Computer Software - The Meaningful Learning Research Group
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1. KIK P 100 90 80 70 60 50 40 30 20 10 0 10 20 30 40 50 60 70 80 90100110120130140150 1 values Position as a function of time Rate of change of position 50 60 time s 40 50 60 time s Sketch graph L values Sketch graph Values Figure 2 From graph to motion The graph was sketched with the mouse The motion of the athlete can be obtained from the graph of position or from the graph of rate of change in position graph on the right done with CHANGE Teodoro 1992 Sistema Janelas Opcoes Dinamix Jw eeke l a Rectilinear motion 0 5 Figure 3 After writing an equation dx dt vx the user can move an object a stroboscopic representation is shown down right and see a graph of position as a function of time top right Done with DINAMIX Lobo 1991 ROOTS OF EXPLORATORY SOFTWARE Papert and LOGO Since Papert wrote Mindstorms 1980 learning with computer based exploratory environments in science and mathematics has become one of the predominant views of computers in education Papert was the first to argue that a computer is a tool that students can use to change the nature of conceptual objects Stated most simply my conjecture is that the computer can concretize and personalize the formal Seen in this light it is not just another powerful educational tool It is unique in providing us with the means for addressing what Piaget and many others see as the obst2. 1993 Conference Date August 1 4 1993 Contact Information correct as of 12 23 2010 Web www mlrg org Email info mlrg org A Correct Reference Format Author Paper Title in The Proceedings of the Third International Seminar on Misconceptions and Educational Strategies in Science and Mathematics Misconceptions Trust Ithaca NY 1993 Note Bene This paper is part of a collection that pioneered the electronic distribution of conference proceedings Academic livelihood depends 1 upon each person extending integrity beyond self interest If you pass this paper on to a colleague please make sure you pass it on intact A great deal of effort has been invested in bringing you this proceedings on the part of the many authors and conference organizers The original publication of this proceedings was supported by a grant from the National Science Foundation and the transformation of this collection into a modern format was supported by the Novak Golton Fund which is administered by the Department of Education at Cornell University If you have found this collection to be of value in your work consider supporting our ability to support you by purchasing a subscription to the collection or joining the Meaningful Learning Research Group Designing Computer Exploratory Software for Science and Mathematics Vitor Duarte Teodoro Faculdade de Ci ncias e Tecnologia Universidade Nova de Lisboa 2825 Monte de Caparica Portugal Abstra
3. difficult to see how the computer could be used as a tool most computer tools were so difficult to use that nearly all potential users were intimidated by them e g word processors and spreadsheets were still in their infancy Now with graphical interfaces it is possible to have computer software that almost dispenses with manuals or specific instructions on how to use it Strongly related to graphical user interfaces is the concept of direct manipulation proposed by Shneiderman 1983 This concept is based on the idea that most actions on the screen need not be mediated by any written language Screen objects should have properties and reaction similar to those of real objects For example if we want some screen object to change its position on the screen we only need to hold that object with the mouse and move it to another position The concept of direct manipulation is crucial to the design of exploratory environments but it raises problems when it refers to conceptual objects if conceptual objects such as a vector are human constructs what does it mean to directly manipulate something that does not exist as a real object This problem shows that exploratory software can be another source of misconceptions in science and mathematics We must then be very careful about the use of direct manipulation in regard to conceptual objects A MODEL TO DESIGN EXPLORATORY SOFTWARE In the above sections I tried to define explo
4. learning How can we characterize a constructivist view of learning Novak 1990 claims that human beings all have an enormous capacity for meaning making and the use of language to construct and communicate meanings I seek to conflate issues that deal with the nature of knowledge construction into the issues that deal with the psychology of meaning making In both cases I see human capacity for meaning making and the nature of that process as the bottom line What really counts in my view is how to empower human beings to optimize their phenomenal capacity for meaning making including their awareness and confidence in processes that are involved This capacity for meaning making is what I refer to as human constructivism p 20 Accordingly to Forman and Pufall 1988 constructivism embodies three properties epistemic conflict self reflection and self regulation 1 Epistemic conflict involves two knowing systems These systems may originate in different individuals and it may be that in early development we are more dependent on externally induced conflict than we are subsequently Whatever the source of conflicting epistemic stances if there is a resolution it is within the individual experiencing the conflict that is it is an individual construction If the resolution is developmental in the strict sense it means constructing a new way of thinking about reality and is marked by logical necessity p 236
