USING THE SOFTWARE MODELLUS TO HELP THE “BASED LEARNING PROBLEMS” Prof. Dr. Luiz Adolfo de Mello Orientandos: Ponha sua Marca

INTRODUÇÃO Vamos mostrar aqui como o software educacional Modellus pode ser usado para se construir “exemplos virtuais” de problemas de física, que quando usados com um conjunto apropriado de questões pode tornar-se uma poderosa ferramenta de ensino no espírito do construtivismo e na metodologia de aprendizado por problemas (based learning problems).

INTRODUÇÃO Baseado em problemas tirados de livros textos construímos aqui um conjunto de modelos que podem ajudar ao aluno compreender o que o autor almeja que ele faça. Além do mais, os modelos virtuais ajudam ao aluno compreender qual a relação entre os problemas de física e o mundo “real”, dando vida a estes exercícios e permitindo que o aluno veja que sua solução não é apenas um exercício numérico, mas sim, uma “foto” de um conjunto de eventos.

Aprendizado Baseado em Problemas PBL is based on the educational theories of Vygotsky, Dewey, and others, and is related to social-cultural constructivist theories of learning and instructional design [11]. The characteristics of PBL are: Learning is driven by challenging, open-ended, ill-defined and ill-structured, practical problems.

Students generally work in collaborative groups Students generally work in collaborative groups. Problem based learning environments may be designed for individual learning. Teachers take on the role as "facilitators" of learning. Instructional activities are based on learning strategies involving semantic reasoning, case based reasoning, analogical reasoning, causal reasoning, and inquiry reasoning,

Instructional activities are based on learning strategies involving semantic reasoning, case based reasoning, analogical reasoning, causal reasoning, and inquiry reasoning. These activities include creating stories; reasoning about cases; concept mapping; causal mapping; cognitive hypertext crisscrossing; reason analysis unredoing; analogy making; and question generating;

Responsabilidade do Aprendizado In the PBL (Problem-Based Learning) the responsibility of learning is transferred from teacher to the student. The student no longer is a passive element of learning process, whose only educational function is to take lectures notes, but become a major generator agent of the knowledge to actively seek information that his need to resolve determined problem. The education, or better, the learning process is oriented by the problems suggested to the student and his need to solve independently.

Aprendizado Resolvendo Problemas It is important to have a clear understanding of the distinction between learning via problem-solving learning and problem-based learning (PBL) [12]. In engineering and physics the use of problem-solving learning is well established. In this method the students are first presented with the material, usually in the form of a lecture, and are then given problems to solve.

These problems are narrow in focus, test a restricted set of learning outcomes, and usually do not assess other key skills. The students do not get the opportunity to evaluate their knowledge or understanding, to explore different approaches, nor to link their learning with their own needs as learners. They have limited control over the pace or style of learning and this method tends to promote surface learning. Surface learners concentrate on memorization whereas deep learners use their own terminology to attach meaning to new knowledge.

O QUE É O MODELLUS

INTRODUÇÃO Modellus é um ambiente computacional que permite a construção e simulação de modelos de fenômenos físicos, químicos e matemáticos utilizando equações matemáticas que representam esses fenômenos. Desta forma o usuário descreve o modelo matemático que representa o fenômeno, o Modellus realiza a simulação computacional  deste.

A idéia básica do projeto é de que o aluno se preocupe mais com a interpretação do significado desses modelos do que com as equações matemáticas. Ele permite que alunos e professores realizem experiências com modelos matemáticos, a onde eles podem controlar variáveis como tempo, distância e velocidade e analisar a variação da função graficamente, preparar animações, resolver exercícios e criar os seus próprios exercícios dentro do contexto do autor do Modellus.

In this way the user (the student) construct the mathematical model to the physical problem and its graphical representation, and the Modellus make the computational simulation of this. The Modellus is a free software [3] and allow us make conceptual exercises constructed from functions, equations, systems of equations, differential equations, change rates and finite difference equation, as it is write in text book and learning in classroom.

