PALESTRA Concepções de Modelagem Matemática

Name: PALESTRA Concepções de Modelagem Matemática
Uploaded: 2021-02-23T07:20:18.000Z
Duration: 2 h 28 min 31 s

Introduction to Mathematical Modeling

The Role of Teachers in Education

The importance of teachers is emphasized as the foundation for all achievements, highlighting that every good beginning has a good teacher.

Acknowledgment of the various fields where teaching plays a crucial role, including architecture and surgery, illustrating the broad impact of educators.

Overview of the Session

Professor Márcio Léo Rodrigues introduces himself and outlines his affiliation with the University of the State of Mato Grosso, focusing on mathematical education.

The session aims to discuss mathematical modeling concepts as part of a formative course for mathematics teachers in graduate studies.

Engagement with Participants

Participants are encouraged to share their thoughts and questions via chat during the 60-minute presentation featuring renowned researchers.

The goal is to explore different perspectives on mathematical modeling and understand how various individuals conceptualize it.

Understanding Mathematical Modeling

Historical Context and Development

Emphasis on democratizing knowledge by sharing information across Brazil, not limited to specific academic circles.

Introduction to systematic presentations aimed at aligning concepts from distinguished researchers in mathematical modeling.

Evolution of Mathematical Modeling in Brazil

Discussion on how mathematical modeling began being addressed in Brazil since the 1970s, initially focused on applying mathematics to real-world problems rather than educational contexts.

Recognition that over 300 master's and doctoral research projects have been conducted over four decades, indicating significant academic interest in this area.

Diverse Perspectives on Definitions

Acknowledgment that no single definition encompasses all aspects or levels of mathematical modeling; instead, multiple definitions exist based on various research findings.

Importance placed on understanding diverse conceptions so researchers can select frameworks that align with their own work.

Understanding Mathematical Modeling Perspectives

Importance of Defining Perspectives in Research

The author emphasizes the necessity of defining perspectives in research, particularly when discussing mathematical modeling, as there are multiple definitions and viewpoints.

It is crucial to align the current work with established conceptions commonly referenced in mathematical modeling literature.

Key Figures in Mathematical Modeling

Professor Rodney is highlighted as a charismatic figure in education and a pioneer in mathematical modeling literature, with his 2002 book being highly cited among mathematics educators.

He has been influential in Brazil's mathematical education landscape, having guided early works in the field while working at Unicamp and later at the Federal University of ABC.

Practical Application of Mathematical Modeling

Professor Rodney not only approached mathematical modeling theoretically but also engaged practically by conducting workshops across Brazil to disseminate these ideas during the 1980s and 1990s.

His focus was on making mathematics meaningful for students and teachers alike, aiming to bridge theoretical knowledge with real-world applications.

Definition and Process of Mathematical Modeling

In his classic educational text, Professor Rodney defines mathematical modeling as transforming real-world themes into solvable mathematical problems while interpreting solutions back into real-world language.

He describes a mathematical model as a set of symbols and relationships that represent studied objects or phenomena.

Steps Involved in Mathematical Modeling

According to Professor Rodney, effective mathematical modeling involves several stages: experimentation, abstraction (defining variables), resolution (solving), validation (checking solutions against original problems), modification (adapting models), and application (relating findings back to reality).

His influence extends through various scholars he mentored, including notable figures like Professor Dionísio Burak and Maria Salett Biembengut.

Contributions of Professor Rhoden and His Influence on Mathematical Modeling

Overview of Academic Lineage

Professor Rhoden has guided notable figures such as Professor Dionísio and Professor Maria Salete, who have in turn supervised numerous doctoral candidates. This academic lineage continues to influence new masters and doctors in mathematical modeling.

Transition to Federal University of ABC

Currently, Professor Rhoden is affiliated with the Federal University of ABC, showcasing a shift in his academic environment while continuing his contributions to mathematical education.

Insights from Professor Maria Salete on Mathematical Modeling

Role and Achievements

Maria Salete is a prominent figure in Brazil's mathematical modeling landscape, having founded the Center for Reference in Mathematical Modeling at the Regional University of Blumenau. She has published significant works across various educational levels.

Definition of Mathematical Modeling

In her book "Mathematical Modeling: Implications for Teaching and Learning Mathematics," she defines mathematical modeling as creating a model that connects mathematics with reality through symbols and relationships that represent studied phenomena.

