Yishay Mor
email: y.mor@ioe.ac.uk

Jakob Tholander
email: jakobth@dsv.su.se

Jesper Holmberg
email: jesperh@dsv.su.se

Designing for cross-cultural web-based knowledge building

Keywords: Iterative design, Design experiment, Web-based collaboration, Constructionism, Activity Theory

This paper describes the iterative design of a web-based collaborative workspace used in educational practice, called WebReports. The system's unique feature is that it allows participants to discuss mathematical and scientific concepts using programmed animated and interactive models of their ideas. Rather than focusing on the specific features of the collaboration tool, we analyze it as part of a constructionist activity system. We describe the context in which the system was developed and used and compare our approach to previous research in the field. Further, we then present two scenarios which demonstrate the system in action. Following that, we attempt to map our cases to an activity theory framework. We highlight several issues in the process of the systems' development, where the contradictions between the WebReports system and other elements in the activity system shaped its design, and comment on several issues which go beyond the activity theory framework.

INTRODUCTION: KNOWLEDGE BUILDING FROM A EUROPEAN PERSPECTIVE

WebLabs is a 3 year EU-funded educational research project oriented towards finding new ways of representing and expressing mathematical and scientific knowledge in communities of young learners1 . Our work focuses on the iterative design of exploratory activities in domains such as numeric sequences, cardinality, probabilistic thinking, fundamental kinematics, and ecological systems. WebLabs utilizes two main media for its activities: ToonTalk (a programming environment) and WebReports (a web-based collaboration system).

One of the central aims of our work is to extend the idea of knowledge building. Building on the constructionist tradition (Papert & Harel, 1991;[START_REF] Hoyles | Windows on Mathematical meaning:Learning Cultures and Computers[END_REF] we combine software model construction activities with web-based collaborative knowledge building. By doing so we expand the range of communication forms learners have at their disposal. Participants can express their ideas as working models, and present these as arguments in a discussion. Moreover, computational models also allow students to explore aspects of mathematics and science that were simply were not available to study in other representations. This possibility is especially powerful in a multi-cultural environment. When students lack a common spoken language, the availability of a common visual modeling language is an enabling factor for collaboration.

CSCL and knowledge building

A majority of the CSCL work focuses on sharing of knowledge through language. This fact limits the potential of incorporating knowledge expressed through non-verbal artefacts in the process of knowledge building. Moreover, there is an obvious problem with this if one wants to achieve cross-cultural interaction and knowledge building (where students do not share a common spoken language). The paradigmatic computer support for knowledge building is the CSILE system (Scardamelia & Bereiter, 1996). CSILE is basically a discussion board where students can post notes on different topics and then comment on each other's notes. The first interesting aspect regarding the system is its close connection to the so-called knowledge building community model of education and learning. This model builds on sociological descriptions of how knowledge is created and refined in scientific communities (Latour, 1986). It describes learning as a process of collective construction of knowledge. Topics are discussed, elaborated, and continuously refined by a community of learners (or perhaps knowledge constructors). The mutual influences of individuals' actions within a community compel people to adapt to each other. Adaptation is not only a positive contribution to efficient knowledge building, but it is also a necessary requirement for a knowledge building community to arise at all. CSILE unique innovation was its scaffolding feature: built-in structure which guides students to focus on particular knowledge building aspects of their discussions. These scaffolds include prompts that encourage students to clarify problem statements, develop theories, state difficulties in understanding certain issues, tag new information on a topic, and summarize what they have learned. Scaffolds are designed to structure the students' discourse to replicate the work of a scientific research team or a research community. Two issues that the extensive research of the use of CSILE in classrooms settings have shown is the need to focus on community building and on organisation of learning activities aiming to achieve productive use of the technology (e. g Hewitt 2001;[START_REF] Hakkarainen | Epistemology of Inquiry and Computer-Supported Collaborative Learning[END_REF]. These two issues have also been addressed in the work discussed in this paper.

Another well-known system based on the knowledge building model is KIE (Knowledge Integration Environment) [START_REF] Linn | Designing computer learning environments for engineering and computer science. The scaffolded knowledge integration framework[END_REF]. Whereas CSILE is domain independent, KIE is targeted towards science education and the particular properties of that domain. It is based on an educational model called Knowledge Integration. This model highlights conceptual change, focusing on fostering students' conceptual understanding of scientific phenomena as the integration of facts, argumentation, and evidence. KIE provides software scaffolding for students to build arguments (the SenseMaker component) and to collect and categorize pieces of evidence such as facts and notes in a reflective manner (the Mildred component). With the SenseMaker [START_REF] Bell | Using Argument Map Representations to Make Thinking Visible for Individuals and Groups[END_REF] component, students collect evidence that they connect to claims as either support or contradictions of the argument they are making, hence, combining models for scientific argumentation with personal understandings. The Mildred component [START_REF] Bell | Designing Mildred: Scaffolding Students' Reflection and Argumentation Using a Cognitive Software Guide[END_REF] focuses on the content of the evidence and the claims that are used to build the scientific arguments. A particular aspect is the meta-cognitive support focusing on supporting students to reflect upon the information they are collecting in their projects.

Designing for systems of activity

Over the last decade, activity theory has been gaining attention as an aid for designing computer interfaces (Nardi, 1996) and CSCL in particular [START_REF] Kaptelinin | Individual and Collective Activities in Educational Computer Game Playing in Proceedings of Computer Support for Collaborative Learning[END_REF][START_REF] Jonassen | Revisiting Activity Theory as a Framework for Designing Student-Centered Learning Environments[END_REF][START_REF] Fjuk | The Complexity of Distributed Collaborative Learning: Unit of Analysis in Proceedings of CSCL[END_REF]. Activity theory spans from the idea, put forth by [START_REF] Vygotsky | Thought and language[END_REF]1987), that human actions are directed at objects and mediated by instruments. These objects define the focus of our attention, while the mediating instruments shape our perception. Hence, the three form a minimal unit of analysis in understanding consciousness and learning. Objects and instruments are artefacts of culture, developed though its history. A comprehensive analysis needs to take these factors into account as well. Thus, cognition and learning are always situated in a particular socio-cultural context. Vygotsky's method is dialectic and emphasizes how the different components of the system shape and change one another, hence building upon a Marxist tradition and on the ideas of Hegel.

These ideas have been elaborated by [START_REF] Engeström | Learning by expanding[END_REF]1999. Cole & Engeström, 1993), to include the community in which the subject (acting agent) operates, the outcomes, or aims, of the activity, the rules which define the subjects relations with the community and the division of labour between subjects. As a dialectic method, activity theory is never content with describing these constituents in isolation, but focuses on the relations and tensions between them. Indeed, learning is often driven by the need to resolve contradictions within the system.

The novelty of our project lies in the integration of constructionist modelling activities with web-based knowledge building discussions, to support a community of learners distributed across six European countries. For us, this means looking beyond the isolated constituents of educational design, and exploring the activity system as a whole. This system includes a combination of components such as technological development, design of novel learning activities, and organizational efforts to support teachers and students in different countries. In this analysis we use activity theory due to its emphasis on understanding human action as systems of activity in social, cultural, and historical settings. By viewing our design efforts not only as particular technological developments (in the form of new ways to support programming or a new system for collaboration) but as the design of system consisting also of new educational activities and organisational changes, we intend to show how all these components interact to form the system in which the students are central actors. This allows us to get a richer understanding of the educational context that the students will be set in. Note however, that this does not mean that technical developments are not important contributions of our work, but rather that these developments need to be understood in the context of the activities and the settings where they are used. By introducing new technologies in an activity system, the system itself is changed which may be the source of contradictions between the different components in the system. [START_REF] Fjuk | The Complexity of Distributed Collaborative Learning: Unit of Analysis in Proceedings of CSCL[END_REF] discuss how contradictions in the use such instruments arise from their multiple purposes, and how the particular purpose within one activity system is shaped by the activities that accompany the use of the instruments from another. They demonstrate how contradictions between different purposes of an instrument may afford contradictory activities. Their analysis suggests that in order to understand the design of educational technologies we need to analyse these within the context of the activity and settings where they being used. This viewpoint has been a guiding element in the analysis of the present paper. Our system was designed in tandem with the educational activities, and the analysis is done in their context. These activities do not occur in a void; we need to consider all the components of the activity system:

• The structure of the community of researchers, teachers and students.