5. thinking Self explanatory interface Figure 4 A model to guide the design of computer exploratory environments Along the theoretical line we have three issues to consider First the design of exploratory software should be based on research on concept formation and on misconceptions We have now an enormous body of literature about concept formation and misconceptions specially in science and mathematics This research can be taken as basic research to identify relevant learning experiences and sources of difficulties in concept formation Second we pose a specific view on learning Such a view assumes that understanding as a result of learning is not a metaconcept but a much less ambitious concept We understand when we are familiar with ideas and representations shared by members of a community Understanding scientific ideas is I assume a process of enculturation This 14 process is facilitated when learning occurs in the zone of proximal development Vygotsky 1978 Third we also pose a view on science as a process of creating testing and communicating representations of the world Along the methodological line we point out five issues First the development of exploratory software is a team project involving different specialists experienced teachers software designers programmers graphic specialists cognitive psychologists Second exploratory software should be designed after the identification of the most
6. variables such as method of teaching But decades of educational thinking and practice show that there are no such variables as independent variables All variables are mutually dependent when we think of learning environments To think that computers alone and exploratory software in particular can change education is an expectation that can block out the most important steps that should be taken to transform schools into learning communities REFERENCES Ausubel D P Novak J D Hanesian H 1978 Educational Psychology A Cognitive View 2nd edition NY Holt Rinehart and Winston Bliss J et al 1992 Summary Report of the Tools for Exploratory Learning Programme London King s College Brown J S Collins A Duguid P 1988 Situated Cognition and the Culture of Learning IRL Report No IRL 88 0008 Palo Alto Institute for Research on Learning Chi M T H Feltovitch P J Glaser R 1981 Categorization and Representation of Physics Problems by Experts and Novices Cognitive Science 5 121 152 This note was inspired in the final talk given by Bob Glaser and in the talk given by Gavriel Salomon at the NATO ASI Psychological and Educational Foundations of Technology Based Learning Environments held at Kolimbari Crete July 1992 20 Educational Technology Center 1988 Making Sense of the Future Cambridge Mass Harvard Graduate School of Education Forman G Pufall P B 1988 Constructivis
7. 2 Self reflection is construed as a response to conflict 3 Self regulation is the developmental restructuring of thought These authors point that the self organizing properties of the knower allow him to abstract structure from action not necessarily with conscious processes Forman amp Pufall 1988 p 236 11 More recently the educational community is recognizing that the constructivist view of learning must be combined with the recognition of the consequences of the fact that learning takes place in social environments where the interaction between students teachers and students and all other social actors are crucial in the process of making sense that is the process of generating knowledge As Brown Collins and Duguid 1988 p 7 wrote learning is we believe a process of enculturation Under a constructivist view of learning abstracting structure from action is not necessarily a conscious process Then in a certain way learning can be viewed as a process by which new knowledge is not necessarily new explicit knowledge we can know without knowing This idea can be re stated by defining learning as a process of becoming familiar with knowledge not as constructing new explicit knowledge Learning most of the scientific and mathematical ideas at secondary school can then be seen as a process of becoming familiar with them True understanding of an idea is most of the times a strong degree of familiarizati
8. Manual Veenman Marcel V J Elshout Jan J Hoeks J in press Determinants of Learning in Simulation Environments across Domains In Ton de Jong Hans Spada Doug Tawne eds The Use of Computer Models for Explication Analysis and Experiential Learning Berlin Springer Vigotsky L S 1978 Mind in Society Cambridge Mass Harvard University Press 22
9. Third Misconceptions Seminar Proceedings 1993 Paper Title Designing Computer Exploratory Software for Science and Mathematics Author Teodoro Vitor Duarte Abstract The aims of this paper are 1 to characterize computer exploratory software 2 to identify the roots of this kind of software 3 to present a model to design computer exploratory environments for science and mathematics 4 to discuss some of the basic issues of the model and 5 to analyze some programs developed in the framework of the model The model is based on findings in learning and in recent developments of computer graphic environments It assumes that 1 learning is a process of enculturation a process of becoming familiar with ideas and representations 2 exploratory software should be integrated with other resources 3 exploratory software should allow direct manipulation of concrete abstract objects and the exploration of multiple representations of a phenomenon Keywords science education mathematics education computers simulations exploratory environments learning General School Subject Specific School Subject science amp math Students high school Macintosh File Name Teodoro Computer Software Release Date 9 15 1994 I Publisher Misconceptions Trust Publisher Location Ithaca NY Volume Name The Proceedings of the Third International Seminar on Misconceptions and Educational Strategies in Science and Mathematics Publication Year
