Problem-based learning (PBL) is a teaching method that appeared in the early 1960s and is widely applied in distinct areas nowadays. In the presented manuscript, we describe a PBL methodology use restricted to applied mathematics for problem solving among a group of engineering students in a Portuguese university. In the pandemic context, it was a huge challenge both for the students and for the teacher. Supported by the available literature, the experiment was defined. As it is well known, teachers are not only knowledge transmitters but also designers of teaching initiatives. Thus, teachers and students both have a large role in PBL methodologies, where collaboration, reflection and concepts discussion are essential. In the presented pedagogical challenge, students were devoted to integrating the previous knowledge acquired and the one acquired during the project. This process improved their new competences—both personal and team work. Despite being a recent pedagogical method, PBL is revealed to be an important teaching tool.

A methodology to predict PM₁₀ concentrations in urban outdoor environments is developed based on the generalized linear models (GLMs). The methodology is based on the relationship developed between atmospheric concentrations of air pollutants (i.e. CO, NO₂, NO_x, VOCs, SO₂) and meteorological variables (i.e. ambient temperature, relative humidity (RH) and wind speed) for a city (Barreiro) of Portugal. The model uses air pollution and meteorological data from the Portuguese monitoring air quality station networks. The developed GLM considers PM₁₀ concentrations as a dependent variable, and both the gaseous pollutants and meteorological variables as explanatory independent variables. A logarithmic link function was considered with a Poisson probability distribution. Particular attention was given to cases with air temperatures both below and above 25°C. The best performance for modelled results against the measured data was achieved for the model with values of air temperature above 25°C compared with the model considering all ranges of air temperatures and with the model considering only temperature below 25°C. The model was also tested with similar data from another Portuguese city, Oporto, and results found to behave similarly. It is concluded that this model and the methodology could be adopted for other cities to predict PM₁₀ concentrations when these data are not available by measurements from air quality monitoring stations or other acquisition means.