• The division of labour between these three groups and within them.

• The social rules which govern interactions between students and between students and teachers / researchers.

• The web of connections which tie local groups and global communities.

• Other instruments in the environment, such as the programming environment and spreadsheets, traditional tools, such as whiteboards and paper, as well as specifically designed objects for collaborative group activities.

• The mathematical and scientific objects which are explored and the educational outcomes of these explorations.

COMPONENTS OF THE WEBLABS ACTIVITY SYSTEM

In the following we discuss the four central components involved designing the Weblabs activity system: the activity sequences, the WebReports system, the ToonTalk programming environment, and the educational and school settings that are involved in our work.

Activity sequences

Our methodology of activity design has emerged through a process of iterative refinement. Our approach interleaves modelling tasks and discussions (face-to-face and on-line). The former builds intuitions in the domain area, while the later forges these into formal argumentation. Our activities follow a common cycle: first a scientific phenomenon or research question is introduced via a group discussion and specific modelling tasks are derived from it. Students then work individually or in pairs, exploring the question at hand through modelling in ToonTalk. Once done, they use a specialized template to publish (on the web) a written report on their findings. The models they have developed are embedded in this report. These reports are then used as input for a group discussion, which concludes with the publication of a group report. When possible, this report will be reviewed by groups from other countries, working on the same topic, to initiate inter-group discussions.

The evolution of our methodology is in itself an interesting example of the mediating role of technology. At an early stage of the design, we realized that if we want to interleave on-line discussion with modelling, the WebReports system (described below) would have to support this practice. Among the required features were streamlined embedding of coded models in a textual report and templates which scaffold students' writing. Only after these features were available did we realize that they enable us to create a new tool, and a new related practice, which we called task templates. These are report templates which include task instructions and questions. The novelty of this tool is that all the tools required for the task are embedded in the template. Students click on the tools they need, work their way through the modelling task, and eventually replace the question text in the template with their own observations.

The ToonTalk programming environment

We see software programming as playing a key role in individual and group learning. Children explore and test their conceptions of the phenomena through programming. Furthermore, by sharing programmed models, they communicate ideas in a concrete yet accurate form. We are programming with ToonTalk [START_REF] Kahn | ToonTalk -An Animated Programming Environment for Children[END_REF]1999; http :// www . ToonTalk . com ) a language used in the past with younger children to construct video games [START_REF] Hoyles | Rethinking the Microworld Idea[END_REF]. ToonTalk is a computer game, programming environment and programming language in one. In ToonTalk programs take the form of animated cartoon robots. Programming is done by training these robots: leading them through the task they are meant to perform. After training, programs are generalised by "erasing" superfluous detail from robots' "minds".

Train the robot to take a number 1 from the toolbox and drop it on the input, to increment it.

Generalise the program by erasing the value of the input from the robots memory.

Give the robot its input box. The robot will continuously repeat the actions it has been taught. In fact, we only have to train the robot to "add 1" to a number and then generalise it to any number.

The robot iterates the actions it was trained to do, for as long as the conditions it expects hold true.

The Webreports system

The individual and collaborative facets of learning are intertwined at all stages of our activities. The WebReports system (Figure 2) was set up to support both. The primary aim of this system is to allow learners to reflect on each others work by sharing working models of their ideas. The "atomic unit" of content in the system is a web report: a document containing formatted text, along with multi-media objects, Java applets, and most important -ToonTalk models. These models are embedded in the report as images, which link to the actual code object. Since our primary focus was on the design of a system consisting of technology, activities, and organizational interventions we made a strategic decision to use (and enhance as needed) existing "vanilla flavour" open source systems. Our first prototype was built upon JSPWiki (http://www.jspwiki.org) whereas the current system is based on Plone (http://www.plone.org). This led us to focus on the functional and usability design, and minimize our implementation efforts.

Reports are edited using a visual editor. Apart from standard text formatting features, this editor allows users to easily embed media including Java applets of their models as well as objects embedding the ToonTalk code in their reports. Students can grab any program object in their ToonTalk environment, and copy it instantaneously into their report.

Reports are catalogued along three axes: topic, site and function. The first categorizes reports by their subject content (e.g. Infinity, Sequences, 1D collisions). The second lists the reports by the real-world team of the author (school, class or club). The function heading presents content by the way it was conceived to be used (programming component, personal report, tutorial, etc.).

School settings

Working across six European countries means having to acknowledge more than language differences. We encounter a wide range of classroom cultures and practices, which have to be accounted for in our design.

First, there are pragmatic issues: school times, session length, and firewalls. As mundane as they seem, these had an actual impact on the success of activities, primarily in cases where our design was in contradiction with existing rules.

One such example regards the use of web reports between sites. Our original plan was to have two groups work on a topic in parallel, publish concluding group reports, and then comment on each others' reports. In practice, synchronizing between sites proved impossible: even if one succeeded in scheduling an activity to start at the same time in both sites, the difference in session duration dictated by the local educational system meant that one group would be well into the next activity before the other published its concluding report. This realization led us to shift the emphasis to individual reports, as a means of collaborative knowledge building within groups.

Other issues are much more subtle, and relate to established classroom rules and norms regarding knowledge sharing. The first issue we encountered was that in most educational institutions, sharing knowledge goes against the grain of standard practice; often it is called cheating. This problem was easy to overcome. A much more difficult issue was getting students to publish work in rudimentary form. Our design builds on iterative refinement of knowledge through social interaction. This requires students to publish work that is not "correct" or finished, acknowledge public feedback, and republish. Again, this contradicts standard educational practice. In school, you submit a paper or exam when you think it is right, and the feedback you receive is judgmental.

To our surprise, the main hurdle in this case was put forth by teachers. In some cases, teachers found it hard to accept that students publish scientifically or mathematically incorrect texts for fear that this might be interpreted as a lack of proficiency on their side. Similar conflicts in norms and values will be further discussed below

CASE STUDY EXAMPLES FROM SCIENCE EDUCATION ACTIVITIES WITH THE WEBLABS SYSTEM

Below we present two case study examples from our work. These two differ in several respects and have therefore been important to our understanding of the activity system as a whole. The first activity, called "Guess my robot", focuses on the intense collaboration and exchange between students in England and Bulgaria using small pieces of program code representing number sequences. The collaborative setting here works as way for students to respond and act on each other's models on a day-to-day basis. The second activity, called "EcoModelling", focuses on students' illustration and presentation of their understanding of foodweb systems.

Here, the collaborative setting has more of an indirect role but still significantly shapes the models that the students are building with less focus on day-to-day exchanges. Our analysis is aimed at identifying contradictions in the system. Contradictions are central to the development and changes of all activity systems [START_REF] Engeström | Learning by expanding[END_REF] and therefore useful as analytical tools [START_REF] Fjuk | The Complexity of Distributed Collaborative Learning: Unit of Analysis in Proceedings of CSCL[END_REF].

