Introdução Semiótica I

Summary

In this video, the speaker introduces a semiotic approach to understanding mathematical thinking and learning. The focus is on how mathematical knowledge is constructed through signs and representations, with theoretical foundations from Ferdinand de Saussure and Charles Sanders Peirce. While Saussure's semiology centers on linguistic signs, Peirce's semiotics explores a broader relationship between objects, meanings, and representations. The speaker emphasizes the importance of understanding how students interpret and represent mathematical concepts, utilizing signs to develop deeper cognitive structures in mathematics. This approach aims to enhance teaching strategies by focusing on the semiotic processes that shape students' mathematical thinking.

Takeaways

• 😀 Semiotics is a key approach to understanding how people develop mathematical thinking and knowledge.
• 😀 The main theoretical references for the semiotic approach to mathematical cognition are Ferdinand de Saussure and Charles Sanders Peirce.
• 😀 Ferdinand de Saussure is considered the father of linguistics, and his work laid the foundation for structuralism in the 20th century.
• 😀 Charles Sanders Peirce is the primary theoretical reference for the semiotic approach in this context, contributing to logic, mathematics, and the philosophy of science.
• 😀 Peirce introduced the concept of 'abductive reasoning', which is essential to understanding logical reasoning, alongside deduction and induction.
• 😀 For Peirce, signs mediate the relationship between objects (the world) and interpretants (the knowledge or meaning generated by the signs).
• 😀 Semiotics, as defined by Peirce, is a process where signs represent objects and create interpretants, focusing on the process of meaning production.
• 😀 Semiology, as proposed by Saussure, focuses on systems of signs in society, such as rituals and cultural systems, while semiosis in Peirce’s theory focuses on meaning-making processes.
• 😀 Understanding how mathematical knowledge is constructed involves analyzing how students use signs and representations in the classroom to develop more complex concepts.
• 😀 The semiotic approach helps in understanding how students think mathematically by observing how they create and interpret signs, facilitating more effective teaching strategies.
• 😀 The main objective is to understand how mathematical concepts are constructed through signs, emphasizing the importance of representation in cognitive development and teaching.

Q & A

What is a semiotic approach in the context of mathematical thinking?

A semiotic approach refers to the way mathematical thinking is developed through the use of signs and representations. It emphasizes how knowledge is constructed and understood through signs, and how these signs mediate the relationship between objects (mathematical concepts) and meanings (cognitive interpretations).

Who are the key theorists in the semiotic approach to mathematical thinking?

The key theorists discussed in the transcript are Ferdinand de Saussure, Charles Sanders Peirce, Immanuel Kant, Jean Piaget, and Michel Frederico Viotti. While Saussure is important for linguistics, Peirce is the central figure for the semiotic approach in this context, particularly in relation to mathematical thinking.

What is the difference between semiology and semiotics?

Semiology, as proposed by Saussure, focuses on the study of signs within the context of language and communication, treating it as a branch of linguistics. In contrast, semiotics, as defined by Peirce, is broader and includes the study of all processes of signification, encompassing various systems of signs like images, music, mathematics, and culture.

How does Peirce's concept of 'abductive reasoning' relate to mathematical thinking?

Peirce introduced the concept of abductive reasoning, which complements inductive and deductive reasoning. In the context of mathematics, abductive reasoning helps explain how individuals generate hypotheses or explanations based on incomplete or ambiguous data, a process central to problem-solving and mathematical discovery.

What role do signs play in mathematical cognition according to Peirce?

For Peirce, all thought occurs through the use of signs, which mediate the relationship between objects (the content or concept) and their meanings (the understanding or interpretation). In mathematics, signs are essential for representing concepts and facilitating cognitive processes that lead to understanding.

Why is Peirce's approach considered innovative in mathematics and education?

Peirce's approach is considered innovative because it integrates semiotics with mathematical thinking. His focus on the relationship between signs, objects, and meaning provides a unique framework for understanding how mathematical concepts are represented, interpreted, and learned, which is valuable in educational settings.

What is the significance of semiotics in the classroom, according to the transcript?

Semiotics plays a crucial role in the classroom by helping teachers understand how students think and learn. By observing how students represent concepts through signs, educators can better comprehend the cognitive processes involved and develop more effective teaching methods that encourage deeper mathematical understanding.

How does Peirce's concept of 'interpretants' relate to mathematical learning?

Interpretants, in Peirce's theory, refer to the cognitive understanding or the meaning generated when a sign is interpreted. In mathematical learning, the interpretant is how students make sense of mathematical signs and concepts, facilitating the construction of knowledge and understanding.

What is the role of objects and symbols in Peirce's semiotic theory?

In Peirce's semiotic theory, the world consists of two essential types of things: objects and symbols. Objects are the things being represented (e.g., mathematical concepts), while symbols are the signs or representations that mediate the relationship between the objects and the interpretation (i.e., the student's understanding of the concept).

How can the semiotic approach be applied to teaching mathematics?

The semiotic approach can be applied by focusing on the process of how students represent and interpret mathematical concepts. Teachers can observe and guide students in how they use signs (e.g., symbols, diagrams, language) to make sense of mathematical ideas, helping them develop more sophisticated and structured mathematical knowledge.