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Blothiaux_09671900_2024.pdf
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- Abstract
- In this work, we will explore the world of complex numbers from multiple angles, with a particular focus on their teaching at the secondary level and proposing pedagogical improvements. This work is divided into three parts. In the first part, we will delve into the theoretical foundations of complex numbers, structuring our exploration into three distinct sections. We will begin by detailing the different representations of complex numbers, highlighting their diversity and relevance in various mathematical operations. Next, we will illustrate concrete examples of the application of complex numbers, demonstrating their advantages in various fields. Finally, we will focus on numbers, examining their set-theoretic extension and revealing the conceptual obstacles inherent in each set. We will also trace the historical evolution of numbers and analyze the order in which they are taught. The second part will focus on the teaching of complex numbers in so-called "scientific" tracks. We will explore the curricula for teaching complex numbers. We will also examine the place of the complex numbers chapter in the context of modern mathematics. Subsequently, we will look into the different structures adopted by teachers to approach this chapter. Particular attention will be given to the transfer skill, often neglected in the teaching of complex numbers. We will then explore various possible approaches to introduce this chapter, thus offering a variety of pedagogical perspectives. Additionally, we will analyze how students grasp complex numbers, examining their initial reactions to this abstract concept as well as the errors and difficulties frequently encountered in exercises and assessments. Finally, we will answer the question: why teach complex numbers in secondary education? The third part will concern my personal reflections. I will describe the pedagogical tools I plan to implement in my own classes. This description will be based on the overall analysis of observed practices, with the aim of enriching the teaching of complex numbers at the secondary level. This work aims to offer a comprehensive view of the teaching of complex numbers, integrating theoretical, practical, and pedagogical perspectives. We hope thus to contribute to a better understanding and improvement of the teaching methods of this fundamental mathematical concept.