A comprehensive analysis of the system would need to analyse these cases, and others, with respect to all the elements of the activity system. We need to identify contradictions, and resolve them by modifying the various aspects of the design. Such an undertaking would be far beyond the scope of this paper. We restrict ourselves to several of the more illustrative issues in each case.

Collaboration and "discussion" in the guess my robot activity

One of the activities we designed was the Guess my Robot (GmR) game. This game is a pivotal activity in our explorations of number sequences. Most students enter it with very little formal knowledge of sequences, and minimal ToonTalk experience. After GmR they move on to more advanced topics, such as the Fibonacci sequence, convergence and divergence, and cryptography. See (Mor, Y., Hoyles, C., Kahn, K., Noss, R. & Simpson, G. 2004) for a discussion of the mathematical-educational context of this game.

In this game, proposers train a robot to generate a numerical sequence, and publish its first few terms as a ToonTalk "box" in a WebReport, using a special purpose template. Responders build a robot that will produce this sequence, and thus show that they have worked out the underlying rule. As one girl said: "So, like, the robot is my proof that I got it?"

We first experimented with this activity in 2002/3 (Mor and Sendova, 2003). Our experience from this pilot informed both the design of the activity and of the WebReports system. In 2003/4 we expanded the experiment, with significantly greater response (Mor and Noss, 2004;Matos et al, 2004). This iteration included far more students and resulted in rich interactions.

We now analyze this case, using the activity theory framework as a guideline. We will focus on the role of the WebReports system, both as an instrument and as an arena for the activity. As mentioned above, the constituents of the system are not seen in isolation, but rather in relation to one another.

Outcome:

The proposers' explicit outcome is the challenge, and the responders' the responses. Yet the game had additional implicit outcomes -the collaborative construction of knowledge about sequences. The WebReports system supports both, yet our activity design supported the former, but neglected the latter.

The explicit outcomes are embodied in models of number sequences, as ToonTalk boxes or robots. These can be seamlessly embedded in both challenge reports and response comments. The implicit outcomes are higher level abstractions and arguments about sequences. These are the more important outcomes from the educational viewpoint. They can be represented verbally, or as situated abstractions [START_REF] Hoyles | Windows on Mathematical meaning:Learning Cultures and Computers[END_REF] by ToonTalk models. The system is flexible enough to support both. However, we failed to design the activity in a way that would promote them and make them explicit. To use Wenger's terminology (1998), we failed to foster a sense of joint enterprise (although, in some exceptional cases, this sense emerged from the students' initiatives).

Subject:

We wish to focus on two relationships -that between subject and instruments, and that between subject and community.

On the issue of subject and tools, we find Ivan Illich's notion of conviviality a useful benchmark:

Convivial tools are those which give each person who uses them the greatest opportunity to enrich the environment with the fruits of his or her vision… Tools foster conviviality to the extent to which they can be easily used, by anybody, as often or as seldom as desired, for the accomplishment of a purpose chosen by the user… They allow the user to express his meaning in action. [START_REF] Illich | Tools for Conviviality[END_REF] Students developed a convivial attitude towards ToonTalk. They used in ways we had not expected, to test conjectures and express mathematical arguments (Mor and Noss, 2004). However, while some students (and teachers) approached the WebReports with conviviality, bending it to their needs and expressing themselves freely with whatever means it provides, others did not. Students' inability to post challenges and responses in the prescribed way hampered collaboration and undermined the success of the activity. We see the causes in two other aspects of the activity system: insufficient attention to the rules imposed by local settings, and a lack of investment in the roles of facilitation and tutoring.

Object:

The objects in focus were numeric sequences. Having those as the play-things in the game eliminated a contradiction often found in educational games, where the learning objects are exogenous to the activity (Squire, 2002).

Instruments: Access to the mathematical objects was mediated by the computational media: ToonTalk programming and Excel worksheets. Each one has its own affordances and disaffordences. While ToonTalk allows the students to construct surprisingly complex sequences, in many cases they preferred to use excel as an analytic tool. We are not sure whether this preference indeed originated with the students, or rather reflects the techno-cultural background of their teachers. ToonTalk mediating role was facilitated by the WebReports equal treatment of text and models.

Rules: [START_REF] Engeström | Learning by expanding[END_REF] identifies rules as mediating between the subject and the community. In our case, the main design challenge of GmR was setting the rules of the game. These rules cannot be designed in isolationthey need to acknowledge of existing rules: those which regulate the social system of the classroom, and those which are constructed when students engage with remote peers. In fact, we had supplied the students with very little other than these rules. The activity is defined by the roles of proposer, responder and their protocol of interaction. Indeed, when these rules were observed, the activity followed a productive path. To our disappointment, this happened in less then half the cases (21 out 45 challenges and 15 of 33 responses). We read a very strong message here, which relates to the issue of division of labour, discussed bellow.

The design of GmR demonstrates a relation which is not usually observed: the mediating role of technology in the construction of rules and their relationship with subjects and objects. As an example, the communication afforded by a web-based system is very sparse compared to face-to-face interaction. This meant that for interactions to be successful, each utterance had to rich in content. In part, this limitation was overcome by a virtue of the tools: the animated code fragments participants embedded in their texts served as avatars, or proxies, in delivering their ideas.

Division of labour:

As mentioned above, the success of the activity was impeded by participants' failure to adhere to its rules. This failure was a result of a contradiction between the designed rules and those which participants had appropriated in common classroom practices. For instance, the emphasis on using code fragments as an element of communication was a completely novelty. In vernacular activity systems, the rules are transparent: they are maintained by consensus of the community, and new members learn them by Legitimate Peripheral Participation [START_REF] Lave | Situated Learning: Legitimate Peripheral Participation[END_REF]. In designed activity systems -such as ours -the rules need to be consciously accepted by all members of the community at once. This creates the need for a facilitator, a person whose role is to monitor adherence to the rules. The facilitator regularly scanned the WebReports system for GmR contributions. When they were ill-formed, he would alert the authors to their mistakes, and guide them in correcting them. In other cases he would point participants to contributions which they would find interestingan action that would have not been necessary had the authors of these contributions observed the rules.

Construction and presentation of eco-system models -ecomodelling

The ecomodelling activity sequence focused on allowing students (5 th grade) to program their own models of food webs where an endangered species plays a central role. The students chose to focus on animals such as the giant panda, killer whales, and Siberian white tigers. The specification of the activity sequence include on as well as off the computer activities where students design, program and discuss their models. The activity sequence was presented to the students as having the goal of producing models that could be published as WebReports and that others could try out, discuss, and comment upon. The students also used the WebReports system to report on their progress in the form of diaries including partial models.

Figure 3: The Whale game by two students exploring the life conditions of killer whales "I and The Best have made a whalegame. The endangered species is the killer whale. The threat is the net. The killer whale is supposed to try to catch the fish. When the killer whale touches a fish it grows. If it touches the net it blows up, same thing if the fish touch the net"

Goals of activity sequence:

The practice that we aimed to stimulate in this activity sequence was twofold. First, to support students in constructing models of their ideas and knowledge about ecological systems. Second, for students to publish their models of these along with textual explanations and description. Receiving students would analyse the models and modify and comment upon these. The intended outcome would thereby be the joint enterprise of knowledge production of ecological phenomena. The two central mediating instruments in the production of models and knowledge are the programming tools used for building models and the webreports system used for publishing models, and commenting and discussing these. These instruments serve dual purposes, both to shape the artefacts but also as mediators in the production of knowledge. Thereby, the students were engaged in two different roles throughout the activities, both as producers of models of ecological systems and as actors in the knowledge production community that we aimed to promote. Moreover, these two roles also occurred at two different levels of collaboration. Both at the level of individuals and small groups producing models and at the community level of knowledge building using the webreports system.

