Effective learning is viewed as an evolutionary process, and as such, it involves an expanded version of the Crenshaw-Collins view of "intersectionality." It demands an in-depth view of the complex socio-cultural-ethnic milieu in which students are embedded. Even more, effective learning requires effectance problem-solving, investigation…

Teaching and learning Calculus concepts and procedures, particularly the definite integral concept, is a challenge for teachers and students in their academic careers. In this research, we supplement the analysis made by different authors, applying the theoretical and methodological tools of the Onto-Semiotic Approach to mathematical knowledge and…

We present a synthesis of the Onto-semiotic Approach (OSA) theoretical system to mathematical knowledge and instruction, while highlighting the problems, principles and research methods that are addressed in this approach and considering the didactics of mathematics as a scientific and technological discipline. We suggest that Didactics should…

In this paper, we present an activity to introduce the idea of public-key cryptography and to make pre-service STEM teachers explore fundamental informatics and mathematical concepts and methods. We follow the Theory of Didactical Situations within the Didactical Engineering methodology (both widely used in mathematics education research) to…

The objective of this qualitative research is to study the mathematical work when solving a mathematical task in the domain of probability presented by Chilean high school mathematics teachers in pre-service and in-service training. We consider as theoretical support the Mathematical Working Space model and methodological design of a collective…

An onto-semiotic analysis of the mathematical connections established by one in-service mathematics teachers and university students when solving a problem about launching a projectile using the derivative was carried out. Theoretically, this research was based on the articulation between the Extended Theory of Mathematical Connections and the…

Engineering educators express concern that undergraduate engineering students solve problems procedurally without the necessary conceptual understanding. While research in engineering dynamics has focused on using technology to improve student performance, this article focuses on using representations for modelling problem solving in the lecture.…

The aim of this study is to analyze and document the extent to which high school teachers rely on a set of technology affordances to articulate epistemological and cognitive actions in problem solving approaches. Participants were encouraged to construct dynamic representations of tasks and always to look for different ways to identify and support…

Reports and surveys by the U.S. government and international organizations have repeatedly acknowledged the achievement problem in math in K-12 regardless of various efforts (e.g., by the U.S. Department of Education) to diminish it. To address the problem in math achievement in K-12, teachers, scholars, and the U.S. government have developed…

Semiotic representations have been an important topic of study in mathematics education. Previous research implicitly placed more importance on the development of institutional representations of mathematical concepts in students rather than other types of representations. In the context of an extensive research project, in progress since 2005,…

The importance of mathematical visual images is indicated by the introductory paragraph in the Statistics and Probability content strand of the Australian Curriculum, which draws attention to the importance of learners developing skills to analyse and draw inferences from data and "represent, summarise and interpret data and undertake…

Balancing content and students' participation in the mathematics classroom is an area of both practical and theoretical interest. In this article we relate and contribute to these two interests by analyzing classroom data from an intervention project aiming at teaching mathematics through problem solving. The study shows that several aspects such…

Research in the didactics of mathematics has shown the importance of the problem of the particular and its relation to the general in teaching and learning mathematics as well as the complexity of factors related to them. In particular, one of the central open questions is the nature and diversity of objects that carry out the role of particular…

Clay's Reading Recovery has been one of the most effective one-to-one tutorial sessions. To make the daily lesson more interesting and fully engage the at-risk readers, the author modified Clay's Reading Recovery Program by conceptualizing phonics and semiotics into early intervention. In this case study, three at-risk first graders formed an…

Background: Games centred approaches (GCA) such as TGfU, Game Sense, and Tactical Games are widely promoted as alternatives to traditional forms of teaching games within physical education. These approaches are promoted on the basis of their capacity to engage students in meaningful and enjoyable physical activity and to promote problem-solving…