10. acle which is overcome in the passage from child to adult thinking I believe that it can allow us to shift the boundary separating concrete and formal Knowledge that is accessible only through formal processes can now be approached concretely And the real magic comes from the fact that this knowledge includes those elements one needs to become a formal thinker p 21 According to Papert exploratory computer tools are seen as tools to overcome the boundary between lower and higher cognitive stages This can be done because computers allow users to approach concretely what without the computer can only be approached in a formal way Papert s view is a compromise between the use of a computer as a new kind of tool in education and a more traditional view of the computer as an object to be programmed I see this compromise as rooted in the personal history of Papert a mathematician and a computer scientist who after some work with Piaget became interested in how students learn Papert s work was based on a computational metaphor programming that is too elementary to allow the exploration of many fields Programming even in a high level language such as LOGO uses primitives that are too primitive to allow meaningful exploration of most scientific ideas With a programming language it is possible to explore most scientific ideas but the programming language itself behaves as a mediator that does not have the properties of th
11. an teach the computer how to do things e g build a mathematical model of an object that falls on the earth or on any other planet move an angle that produces a graph etc and then get feedback about the reasonability of what they have done In a computer exploratory environment there are three possible kinds of objects Table 2 Kinds of objects in a computer exploratory environment Type I real objects objects that represent real objects e g a planet a car a particle with more or less perceptual fidelity Type II conceptual objects objects that are pure conceptual objects e g a variable a vector that have no perceptual fidelity Type III relations between propertiebjects that represent relations between properties of other objects e g a graph an equation Type II objects of a computer exploratory environment acquire a new status as compared with traditional modes of concept learning Hebenstreit 1987 argues that they are a new genre of objects concrete abstract objects L objet sur lequel l usager agit pendant une simulation est concret en ce sens qu il r agit aux actions par l interm diaire du clavier ou d une souris comme le ferait in objet r el mais cet objet est cependant abstrait car si son comportement apparait sur l cran de l ordinateur il ne peut cependant tre vu ou touch comme le serait un objet concret p 1 These concrete abstract objects are concrete in
12. ct The aims of this paper are 1 to characterize computer exploratory software 2 to identify the roots of this kind of software 3 to present a model to design computer exploratory environments for science and mathematics 4 to discuss some of the basic issues of the model and 5 to analyze some programs developed in the framework of the model The model is based on findings in learning and in recent developments of computer graphic environments It assumes that 1 learning is a process of enculturation a process of becoming familiar with ideas and representations 2 exploratory software should be integrated with other resources 3 exploratory software should allow direct manipulation of concrete abstract objects and the exploration of multiple representations of a phenomenon Keywords science education mathematics education computers simulations exploratory environments learning WHAT IS A COMPUTER EXPLORATORY ENVIRONMENT Some ideas are difficult to verbalize The concept of computer exploratory environment seems to be one of those ideas As with many other concepts to build this one into the cognitive structure each of us needs to know and more important to be familiar with the use of computer exploratory environment As one becomes more and more familiar with this kind of software environments the concept becomes more precise and accurate Taylor 1980 suggested that all instructional uses of computers fall under th
