Research, Education and Problem Solving as a Virtuous Circle

Transcription

1 The nd International Symposium on Interatin Research, Education, Problem Solvin: IREPS 01 Research, Education Problem Solvin as a Virtuous Circle Horacio E. Bosch Mercedes S. Berero Mario Di Blasi Maria C. Rampazzi Grupo de Investiación Educativa en Ciencias Básicas, FRGP, Universidad Tecnolóica Nacional Gral. Pacheco, Pcia. de Buenos Aires (1617), Arentina

2 ABSTRACT The world is concerned about science mathematics education for both secondary university students, in order to become the future workforce. Since many years, several attempts to describe smart tutorial systems have been made. Present technoloies are needed to assist learners. The National Science Foundation has supported the Innovative Technoloy Experiences for Students Teachers Proram in order to call for proposals about this subject matter. The present authors, inspired on this Proram, submit innovative experiences for sciences mathematics learnin. A chane in spaces with combined classroom laboratory facilities is needed in order to implement an automatic system for data acquisition, processin representation. Open educational reurces are desined with new technoloies for representin, manipulatin, communicatin data, information, ideas focused on practices in STEM fields. Technoloy should be used to support student interaction with STEM content in ways that promote deeper understin of complex ideas, enae students in lvin complex problems, create new opportunities for STEM learnin. The present paper contents me examples on how to deal with real life problem lvin at the intersection of various sciences disciplines, technoloy, enineerin mathematics. These open educational reurces are free can be used by those teachers who have been trained durin several workshops. Keywords: experiences, sciences, mathematics, technoloy, teachers, students. 1. INTRODUCTION The World is very much concerned about the application of present technoloies as tools for students performances both in hih school university. Several proposals for helpin student s learnin, particularly in science mathematics, have been done (Cataldi 009) (Chipan et al., 005), more recently, U.S. Department of Education, Office of Educational Technoloy, Transformin American Education: Learnin Powered by Technoloy (DOE, 010). The new students eneration is usin video ames they have acquired practice in dealin with simultaneous processes in very short times with hih density knowlede. So, if a new tutorial system will be desined, it has to be accordin to those practices.. APPLICATION OF SCIENTIFIC METHOD FOR SCIENCES AND MATHEMATICS TEACHING The application of scientific method to sciences mathematics teachin has been applied for a lon time, but the way it is applied at present is no loner valid, accordin the way scientific research is dealin with in the XXI Century. Technoloy is now present in almost any research, in contrast with science mathematics teachin. This is not motivational students find it borin. 3. OPEN EDUCATIONAL RESOURCES DESIGN AND MANAGEMENT Our Education Research Group in Basic Sciences has implemented a Proram based on a tutorial system for experimental sciences mathematics learnin accordin to STEM Pedaoy (Science, Technoloy, Enineerin Mathematics).(Geore Washinton University 009), (CRS Report for Conress, 006), (Meet the Future Summit 010), Success in STEM Education 011). This Proram is inspired on the National Science Foundation Innovative Technoloy Experiences for Students Teachers (ITEST) Proram (NSF, 011). Accordin to the US Department of Education Report (DOE, 010), new technoloies for representin, manipulatin, communicatin data, information, ideas have chaned professional practices in STEM fields. Technoloy should be used to support student interaction with STEM content in ways that promote deeper understin of complex ideas, enae students in lvin complex problems, create new opportunities for STEM learnin. The value of open educational reurces is now reconized around the world, leadin to the availability of a vast array of learnin, teachin, research reurces that learners of any ae can use across all content areas. 4. LABORATORY EXPERIMENTS In contrast with most of Sciences Mathematics textbooks, we emphasize experimentation, as it permits to work with concepts, laws processes applications to real life (Duschl, 004), (Lederman, 004). The instructional unit enaes the students in a carefully structured sequence of hs-on laboratory investiations interwoven with other forms of instruction. For each Experimental Session, a sequence of experiences is presented, in order that each one ives rise to the followin, that is to say, they are linked between what has been done what will be done. Accordin to this sequence, students learn how to observe, how to reister information, how to introduce a scientific model, how to arrive at conclusions, in such a way that they acquire the scientific method. These Series of Experimental Sessions have the objective To provide students with sufficient activities to develop scientific knowlede concepts on sciences mathematics; To acquire attitudes of inquiry data analysis in order to create, test refine models; Scientific modelin is a core element in several innovative laboratory- centered science curricula that appear to enhance student learnin. The development of each experiment encompasses the followin activities Experimental arranement assisted by new elements new technoloies for automatic data processin representation; Experiment performance with automatic simultaneous representation of data atherin; Derive a model its predictions; Fittin model predictions with experimental data; Derive conclusions propose new experiments. The use of these reurces raphics interpretation constitutes an important tool that students are encouraed to measure, to experiment, to discover relationships between variables, makin hypothesis, derive conclusions, communicate them.