Collaborative Work with Nelson

Conceptual Framework

In collaboration with Professor Nelson, Salete describes mathematical modeling as an art form that not only solves specific problems but also serves as a foundation for future applications and theories. This highlights the dual purpose of models in both immediate problem-solving and broader theoretical support.

Interconnection Between Mathematics and Reality

Theoretical Perspectives

Salete emphasizes that mathematics and reality are interconnected sets; modeling serves as a bridge between them, integrating structural mathematics with physical phenomena to create comprehensive models explaining their functions.

Importance of Real-world Applications in Teaching

Mathematicization Process

The process involves bringing real-world phenomena into math teaching (e.g., using bacterial growth to teach exponential functions), ensuring students grasp the relevance of mathematical concepts within practical contexts. This approach aims to enhance comprehension by linking theory directly to observable realities.

Stages of Model Development According to Maria Salete

Three Main Stages

Salete outlines three stages for developing models:

Interaction: Recognizing problems and familiarizing oneself with relevant topics.

Mathematization: Formulating problems mathematically.

Modeling: Interpreting solutions and validating models.

This framework simplifies complex processes into manageable steps while maintaining depth through sub-stages within each main stage.

Engaging Students Through Relevant Problems

Enhancing Interest in Mathematics

By incorporating real-life issues into lessons, educators can spark student interest in previously unfamiliar mathematical topics while simultaneously teaching them how to model mathematically effectively—demonstrating the practical applicability of their learning objectives within curricula.

Contributions from Professor Dionísio Burak

Research Background

Dionísio Burak is recognized for his extensive research on mathematical modeling over more than 30 years, contributing significantly to its application within mathematics education across Brazil through mentorship at various academic levels including master's and doctoral studies. His work reflects deep theoretical engagement with the subject matter since his doctoral thesis in 1992.

Mathematical Modeling: Understanding and Application

Definition and Purpose of Mathematical Modeling

Mathematical modeling is described as a set of procedures aimed at creating parallels to explain everyday phenomena, assisting in predictions and decision-making.

The definition aligns closely with the concepts presented by Professor Rhoden and Professor Maria Salete, emphasizing the connection between real-world phenomena and mathematical content.

Stages of Mathematical Modeling

The author outlines five stages of mathematical modeling, starting with theme selection followed by exploratory research to gather relevant data.

Identifying problems is crucial; it involves determining what needs resolution based on the gathered data before moving on to problem-solving and content development.

The final stage includes critical analysis of solutions, reflecting on how these steps were initially influenced by applied mathematics perspectives.

Evolution of Methodology

Initially focused on model construction defined by researchers, the methodology has evolved to emphasize meaningful engagement with students' interests in real-world contexts.

In 2010, a reformulation highlighted that problems must resonate with students’ realities for effective exploration and interest in research.

Importance of Contextualization

Emphasizing student interest is vital; problems should be relevant to their context for meaningful exploration and data collection.

Teachers are encouraged not to provide ready-made data but rather facilitate students' active investigation into relevant issues.

Significance of Meaningful Engagement

The work emphasizes that mathematical modeling should not only be technical but also contextualized, giving significance to mathematical content through student engagement.

Reflecting on teaching practices raises questions about whether the topics taught align with students' interests and daily lives.

Influences in Educational Mathematics

Acknowledgment is given to earlier researchers like Professors Maria Salete and Dionísio who were influenced by Professor Rhoden's work in educational mathematics.

Introduction of new perspectives emerged around 2000, particularly from Professor Jonei Cerqueira Barbosa’s contributions regarding mathematical modeling.

Contributions from Jonei Cerqueira Barbosa

Barbosa's doctoral thesis published in 2001 introduced a distinct conception of mathematical modeling that diverged from previous frameworks.

Modeling as a Learning Environment

The Role of Modeling in Education

The concept of modeling is presented as a learning environment where students are invited to engage actively. The importance of this invitation lies in the teacher's role to motivate and encourage inquiry among students.

Emphasis is placed on exploring non-mathematical situations through mathematics, highlighting the need for interdisciplinary connections that enrich the learning experience.

The term "environment" is defined as a space that encourages investigation into real-world situations using mathematical tools, fostering an engaging atmosphere for students.

Interdisciplinary Connections

The discussion includes various relationships between mathematics and other subjects such as physics, geography, and biology, promoting dialogue among students about these interconnections.