Community, rules, and norms:

The students' model construction and sharing were significantly influenced by the cross-cultural setting. This was the case even though at the time of this study the WebReports system was just recently up and running so collaboration with students from the other countries only happened to a limited extend. We would like to focus on two relationships that we identified as important sources of the contradiction in the activity system. Those were the relations between subjects and the surrounding community and that between subjects and rules and norms. The relation between the students and the surrounding community influenced the models that they students produced as well as the final outcome of the activity in two ways. First, the nearby group participants actively contributed to the shaping of the models that the students produced through discussions and comments that occurred in local activities and through use of the webreport system. Moreover, the local community also affected the students through the social relationships between the different students. This indirectly shaped the final outcome in that students were highly engaged in the particular impressions their models would make on other local community members. The following fragment illustrates this issue. The four students are discussing the model that is being built by two of their friends (Sebastian and Jonathan) that aims to illustrate how a drought may influence the life conditions of rats and sunflowers. 1. Tobbe: Their huge sun flower in the middle of the screen is… 2. Jonna: Really, seriously speaking their sun flower is kind of … 3. Tobbe: The rat is not really that pretty either, do you think 4. Tina: Yeah, I thought that … 5. Mimmi: Tina please let our buffalo be part of your game

The most important thing that happens in this episode is not how the students exchange specific ideas about how to implement something in their models, nor that they find specific suggestions relevant to their own work by studying what their friends are doing. Instead, what we find to be most important is that the students relate to and compare what they are doing to the work of their friends on a social level. Most of the influence of the collaboration does not concern the specific scientific content of the models they are building. It is rather about comparing and discussing each one's work in relation to everyone's overall progression. There is also extensive engagement in making sure that what they are building complies with the agreed upon overall norm for what they find the activity to be about. The two girls, Mimmi and Jonna, here come over to Tina and Tobbe to compare with their own work, to discuss the work of the Sebastian and Jonathan, and to try out the game that Tina and Tobbe have built. Hence, the role played by social influences for the modelling and programming of their system is mostly as a motivator for the progression of the activity as a whole, rather than having implications for specific considerations concerning knowledge about modelling of ecosystems.

Second, even though there was only limited immediate interaction between groups of students in different sites, the student's awareness of a larger community significantly influenced how they approached the production of ecosystem models. This relates to a contradiction that we identified in the different ways that the WebReports system may be used. In the EcoModelling activities the students mostly used WebReports as a tool for presentation of the models they had produced (see Fig 3) and much less as a tool for discussion and sharing of knowledge. This is a consequence of a contradiction between the goals that students developed in the local group activities and the community level activities. We see this as an example of a more general issue: the contradictions between motives and goals of the different actors (students and teachers) within educational activities. In our case the students' motives was partly to jointly discuss their ideas and thereby be co-producers of knowledge. However, we discovered that for the students, the goals of joint knowledge production often stood in contrast to the more immediate goal of actually designing and implementing their models in the programming tools. These two goals are different in character and may therefore subsequently lead to a different set of subactivities; the practical activity producing a working computational artefact vs. the activity of discussing the ideas that the artefact represents.

This contradiction has important consequences not only for the activities that students engage in but also for how we as designers of the system should approach the redesign of the different components and subactivities. We see that a significant source of this contradiction is found in the underlying values of these two activities. The model construction activity has clear resemblances to the established practice of schooling: performing a task by following instructions, which here involved building a model using this particular tool. On the contrary, knowledge building as a joint activity requires the fostering of a new set of social rules and norms for what the school activity should be about. To resolving these contradictions we would need to redesign the WebReports system and the activity sequence, but also to raise awareness to the unorthodox rules we wish to establish.

CONCLUDING DISCUSSION

We have reviewed two example of educational activities designed and tested by the WebLabs project. While both cases were fairly successful, they both had their weaknesses. These activities differ in their knowledge domains, but also in their interpretation of Knowledge Building, Constructionism and CSCL. While the GmR had more elements of the traditional knowledge building interactions, ecomodelling had a larger focus on model building and presentation. GmR used ToonTalk's low level programming facilities, whereas ecomodelling applied a component-based approach. In GmR WebReports served as a platform for discussion, in ecomodelling they functioned primarily as a display medium.

A key result regards how the students perceived the expected outcome of the different activities in the two case studies. In the ecomodelling activity the students largely focused around creating their models and presenting them to their peers, both over the web and in group presentations. Thereby, the web-based collaboration did not become an aspect of the actual model building activity. In the Guess my Robot activity on the other hand, the students focused on using the WebReports system to create challenges and respond to each others challenges, and the intense web-based collaboration became a prerequisite for successfully engaging in the game. Thereby, the web-based collaboration provided additional benefits to the outcome of the activity as a whole than the students would get from local collaboration only.

In both our case study examples we saw how the goal of the technologies that we have designed sometimes stood in contrast to the already existing classroom practices. The two technologies also partly brought conflicting goals with them. Hence, design efforts to a large extent involved fostering students and teachers to find ways to incorporate these technologies into their classroom practices. The changes and extensions we made to our systems were hence always accompanied by changes to the activity sequences. In particular since the kind of activity that we aimed to foster involve a range of different social (schools, research practice, virtual places) and technological contexts (websystems, programming tools) it has been central to our design efforts to always take this range of aspects into account.

Three themes are common to all our other activity sequences and contributed to their success:

• An attempt to blend ideas of knowledge building, as a social practice, with constructionist modelling, as an individual (or small-group) endeavour. • A view of designing, and analyzing, the epistemic activity system as a whole: the tasks, their aims, the tools (ToonTalk programming and WebReports collaboration), school settings and community practices. • An iterative process, in which the activity system evolves through cycles of design, critical evaluation and refinement.

These themes are tightly bound. An activity-theoretic view leads us to the understanding that the individualcognitive and social factors of learning are intertwined. In our case, these are reflected as construction and discussion. It also suggests that the historical process of refinement (even at the micro-level of iterative design) is inevitable; Instruments, both concrete and social, are invented for a purpose -but their full potential is realized through use. In our case, testing the activity sequences with one version of the tools led to insights regarding the refinement of both the tools and the activity design.

Figure 1 :

 1 Figure 1: Training a robot to count Figure 1 shows three snapshots of what it means to write a program (train a robot) to count through the natural numbers.In fact, we only have to train the robot to "add 1" to a number and then generalise it to any number. The robot iterates the actions it was trained to do, for as long as the conditions it expects hold true.

  When clicked, they automatically open in the reader's ToonTalk environment -which could be in another classroom or another country. The reader can then manipulate the object, modify it, and even respond with a comment that may include her own model. Note that by including a revised or alternative model the students have several ways of building on each others knowledge. This last point is crucial: rather than simply discussing what each other thinks, students can share what they have built and rebuild each others' attempts to model any given task or object.

