In this paper, we develop a review of the research focused on the teaching and learning of ordinary differential equations with the following three purposes: to get an overview of the existing literature of the topic, to contribute to the integration of the actual knowledge, and to define some possible challenges and perspectives for the further research in the topic. The methodology we followed is a combination of a systematic literature review and a bibliometric analysis. The contributions of the paper are given by the following: shed light on the latest research in this area, present a characterization of the actual research lines regarding the teaching and learning of ordinary differential equations, present some topics to be addressed in the next years and define a starting point for researchers who are interested in developing research in this field.

Modelling has become mandatory in the school curricula in many countries across the globe, often without providing teachers the training needed to address this challenge. With a qualitative case study, we analyzed the tasks designed by secondary mathematics pre-service teachers. We recognized how participants manage their knowledge for teaching modelling in the absence of training. Elements of knowledge for teaching such as translation between languages, recognizing unknown data, covariation, and usefulness of representations for understanding and solving problems, were identified. Our results also reveal that future teachers have a tendency to create word problems when first attempting to teach modelling.

With an empirical study, we explore the process of designing modeling tasks for teaching mathematics in a Dynamic Geometry environment. We address the research questions: What are the characteristics of the tasks that pre-service teachers design to teach mathematics in digital and modeling environments? What are the activities like that these tasks encourage in students? By means of a qualitative methodology, we characterize the tasks designed by secondary pre-service mathematics teachers and identify the activities that these tasks encourage in students. By analyzing the process of designing and planning a class, we can determine how the characteristics of the modeling tasks are modified based on the software used. In this context, the software also acts as a medium that reflects aspects of the models involved, the objectives of the tasks, and the activities intended for the students. The results contribute to the discussion regarding task design, where technology is a means of supporting the exploration, understanding, and study of different phenomena.

The wide availability of digital tools, as well as the current global pandemic has transformed the way in which teachers and students interact. This of course will have consequences on the learning of in physics and mathematics in the medium and long term. The objective of this research is to explore what are the feelings, difficulties and adaptations of the teachers to develop online classes. We reach this goal with support on the tetrahedron model for a didactical situation, which describes the interactions between student, teacher, content, and technology. Following a qualitative methodology, a survey of 48 in-service teachers was conducted to explore how teachers’ knowledge and their use of digital tools influence teacher-student-technology interactions. The results showed that 65% of the participants feel prepared for online teaching, while 35% feel. However, there is not a big difference in the interactions they promote with the students. Teachers experiment a high level of negative emotions such as frustration and anxiety, many of these emotions were recognised in teachers feeling online teaching. The findings explain how emotional and infrastructural factors are related to the interactions in online teaching. The results have implications in physics and mathematics teacher training programs, the ways we teach physical and mathematical content, insofar we highlight those aspects into account to improve the students’ learning.