound interest through an exploration of the mathematical structures underlying these concepts. Financial numeracy concepts (simple and compound interest, interest rates, interest period, present and future value, etc.) have been added to the mathematics curriculum of the…

Procedural fluency and strategic competence in operating and mathematizing with natural and rational numbers are based on a flexible and meaningful use of mental models, strategies, and procedures. The study to be presented in this paper pursued the question as to which subdomains or tasks relating to procedural fluency and strategic competence at…

This study explores the integration of game play into an inclusive, hands-on computing project in Calculus class. The project is focused on designing and analyzing priority switches for applications competing for computational resources on embedded devices such as smart watches and tablets. By engaging students in real-world problem-solving…

Examining students' inclinations to use algorithms and rules to solve a task was a fruitful area of research in chemical education in the last four decades. This research aimed to examine whether students read the task request carefully, considering its meaningfulness, or they approach it mechanically, applying a set of algorithms by default. The…