Learning Math Concepts by Visually Programming Robots.

Transcription

1 Learning Math Concepts by Visually Programming Robots. E. Bilotta, P. Pantano and V. Talarico Centro Interdipartimentale della Comunicazione, Università della Calabria Arcavacata di Rende CS Italia Keywords: VPLs, AgentSheets, Pedagogical agents, Cognitive and user-interface design issues. Abstract For improving the use of visual programming language many are the systems that have been built for the primary school users. Some applications are about science learning and some deals with Mathematics. This paper presents an educational environment developed by AgentSheets system, devoted to math learning for elementary students and it is a follow up of a computational system in which an autonomous robotic agent, through its sensors and a simple set of behaviours, is able to develop a specific sensorial language. The environment is so organized. There is a pedagogical agent which explores the environment and classifies the objects it finds. The objects are stored in the system memory and the agent makes mathematical operations on this stored information. The agent has all math rules for calculus, formal logic, sets theory, topology and space concepts. These rules are displayed on the worksheets since the agent creates enganging situations and are transferred to the users by demonstration, through and highly dynamic interaction. In fact, the user can interact with the system and learning by doing. 1. Introduction The use of visual programming languages to support science learning is flourishing and spreading widely in this period (see for example the applications developed with AgentSheets [1], Cocoa [4], StarLogo [12]). Starting from the classic literature on this topic (Logo e Karel the Robot, for example) languages have become more and more flexible in offering new modalities of representation which not only visualize the phenomena taught to students, but also create environments in wich subjects build rules which underlie the same phenomena (cause-effect relations, analogies, differences between phenomena, cascade of contents, etc.). These languages can change learning in the scientific research praxis and support the construction of virtual laboratories in which the students can modify all the variables involved in a given phenomenon, using both the experimental and the observative methods. Moreover VPLs allow, by building enviroments for beginners, the use of cognitive programming skills, improving the contents' acquisition and representing self-organization, decentralization, complexity of systems [7]. Learning in such environments means making more comprehensible phenomena through practical examples, providing teachers with the possibility to organize contents they want to supply and students with the possibility to verify their understanding step by step. In this systems, students, by manipulation and methods of metaphoric rewriting, are able to demonstrate the way laws are built, instantiating models close to what Bruner [3] calls enactive and iconic moments in development. Among these languages, AgentSheets [8], [9], [10] allows: a) new methods of interaction (highly modifiable systems); b) modularity: presence of agents allowing decomposition of complex phenomena in many simpler phenomena;

2 c) abstract rules referred only to agents behaviour; d) ease of programming; e) interface as theater; f) tactile methods of programming through manipulation [11]; g) possibility to build the pragmatic of scientific models construction [6]. In this work we present a pedagogical agent, developed by AgentSheets, which explores the environment and classifies the objects it finds. The objects are stored in the system memory and the agent makes mathematical operations on this stored information. The agent has math rules for calculus, formal logic, sets theory, etc. These rules are displayed on the worksheets since the agent creates enganging situations and are transferred to the users by demonstration, through and highly dynamic interaction. the various mental processes involved with analysis and classification of objects and into communication phases. For this end we have divided our worksheets into two distinct areas: the former, located at top left, representing the autonomous agent s physical work space and the latter dedicated to agent s memory. The memory space is subdivided into three parts which together are the necessary structure to a spatial memory representation of the physical environment, to analysis and to classification.. 2. The autonomous robot We have developed the actual implementation devoted to math teaching/learning from a computational system in which an autonomous robotic agent, through its sensors and a simple sets of behaviours, is able to develop a specific sensorial language [2]. This language will be used in different domains of activity in order to set up a knowledge base which will be sharable with any other agents developed and implemented following the same evolutionary process. The agent s basic knowledge will involve two kinds of information: spatio-temporal relations between objects and situations and attributes concerning the physical properties of objects. By building up the sensorial language, the agent will be able to record complex experiences in the past and to reflect on new upcoming situations. This leads the agent to recall all procedures used in similar and less complex situations, to apply them to new ones and to augment its knowledge base. The computational prototype, is based on the idea of creating a completely visual simulation environment, which allows the robot s user/programmer to see what the robot itself is doing at any time. Moreover the user has the possibility of doing real time interventions, without stopping the simulation, changing the algorithms underlying the robot s program, causing perturbations and hence exploring new possibilities. Besides, it was our interest to be able to create a visual representation of robot s memory allowing the user to comprehend and control the agent s cognitive process. In the robot application, the first problem we had to face was to represent into a worksheet, the agents working space in Agentsheets, both the physical environment the autonomous agent perceives and operates into, and all Figure 1. The World of Animals For implementing the system devoted to math learning, we have used the robot s behaviours since it was necessary to give to the visual robot, we have called Noè, the possibility to operate like the autonomous agent did. This in order to : 1. Decide if an object is on the left or on the right of another object; 2. Decide if an object is below or above another object; 3. Count categories; 4. Count elements contained into each class and do numerical confrontations; 5. Associate a random symbol to every class. This allowed us to equip the robot Noè with mathematical skills of a numerical, logical and setrelated nature.