3 5. LABORATORIES AND EQUIPMENT Combined laboratory-classrooms can support effective laboratory experiences by providin movable benches chairs, movable walls, peripheral or central location of facilities, wireless Internet connections trolleys for computers, fume hoods, or other equipment. These flexible furnishins allow students to move seamlessly from carryin out laboratory activities on the benches to small-roup or whole-class discussions that help them make meanin from their activities. All computers may be equipped with Computer Alebraic Systems (CAS) (Hohenwarter, M., 004); Wolfram Research Institute, 011). 6. EXAMPLES OF REAL LIFE PROBLEM SOLVING Amon different kinds of problem lvin, one chooses the real life scientific problems, the lution of which is done throuh model conceptions. In order to conceive a model one needs to apply a scientific method: parameters identification, measurements, data loin, data processin, alorithm proposal lvin, predictions, aain experiments to check the predictions. In turn, to follow this sequence we need to perform me research to create a new set of knowlede suitable for the problem to be lved. In order to show the results, we need discussions with peers many others people. The whole interaction iterations between research, model, people experiments, will ive rise to a model proposal, finally, to a problem lution. These procedures promote student reflection usin collaborative tools to reveal clarify students conceptual understin thinkin, plannin, creative processes. These studies must be performed at technoloy-enriched learnin environments that enable all students to pursue their individual curiosities become active participants in settin their own educational oals, manain their own learnin, assessin their own proress. Classical experiences must be re created into new experiences oriented to real-life problems lvin. For this purpose new teachin prototypes must be developed. The aim of our Proram is to ive me examples on how to deal with real life problem lvin at the intersection of various sciences disciplines, technoloy, enineerin mathematics. 7. Motion of a body fallin down to earth Generally, the motion of a body of mass m subject to a force F throuh a trajectory s durin time t is described by the interal equation s ds = t Eq. (7.1) w m s 1 W = F ds= m v(s) Eq. (7.) If the force F is a conservative force derived from a potential function V(s), then s 1 W = -dv = V()- V(s)= mv(s) The equation of enery conservation results Eq. (7.3) 1 V() = V(s) + m v(s) = ET, Eq. (7.4) Where E T is the system s total enery (invariant). Let consider the motion of a body subject to the earth ravitational force F potential V(r). If the initial conditions are: H(0) the distance from earth where the body is launched without initial velocity; V(t)=m..h(t) the body potential enery correspondin to a distance h(t) from the earth; then, equation (.4) becomes 1 V(H) = m h + m v(s) = E T Eq. (7.5) In order to validate equation (7.5), let take a body that falls from the distance H =,4 m down to a distance h = 1,3 m from the experimental table; let consider the followin experimental arranement shown in Fi. 1. A ball is fallin down; the position velocity of it are reistered by ultranic radar. The correspondin values are displayed in Table 1. Fi. 1 represents the eneries raphs from data iven in Table 1. Fiure 1. Experimental arranement for displacement velocity reistration of a fallin body from a distance of,4 m down to 1,3 m. Reistration is taken by ultranic radar coupled to an interface computer. t (s) disp (m) veloc.(m/s) 0,75,40 0,09 0,8,37 0,30 0,85,35 0,65 0,9,31 1,08 0,95,5 1,54 1,16 1,99 1,05,05,44 1,1 1,91,87 1,15 1,76 3,30 1, 1,586 3,70 1,5 1,39 4,09 1,3 1,17 4,47 Table 1. Displacement velocity values reistered correspondin to the ball fall from heiht,4 down to 1,3 m durin almost half second.

4 Enery J Heiht m Fiure. Graphs representin the body potential, kinetic total enery vs. heiht. The kinetic enery does not fit exactly with a linear function since there is a sensible friction of the ball with air. Consequently total enery is constant at the beinnin where both velocity friction are low. When velocity increases, friction too, total enery is reduced up to 5 %. 8. Motion of a body fallin down within a fluid We studied the displacement of a body fallin down within a fluid due to the ravitational attraction. In this case there exists a dra force pullin up the body aainst the ravitational force. In the experimental set up, we choose a coffee filter as a body the atmospheric air as a fluid. We use an automatic system to determine the body s velocity displacement. Ultranic radar is coupled to an interface connected with a computer. A correspondin proram is used to determine the variation of the abovementioned parameters as function of time. Fi. 6 shows the experimental arranement. Fi. 7 illustrates the velocity raphics as function of time showin the velocity limit reached by the body. At he beinnin, the velocity varies linearly with time, later chanes linearity, approachin the velocity limit v (1 e kt ). Eq. (8.3) k The velocity limit is v =. Eq. (8.4) k Replacin the experimental values one ets v(t) =,97 (1- e 3,3 t ), Eq. (8.5) Second Assumption We developed another mathematical model assumin that the dra force actin on the body is proportional to the square of its velocity. The resultant force is expressed by F(t)= m a e y = m e y k m v² e y. ivin rise to the differential equation Velocity (m/s) Fiure 3. Experimental arranement for body s velocity displacement reistration. v =, 97 m s First Assumption We developed a mathematical model assumin that the dra force actin on the body is proportional to its velocity. That is to say, the total force F actin on the body has two components. The resultant force is expressed by F(t) = m a e y = m e y k m v e y. Eq. (8.1) where e y is a unitary vector pointin down to the earth s center. From eq. (8.1) a differential equation is derived ( kv) = dt, Eq. (8.) with the initial condition for t = 0 is v = v 0 ; y = y 0 = 0. From the experiment is v 0 = 0, then Time (s) Fiure 4. Body s velocity reistration as function of fallin time. dt (kv ) Eq. (8.6) In order to homoenize the forces actin on the body, the k constant is expressed as function of two parameters y ² that k.the constant must have a velocity dimension; we choose its value bein the velocity limit =.97 m s. Then the differential equation is set dt. Eq. (8.7) v 1