Figure 2 :

 2 Figure 2: WebReports front page (http :// www . weblabs . org . uk / wlplone / )

http :// www . weblabs . eu . com


Denis Bouhineau
email: denis.bouhineau@imag.frjean-francois.nicaud@imag.fr

Jean-François Nicaud

Hamid Chaachoua
email: hamid.chaachoua@imag.fr

Marilena Bittar
email: marilena@dmt.ufms.br

Alain Bronner
email: alain.bronner@montpellier.iufm.fr

TWO YEARS OF USE OF THE APLUSIX SYSTEM

Keywords: ALGEBRA, EQUIVALENCE, EXPERIMENT, FEEDBACK, ITS, LEARNING, MICROWORLD, TEL

APLUSIX is a learning environment for helping students to learn algebra. This system is designed and developed in the IMAG-Leibniz laboratory. Its basic training mode consists of letting the students perform their owns calculations, thanks to a two-dimensions editor of algebraic expressions, providing feedback on the correctness of the calculations and on the end of the resolution. APLUSIX has now been used for two years at school, in different contexts. One use was made by four teachers during two entire school years in France, in the computer room, for each algebraic activity of their grade 10 classes. Their main outcomes were very positive. APLUSIX has also been used in the hospital for children having a long illness. The results were very positive too. Several experiments of Aplusix have been realised with a pre-test and a post-test to measure the learning. One experiment, in France, with 28 students and 50 minutes training, shows an improvement of the abilities increasing of 70% to 250% depending of the type of exercise. Another one, in Brazil, with 1120 students and 25 minutes training, shows a global improvement of 30%. These good results led us to realise a version of APLUSIX for home usage in addition to the version for schools. This home version is now available as a shareware in several languages.

INTRODUCTION

In the domain of Technology Enhanced Learning (in short TEL), most of the work done by researchers stay confined inside the laboratories and universities, those works almost permit the development of the academic knowledge but most of them decayed without having been used by everyday students in standard school. Fortunately, it is not always the case. Few works have been exported out of the research area into the real world. The best example is given by the success story of the microworlds for dynamic geometric leaded by Cabri-Géomètre [START_REF] Laborde | Designing intelligent tutorial systems: The case of geometry and cabri-géomère[END_REF]). In the domain of algebra, no success as big has been noticed yet. In the last ten years, almost two academic projects have been commercialised [START_REF] Beeson | Design principles of mathpert: Software to support education in algebra and calculus[END_REF][START_REF] Koedinger | Intelligent tutoring goes to school in the big city[END_REF][START_REF] Koedinger | Intelligent tutoring goes to school in the big city[END_REF]). Unfortunately, they did not compete with the use of computer algebra systems (in short CASs) available on the student's symbolic calculators. CASs and spreadsheet are use even if they have not been built with any learning purpose. Teachers and researchers in education have shown that CASs are certainly not neutral and safe objects, and, moreover, the use of those tools can introduce important difficulties for the learning of algebra [START_REF] Trouche | Calculatrices symboliques[END_REF]. For example, in the same direction that, years ago, it has been shown that calculators lead to annihilate the differences between large integers and floating point numbers (because of the scientific notation), between the decimals, the rationales, the algebraic numbers and the true real number (because of the truncated decimal representation), CASs tend to make disappear the differences between one given expression, the same expression factored and the same expression expanded, reduced and ordered. For all of these expressions, the student can find zeros, limits for infinite values, derivatives, etc., with the same action, not depending on the form of the expression.

In 2000, our team, mainly two computer scientists, the two first authors (who, at this moment, were at the University of Nantes, France), restart from scratch the development of a new TEL environment with two main goals. The first main goal was to create a TEL environment for learning algebra allowing the student to freely build and transform algebraic expressions. The environment should provide epistemic feedback that can help in the first stages of the learning of algebra. At that time, there were no TELs for algebra that allowed the student to freely build and transform algebraic expressions, as he/she can do on paper, and to follow his/her own algebraic reasoning; the existing TELs were, and most of them are still, command-based systems that did not allow the student to proceed without applying a command chosen from a menu. See MathPert, [START_REF] Beeson | Design principles of mathpert: Software to support education in algebra and calculus[END_REF] as a good example of these command-based systems. So we decided to build a system to help students solve exercises in numerical calculations and formal algebra, where they would perform their own calculations by typing the expressions and making the steps they want, as on paper. The system, called APLUSIX (this is what is pronounced in French when you read "a+x"), would gives feedbacks, mainly whether the calculations are correct or not, and whether the exercise is solved or not, those feedbacks depending on the semantics of algebraic expressions, and the syntactic form of the expression, see [START_REF] Nicaud | Syntax and semantics in algebra[END_REF]) for a complete explanation of the semantics aspects. The second main goal was to create a TEL environment that would be used for real. This goal requires building an easy to use and useful system. We considered two main points for usefulness: Encompassing a large mathematical domain and having several modes of functioning. And we also kept in mind that teachers will be the first users of the environment. For them, also, the environment must be user friendly and must provide useful tools. APLUSIX does not directly teach the rules and the methods. Rather, by providing adequate information, it helps students learn to apply the rules and methods correctly. The teacher is still in-charge of the teaching and learning process, for him/she APLUSIX is just another tool in order to achieve his/her goals. In fact, APLUSIX impacts the learner rather than making the teacher more efficient. Aplusix participates to the global movement observed about education and TEL: computers are slowly but steadily moving educational programs from teaching to learning. Section 2 will give a short description of the system. Section 3 will describe experiments done by researcher in education with it. Section 3 will report comments given by teachers having use APLUSIX during the last two years. Section 4 will relate the efforts done to achieve a real distribution of the system.

THE APLUSIX SYSTEM

APLUSIX is organized on the base of two editors, an advanced editor for algebraic expressions, an editor for algebraic reasoning; these two editors have been constructed as microworlds. They permit numerical calculations and formal algebra activities like expansion, factorisation, and resolution of equations, inequations, and systems of equations with verification of the equivalence (or equality) of expressions during the reasoning. There is an immediate feedback showing whether two consecutive expressions are equivalent or not.

The domain allowed correspond to numerical expressions with integers, decimals, fraction, square roots; algebraic expressions with degree less or equal to 4 (polynomials or rational expressions with sum of degree less or equal to 4); equations, inequations or systems of equations. Strategic information is given to the students about the state of the problem in order to help them move toward a solution. Gauges 'Reduced', 'Sorted', 'Expanded', 'Factored' (for numerical and polynomials factors), 'Equation' are available.

Commands for executing certain algebraic actions are available. These commands can be visible or not, powerful or not, according to parameters set by the teacher, (they have to be adapted to the current level of understanding of the students in order to only present calculations they can do without difficulty). With this feature, such a computer system can provide an introduction to the proper use of a Computer Algebra System. There are 'Calculate', 'Expand and reduce', 'Factor' and 'Solve' commands.

Last, the microworlds are embedded in a piece of software whose concern is the practical organisation of the learning process (login of the students, organisation of their work according to some prepared scenario, recording of the activities, scoring and statistical analysis of these activities made available for the teacher, tuning of the software with parameters, automated generation of exercises, ...). A longer description is given in [START_REF] Nicaud | Mixing microworld and CAS features in building computer systems that help students learn algebra[END_REF]).

Let's see an example of use of APLUSIX. First, the student starts with an expression (14 -8)(18 -15) and a direction 'Calculate', figure 1. Then, figure 2, the student, tries to calculate the product, see the negative feedback, correct him/herself, and make a significant step.

Figure 2: Three moments in the calculation. First the student ask for a new step (no equivalence is shown in blue, the colour of the question mark, between the first step and the second unfinished one), then the student proposes an erroneous expression (a negative feedback is given in red), after correction, the student finds the correct expression.

THE EXPERIMENTS

The first users of APLUSIX are our colleagues from math education. They organize large experiments in ecological conditions to record via APLUSIX the activity of students with this light software very close to the paper and pencil environment (especially when no feedback is given to the students, as it can be parameterised in APLUSIX)

Experiment '9-2'

Quantitative information:

-When: September and October 2002 -How many sessions: 3 sessions, the first session without any feedback from the software, the second session with feedback on equivalence available to students when they ask for it, the third session with permanent feedback.

