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 this study, effects of asking participants to make different types of considerations when solving a realistic word problem were investigated. A two-factorial experiment with the factors "addressing realistic considerations" (with vs. without) and "addressing mathematical operations" (with vs. without) was conducted. It was…

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.…

The growing use of programming in mathematics classrooms presents a challenge linked to implementation in general and task design in particular. This article presents design ideas for mathematical problems incorporating programming in which the focus remains mainly on learning mathematics and less on learning programming. The article starts by…

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…

Comprehending and formulating strategies for geometry problems that require higher-order thinking skills (HOTS) is crucial in enhancing mathematics education. This study implements a qualitative case study approach to comprehend how prospective mathematics teachers with varying Adversity Quotients (AQ) solve geometry Higher-Order Thinking Skill…

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…

This study contributes to Action, Process, Object, Schema (APOS) theory research by showing two approaches used by advanced mathematics students to construct relations between higher-order derivatives to solve complex problems. We show evidence of students' ability to perform Actions on their graphing derivative Schema, that is, of its…

Mathematical modelling has acquired relevance in different fields at an international level, both in education and research. This article states that, throughout the construction of the theoretical corpus of this mathematical process and competency -- among others -- two big issues have occurred: one of terminological nature since the definitions…

In tracing recent research trends and directions in mathematical problem-solving, it is argued that advances in mathematics practices occur and take place around two intertwined activities, mathematics problem formulation and ways to approach and solve those problems. In this context, a problematizing principle emerges as central activity to…