Le Indicazioni Nazionali come strumento di progettazione didattica: analisi delle convinzioni degli insegnanti di matematica di scuola secondaria di I Grado

Teaching and learning of mathematics play a fundamental role in the global educational system as it supports the development of logical skills and could stimulate students' critical and creative thinking. However, its effectiveness is influenced by various factors, including teaching practices, teachers' beliefs, and students' attitude towards mathematics. This thesis focuses on lower secondary schools and analyzes the influence of mathematics teachers' beliefs about the National Guidelines and their impact on teaching practices. The aim is to understand which factors, according to teachers, hinder the achievement of specific competencies by examining teachers' views on these factors through the lens provided by the causal attributions, such as locus, stability, and controllability. The research is conducted through a qualitative approach based on semi-structured interviews with 39 mathematics teachers. The interview is divided into three parts: the first explores teachers' knowledge and beliefs about the learning goals they pursue and about the National Guidelines; the second examines the stated teaching approach; the third gathers personal information, such as academic profile and professional experience. Moreover, the thesis explores teachers' beliefs about mathematics, with a particular focus on geometry, highlighting specific educational challenges. The research findings indicate that teachers tend to perceive many critical factors in teaching mathematics as external, stable, and partially uncontrollable, such as the complexity of the content. This view may reduce their sense of personal efficacy, leading some teachers to feel powerless in altering educational circumstances. However, a positive aspect emerges: many recognize their own actions as an internal, controllable, and relatively stable factor, with individual differences. Some teachers see continuity between students' experiences and their teaching practices, while others report significant changes, attributed to critical reflections and continuous professional development. This reflects a positive awareness of their ability to influence the teaching process, in line with the National Guidelines, which promote adaptability and the personalization of teaching. Regarding geometry, the findings of the research indicate that teachers, although recognizing the importance of objectives such as the understanding of definitions and properties of plane figures and problem-solving, struggle to define these concepts clearly, making it difficult to integrate these objectives into teaching practices. Among the difficulties reported, there are issues with argumentation and with harmonizing the conceptual and figurative components of geometry. Students tend to focus on the visual perception of figures, ignoring their conceptual properties, and many teachers adopt rigid approaches that reduce geometry to a mechanical exercise, neglecting its relational aspects. This procedural approach, which prioritizes "products" over "processes," limits deep understanding and the integration of critical skills, counteracting the goals set by the National Guidelines. In conclusion, the research emphasizes the importance of continuous teacher training to address the challenges in teaching mathematics. Professional development courses should provide practical methodologies, aligned with the National Guidelines, to enhance teaching approaches and support teachers in assessing students' cognitive processes. This approach fosters a positive learning environment, promoting greater teacher awareness and encouraging a proactive attitude toward teaching challenges.