Collaborative learning is a group learning paradigm in which individuals or students work together to solve problems or complete tasks, exemplifying the essence of collective educational efforts. There are a lot of collaborative learning methods available; however, finding one that is suitable for the complex nature of mathematical problem-solving…

In XVII century, presumably between 1637 and 1638, with a note in the margin of Diophantus' "Arithmetica", Pierre de Fermat stated that Diophantine equations of the Pythagorean form, x[superscript n] + y[superscript n] = z[superscript n], have no integer solutions for n > 2, and (x, y, z) > 0. Of this statement, however, Fermat…

Background/purpose: Learning mathematics often presents challenges for students, particularly in problem-solving and establishing mathematical connections. Self-regulated learning allows students to direct, adjust, and control their learning processes. This approach is essential in encouraging students to manage their learning strategies…

This paper aims to understand how primary students use gestures to solve partition tasks and to what extent these gestures may promote fraction understanding. Analysis of six selected students' answers to partitioning tasks, classroom observation, and post-lesson interviews indicates that co-thought representational gestures play a critical role.…

This article examines what constitutes a 'good' mathematical problem and proposes to conceptualize the notion of "collective mathematical problems" as phenomena that arise through and by way of the inter-actions enabled by the collective itself. The author examines how these collective mathematical problems can emerge in the classroom…

The increasing use of complex machine learning models in education has led to concerns about their interpretability, which in turn has spurred interest in developing explainability techniques that are both faithful to the model's inner workings and intelligible to human end-users. In this paper, we describe a novel approach to creating a…

The aim of this study is to investigate the production and dissemination of mathematical modeling-based projects by gifted students, intended to solve real-life problems, over the four-year Project Production and Management Program (PPMP). The longitudinal research methodology was utilized to examine the project production process among…

Effective mathematics teaching practices include not only probing student thinking and selecting student strategies to share but also facilitating discourse and encouraging reflection about important mathematical ideas (National Council of Teachers of Mathematics [NCTM], 2014, pp. 36-37). Encouraging students to use precise academic vocabulary to…

This article considers the rise of generative Artificial Intelligence (GenAI) in the context of secondary mathematics education, focusing on its responses to cognitively demanding tasks and the pedagogical implications of these interactions. Using tools such as ChatGPT (OpenAI) and Gemini (Google), we investigate how GenAI engages in complex…

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…

Teacher gestures support mathematics learning and promote student collaboration. Aligned with speech, gestures can help students to notice the important visual information of geometry tasks. However, students' visual attention to the teacher's gestural cues during collaborative problem solving remains a largely unexplored field in mathematics…

Background/purpose: This study aims to analyze students' ability to solve differential calculus problems in relation to their prior mathematical knowledge (PMK). Materials/methods: A qualitative research design method was employed. Participants in this study were 103 third-semester students at the university enrolled in the Differential Calculus…

Research literature about visually impaired students' approach to mathematics is still very scarce, especially in the case of algebra, even though mathematical content is becoming increasingly accessible thanks to assistive technologies. This paper presents a case study aimed at describing a blind subject's process of algebraic symbol manipulation…

This study investigates the ability of ChatGPT to generate mathematical problems creatively, focusing on fluency, flexibility, and originality. The findings indicate that ChatGPT can produce a vast number of problems, demonstrating a high level of fluency. Additionally, it tends to prioritize the most original problem among its generated outputs.…

Productive struggle (PS) has emerged as a critical construct in mathematics education, emphasizing the importance of persistence, cognitive engagement, and conceptual understanding in problem-solving. However, inconsistencies in its conceptual and operational definitions have hindered its effective implementation and assessment. This study…