Reference is made to Barbosa's conception of autonomy in education, aligning with Paulo Freire’s ideas about student independence in learning through mathematical modeling.

Inquiry-Based Learning

Understanding modeling involves inquiry beyond merely stating problems; it requires a mindset that accompanies the entire problem-solving process. Students must develop questioning skills essential for their engagement.

For effective dialogue and discussion within the modeling environment, it is crucial for students to find relevance and meaning in what they are studying; otherwise, their participation may be limited.

Creating an Effective Learning Environment

A call for open-ended situations reflects real-world complexities where disciplines are interconnected rather than isolated. This approach aims to break down traditional educational silos.

Barbosa advocates for creating environments where exploration, dialogue, and discussion are central. It emphasizes that discussions should resonate with students' experiences and interests.

Real-Life Applications in Mathematics

Teachers should present real-life scenarios instead of fictional ones to enhance student engagement. Real contexts can lead to meaningful discussions around mathematical concepts.

Three methods are proposed for configuring a learning environment: problematization of real situations, presenting problems based on data collected by students, or using themes generated by student interest.

Problem-Solving Approaches

The first method involves teachers introducing specific tasks with all necessary data provided for collaborative resolution among students during class discussions.

In the second method, teachers present problems from reality while allowing students to gather relevant information themselves—encouraging independent research alongside guided instruction.

An example illustrates how students might investigate local cellular service providers' effectiveness based on gathered data—a practical application reinforcing their analytical skills.

This structured overview captures key insights from the transcript while providing timestamps for easy reference back to specific points discussed.

Importance of Project-Based Learning in Mathematics

The Need for Practical Applications

Discussion on the absence of a swimming pool at school raises questions about costs and logistics, highlighting the need for qualitative and quantitative research by students.

Emphasis on project-based learning where students can propose real-life situations, such as constructing a swimming pool, to explore practical applications of mathematics.

Social Relevance and Community Impact

Building a swimming pool could enhance community quality and address social issues, indicating that mathematical problems can have significant societal implications.

Encouragement for creating an open environment where students engage with both mathematical and non-mathematical contexts.

Active Learning Through Problem Solving

Professor Barbosa advocates for presenting new problems rather than traditional content delivery, promoting active student engagement in problem-solving.

The goal of basic education is to prepare students for citizenship; thus, math classes should incorporate real-world scenarios beyond just mathematical concepts.

Modeling Mathematics as an Educational Tool

Bridging Theory with Real-Life Situations

Mathematical modeling addresses student inquiries about the application of math in society while maintaining a balance between theoretical knowledge and practical use.

Distinction between "educating for mathematics" (focusing on outcomes) versus "educating through mathematics" (emphasizing the process).

Perspectives from Educators

Introduction of Professor Lurdes Wesley de Almeida's view on mathematical modeling as a pedagogical alternative that integrates non-mathematical problems into math education.

Almeida’s approach aligns with Barbosa’s perspective, emphasizing the importance of engaging students in meaningful problem-solving activities.

Phases of Mathematical Modeling

Defining Mathematical Modeling

Definition provided by Almeida et al. describes mathematical modeling as transitioning from an initial problematic situation to a desired solution using necessary procedures and concepts.

Dynamic Nature of Modeling Activities

The authors outline four phases involved in mathematical modeling: understanding the problem, mathematization, solving problems, interpreting results, and validating findings. These phases are not strictly linear but dynamic.

Exploring Mathematical Modeling in Education

The Process of Problem Solving

The initial phase involves exploration and conjecture formulation, where students attempt to construct solutions for real-world problems without predefined procedures.

Data collection is crucial; students seek information to begin the process of mathematization, emphasizing the importance of contextualizing mathematical problems within everyday situations.

Perspectives on Mathematical Modeling

Professor Lurdes aligns with other educators like Professor Barbosa, focusing on strategies that define actions related to problem-solving in mathematics education.

Renowned educator Ademir Donizeti Caldeira emphasizes integrating mathematical modeling into curricula while maintaining universal mathematical concepts rather than rigidly adhering to existing curricular content.

Fundamental Concepts in Mathematics

Key mathematical concepts discussed include those outlined by Bento de Jesus Caraça, which transcend various branches of mathematics and should not merely replicate traditional curriculum structures.

Caldeira advocates for viewing modeling as a learning system that enhances understanding of educational issues in mathematics, linking social themes to citizenship education.