13. e scientific ideas that we want to explore For example if we want to explore how velocity of an object changes with time under certain circumstances we must have direct access to a representation of velocity such as a vector With LOGO or any other programming language that can only be done with a big programming effort because programming languages are not domain specific and only have general primitives and procedures Exploratory environments unlike programming languages are domain specific What a user can do with an exploratory environment depends on the domain On the one hand this gives very powerful primitive actions such as showing a velocity vector just by clicking the mouse on the other hand however it narrows the range of the capabilities of the software But this is usually not a real problem because of the domain specificity of each exploratory environment Constructivism Papert s work and exploratory approaches to software are in accordance with a major shift on the dominant view of how humans learn Decades of work by Piaget and collaborators and many others including critics of Piaget s work such as e g Novak 1977 have given clear evidence that learning is an active and constructive process The delivery paradigm of education doesn t seem to be accepted by educators any longer it is now widely recognized that the mental activity of the learner and his her own experiences are the major factors that support
14. friction switch no strobe stroboscopic trajectory choose vector switch vector value choose vector components gravity reference frame zoom in zoom out choose wall flash when a particle is out of screen edit particle data Figure 5 Control panel of the first level left and of the fifth level right of NEWTON As the level increase the complexity of the features of the software increase 4 Direct manipulation of concrete abstract objects is no doubt a subject that deserves more research As argued above this can be a powerful way to explore scientific constructs but it can also be a source of misconceptions or naive epistemologies about them specially if we take into consideration that novice learners tend to be distracted by surface features 5 Multiple representations is one of the most important features of exploratory software This feature gives users the possibility to interact with different coordinated representations of a phenomenon Multiple representations can easily lead to information overload in learners that is Access to different levels is done with passwords This prevents students from using capabilities of the software that are too complex for their conceptual level or for their level of progression in the study of the domain 17 one of the reasons why exploratory software should have different levels of complexity Until some years ago exploratory software only had limited ca
15. learning materials such as books Exploratory software can be very powerful but learners can Vigotsky 1978 p 86 defines this concept as the distance between the actual development level as determined by independent problem solving and the level of potential developlement as determined through problem solving under adult guidance or in collaboration with more capable peers 15 only explore what they already know not what they don t know Well written materials combined with good graphics still have the most important characteristics to present lines of argument Ideally exploratory software should serve as a complement to books allowing students to explore what they read giving them the capabilities that no book has unlike well designed software As any other educational material exploratory software is a resource for learners Programs are like artist tools tools can help artists but they don t produce art Only artists do But exploratory software has a unique characteristic when well designed it fosters interactions between learners in particular if students work in pairs or in small groups Exploratory software can then help the formation of communities of learners that can explore test and communicate ideas of science 2 Balancing exploratory learning and direct instruction is a fundamental issue in the design of learning packages and in the creation of good learning environments Research shows that exp
16. loratory learning is difficult e g Bliss et al 1992 Njoo amp Jong in press Veenman et al in press Teachers should always bear in mind that learners cannot explore what they don t know already This statement can be seen as a corollary of Ausubel s famous principle The most important single factor influencing learning is what the learner already knows Ascertain this and teach him accordingly Ausubel et al 1978 p iv The balance between exploratory learning and direct instruction must be managed by the teacher and should be one of his concerns As Chi et al 1981 have shown that novice learners tend to be distracted by surface features of display presentations Exploratory software can increase distraction because surface features of a domain are usually easily accessible 3 One way of facilitating the balance between exploratory learning and instruction is developing software with increasing levels of complexity such has NEWTON Teodoro 1992 Figure 5 Progression of complexity is based on research on concept formation In each phase of learning each learner can have an environment which is as close as possible to his zone of 16 proximal development so as to avoid one of the most crucial problems in educational software design i e information overload erase back to zero time strat stop replay pause stop rewind time forward time apply a force on this direction choose the value of force
