USING THE SOFTWARE MODELLUS TO HELP THE BASED LEARNING PROBLEMSLuiz Adolfo de Melloladmello@uol.com.brCentro de Cincias Exatas e Tecnologia - UFS

INTRODUO Vamos mostrar aqui como o software educacional Modellus pode ser usado para se construir exemplos virtuais de problemas de fsica, que quando usados com um conjunto apropriado de questes pode tornar-se uma poderosa ferramenta de ensino no esprito do construtivismo e na metodologia de aprendizado por problemas (based learning problems). Baseado em problemas tirados de livros textos construmos aqui um conjunto de modelos que podem ajudar ao aluno compreender o que o autor almeja que ele faa. Alm do mais, os modelos virtuais ajudam ao aluno compreender qual a relao entre os problemas de fsica e o mundo real, dando vida a estes exerccios e permitindo que o aluno veja que sua soluo no apenas um exerccio numrico, mas sim, uma foto de um conjunto de eventos.

ABSTRACTWe will expose here how the educational software Modellus can be used to create a set of virtual physical examples that when used with a set of appropriate questions becomes a powerful teaching tool in the spirit of constructivism and in the based learning problems. Here I proposed/construct the models based in problems of text physics book that can be used to illustrate it. How I will show below, the virtual models help the student imaging what the problem wants. I suggest that the virtual models can help the student understand what is the relation between the problem and real word.

Key words: Ensino de Fsica; Modelagem matemtica; software de ensino; aprendizagem baseada em problemas.

INTRODUCTION

Modellus was created by Teodore[1,2] and it is a computational environment that allows the construction and simulation of physical and mathematical phenomena using mathematical equations. 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. As in the Matlab software tool called simulink [4], you can express all our integral equations in a differential form. It prepares the student to use the powerful engineering tools as Matlab. It is largely used to help laboratory and classroom tasks in the high school. Some authors suggested that it can be used in school where the laboratory of physics is poor. I suggest that it can be used as a kind of juniors table control or juniors matlab. 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. 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].By the above argument who doesnt 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, that 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. More details see Teodore [1,2 and 4]. And it shows the graphics and table of the variables we want, figure 2. The program use numerical integration, so all variable are defined as function of t (time or integration step) or free parameter. As it allow us create bottoms controls or indicators to free parameters, figure 3, we can use it as simulator controls. So the student/user can acquire the full meaning of the system of equations as he play/explore the model. So the software Modellus solve one of the major problems of modern science, i. e. generaly we learn mathematics as will be a mathematician no a natural scientist (physics, chemist, biologist or engineer) that can use the mathematics as a tool to describe the physical world.

Fig.1 Modeling a car movement with uniform movement

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

Fig3. You can change the velocity of the object as the car moves.

Theory

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. These activities include creating stories; reasoning about cases; concept mapping; causal mapping; cognitive hypertext crisscrossing; reason analysis unredoing; analogy making; and question generating;

In PBL, students are encouraged to take responsibility for their group and organize and direct the learning process with support from a tutor or instructor. Advocates of PBL claim it can be used to enhance content knowledge and foster the development of communication, problem-solving, and self-directed learning skill.In some ways what PBL is seems self-evident: it's learning that results from working with problems. Official descriptions generally describe it as "an instructional strategy in which students confront contextualized, ill-structured problems and strive to find meaningful solutions." 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. 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.In PBL, the students determine their learning issues and develop their unique approach to solving the problem. The members of the group learn to structure their efforts and delegate tasks. Peer teaching and organisational skills are critical components of the process. Students learn to analyse their own and their fellow group members learning processes and, unlike problem-solving learning, must engage with the complexity and ambiguities of real life problems. It is ideally suited for the development of key skills, such as the ability to work in a group, problem-solving, critique, improving personal learning, self-directed learning, and communication.

Methodology

As a first problem lets 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 concave mirror.

As a second example let see the problem of a man that parachute jump of a airplane that move uniformly with velocity Vav, subject to air resistence.Problem A man parachute 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.6 Open the graphical windows and discuss what happen with the curve of velocity of the movement after he opened the parachute.7 In the model you can made the parachute air resistance equal zero. Its correct? What is the air resistance minimum value?8 You think that with professional software we can simulate a paraglider 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 wasnt one, it can replace it. Its 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.

References

[1] V.D. Teodoro, Modellus: Learning Physics with Mathematical Modelling. Unpublished PhD Thesis, Universidade Nova de Lisboa, Lisboa, 2002. [Links] [2] V.D. Teodoro, J.P. Vieira and F.C. Clrigo, Modellus, Interactive Modelling with Mathematics (Knowledge Revolution, San Diego, 1997). [Links] [3] TEODORO, V. D.; VIEIRA, J. P. D.; CLRIGO, F. C. Modellus 2.01: interactive modelling with mathematics. Monte Caparica: Faculdade de Cincia e Tecnologia - Universidade Nova de Lisboa, 2000.[Links] [4] TEODORO, V. D. Modellus: experiments with mathematical models. Disponvel em: < http://phoenix.sce.fct.unl.pt/modellus/ > . Acesso em: 20 maro 2002.[Links] [5] TEODORO, V. D. From formulae to conceptual experiments: interactive modelling in the physical sciences and in mathematics. In: INTERNATIONAL CoLos CONFERENCE NEW NETWORK-BASED MEDIA IN EDUCATION, 1998, Maribor, Eslovnia. [S.l.: s.n.], 1998. p. 13-22.[Links] [6] KRAPAS, S.; QUEIROZ, G.; COLINVAUX, D.; FRANCO, C. Modelos: uma anlise de sentidos na literatura de pesquisa em ensino de cincias. Invest. Ens. Ci., Porto Alegre, v. 2, n. 3, p. 185-205, set./dez. 1997.[Links] [7] GRECA, I. M.; MOREIRA, M. A. Mental, physical, and mathematical models in the teaching and learning of physics, Science Education, v. 86, p. 106-121, 2002.[Links] [8] E.A. Veit, V.D. Teodoro. Modelagem no Ensino/Aprendizagem de Fsica e os Novos Parmetros Curriculares Nacionais para o Ensino Mdio. Rev. Bras. De Fsica. Vol.24, n-2, So Paulo, June 2002.[9] F. Ornek, Models in Science Education: Applications of Models in Learning and Teaching Science. International Journal of Environmental & Science Education, 2008, 3 (2), 35 45

[10] I. Halloun, Schematic Modeling for Meaningful Learning of Physics. Journal of Research in Science Teaching, Volume 33 Issue 9,Pages10191041 Published Online: 7Dec1998

[11] en.wikipedia.org/wiki/Problem-based_learning

[12] http://physics.dit.ie/programmes/pbl.html