Eigentheory concepts are central in mathematics and physics; they serve multiple functions, such as symbolizing physical phenomena and facilitating mathematical computations. Words and meanings associated with eigentheory develop and vary over time, as do their associated symbols. In this study, we investigate how "eigen" develops over…

This paper initiates a teaching sequence that focuses on building up equivalent definitions to the standard ones for the limit concept in Real Analysis. It comprises two parts: The first provides a classroom assignment where students, guided by Analysis lecturers, are led to develop an alternative definition to the [epsilon] - [delta] one for…

Mathematical ideas are developed and spread during argumentative whole class discussions between a teacher and her students. The goal of the current study is to characterize how ideas about quadratic functions emerge and are spread during a whole-class discussion among ninth graders. To this end, we recorded both discussions between pairs of…

This article presents a theoretical-didactic perspective on the formation and development of concepts concerning mathematical objects as a result of research on didactic difficulties in dealing with concepts in school. The theoretical foundation that supports the research is based on the contributions of the materialist approach to the theory of…

As students have struggled to use the "chip model" (i.e., red and yellow chips representing positive and negative numbers) to model integer addition and subtraction and have found it confusing, the authors developed a series of activities based on adding and removing opposite objects to and from a boat to better help students in this…

We introduce learning modules in cryptography that can be crafted to motivate many abstract mathematical ideas, and we illustrate with a sample module. These modules can be used in a variety of ways, such as the core for a cryptography course or as motivating topics in other courses such as abstract and linear algebra or number theory.

The study examines the levels of understanding logarithmic expressions within the frames of a mathematical card game. The game is based on the popular card game Saboteur. In this paper, we analyse the progress of a group of six undergraduate students participating in a remedial course using games for recalling some fundamental mathematical…

Pre-service teachers (PSTs) often encounter challenges grasping the conceptual understanding of fractions, which can affect their readiness to teach this topic. This study investigates a novel approach to enhancing PSTs' comprehension of fractions by focusing on the fraction-as-a-measure meaning within a measurement context. Through a modified…

There has been a consensus that students' conceptual understanding of mathematical operations (such as multiplication) can be developed through communication about multiple representations. However, learning opportunities have often appeared to be limited to surface translations (in which only obvious similarities such as numbers have been…

This article discusses two mechanisms through which understanding static mathematical concepts (basic and more advanced mathematical concepts) in terms of fictive motions or motion events enhance our understanding of these concepts. It is suggested that at least two mechanisms are involved in this enhancing process. The first mechanism enables us…

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…

First-year college students experience difficulties in understanding the concepts of derivatives and integrals. At the postsecondary level, the use of static visualization and other traditional instruction delivery methods often are unable to meet students' needs in calculus. This problem is current and essential in the field of education and…

Cutting-edge technology enhances the teaching-learning process, with Multimedia-Based Instruction (MMBI) emerging as a powerful tool to achieve educational goals. MMBI creates visually engaging, resource-rich materials that support students in understanding abstract mathematical concepts, boosting interest and curiosity. According to Mayer (2001),…

Baseball. Subway line. Maps. A flower. Each of these contexts involves some form of varying motion or constant change over time: the bi-directional motion of a fly ball, the speed of a subway car, or the growth of a flower until bloom. This article does not highlight students' calculus problem-solving abilities, but rather describes a set of…

This paper examines Grade 10 students' conceptions of proof in a secondary school in Singapore. Using a purposive survey of 9 mathematical items, proofs by 8 students for two items, one on Number and Algebra and another on Geometry and Trigonometry, were coded using Harel's proof schemes. The findings show that the students' proofs for the two…