-How much time: 50 minutes for each session.

-How many students: 246 students, three levels involved: 91 students aged 14-15, 108 students aged 15-16 and 47 students aged 16-17.

-What were the exercises: Each session, and each level get a particular list of exercises from every type of problems available in APLUSIX. For example, there were the following exercises:

expand (7x-2)²-(3x+12)(3x-12), solve (3x+5)(- x+9)=0, solve (-3x+9)(2x+4)-(-3x+9)(7x-1)=0, solve x 2 = 3, solve ( 2 4
)(5 3 ) 0 4 ( 1)

x x x x + - = + , solve 2 2 1 5 3 x x - = - , solve 6x-(5- 3x)<-3(x+1).
-What is the average score (in terms of well-solved exercises) obtained on exercises: it was about 30% for 14-15 years old students, 40% for 15-16 years old students and 60% for 16-17 years old students.

Qualitative information:

The goal of the experiment '9-2' was to collect an important amount of protocols in order to analyse and determine typical conceptions of students. Each list of exercises consisted of about 30 exercises organised to minimize the effect of learning. For example, the first session, for 15-16 years old students was made of 3 'calculate' problems interleaved with 8 'expansion' and 6 'factorisation' about second degree polynomials, and 13 'solve' problems about linear, second degree equations and systems of linear equations. Most of the numbers were integers. However, in 5 problems, they were rational numbers and radicals in 1 problem.

Two different analyses of the results have been made by hand:

-Construction of a collection of correct and incorrect transformation rules used by student. This has been made by means of an analysis by hand of the protocols. From an epistemic point of view, regarding the movements of terms in linear equation and inequation, there can be found 648 transformation rules. The library of transformations rules used in algebra allowed the construction of an algorithm to diagnose the transformation made by students. This algorithm permitted the second analysis which aim at: -Construction of typical conceptions of students learning algebra. The algorithm for diagnostic of transformation gave good results, but we have not be able to construct typical conceptions of student, because we did not get enough data on one domain for every student. The principal reason was that we have targeted a too large domain (too many types of problems and sort of expression). As a consequence, we decided to organize a second experiment, where the domain (type of problems, type of expressions) would be smaller, in order to get more actions for each student on one domain.

Experiment '9-3'

Quantitative information:

-When: September and October 2003 -How many sessions: 3 sessions, the first session without any feedback (pre-test), the second session with punctual feedback on equivalence available to students, the third session without any feedback (post-test).

-How much time: 50 minutes for each session.

-How many students: 167 students aged 16-17.

-What were the exercises: the exercises were mostly linear equations and inequations. For example: solve 2x+4=7+5x, solve 3x+2<6x+11, solve 5(x-2)-(1-x)=0, solve (x+1)(x+2)<(x+3)(x+4). The exercises of the third session were close variations of the exercises from the first session (5(x-2)-(1-x)=0 replaced by 3(x-2)-(5-x)=0) -What is the average score obtained on exercises: we pay attention to the evolution of the score between pre-test and post-test for 28 students from one high school (the score is the number of exercises well-solved by all the students over the number of students). On the average, this score have been up of more than 100%: Exercise of pre-test Similar exercise of post-test Score at pre-test Score at post-test

3-2x=3x-6 2x+4=7+5x 37% 64% 3/2+x=1/3-1/2 3/2+1/2x=1/3-1/2x 10% 32% -4x-1>0 -4x-1>2x 16% 42% 3x-8<2-2x 3x-8<2-2x 33% 66%
Figure 3: Evolution of the score between pre-test and post-test.

Qualitative information:

The goals of the experiment '9-3' were to collect protocols about a restricted domain of algebra to analyse, and to determine typical conceptions of students on this domain. As a derivative result, we would like to obtain also some preview about the learning achieved with APLUSIX. The restricted domain was about solving linear equations and inequations. We have focused on the transformation rules of movement in linear equations and inequations. For example, about the transformation 3x=4 x=4/-3, we have associate the rule 'MultiplicativeMovementInRelation' applied to term '3' with attributes (LeftToRight, NumeratorToDenominator,SignArgumentChanged, Incorrect) Protocols have been processed by the algorithm to diagnose the transformation rules used by the students. Among 4570 resolutions, we have diagnosed 4756 transformation rules concerning movement. This has produced vectors containing information about the context and the transformation rules used. Those vectors can take 192 different values. For each student, we have tried to correlate context and transformation rules in order to determine the conception of the students about movement in linear equations and inequations. We have found 4 conceptions based on the sign of the moved terms, and 4 conceptions based on the sense of the inequations.

3.3

Experiment 'BRA-1'

Quantitative information:

-When: March, April 2004 -How many sessions: 2 sessions. Each session began with permanent feedback on equivalence (25 minutes), and ended with no feedback (test during 25 minutes).

-How many students: 1121 students aged 13-14.

-What were the exercises: the tests consisted of 20 exercises on linear equations and inequations. Coefficients were mostly integers. Few exercises contained rational numbers.

-What is the average score obtained on exercises: the first test had only 10,7% of success on equations and only 8,9% of success for inequations. The rate of well solved was up 30% for the second test. From a general point of view, the scores were very low. This was surprising because the resolution of linear equations and inequations were supposed to be known at that age.

Qualitative information:

The goal of the experiment 'BRA-1' was to test the use of APLUSIX for learning with a very large number of students.

During the first session, the first part, with permanent feedback, corresponded to an introduction to the system. During the second session, the first part was thought of as a learning phase (25 minutes). In both sessions, the second part, without feedback, was a test: pre-test for the first session, post-test for the second session.

Unfortunately, the length of the experiment was not sufficient to conclude that any learning occurred for students. Nevertheless, we have verified an increase of the student's scores between the two sessions. The observed improvement was not related to one particular type of exercise but related to the global set of exercises. For example, we have noticed a score of 25% of success for the exercise X/3=4 from test 1, and a score of 30% of success for the exercise x/7=2 from test 2. It means a noticeable improvement. But for the exercise 4x-6=2x+5 from test 1, we had a score of 21% which did not evolve with test 2: we got a score of 22% of success for the exercise 8x-2=4x+3 from test 2.

For both tests, statistics have shown that the score for equations is quite twice the score for inequations: 27% for equations, 14% for inequations. This is a normal. Equations have been studied by students during the previous two years. Equations are worked out all along these two years, either as exercises, either as problems leading to equations.

Inequations did appear at the same time but the frequency is very low, even null in some manuals (equations do appears always in manuals)

Experiment 'BRA-2'

Quantitative information:

-When: March, April 2004 -How many sessions: 2 sessions. The first one, without feedback, began with an introduction to APLUSIX and ended with a test on linear equations (30 minutes). The second session began with a test on linear inequation (20 minutes). The end of the second session was free, students had permanent feedback.

-How many students: 1340 students aged 13-14.

-What were the exercises: the tests consisted of 16 exercises on linear equations and inequations. Coefficients were always integers. For example: 3x-5=7, 4x-6=2x+5 and -2(5x-2)>-3(x+2). Exercises relied mainly on numerical calculations, expansions and reductions.

-What is the average score obtained on exercises: the average score (all protocols evaluated together) is very low, varying from 3% to 26% according to the exercise. Statistics computed by high-school can vary from 35% to 60%. Score for equations are higher than for inequations. Score for equations and inequations is lower with negative coefficient for x.

Qualitative information:

The goal of the experiment 'BRA-2' was to collect a large number of protocols to continue the study of transformation rules and conceptions of students about linear equations and inequations.

Teachers reported that students did not have difficulties with the software but with the proposed exercises.

