This paper presents our research efforts to support students' collaborative process when learning mathematics and science as they interact in microworlds and engage in discussions and structured arguments. From a pedagogical perspective, the system provides students with an environment to explore challenging problems and encourages them to collaborate. The collaboration takes place in a discussion environment that is integrated with microworlds, allowing students to discuss and argue with one another and share their rationales and insights. The challenge of this work lies in providing students, teachers, and researchers with coherent, unified feedback within the system as a whole. To accomplish this, the system must combine and analyze student actions across tools, and results of those actions. We conclude that the integration of these two types of software tools provides a solid foundation for intelligent analysis of student collaboration.
1 Introduction
Technological advances and research in technology-enhanced learning (TEL) have
enabled at least two ways in which computer-based environments can support the way
students learn mathematics and science. The first is through Exploratory Learning
Environments (ELEs) including microworlds and simulations, which hold the promise
of making abstract ideas concrete and manipulable [
The work presented here attempts to blend these two approaches to learning by
integrating ELEs with a discussion and argumentation environment, thus enabling the
possibility to learn in ways that were not previously possible. Some prior steps have
been taken in this direction; for instance, the CoChemEx project explored the
combined use of a virtual laboratory environment with a collaborative discussion
environment, finding that scripted use of the integrated environment was easier for
students than a non-scripted environment [
Integration of discussion and exploratory learning environments has the potential to provide unique learning opportunities. Students can support each other by sharing domain knowledge (a form of peer tutoring), and students arguing about their work can promote deeper understanding than the students could gain working independently. However, there is a large potential for confusion, or missed opportunity when students are working in different tools and with different conceptual knowledge. The unique aspect of this work is our attempt to use an intelligent support system to recognize differences in student’s knowledge, and to support the movement between different tools in such a way that students gain the benefits of peer support and argumentation about constructed knowledge.
This work is being done within the context of an EU-funded project (Metafora1), which aims to provide a holistic environment in which students will collaboratively plan and organize their work, as well as collaborate in solving challenges and problems over a relatively long time period.
This paper presents a particular use case in mathematics and introduces the
challenges that we face in our efforts to analyze students’ collaborative process while
they interact in a mathematical microworld and simultaneously have the opportunity
to engage in discussions and structured arguments. In the microworld, called
eXpresser, students construct patterns of repeated building blocks of square tiles and
their associated algebraic rules, as described in more detail in the next section.
Underlying this goal, the main objective is to promote students’ appreciation of the
power of algebra [
Both of these tools have analysis agents that can provide intelligent support.
Several computational components analyze students’ interaction in eXpresser and a
rule-based system offers suggestions or hints designed to help them complete the task
they are undertaking [
The Metafora system incorporates these tools (as well as other tools not mentioned here), providing communication and control abilities across tools. The tools, and their associated intelligent support components, are linked both through interface elements 1 http://www.metafora-project.org 2 eXpresser was developed in the context of the MiGen project (see http://www.migen.org) 3 http://cscwlab.in.tu-clausthal.de/lasad/ and data sharing components. Each tool records lower-level events (termed indicators) that note instances or summary of student activity, and higher-level events (termed landmarks) that note a significant accomplishment or evaluation of student work. An overall analysis component analyses these events to identify situations where intervention might encourage peer support or shared knowledge evaluation. To concretize the purpose, architecture, and usage of the system, section 2 presents a specific use case to illustrate how students might work within the system, and how the system might respond. Section 3 discusses our generic cross-tool analysis approach and section 4 concludes that this approach of integration and analysis across tools provides a solid foundation for supporting student collaborative process. 2 The Integrated Microworld and Discussion Environment in Use This scenario is meant to highlight the potential benefits and challenges of integrating microworld and argumentation tools in a pedagogically meaningful way. We seek to demonstrate how analysis from the individual tools can be combined to recognize when students should be prompted to use a specific tool, and how they might be prompted to do so.
The challenge given to students in this scenario is to use eXpresser to derive algebraic rules that correspond to structures of their own design, and are general across variable values. Specifically, in eXpresser, students construct their own models made of square tiles. These models contain variables that can be changed dynamically to test their structural generality. For example, