Ler, escrever e resolver problemas | Kátia Smole e Maria Diniz (Org.) I Capítulos IV e V

Summary

In this video, the presenter explores two chapters from a book on problem-solving in mathematics education. Chapter 4 covers the evolution of problem-solving methodologies, detailing three key conceptions: as a skill, a process, and a competence. It also traces the history of problem-solving in the 1980s and 1990s, highlighting shifts toward investigative, non-conventional methods. Chapter 5 critiques conventional textbook problems, urging educators to adopt more dynamic, problem-based learning that encourages critical thinking. The video stresses the importance of a methodological approach and effective communication in fostering deeper understanding in mathematics.

Takeaways

• 😀 Takeaway 1: Problem-solving in math education has evolved through multiple conceptual phases, from a basic skill to a process and an ability to resolve new situations.
• 😀 Takeaway 2: In the 1980s, problem-solving was largely seen as a skill necessary for participating in society, and it was linked to specific mathematical knowledge.
• 😀 Takeaway 3: The 1990s brought a shift where problem-solving became more methodological, involving a set of strategies for learning math effectively.
• 😀 Takeaway 4: The methodological perspective on problem-solving includes not just the methods, but also a broader teaching philosophy that values student independence in learning.
• 😀 Takeaway 5: Conventional problems in textbooks often limit students’ engagement, and the script encourages confronting these problems to make them more investigative and enriching.
• 😀 Takeaway 6: One key characteristic of effective problem-solving is allowing students to question both the problems and their initial situations, promoting deeper analysis.
• 😀 Takeaway 7: The resolution of problems in the classroom must be carefully planned, with clear objectives and activities that guide students to achieve these goals.
• 😀 Takeaway 8: The distinction between conventional and non-conventional problems is essential; non-conventional problems stimulate critical thinking and deeper learning.
• 😀 Takeaway 9: In problem-solving, integrating content with methodology is crucial; teachers should not separate the two but should plan problems that connect both.
• 😀 Takeaway 10: Mathematical communication plays a critical role in the problem-solving process, as it helps students articulate and refine their understanding of concepts.

Q & A

What is the main topic of the video?

The main topic of the video is focused on problem-solving methodologies in mathematics education, specifically discussing the different perspectives on how problem-solving is approached in the teaching and learning of mathematics.

What are the three key conceptions of problem-solving in mathematics discussed in the video?

The three key conceptions of problem-solving discussed are: 1) Problem-solving as a complete process, 2) Problem-solving as a process that applies previous knowledge to new situations, and 3) Problem-solving as a basic skill necessary for participation in society.

How does the video describe the evolution of problem-solving approaches in mathematics education?

The video explains that the understanding of problem-solving in mathematics evolved through different decades. In the 1980s, problem-solving was seen as a skill, a process, or as the foundation of teaching math. In the 1990s, a shift occurred, where problem-solving gained new dimensions as a methodology for teaching math, incorporating strategies that go beyond traditional problem types.

What is the perspective methodology of problem-solving as described in the video?

The perspective methodology of problem-solving is a teaching approach that includes not only methodological aspects but also a particular stance on what teaching and learning mean. It emphasizes breaking away from conventional problems and encourages more investigative, open-ended problems to deepen understanding.

What are 'conventional problems' in the context of the video, and why are they problematic?

Conventional problems in the video refer to typical, textbook-style problems that often do not promote critical thinking or deeper investigation. They are seen as problematic because they limit the learning process and do not encourage students to explore different methods or engage in deeper problem-solving.

What role does 'questioning' play in the perspective methodology of problem-solving?

In the perspective methodology of problem-solving, 'questioning' plays a crucial role in both questioning the problems posed and questioning the initial situation of the problem itself. This approach enables a more qualitative analysis of the problem, fostering deeper critical thinking and understanding.

What is meant by the integration of content and methodology in the perspective methodology?

The integration of content and methodology means that teaching should not separate the subject matter from the teaching approach. Both should be carefully planned and aligned, ensuring that the method of solving problems is directly tied to the mathematical content being taught.

How does the video suggest transforming conventional textbook problems?

The video suggests transforming conventional textbook problems by questioning their assumptions, modifying them to make them more investigative, and creating problem situations that encourage deeper engagement and exploration of mathematical concepts.

What are the three characteristics of the perspective methodology of problem-solving mentioned in the video?

The three characteristics of the perspective methodology of problem-solving are: 1) Considering all situations that can be problematized, 2) Including the actions of questioning the problems and the initial situation, and 3) Carefully planning the problem-solving activities to ensure they are aligned with educational goals.

What is the significance of students perceiving themselves as the introducers of their own knowledge?

The significance of students perceiving themselves as the introducers of their own knowledge is that it encourages active learning and self-directed exploration, where students take ownership of their learning process, thus fostering deeper understanding and personal engagement with mathematical concepts.