Laboratório de Física Ele é muito usado no auxilio à aulas teóricas, complementando laboratórios ou substituindo a onde eles não estão disponíveis. Área de Pesquisa Realidade virtual X Mundo Físico

Modelagem Matemática Nowadays the mathematical modeling understands as a generalization of physical paradigm (Galileo Galilei) that the physical World can be explained in mathematical language. This is a new area that uses the Mathematics and Computation methods in the elaboration of mathematical models and simulations to find solutions to the problems in several areas of knowledge.

Modelagem Matemática So the first meaning of mathematical modeling that we are using is that we are representing some object or real system through mathematical correlations (with more or less simplified suppositions) to computational implementation. The second meaning of model is the physical models [5,6]: descriptions simplified and idealized systems or physical phenomena accepted by the community of physicists, involving elements such representations (external), semantic propositions and inherent mathematical models [7 - 10].

Física x Matemática By the above argument who doesn’t dominate the mathematical tools would not be able to made mathematical modeling. The Modellus solves partially this problem. As was stated above the software interprets the mathematical equations, this is, solve it and we can “say” to the program that an object has coordinates that behaved as a solution of the equation, figure 1.

Fig.1 – Modeling a car movement with uniform movement

Fig.2 – Modellus made table and graphics simultaneous to the movement

Methodology   As a first problem let’s analyze the simple problem of find the position and height of an image of a man in front of a mirror. Problem – Find the position and height of an image of a man that is a 2 meters from an ideal mirror. Consider that his height is 2.90m.

Conceptual questions: 1 – Solve the problem geometrically and analytically. 2 – Open the model convex_mirror and change the mirror radius. What is the difference between a convex and a concave mirror? 3 – Where in the model we use the fact that the mirror is ideal? 4 – How we could improve the model to make a non ideal mirror?

5 – Take the mirror equations (1/f = 1/p + 1/p’ and A = hi/ho) and put the Xi (=p’) and hi (image position and its height) variables in evidence, and verify if you get the same equations of the model. 6 – You think that a computer, with a right program, could control the image formation of a picture?

Fig.4 – An optical model - position and height of an image of a man in front of a mirror.

Segundo Exemplo As a second example let see the problem of a man that jump of a airplane that move uniformly with velocity Vav, subject to air resistence. Problem – A man jump of an airplane traveling horizontally with initial velocity equal to 200km/h. If he is in free fall with open legs and arms the air resistance can be considered linear with his velocity. What are his maximal velocity and the horizontal distance that he travels? Consider the air resistance in the horizontal distance equal to the vertical.

Conceptual questions: 1 – What is the function that represents the velocity of the man? 2 – If the air resistance were considered zero what kind of movement we will obtain? 3 – Open the model parachute1 and argue your answers. 4 – How you can make a model that we could model a man opening a parachute after t second after he jump the airplane? 5 – Open the model parachute2 and compare it with your model.

Conceptual questions:  6 – Open the graphical windows and discuss what happen with the curve of velocity of the movement after he opens the parachute. 7 – In the model you can made the parachute air resistance equal zero. It’s correct? What is the air resistance minimum value? 8 – You think that with professional software we can simulate a parachutist stunts or an airplane flying?

Fig.4 – Parachute model with velocity, and aerodynamics coefficients controls.

Conclusion The Modellus software can be used to illustrate some problems of physics find in text book and make the student think about the possibility of this knowledge be applied in the real world as the questions 1.6 e 2.8 suggest. It can be used together if the physics laboratory or, when there wasn’t one, it can replace it. It’s a powerful teaching tool to demonstrate to the student the relevance of the physical way of think: to use the mathematical models to represent the natural world.

Prof. Dr. Luiz Adolfo de Mello Áreas de Atuação Modelagem Matemática Ensino de Matemática Dinâmica Molecular Cálculo de Estrutura Eletrônica