17. m Solving In S Lajoie amp S Derry eds Computers as Cognitive Tools Hillsdale NJ Erlbaum Rouse J 1987 Knowledge and Power Toward a Political Philosophy of Science Ithaca NY Cornell University Press Salomon G in press Differences and Patterns Studying Computer Enhanced Learning Environments In S Vosniadou ed Psychological and Educational Foundations of Technology Based Learning Environments Berlin Springer Verlag 21 Salomon G 1991 Transcending the Quantitative Qualitative Debate the Analytical and Systemic Approaches to Educational Research Educational Researcher 20 10 18 Schank R C 1986 Explanation Patterns Hillsdale NJ Erlbaum Shneiderman B 1983 Direct Manipulation A Step Beyhond Programming Languages IEEE Computer 16 57 69 Striley J 1988 Physics for the Rest of Us Educational Researcher Aug Sep 7 19 Taylor R P ed 1980 The Computer in the School Tutor Tool Tutte NY Teacher s College Press Teodoro V D 1992 Direct Manipulation of Physical Concepts in a Computerized Exploratory Laboratory In E de Corte M C Linn H Mandl L Verschaffel eds Computer Based Learning Environments and Problem Solving Berlin Springer Teodoro V D Batalha J C 1992 VARIACOES Investiga es sobre Gr ficos e Varia es Manual de Utiliza o Monte de Caparica Universidade Nova de Lisboa 1992 CHANGES Investigations about Graphs and Changes User s
18. m in the Computer Age A Reconstructive Epilogue In G Forman amp P B Pufall eds Constructivism in the Computer Age Hillsdale NJ Erlbaum Hebenstreit J 1987 Simulation et P dagogie une Rencontre du Troisi me Type Gyf Sur Yvette Ecole Superieure d Electricit mimeo Lobo M S Teodoro V D 1991 DINAMIX um sistema de modela o din mica Manual de Utiliza o Monte de Caparica Universidade Nova de Lisboa DINAMIX a dynamic modelling system User s Manual Mestre J P 1991 Learning and Instruction in Pre College Physical Science Physics Today Sep 56 62 Njoo M Jong Ton de in press Supporting Exploratory Learning by Offering Structural Overviews of Hypotheses In Ton de Jong Hans Spada Doug Tawne eds The Use of Computer Models for Explication Analysis and Experiential Learning N Y Springer Verlag Novak J D 1977 An Alternative to Piagetian Psychology for Science and Mathematics Education Science Education 61 453 477 Novak J D 1990 Human Constructivism A Unification of Psychological and Epistemological Phenomena in Meaning Making Paper presented at the Fourth North American Conference on Personal Construct Psychology San Antonio Texas July 18 21 Papert S 1980 Mindstorms Children Computers and Powerful Ideas NY Basic Books Reusser K 1992 Tutoring Systems and Pedagogical Theory Representational Tools for Understanding Planning and Reflection in Proble
19. n But the computer program CHANGE can be used with young students aged 12 or even less who can then easily discuss powerful concepts such as rate of change and function without using complex formal mathematics Older students can also use this program as a foundation to more formal approaches to the exploitation of those concepts 7 Finally exploratory software must have a self explanatory interface Students as other software users do not like to read computer manuals If a student who has already been introduced to a scientific domain cannot use an exploratory piece of software about that domain then the software cannot be widely used Text buttons icons if used with parsimony context dependent on screen help self presented examples etc are now easily available for programmers on most computer languages from resources workshops 19 they are essential for the implementation of exploratory software which is easy to use A NOTE AS CONCLUSION After all that has been written above one could expect exploratory software to have the potential to radically change science and mathematics education This is not true the power of any computer environment is not on the computer it is on the environment the cluster of systemic relations among learners teachers technology devices such as computers books etc Naive conceptions of educational change assume that educational change depends on the change of independent
20. on as function of time Using this button it is possible to foster discussions about the relations between the rate of change of a function and the value of the function about the relations between the graphical representation of a function and the phenomena that it represents etc 6 Another important issue about the design and use of exploratory software is the relation between semi quantitative learning and quantitative learning Semi quantitative learning is characterized as non algorithmic learning I can discuss relations between variables without the need of formulae Quantitative learning is on the contrary algorithmic learning Relations between variables are expressed through symbolic equations Some authors consider semi quantitative learning as the most important issue on learning science and mathematics e g Mestre 1991 Teachers and researchers are well familiar with students who are almost perfect algorithmic problem solvers but do not know anything about the meaning of the problem about the plausibility of the solutions about the validity of their claims etc Well designed exploratory software can bring semi quantitative learning to a high level because students can concentrate on meanings not on rules or algorithms For example the situation presented in Figure 6 is usually discussed only with senior high school students and first year undergraduates when they are introduced to calculus derivatives and integratio