3 3. The math application Using the siystem described in the previous section and the robotic agent s behaviour (adapting some algorithms to the functions we wanted to realize), we have developed a pedagogical visual agent, the robot Noè, which helps the user, either teacher or student, in math teaching and learning activities. Such application is so organised: a) a gallery of agents subdivided in: i) animals; ii) plants; iii) arabian numerals; b) some worksheets visualizing the environments in which math units are organised. Such environments are: i) the world of animals ii) the Ark iii) Noè s laboratory. Following, some practical examples concerning sets and number theory are discussed. Noè and the world of animals. The aim of this environment is to make students familiar with concepts of grouping and sets. The worksheet World of Animals looks like figure 1. The world of animals is filled with some animals (agents), picked from the gallery. Noè has to find all the animals, take them to the Ark and insert them in the space assigned to each species. Noè explores the worksheet and begins classifying, grouping, storing and sets building behaviours. The students can look at these processes.. Figure 2. The World of Animals at the end of the process. Once this phase is over, Noè proposes a series of exercises on these concepts. Then the users are also able to activate some contructivist games (or a custom construction of the worksheet), to repeat the same activities Noè did or just to play back what Noè did.in figure 2 is shown the worksheet at the end of the process. The second activity provides the notion of sets comparison, in order to see if the elements contained in a set are in a number major, minor or equal to those of (a) (b) another set. Other worksheets have been organised in order to represent concepts of belonging, subset, Vien s diagram. Figure 3. The empty Wax Tablet (a), The filled Wax Tablet (b), The Bag filled with Little Stones (c). Noè and the world of numbers. Also in this case, the Noè s Ark metaphor helps us to make the concept of number more familiar to the users.noè has also some other objects which he uses in his work, a wax table in which he takes notes and some bags which are filled with little stones(see fig. 3 a, b, c). Noè spots the species hosted in the ark (classes stored in memory), uses his wax tablet to report these species and starts to count the number of animals for every species, by writing a check mark for each animal belonging to a given species (see fig. 3 b). When this process is over, Noè assigns symbols as 1, 2, 3 to each set, starting from the smallest, caring of assigning the same symbol to sets having the same number of elements. We have chosen to represent the concept of zero using the metaphor of an empty cage, tens and arabian positional notation for numbers. Noè owns also a number of coloured bags equal to the number of species of animals. As he counts all the animals belonging to a species, he inserts in the corresponding bag a little stone (see fig. 3 c). Every bag (c)