Community Context and Relevance

Emphasizing the significance of real-world problems relevant to students' communities is essential for effective teaching; abstract topics must connect with local contexts.

The model encourages teachers to consider how mathematics can transform community engagement rather than focusing solely on theoretical constructs disconnected from students' realities.

Rethinking Curriculum Design

Caldeira proposes that mathematical modeling serves as a pathway for teaching and learning math through observation and inquiry-based discussions about real-life challenges.

He critiques linear curriculum designs, suggesting they limit opportunities for meaningful engagement with real-world applications of mathematics.

Creative Insubordination in Teaching

The concept of "creative insubordination" emerges as a critical theme; educators should question what is truly necessary to teach based on student needs rather than strictly following prescribed curricula.

A flexible approach allows teachers and students to redefine educational priorities, ensuring relevance and dynamism in the learning process.

Modeling in Mathematics Education

The Importance of Critical Competence

Modeling transcends mere methodology; it fosters a dynamic and investigative approach driven by critical thinking, as emphasized by Caldeira and other mathematical educators.

Developing Critical Thinking through Real Problems

Fostering students' critical competence involves engaging with fundamental doubts, leading to the conception of mathematical modeling that starts from real-world problems, allowing for multiple answers rather than fixed curriculum paths.

Breaking Traditional Curriculum Structures

The proposal by Caldeira suggests a broader scope beyond simple content teaching, addressing political, social, and human concerns relevant to the community where students are situated.

Diverse Perspectives on Mathematical Modeling

Various educators like Bazzanesi and Maria Salete view mathematical modeling as a strategy for learning math content. Their approaches highlight the importance of student interest and real-life problem-solving in education.

Characteristics of Effective Mathematical Modeling

Almeida Silva Everton views modeling as a pedagogical alternative while Barbosa emphasizes its role as a learning environment. These perspectives contribute to understanding how modeling can enhance educational practices.

Contextualizing Learning within Students' Reality

The initial definitions focus on content but evolve to emphasize that learning must connect with students' realities and interests, fostering engagement in their educational journey.

Engaging Students in Active Learning

Analyzing various conceptions reveals both distances and proximities among them; teachers should consider these when implementing mathematical modeling strategies tailored to their classroom contexts.

Principles for Implementing Mathematical Modeling

Educators should identify which conception aligns best with their teaching style while recognizing that different approaches can effectively address real-world problems through mathematics.

Creating an Interactive Learning Environment

Emphasizing active student participation is crucial; learners should engage in data collection and problem-solving activities that resonate with their everyday experiences.

Interdisciplinary Approach to Mathematics Education

A successful model integrates multiple math concepts across disciplines, promoting interconnectedness rather than isolated lessons focused solely on specific topics like percentages or ratios.

Collaborative Problem Solving in Classrooms

Encouraging group discussions allows students to explore various solutions collaboratively. Teachers play a mediating role, guiding discussions about different approaches to problem-solving.

Understanding Perspectives in Mathematical Modeling

Active Role of Students in Learning

The presentation emphasizes the active role students play in their learning process, highlighting the importance of engagement and participation.

Seven different conceptions were presented, suggesting that individuals may identify with multiple perspectives simultaneously.

Research Perspectives and Methodologies

It is crucial to define one or more research perspectives when engaging with mathematical modeling as a pedagogical approach.

The discussion includes insights from various researchers who have contributed to the understanding of mathematical modeling as an alternative teaching method.

Diverse Conceptions in Education

The focus is not on identifying a single best conception but rather recognizing the diverse viewpoints offered by different researchers.

The concept of "excessive vision" (excedente de visão), introduced by Bakhtin, encourages humility and openness to feedback from others regarding one's work.

Collaborative Learning Environment

The speaker aims to foster dialogue among colleagues and educators at various levels, promoting open discussions beyond just classroom settings.

Engagement metrics indicate strong participation, with over 100 comments and significant attendance during live sessions, reflecting interest in collaborative learning.

Importance of Multiple Perspectives

All materials related to the course will be made available for further study, including slides and links for downloading resources.

Emphasis is placed on understanding that all educational practices are informed by various concepts viewed through different lenses.

Closing Thoughts on Educational Growth

Respecting diverse viewpoints fosters personal growth and learning; this message is central to the speaker's philosophy as an educator.

A reminder about upcoming discussions on mathematical modeling research in Brazil concludes the session.