Visualization and argumentation are central processes in the learning of geometry, giving rise to specific lines of research in mathematics education. However, it is worth asking whether they should be developed independently or if it is possible and in what way an articulation between them can be promoted. The objective of this paper is to search…

Mathematics teacher candidates enter teacher education with knowledge that could support or limit their learning. It is therefore important to gain insights of this knowledge to inform teacher education. This paper offers such insights for prospective mathematics teachers' initial knowledge of problem solving (PS) for teaching at the beginning of…

Algebraic Thinking (AT) and Computational Thinking (CT) are pivotal competencies in modern education, fostering problem-solving skills and logical reasoning among students. This study presents the initial hypotheses, theoretical framework, and key steps undertaken to explore characterized learning paths and assign practice-relevant tasks. This…

This article aims to delve into the meaning of school mathematical concepts by their semantic analysis. Concretely, this paper aimed primarily to describe and characterize the meaning of derivative of a function at a point expressed by mathematics pre-service teachers. In order to achieve this goal, we use a semantic framework, in which the…

Spanish educational curriculum adopts a mathematical process-based approach, which encompasses problem solving, reasoning and proof, communication, connections and representation. A fundamental role in the integration of these processes in mathematics teaching is played by teachers' professional practice of designing tasks. According to this, our…

This work describes how the combination of the mistakes committed by a group of pre-service teachers when solving a Fermi problem, with the representation of the temporal analysis of their resolutions, can offer more in-depth information about their conceptual misconceptions regarding mathematical and modelling concepts. The combined…

The development in mathematical flexibility should be included in the mathematics teaching training of students in Primary Education Degree. Teachers in training have to acquire the skill to modify the problem resolution and be able to break with stereotyped methods. This document presents an analysis of spontaneous mathematical flexibility…

This paper presents an analysis of the classroom events that a group of future teachers of Secondary Education mathematics identified from their own experience when using GeoGebra to solve problems. The data analyzed are from the written materials by twelve mathematics majors who were studying the Mathematics for Teaching course. The students, in…

In the particular case of Spain, student and teacher difficulties associated with the mathematical discipline have been evidenced in PISA and TEDS-M reports. As we consider that the teachers' difficulties are connected to the students' performance, we propose a multi-disciplinary approach to deliver specific didactic/mathematical knowledge to the…

In this paper, we analyse the results of an experience designed and implemented to evaluate the epistemic and cognitive conflicts identified in the study of proportionality, carried out by a group of 21 students in their last year of primary education. Initially the students exhibit difficulties to recognize situations where proportionality can be…

This study explores the potential of modern board games to foster key competences in primary education. A total of 238 students and 17 teachers from Spain, Romania, and Greece implemented 29 board games targeting Linguistic Communication, Mathematical Competence, and Learning to Learn. The intervention included teacher training, pedagogical…

The curricular perspective based on teaching processes which takes formal mathematical knowledge as a starting point has been severely criticized. This traditional perspective considers that the formal mathematical knowledge has to be taught prior to the application so, once taught, it can be used to solve problems. Along with this criticism,…

Introduction: This paper analyzes the arithmetic problems posed by a group of mathematically talented students when given two problem-posing tasks, and compares these students' responses to those given by a standard group of public school students to the same tasks. Our analysis focuses on characterizing and identifying the differences between the…

We conducted a qualitative research of case studies based on think-aloud protocols. The aim was to carry out in-depth analyse secondary students' cognitive difficulties appearing in early stages of transfer processes in problem-solving. The task was to relate several source problems to a target problem, in order to solve it effectively. Source and…

This paper analyses the role of Computer Algebra Systems (CAS) in a model of learning based on competences. The proposal is an e-learning model Linear Algebra course for Engineering, which includes the use of a CAS (Maxima) and focuses on problem solving. A reference model has been taken from the Spanish Open University. The proper use of CAS is…