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…

The problem here dealt with concerns physics education, and specifically the concept of force. The idea behind this research is that a historical approach to the teaching of such a notion is of great help for the students to fully understand the meaning of this basic physical magnitude. For, most of scientific concepts can be better grasped by the…

Here we investigate how college students may conceptualize symbolic algebraic properties. This work uses the theory of Grundvorstellungen (GVs) to analyze how learners' conceptions may or may not align with some desired goals of instruction. Through the analysis of interviews with students across a variety of courses, we describe several…

The development of the mathematical concept of the infinite, through the reflections that arise from personal notions and perceptions and the analysis of some ideas of Galileo and Cantor, invites us to investigate the relationship between intuition and formalization for the understanding of the said concept. This paper aims to observe and describe…

Numerous activities and measures can be observed in the context of digitization. However, these are often not interrelated or sufficiently anchored institutionally and structurally with regard to overarching goals. The aim of this study is therefore to carry out a theory-based clustering of connotations with the concept of digit(al)ization in…

Preservice teachers (PSTs) are expected to possess a relational understanding (i.e., knowing how to do and why) of mathematics for ambitious instruction. This study aimed to shed some light on the possibilities of supporting PSTs' development of relational understanding of fractions through engaging them in writing collective argumentation.…

Similarity is a crucial concept introduced in the 8th grade, and it is further developed and reinforced through associations during high school. This research aims to investigate how 8th grade students construct the concept of similarity using concrete manipulative support within the framework of APOS theory. The research was conducted as a…

As education increasingly shifts towards a technology-driven model, artificial intelligence systems like ChatGPT are gaining recognition for their potential to enhance educational support. In university education and MOOC environments, students often select courses that align with their specific needs. During this process, access to information…

Students' perceptions of an activity involving visualization are important in assessing their learning of the task. In view of this, this study was developed with undergraduate students from different courses at a public Brazilian university. The research objective was to determine how three students, who are majoring in different courses…

Massive Open Online Courses (MOOCs) which enable large-scale open online learning for massive users have been playing an important role in modern education for both students as well as professionals. To keep users' interest in MOOCs, recommender systems have been studied and deployed to recommend courses or videos that a user might be interested…

This study explores calculus students' opportunities to learn the concepts of integral by examining one mathematician's videotaped lessons and the textbook. The results show that both lessons and textbook introduced important cognitive resources very briefly and focused on procedures and techniques of integration. Implications to these results…

This qualitative study aims to investigate novice undergraduate mathematics students' first encounter with the First Isomorphism Theorem, which is, more often than not, the pinnacle of a typical introductory course in Group Theory. Several studies have reported on the challenges that this mathematical result poses to inexperienced mathematicians,…

This full paper considers how collaborative discourse can reveal ways upper-class engineering students mechanically reason about engineering concepts. Argumentation and negotiation during collaborative, multimodal discourse using speech and gestures helps establish common ground between learners and fosters reflection on their conceptual…

In this report, we present an advance of doctoral research. We explore teaching alternatives that promote proportional reasoning in Mexican students between 14 and 15 years old with the support of digital technology. We designed a sequence of activities that pretends to signify the concepts of ratio and proportion in their diverse representations…

Using metaphors in education is a very effective method, especially in terms of learning abstract concepts and being memorable. For this reason, teachers use frequently metaphors in order to understand the concepts in their lessons. This study aims to determine teachers' perceptions of freedom and justice concepts through the metaphors they…