21. on with the idea As Schank 1986 p 5 pointed out understanding is not an all or none affair People achieve degrees of understanding in different situations depending upon their level of familiarity with those situations Exploratory software must allow students to get a strong degree of familiarization with the basic ideas of the domain being explored With exploratory software students can see many situations explore what happens in different conditions discuss what happens if they change conditions etc 1 e they can become more and more familiar with the ideas the consequences of ideas and representations of the world When they become more familiar with new ideas and new representations they can establish more meaningful relations with ideas they already have Exploratory software can be a major way to foster familiarity with new ideas Graphical and direct manipulation computer interfaces We can also identify another important root of exploratory software the graphical user interface introduced by Apple in the early 80 s and now used 12 in almost every computer environment such as Windows and OS 2 These graphic environments allow computer illiterate users to become almost immediately involved with computer software by exploring icons buttons pull down menus and other screen objects When Taylor 1980 suggested that all uses of computers in education should be seen either as tutor or tool or tutee it was really
22. pabilities of multiple representations it was only possible to change conditions in one of the representations e g a parameter on an equation and then see the change on the corresponding graph But now it is possible to fully explore the capabilities of multiple representations For example it is possible to change a graph with a mouse and see the corresponding change in an equation It is even possible to sketch graphs with a mouse and then obtain the corresponding phenomena see Figure 2 and Figure 6 lt lt 3 C Values Position as a function of time Rate of change of position 0 time s Sketch graph Values Figure 6 Linking multiple representations The graph of the rate of change of position velocity was sketched with the mouse The motion of the athlete and the graph of the position can then be obtained from the graph of the rate of change in position Done with CHANGE Teodoro et al 1992 One design hint that I found helpful is the use of a button that hides and shows the window with one of the representations For example Figure 6 shows a graph of the rate of change in position of an athlete done with the mouse This graph doesn t have perceptual fidelity The window that has perceptual fidelity the top window where the athlete can run or walk is hidden but it can easily be shown by pressing the button Show The same applies to the left window with the graph of the positi
23. presentations of complex features of real phenomena or of complex mathematical constructs such as fractals falls exploratory software should enable students to see the following representations simultaneously and in real time Figure 1 1 the object moving 2 astroboscopic representation of the motion 3 the vertical and the horizontal components of the positional vector of the object 4 the graphs of position in the y and in the x axis as a function of time Oo E JE position y fitime Figure 1 Multiple representations of a rectilinear vertical motion of a particle stroboscopic representation vertical and horizontal components of the positional vector graph of position in the y and in the x axis as a function of time Done with NEWTON Teodoro 1992 Analyzing further the idea of multiple representations exploratory software should allow students to start from the graph for example sketching the graph with a mouse and then obtaining the corresponding motion Figure 2 Another possibility of the software is that it should allow the student to write an equation and then obtain the motion of an object that behaves according to the equation and simultaneously obtain a graph Figure 3 Linking equations of motion to graphs graphs to motion in real time and motion to equations can be a powerful process to derive meaning of each of the representations and of all of the representations of the same phenomenon
24. ratory software and identify its roots I will now try to outline a model for the design of this kind of software This model is based on reflections aroused by the development of a set of titles of exploratory software in the following domains Newtonian mechanics properties of chemical elements semi quantitative study of functions and rates of change representation of geographical characteristics of a country modeling with differential equations trigonometry and properties of triangles electrical fields descriptive geometry and heredity 13 Figure 4 shows the structure of the model It has two lines of approach one of which is methodological and the other theoretical METHODOLOGICAL THEORETICAL Multidisciplinary team Founded on research on concept 3 formation and on misconceptions Identifi cation of relevant learning experiences View of learning process of becoming familiar with meanings Validation in dif ferent learning through social interaction settings View of science process of creating testing and communicating Successive improvements representations of the world Direct manipulation metaphor Design of computer exploratory environments Integration with other resources books peers teachers Balance between exploration and in struction Conceptual progression Concrete abstract objects Multiple representations linking percep tual fidelity to conceptual fidelity Semi quantitative
