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. 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 problemsolving 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