The analysis of the protocols is not finished yet. Researches are in progress. The by-hand analysis of a few protocols has shown that the incorrect transformation rules used by students correspond to the rules found during experiment '9-3'. This validates the library of transformation rules constructed. The study of these protocols in term of protocols has not been done yet. We project to use the diagnostic algorithm to achieve this study; in particular, because of the large amount of data, a by-hand study is not thinkable.

TEACHER'S OPINIONS

In parallel to experiment done for research, APLUSIX have been used by voluntary teacher. Here are some opinions and example of use of APLUSIX.

Use in normal class

Here are collected opinions from 4 teachers having used APLUSIX during the last two years.

About the software:

-The discovery of the system did not present any difficulty and was very quick.

-The use of the system on the network of the school is appreciated because it permits individual and collective use. -The possibility to set the parameters of the system according to the goals of the learning is appreciated.

-The use of the virtual keyboards is more and more efficient.

-The possibility to supply the students with commands like 'expand or 'factor out' permit to focus the work on one difficulty at a time.

-The preparation of a session is easy, the exercise editor allow to create a personal list of exercises quickly.

About the students: -The students needed less help, were more confident and gained autonomy.

-All the students really worked during APLUSIX sessions, contrarily to the usual paper-pencil sessions.

-Students in difficulty have shown motivation to solve exercises, on their own, out of the lesson; they chose exercises in their text books and solved them with APLUSIX.

-How many times do I have eared "Now, that's it, I have understood!" -APLUSIX forces students to correct themselves their errors and to analyse them. As a consequence, the most important part of the group progress well, for the methodology too.

About the place of the teacher in the classroom: -With APLUSIX, the teacher can circulate much more easily, bring a punctual help and give advices.

-With paper and pencil environment, the teacher mainly validates the results.

-With paper and pencil environment, the teacher spends a lot of time with students in difficulties to find where the errors are located. About the learning: -We have observed a significant progression from the very first hour.

-The benefit of the work with APLUSIX was transferred to the paper-pencil context.

-Progresses are made at the syntactical level.

-After two sessions devoted to systems of equations (Aplusix obliges the students to make steps with equivalent systems), 90% of the students wrote equivalent systems in the paper-pencil environment.

-At the end of the year, the students had better results than the students of the previous year.

-Some errors seem to have disappeared.

-The notion of equivalence seems to have gained sense.

-Students remember to simplify the results.

Example of use:

-Experiment and confrontation of different methods for the resolution of the same problems are facilitated.

-Each student has a computer, first with permanent verification of the equivalence, then with verification on demand.

-Each student has a computer and a list of problems, students can choose the computer or paper and pencil.

4.2

Use at the hospital and at home, for children having long illnesses APLUSIX have been used for ill children, during one year, by one teacher, in two main situations: -Student, in a classroom, who alternatively takes a lesson (alone or in a group of 2 or 3) and work in semi-autonomy; -Isolated student, at home or in a sterile room of the hospital, who alternatively take an individual lesson (by teleconference: the use of Aplusix is shared between the teacher and the student) or work in autonomy.

The student has often less time to work than a usual student, and the duration of its stay in the hospital is not always known in advance. One has to do simple and efficient actions.

Up to now, the use of APLUSIX at the hospital is basic: a brief explanation of the functionalities allows an immediate use of APLUSIX, generally in anonymous mode, to work on numerical calculations (fractions, square roots), algebraic calculations or equations. The first exercises are solved with the presence of the teacher (physical or at distance) who provides the exercises, and quickly the student works in semi-autonomy or autonomy with exercises provided by the teacher or by its own initiative.

Some features of the software are particularly interesting for our specific students: -Lightness: the discovery is very quick the manipulations are simple for the students (the virtual keyboard is appreciated for the laptop we lend to the students); -Efficiency: Aplusix saves the teacher time; it favours the student's autonomy, promotes an exploratory behaviour, asks interesting questions (0.33 is refused for 1/3 and 1,414 is refused for square root of 2); -Attraction: the students like to use the system, even those who would not have been motivated by the same exercises on paper;

-Flexibility: the system is easy to use in an individualized way or at distance; -Reliability: its rigour and logic allow letting, in confidence, the student work alone.

TOWARD A REAL DISTRIBUTION OF THE SYSTEM

These good results led us to achieve our project of real use and to define a version of APLUSIX for home usage in addition to the version for schools, and to try to commercialize both versions. We present shortly modification we have made recently to achieve both versions and work necessary to become a decent product.

5.1 APLUSIX at home. Compared to the software used during the experiments and last years, the version of APLUSIX tailored for home usage has been:

-simplified (fewer menus, parameters, and functionalities, smaller domain of application), -augmented with a generator of exercises, -augmented with an algorithm to score the production of a student. Since, September 2004, APLUSIX is commercialized as a shareware on the web.

5.2

APLUSIX at school The development of APLUSIX continues with a focus on the tools we can give to teachers. We added a new type of problem: the word problem (to find an equation modelling a problem given in natural language). We added tools for the administration of the student's accounts, of the classes, of the teacher's teams. We added a module for doing statistics about the actions of the students.

5.3

Other works We have tried to have APLUSIX become a professional product, with help according to the HLP format of windows, installation setup according the standard of windows. We added key-authentication algorithm to verify that the product have been paid. We have registered APLUSIX at the APP (Agency for the Protection of Programs). We have found a publisher to commercialize APLUSIX in French. We are discussing with publishers for English, Portuguese and Japanese. We also put APLUSIX on the web at http://aplusix.imag.fr .

Our opinion is that all the work done in this subsection (except the diffusion on the web) is not a research work, but is necessary to achieve a real use.

CONCLUSION

The work we began in 2000 has given software which can have been used since 2002. The first users were researcher in education. They collected hundreds of protocols (more than 1 millions of actions have been recorded and are available in a database not described in this article, dedicated to the protocols of APLUSIX). For researchers in education, APLUSIX is a tool which permits to obtain a lot of data. In fact, experiments have given much more data than researchers can exploit since they got it.

Since 2003, APLUSIX is also available on the web, and more than 5000 downloads have been processed (in three languages) With the exception of the few teachers we know and work with us, it does mean that there are teachers, we don't know, who are using APLUSIX in their class. In Italy, in Canada, researchers begin to work with APLUSIX, out of our control, too. We hope this will continue and progress.

7.

Figure 1 :

 1 Figure 1: Starting point of a session with APLUSIX.


Casper Hulshof
email: c.d.hulshof@utwente.nl

Ton De Jong

Using domain-specific and generic knowledge to support discovery learning about geometrical optics in a computer-based simulation

Using domain-specific and generic knowledge to support discovery learning about geometrical optics in a computer-based simulation

Casper Hulshof, Ton de Jong

Introduction

In the context of the project 'Prior knowledge and discovery learning' (subsidized by NWO, the Dutch equivalent of ESF), a number of studies have been conducted. These studies aimed at clarifying some of the constraints of discovery learning in computer-based simulations. For this purpose, the studies focused on the method students from secondary school used to operate a computer simulation on the topic of geometrical optics. The computer simulation (called 'Optics') was designed to elicit scientific discovery learning behavior. The Optics simulation offers a versatile and dynamic learning environment, with built-in tools for the analysis of discovery learning processes. To study discovery learning processes, all actions that students performed in the Optics simulation were registered. Domain-specific knowledge and generic knowledge of mathematical relations were measured before students commenced work in the simulation. The earlier studies that we have carried out (reported in detail in [START_REF] Hulshof | Discovery of ideas and ideas about discovery: The influence of prior knowledge on scientific discovery learning in computer-based simulations[END_REF] show only a limited influence of the level of prior domain-specific knowledge, and a general effect of generic knowledge on discovery learning processes. Learning effects were minimal, which may have been caused by the lack of support students received during learning, in combination with the poor level of prior knowledge about geometrical optics that students possessed. In a first study (see [START_REF] Hulshof | The influence of prior knowledge on scientific discovery learning processes in simulation-based science domains[END_REF] we had already attempted to influence prior domain-specific knowledge about another simulation about a ficitious domain (called 'Bubbles'). It was found that only giving students knowledge about the domain prior to working with the simulation did not render discovery learning more effective. The objective of the present study was to render discovery learning in the Optics simulation effective, by manipulating knowledge during discovery learning. This way, knowledge was used as an active support measure. In the study, domainspecific and generic knowledge were available to a group of students while they were working with the Optics learning environment. Another group, who did not have this type of support available, served as a control group. It was expected that having knowledge available during discovery learning would affect the learning process and lead to more effective learning.

