Over time, teaching materials, such as manipulatives, have acquired a key role in promoting students’ understanding of mathematical knowledge. These materials play an important resource in student learning, including a recreational role that promotes motivation and a dynamic role in the understanding of concepts in which students are involved in the learning activities. Based on these assumptions, this study aims to investigate the contribution of manipulative materials in the learning of geometric figures by elementary school students. Adopting a qualitative and interpretative approach, data were collected through students’ written records, and audio and video record of students’ activities. The results show that students explored, manipulated, and constructed representations of triangles, squares, rectangles, circles, and other geometric figures, distinguishing them from each other through shape and properties. In particular, through manipulation of shapes with manipulatives students realized that a square is a rectangle but the inverse is not true.

This study aims to understand the functional thinking of 10th-grade students while studying functions. Specifically, we intend to answer the following research questions: what are the functional thinking processes used by 10th-grade students when studying functions? What difficulties do students present while learning functions? In view of the nature of this research objective, we adopted a qualitative and interpretative approach. In order to answer these questions, data were collected from the written records produced by the students while solving the proposed tasks, from records of the oral interactions during discussions and from a questionnaire. The results show that functional thinking processes were implicit in the resolution of the tasks proposed to the students. The students expressed an understanding of how the variables were related, presenting evidence of their functional thinking while working on the new concepts represented by the functions addressed in the proposed tasks. Some students expressed difficulties in interpreting the different types of representations associated with the functions, in retaining the necessary information from a graphical representation that would help them to draw conclusions and establish correspondences, in explaining functional relationships, and in interpreting the information provided by algebraic expressions. These difficulties can reduce the recognition of the relationships between variables and their behavior in the different representations, becoming an obstacle to learning for some students.

A multidisciplinary team collaborated on the development of a learning experience involving 10th grade students using a Science, Technology, Engineering, Arts, and Mathematics (STEAM) approach. The experience was based on the development (conception, implementation, and evaluation) of a science cartoon that aimed to highlight different scientific and technological dimensions related to the diversity of marine worms (Phylo Annelida, class Polychaeta) present in the continental shelf off the coast of Aveiro, Portugal (NE Atlantic coast). The study was implemented in a Portuguese high school in the Aveiro region, involving 24 10th grade students, emphasizing a social context close to the students’ lives. All pedagogical interventions occurred in face-to-face sessions during the 2020/21 school year and were oriented by the following research question: What is the role of science cartoons in establishing STEAM connections for solving real-world problems presented to 10th grade students? Following a qualitative and interpretative research methodology, with a design-based research focus, data were collected through a questionnaire, observations, and students’ written records. The content analysis shows that most students learned new concepts related to STEAM areas. Evaluating the impact of the science cartoon reveals that it can be considered an innovative science communication resource due to its educational potential in stimulating a STEAM approach within the students’ learning process.

This study was conducted while 9th grade students learn to solve inequalities and seeks to understand their approach to solving problems with a real-life context. Specifically, the aim is to understand: (1) What are the main characteristics of the students’ approaches to the proposed problems? (2) What is the impact of the real context on the students’ resolutions? A qualitative and interpretative methodology is adopted, based on case studies, with data collected through documentary collection and audio recording of discussions between a pair of students while solving problems. The main conclusions suggest a trend to approach problems without establishing immediate connections with what was being done in the classroom, with students’ decisions being essentially guided by criteria of simplicity. The real context of the problems seems to have the potential to develop in students a more integrated mathematics, focused on understanding and not so much on the repetition of mechanical and meaning-independent procedures. The students’ familiarization with the context in question is one of the aspects highlighted by this study.

The current teaching of mathematics is guided by recommendations that suggest the implementation of various activities in order to raise the understanding of mathematical knowledge. This diversity is related to the characteristics of the tasks proposed in the learning contexts. Among all tasks, the modelling ones call for the application of activities through different representations. So, it is important that teacher training courses promote experiences involving prospective teachers with this type of task. Based on this assumption, we intend to identify the activities that prospective primary school teachers perform in solving modelling tasks, the difficulties experienced in these tasks and the value of the models they determine. From the analysis of the resolutions of two tasks, we find that the prospective teachers translate the information of the data available in tables through graphs and analytical expressions. Some discuss models that determine which best fits the data. In the activities carried out, difficulties arise in determining the proportionality constant that best translates the problem situation, discussing the reasonableness of the values generated by the model, and sketching the graph of the model that best fits the experimental data. As for the usefulness of the model they determine, few prospective teachers are predicting outcomes.

Este artigo debruça-se sobre o papel das TIC no desenvolvimento de aspetos do conhecimento didático (tipo de tarefas e formas de comunicação) e da capacidade reflexiva de futuros professores de Matemática durante o seu estágio. O estudo envolve três estagiários colocados em escolas diferentes. Os dados foram recolhidos através de duas entrevistas a cada estagiário (uma no início e outra no final do estágio) e da análise documental (reflexão de aulas e mensagens de e-mail e do fórum). As TIC permitiram a partilha e a discussão de situações da sala de aula, o trabalho conjunto entre orientadores e estagiários, o que contribuiu para o desenvolvimento do conhecimento didático e da capacidade reflexiva dos estagiários. Estes usaram diferentes tipos de tarefas e promoveram formas de comunicação para além da unidirecional. A interpretação, problematização e reconstrução de alguns momentos contribuíram para verem a própria prática como fonte para aprender a ensinar.