Discutindo os casos e os momentos em Modelagem Matemática

Summary

This video script explores the concept of mathematical modeling in education, focusing on two main approaches: Barbosa's 'cases' and Almeida & Dias' 'moments.' Barbosa presents three models where the teacher's level of control gradually decreases, allowing students more responsibility. Almeida & Dias, on the other hand, emphasize a sequential learning process that helps students gradually become familiar with modeling. The video highlights the differences between these two approaches, providing a comprehensive overview of how mathematical modeling can be introduced in classrooms, fostering both student engagement and critical thinking in real-world scenarios.

Takeaways

• 😀 **Barbosa's Approach to Mathematical Modeling**: Barbosa outlines three levels of teacher involvement in the classroom: Case 1 (teacher-controlled), Case 2 (shared responsibility), and Case 3 (student-controlled). Each case corresponds to varying degrees of autonomy for the students.
• 😀 **Case 1 - Teacher-Controlled**: In this approach, the teacher provides all the necessary data and the students simply solve the problem based on the provided information. It requires minimal student research or decision-making.
• 😀 **Case 2 - Shared Responsibility**: The teacher provides the problem and some data, but students are responsible for gathering additional information and making decisions about how to approach the problem.
• 😀 **Case 3 - Student-Controlled**: Students take full responsibility for the entire process, including selecting the problem, gathering data, making hypotheses, and solving it. The teacher's role is to guide and support as needed.
• 😀 **Almeida & Dias' Approach to Mathematical Modeling**: This approach emphasizes a gradual, step-by-step introduction to modeling, with the teacher's role evolving from full control to minimal intervention.
• 😀 **Moment 1 - Teacher-Controlled**: The teacher presents a problem, leads the discussion, and provides all the necessary data. This is where students begin to engage with the concept of modeling.
• 😀 **Moment 2 - Shared Responsibility**: The teacher provides some initial information but encourages students to make hypotheses and gather additional data. This moment fosters more active student participation.
• 😀 **Moment 3 - Student-Controlled**: The teacher provides no pre-selected data. Students are expected to choose a problem, collect data, hypothesize, and resolve the issue independently, with the teacher providing minimal support.
• 😀 **Key Difference - Barbosa vs. Almeida & Dias**: Barbosa’s approach offers flexibility, allowing teachers to move between the different cases based on time and student engagement, while Almeida & Dias’ approach advocates for a sequential progression from teacher-led to student-led modeling activities.
• 😀 **Sequential vs. Flexible**: Almeida & Dias’ moments are designed to be followed sequentially, promoting gradual student familiarization with the modeling process. In contrast, Barbosa’s cases can be mixed and matched depending on the classroom’s needs.
• 😀 **Emphasis on Teacher Control vs. Student Responsibility**: Barbosa’s model focuses more on adjusting the level of teacher control, whereas Almeida & Dias prioritize student autonomy and gradual development of modeling skills.
• 😀 **Practical Application**: Both approaches aim to engage students in the process of mathematical modeling, but they differ in how they approach student autonomy and teacher control. Teachers can select either model depending on their classroom dynamics and the objectives of the lesson.

Q & A

What are the two main perspectives on how mathematical modeling can be introduced in the classroom?

The two main perspectives are Barbosa's 'cases' and Almeida & Dias' 'moments.' Barbosa's cases focus on different levels of teacher control and involvement, while Almeida & Dias' moments emphasize a gradual progression of student responsibility in the modeling process.

What does Barbosa mean by the term 'modeling' in the classroom?

Barbosa defines modeling as a learning environment in which students are invited to inquire and investigate through situations derived from other disciplines or real-life scenarios, utilizing both qualitative and quantitative data to solve problems.

How does Barbosa’s Case 1 differ from Case 2 and Case 3 in terms of teacher and student involvement?

In Case 1, the teacher controls most of the process, providing all the data and guiding students through problem-solving. In Case 2, students take more responsibility, gathering some data themselves while the teacher still offers guidance. In Case 3, students are fully responsible for all aspects of the modeling process, including identifying the problem, collecting data, and finding solutions.

What is the main difference between Barbosa’s cases and Almeida & Dias’ moments?

Barbosa’s cases are flexible and can be applied in any order, depending on the teacher's needs and the class context. In contrast, Almeida & Dias’ moments must be followed sequentially, with Moment 1 starting with teacher-led activities and gradually increasing student responsibility through Moment 3.

How do the three moments proposed by Almeida & Dias support student learning?

Almeida & Dias propose a gradual increase in student involvement. In Moment 1, the teacher controls the activity. In Moment 2, students take a more active role by making hypotheses and gathering data. By Moment 3, students are responsible for the entire modeling process, which helps them build confidence and understanding.

Why do Almeida & Dias emphasize a sequential approach in their moments of modeling?

Almeida & Dias emphasize a sequential approach to ensure that students are gradually familiarized with the process of mathematical modeling. This helps prevent students from feeling overwhelmed when asked to independently solve a problem, as they can build their skills progressively.

What kind of problems might be used in Barbosa’s Case 1, and how does this impact student learning?

In Barbosa’s Case 1, the teacher provides a problem with all the necessary data, such as a real-life scenario like an internet service plan comparison. This allows students to focus on problem-solving without worrying about data collection, helping them concentrate on applying mathematical concepts.

How does Case 2 in Barbosa's model allow students to take on more responsibility?

In Case 2, the teacher provides the initial problem, but students are asked to gather some of the relevant data themselves. This shift in responsibility encourages students to engage more actively in the process and develop research and analytical skills.

What role does the teacher play in Moment 3 of Almeida & Dias’ approach?

In Moment 3, the teacher’s role shifts to one of guidance and facilitation. While the students are responsible for identifying the problem, collecting data, and solving it, the teacher supports the students’ discussions and makes interventions when necessary to guide their learning.

Can Barbosa’s cases and Almeida & Dias’ moments be used together in a classroom setting?

Yes, it is possible to combine Barbosa’s cases and Almeida & Dias’ moments in a classroom. For instance, a teacher might begin with a Case 1 approach for simpler tasks and gradually move to more student-centered activities in Cases 2 or 3, while following the sequential moments of Almeida & Dias to build student confidence and independence.