5 with the initial condition for t = 0 is v = v 0 = 0. The lution of Eq. (8.7) is obtained throuh the use of the Computer Alebra System iven by 1 v 1 0 tanh tanh t v (t) =,97 tanh(3,3 t). Eq. (8.8) Two hypotheses have been assumed, one, the dra force actin on the body is proportional to its velocity, the other, to the velocity squared. The raphics from Fi. 8 shows the representation of both functions (8.5) (8.8) the experimental one from Fi.5, within the time interval where the dra force is actin clearly on the body, that is to say in the time interval [1,1 ; 1,5]. Velocity (m/s) 3. 0 Function (8.8) Function (8.5) Experimental results Time (s) Fiure 5. Fallin body s velocity raphs accordin to experimental results functions Eq.(8.5) Eq.(8.8). In the time interval between s one observes that function Eq.(8.5) approaches more to the experimental function than function Eq.(8.8). Accordin to these raphics we arrive at the conclusion that the most plausible approximation is that the dra force is proportional to the body s velocity, at least accordin to the experimental arranement of Fi. 3. DISCUSION AND CONCLUSIONS Open educational reurces for teachin sciences mathematics have been proposed by means of application the scientific method assisted by electronic information Technoloies. The experimental sessions are performed with an automatic reistration system (Computer Based Laboratory). Scientific models are proposed to predict the system s behavior confronted with experimental data. A CAS is used to lve differential equations raised from mathematical models. experiment. One has to prove that the differential equation s lution is correct from the mathematics stpoint of view is correct from the real life problem point of view. Multidisciplinary focus in accountin for a lution of a real life problem is a way that promises to be more attractive to students. If one assumes that this is the way to conduct science enineerin education, ettin the correspondin feedback to improve model problem lution, one has created a virtuous circle between research, education problem lvin. REFERENCES [1 ]America's Lab Report: Investiations in Hih School Science (011). (consult: permanent). [] CATALDI, Zulma; LAGE, Ferno J. (009). «Sistemas tutores intelientes orientados a la enseñanza para la comprensión».edutec, Revista Electrónica de Tecnoloía Educativa. Núm. 8/ Marzo (consult:10/10/11). [] CHIPMAN, P., OLNEY, A., & GRAESSER, A. C. (005). The AutoTutor 3 architecture: A ftware architecture for an expable, hih-availability ITS. Proceedins of WEBIST 005: Portual, INSTICC Press. [4 ]DOE (010). U.S. Department of Education, Office of Educational Technoloy, Transformin American Education: Learnin Powered by Technoloy, Washinton, D.C., 010 [5] Duschl, R. (004). The HS lab experience: Reconsiderin the role of evidence, explanation, the lanuae of science. Committee on Hih School Science Laboratories: Role Vision. (consult: ermanent). [6] Hohenwarter, M. (004); Steiun und Ableitun einer Funktion mit GeoGebra. (consult: permanent) [6] Lederman, N.G. (004). Laboratory experiences their role in science education. Committee on Hih School Science Laboratories: Role Vision. (consult: permanent). [6] MEET THE FUTURE SUMMIT (consult: 10/10/11). [7]National Science Foundation (011). (consult: permanent). [8] Science, Technoloy, Enineerin, Mathematics (STEM) Education Issues Leislative Options (006) CRS Report for Conress, Order Code RL33434 [9]Successful STEM Education (1): A Workshop Summary. (consult: 10/10/11). [10] Wolfram Research Institute (011), (consult: permanent). [11]Workshop on Science, Technoloy, Enineerin Mathematics (STEM) Enterprise: Measures for Innovation & Competiveness (009),Geore Washinton University, Washinton, D.C. A Framework for K-1 Science Education: Practices, Crosscuttin Concepts, Core Ideas. (consult: 10/10/11). The examples shown provide an idea on how an open education reurce may be written in the future. First of all, formulas appear as consequence of a physical system study. Second, a model proposition arises from a system description. Thirdly, the model prediction must always be validated by