25. ree modes Table 1 Taylor s 1980 modes of instructional uses of computers tutor the student is taught knowledge by the computer tool the computer assists the student in the learning process but does not direct his her efforts tutee the student teaches the computer This classification has been used since then by many authors as a basis to classify the role of different educational software packages The computer as tutor can be seen as a transposition of the classic role of the teacher to the computer The computer as a fool is a transposition of the role of a pen or a calculator to the computer The computer as tutee is anew kind of educational environment where teaching the computer is seen as a powerful aim that can allow students to get a deep awareness of how knowledge is built Papert 1980 wrote In my vision the child programs the computer and in doing so both acquires a sense of mastery over a piece of the most modern and powerful technology and establishes an intimate contact with some of the deepest ideas from science from mathematics and from the art of intellectual model building p 5 A computer exploratory environment combines two of Taylor s categories tool and tutee It is a tool because it can be used to help students think about one or more knowledge domains doing tasks that could not be done without it or that would take more time than reasonable It can be used in a tutee environment because students c
26. relevant learning experiences in a certain domain A relevant experience is related to the process of concept formation either because it gives anchors to subsume concepts or because it shows a conflictual view with naive thinking Third as learning takes place in many different settings the software should be validated in the different settings where learning occurs We shall not claim that exploratory software should be designed only for classrooms With the increasing diffusion of computers at home in resource centers in libraries etc students can have experiences with exploratory software in many different places outside classrooms and outside teacher control Fourth exploratory software should be based on graphical and direct manipulation interfaces where the user controls his actions directly not mediated by written language Fifth it is not possible to design good exploratory environments without successive improvements based on ecological valid research This research on the software developed should be carried out in real schools with real students and teachers not in ideal settings As output of the model we raise seven relevant issues 1 Exploratory software by itself has very limited use Exploratory software should be considered as a part of learning packages to foster learning communities I think that it is neither possible nor desirable to build exploratory software that is independent from other
27. resentations of the world Rouse 1987 The Educational Technology Center 1988 points out that multiple representations is one of the most fruitful applications of computer technology with particular relevance in science and mathematics domains where knowledge has more than one mode of representation The Educational Technology Center presents two reasons for this First different representations of a complex idea for example a ratio an algebraic function or a concept such as heat emphasize different aspects of the idea and afford different sorts of analyses Understanding the strengths and weaknesses Bliss et al 1992 of various representations and the relationships among them helps mathematicians and scientists select and apply them efficiently in solving problems Second students differ in their ability to understand and use particular representations Thoughtfully designed computer software can present multiple dynamically linked representations in ways that are impossible with static inert media such as books and chalkboards p 10 For example if we want students to see in a reference frame how does the coordinates x and y of a moving object change with time when the object Thanks to computers and their powerful graphical capabilities a new field of science has emerged in the last two decades computer visualization or computer representation One of the aims of this field is to create graphical re
28. the sense that they can be seen and manipulated as real on the computer screen and abstract in the sense they are physical and mathematical constructs One of the most important features of a computer exploratory environment is that it should allow the user to explore the relations between the different kinds of objects in real time or with a different time scale if necessary faster or slower depending on the nature of the problem under investigation The exploration is done under the full user s control not the computer s This means that the computer does not behave as a video projector that presents a previously defined sequence of images but as a device that is fully manipulable by the user who must establish strategies to explore what s he wants to explore choose what when and how to visualize things Another important characteristic of exploratory software is the possibility of linking multiple representations This is perhaps the characteristic that most teachers are interested in Multiple representations can facilitate the process of creating meaning from representations if we assume that meaning is created essentially when students relate different representations We only understand something if we can establish relations between different representations of phenomena The issue of representations is crucial in science and science education Science can even be defined as a means for constructing and improving rep
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