4 can contain only ten stones and the symbols to identify the ten. When the bag is filled, Noè gets it empty and pastes the symbol which identifies the ten on the bag. The same metaphor can be used to introduce base change. It can be done by filling bag with different capacity. For these concept a set of exercises and constructivist games, customizable by the user, are presented too. The metaphor of the robotic agent Noè can be used to build worksheets at different levels of complexity for about all the fields of elementary mathematics, topology, geometry, seriations, formal logic, arithmetic operations. 4. Interaction mechanisms and lerning environments Different interaction mechanisms are present in our application but, for the moment, we focuse on the visualization of the process that Noè is carrying on. The subject watches the robot and then repeats the process. Noè waits for explicit requests from the user, verifies the correctness of the student's actions and replies to them, utilizing a sets of simple verbal statements. This simple scheme of interaction presupposes the system to be organised in order that it suits the students cognitive needs and the subsequent programming of visual functions, activable by the user. Let s see how the system is organised through the exam of functions that can be activated. What does the system do? 1. The rules (represented by the the pedagogical agent s behaviours) are owned and used by the system according to the context that has to be visualized, inside the chosen math unit. 2. The visualization of such rules is done through the expression of the Noè s and the other agents behaviours in the worksheet, which means that the processes Noè accomplishes are all visible at the system memory level. 3. Noé has some "teaching by demonstration" behaviours: a) classification (Noè puts the animals in cages after having discovered that, for example, two animals belong to the same class, i.e. they have some common characteristics; he moves these agents from one cage to another and fills spaces in memory;); b) comparison (the visual robot can make analogy for similitude and analogy for disequality); c) categorization (Noè assigns symbols to such agents and makes comparison between symbols). What do users do? There are two kinds of users: teachers and students. Teachers can interact with the system in two ways: 1. in changing the organization of contents sequences according to the educational objectives he wants to accomplish. This means that the sistem is organised as a path (cascade process), eventually modifiable, and that all the implementation is made of a set of units which are activable on the teacher specific needs; 2. in changing the system s single units. The teacher inserts new agents, new rules (where it is possible), builds new exercises, experiments how some elements of the system work (motivational effect which produces on subjects the activation of better cognitive skills, retention of contents, with respect to traditional methods), the teacher can also evaluate learning by following the heuristics the subject has used in solving a particular problem. The student finds a contructivist environment. According to his/her age and degree of expertise in programming, he/she can activate mechanisms of complete comprehension of the described phenomena, through the same activities the teacher can do at point 2. If the student is not expert, or still too young, he/she has a range of activities which can be compared to the behaviours human infants exhibit in play situations with instruments and/or toys, i.e. the subject observes the system, explores, spots agents, creates cause-effect relations about the agents behaviour. Or, in a more manipulative way, the user drags agents, activates the system, modifies some system s parameters, etc. There are some psychological aspects in VPLs which we are going to explore in further developments: a) the role of motivation in learning environments (curiosity, interest); b) the role of situations involving the affective, cognitive dimension of the play; c) the role of play in education, exploration, manipulation, construction; d) the persona effect [5] which is the presence a life-like character in an interactive learning environment (even one that is not expressive) can have a strong positive effect on student perception of their learning experience; e) the role of the explanatory behaviours on affective perception (involvement) and learning performance.

5 Bibliography [1] AgentSheets: ~l3d/systems/agentsheets/di-projects.html [2] Bilotta E,. Pantano P. and Talarico V., A Sensorial Language for an Autonomous Agent. Proceedings of 10 th PPIG Workshop, Milton Keynes, Open University, /Ricerca/ricerca.html [3] Bruner, J.. Toward a Theory of Instruction. Cambridge, MA, Harvard University Press,1966. [4] Cocoa: [5] Lester J.C., S.A. Converse, S.E. Kahler, S.T.Barlow, B.A. Stone, R.S. Bhoga, The Persona Effect: Affective Impact of Animated Pedagogical Agents. Proc. CHI 97. [6] Rader C., C. Brand and C. Lewis, Degrees of Comprehension: Childeren s understanding of a Visual Programming Environment. Proc. CHI 97. [8] Repenning, A., Agentsheets: A Tool for Building Domain- Oriented Dynamic, Visual Environments, University of Colorado at Boulder, Ph.D. dissertation, Dept. of Department of Computer Science, [9] Repenning, A., Programming Substrates to Create Interactive Learning Environments, Journal of Interactive Learning Environments, Special Issue on End-User Environments, Vol. 4, 45-74, [10] Repenning, A. and T. Sumner, Agentsheets: A Medium for Creating Domain-Oriented Visual Languages, Computer, Vol. 28, 17-25, March [11] Repnning A., J. Ambach. Tactile Programming. A Unified Manipulation Paradigm Supporting Program Comprehension, Composition and Sharing. Proceedings IEEE Symposium on Visual Languages, , Boulder Colorado, [12] StarLogo: /el/projects/starlogo/). [7] Resnick M., Turtles, Termites and Traffic Jams. Explorations in Massively Parallel Microworlds, MIT Press, 1995.