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…

Prior research highlights the role of number manipulation activities in fostering the early mathematical development of children. This study (N = 1,491) explored the effect of a bear-themed intervention on enhancing arithmetic abilities in kindergarten students. Utilizing a pre- and post-test design, the study compared the advancements of children…

Despite the prominence of analogies in mathematics, little attention has been given to exploring students' processes of analogical reasoning, and even less research exists on revealing how students might be empowered to independently and productively reason by analogy to establish new (to them) mathematics. I argue that the lack of a cohesive…

In this paper, we are interested in a dynamic vision of diagrams, focusing on their evocative power, their force in mathematical activity and their potential for interaction with mathematical objects. We are inspired by the work of C. S. Pierce to see diagrams as "inscriptions that organise space and articulate relations" and that of the…

This research aims to determine the thinking activity types dominated by a mental process in producing answers characterized by automatic, unconscious, and subjective-empirical processes (system 1) in solving problems so that the default-interventionist interaction occurs. This research novelty is the formulation of the contents and thinking…

This article investigates the potential mathematical learning opportunities arising from a digital activity designed to enhance students' comprehension of equations. Employing a commognitive-oriented lens, the analysis explores the potential mathematical discourses that could emerge from students' interactions with a digital scale inspired by the…

Building upon the blockbuster success of "Building Thinking Classrooms in Mathematics," Peter Liljedahl has joined forces with co-author Maegan Giroux to bring the Building Thinking Classrooms (BTC) framework to life in this new book, "Mathematics Tasks for the Thinking Classroom, Grades K-5." But this book is so much more than…

Learning mathematics is often justified as supporting students to make rational decisions, an important goal given the misinformation spread through social media every day. However, when asking preservice teachers to engage in a critical mathematics education activity in which they had to produce an argumentation that would persuade people to…

The aim of this qualitative study was to explore the thoughts of primary and secondary prospective mathematics teachers about educating mathematically gifted students. For this purpose, this research was conducted with 40 prospective mathematics teachers, 17 of whom were secondary mathematics prospective teachers, and 23 were primary mathematics…

Despite the burgeoning adoption of informal learning in people's daily lives, the actual effects of informal learning activities, especially technology-related informal learning activities, are much less reported than those of formal learning. Furthermore, there is a notable lack of research on the effects of technology-related informal…

Gaining useful insight into real-world problems through mathematical modelling is a valued activity across several disciplines including mathematics, biology, computer science and engineering. Differential equations are a valuable tool used in modelling. Modelling provides a way for students to engage with differential equations within a…

Research indicates that investigating phenomena, rather than reproducing facts, should be a core experience in the education of prospective mathematics teachers. Corresponding with its centrality to quality teacher education, there are multiple existing methodologies for analyzing the effects of investigation tasks on teachers' mathematical…

Graph theory allows the student to work on problems that require imagination, intuition, systematic exploration, conjecturing, and reasoning. It implies that mathematical investigation skill is essential to be proficient in Graph Theory. In this study, we conduct empirical research that deals with associational research. There were 97 students…

Mathematical inquiry involving hands-on activities has received increasing attention in mathematics education. Besides various customized physical teaching aids, subject-specific information technology, such as Dynamic Geometry System (DGS), finds extensive use in mathematical inquiry activities. However, effects of DGS and physical manipulatives…

These educators share the "how" and "why" behind their use of open middle tasks in the classroom. In this article, the authors share a type of mathematics task, called Open Middle, that exhibits the characteristics outlined above. The authors frequently use Open Middle tasks in their classrooms because they teach students that…