Theoretical framework

The theoretical framework that has been used for all the studies that were conducted in this research project is the SDDS model of discovery learning [START_REF] Klahr | Dual space search during scientific reasoning[END_REF][START_REF] Klahr | Exploring Science: The Cognition and Development of Discovery Processes[END_REF]. During discovery learning with a computer simulation people carry out experiments in a virtual environment to get new information and to modify their existing beliefs (Kulkarni & Simon, 1990). When the process of experimentation and the process of deriving a hypothesis are described as search processes, [START_REF] Newell | Human Problem Solving[END_REF] general theory of problem solving can be extended to incorporate both these processes. Klahr and Dunbar's SDDS model offers a description of discovery learning as a problem solving-like search through two problem spaces: hypothesis space and experiment space. The model states that discovery learning consists of three components: search hypothesis space, search (or: test) experiment space, and evaluate evidence. Each of these processes has its own goal. In hypothesis space search, the goal is to form a fully specified hypothesis. This hypothesis can be tested by performing an experiment. The resulting evidence is evaluated, the goal of which is accepting or rejecting a stated hypothesis. The SDDS , and the extensions that have been added to it by [START_REF] Van Joolingen | An extended dual search space model of scientific discovery learning[END_REF]It can be used as a general framework for studies on discovery learning processes.

One goal in this research project has been to further extend the SDDS model, by focusing on the role of different types of knowledge on the search through hypothesis space and experiment space. Several studies (e.g., [START_REF] Glaser | Scientific reasoning across different domains[END_REF][START_REF] Lavoie | The nature and use of prediction skills in a biological computer simulation[END_REF][START_REF] Njoo | Exploratory learning with a computer simulation for control theory: Learning processes and instructional support[END_REF] have shown that a relation between prior knowledge and discovery learning process and learning performance exists. In these studies, more domain-specific prior knowledge was shown to lead to more effective discovery learning behavior and higher learning effects. Our hypothesis is that knowledge will only lead to more effective discovery learning when it is available, or can be accessed, during learning. In the case of geometrical optics, students had trouble in accessing their knowledge about the subject during learning. In this study, it was attempted to influence this situation, by making knowledge available to students. The main research question of the current experiment was: what differences can be found between students who are not supported in their learning behavior, and students who have support available in the form of domain-specific and generic tips during discovery learning?

We expected differences between an experimental group (who had help available) and a control group (who had no help available) in scientific discovery learning processes and in performance on a domain-specific knowledge test. It was expected that the experimental group would benefit from having knowledge available, which should result in more progress from pretest to posttest on the domain-specific knowledge test.

Method

The subjects who participated in the study were 32 students who were following technical vocational education (mean age 19 years). All students worked for a set amount of time (about 60 minutes) with a version of the Optics computer simulation (see Figure 1). The simulation allows for the manipulation of light sources and lenses, and allows students to make both qualitative and quantitative measurements. Two conditions were used in the study: a 'help'-condition, in which domainspecific knowledge was available to students during learning, and a 'no-help'condition, in which students worked with the simulation but had no help available. Students were randomly assigned to one of the two conditions. In the help condition, tips were used to make domain-specific and generic knowledge available to subjects. Students were free to access the tips, they were not obliged to do so. In total, nine tips were available during learning. The assignment that was given to students was the same in both conditions. Students were encouraged to experiment with the simulation, and to find out the underlying rules.

To measure interaction behavior with the Optics simulation, all operations that students performed were registered by the computer. The resulting 'log files' could be analyzed afterwards. Before they worked with the simulation, paper-and-pencil tests for domain-specific and generic knowledge were administered to students. After working with the simulation, a domainspecific post-test was administered.

The experiment was split over two sessions: in the first session the prior knowledge tests were administered, in the second session students worked with the Optics simulation. Both sessions lasted about 80 minutes.

Results

The results showed that when students had access to information about geometrical optics, they did make use of it. Also, the information that was provided by the 'knowledge tips' helped in manipulating domain-specific knowledge, which in turn led to a statistically significant improvement on domain-specific knowledge from pretest to posttest (see Figure 2). The improvement from pretest to posttest in the help condition is in contrast to the result for the no-help condition. For the latter group, scores from pretest to posttest showed a statistically significant decrease. In the no-help condition a positive correlation between the domain-specific pretest and posttest was found (a replication of results from earlier experiments in which no support was used). This correlation was zero in the help condition. Also, no correlation was found between the number of tips that were accessed by subjects in the help condition, and their performance on the domain-specific posttest.

Results from the analysis of the interaction with the Optics simulation revealed that students in the help condition were less active than students in the no-help condition. When a division was made between students with poor and high generic prior knowledge, an opposite effect was found: students with high generic knowledge were more active than students with poor generic knowledge.

The results lead to the conclusion that discovery learning about geometrical optics can be rendered effective when a relatively minor support measure of knowledge support is used. When knowledge is offered during discovery learning, students are able to make use of it and will access it when they deem it necessary. The findings for the interaction behavior in the computer simulation replicate earlier findings: access to domain-specific knowledge leas students to be less active in their discovery learning behavior. Having generic knowledge of mathematical relations helps students in experimenting with a simulation, causing them to be more active. In terms of the SDDS model, it can be said that more generic knowledge gives students a larger hypothesis space to search, because they know of more types of possible relations between variables (in Van Joolingen and De Jong's extended SDDS model, this is called the 'effective learner space'). Having domain-specific knowledge available during discovery learning partly 'fills in' students' hypothesis space (or 'learner hypothesis space'), which reduces their need to search for further exploration.

Conclusions

The results of this study have both practical and theoretical implications. The practical implications center around the design of effective learning environments that elicit discovery learning. In earlier studies, we concluded that it is important to determine at what moment the availability of information can bring extra support to the discovery learning task and thereby improve performance in simulation-based learning environments [START_REF] Hulshof | The influence of prior knowledge on scientific discovery learning processes in simulation-based science domains[END_REF]. For these environments to be effective, it is important that students have access to (prior) knowledge during learning. Supporting students by giving them access to information during learning also has the potential benefit of motivating them to learn, because it will help them in linking the knowledge they receive with what they already knew about a subject.

On a more theoretical level, the study shows that the SDDS model, in which the search spaces are 'islands' of knowledge, is correct in adhering so much importance to the role of knowledge in discovery learning. Further research can shed more light on other determinants of successful discovery learning, and on the role of prior knowledge in collaborative discovery learning.

Figure 1 .

 1 Figure 1. Example interface of the Optics computer simulation as used in the current experiment.

Figure 2 .

 2 Figure2. Pretest-posttest differences for no-help and help conditions.