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…

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…

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 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…

This paper aims to shed light on an overlooked but essential aspect of informal reasoning and its radical implication to mathematics education research: Decentralising mathematics. We start to problematise that previous studies on informal reasoning implicitly overfocus on what students infer. Based on Walton's distinction between reasoning and…

Knowing functions and functional thinking have recently moved from just knowledge for older students to incorporating younger students, and functional thinking has been identified as one of the core competencies for algebra. Although it is significant for mathematical understanding, there is no unified view of functional thinking and how different…

This study is a contribution to efforts to promote practices for dealing with the difficulties encountered by learners in probabilistic modeling situations. We attempt to elucidate as precisely as possible the types of difficulties that secondary school students face in the process of modeling with probability tools. By referring to a large and…

Recently, the importance of statistical literacy has been stressed, and three central concepts in statistical literacy are the measures of central tendency: mean, median, and mode. This study explores aspects of statistical literacy expressed by 12-13-year-old students, focusing on mean, median, and mode. Their responses were analysed using a…

Manipulative-based instructional sequences have proven to be successful with students with disabilities. However, instruction must not only support the acquisition of conceptual and procedural knowledge but also build on students' strengths. This article describes how teachers can use manipulative-based instructional sequences to support the…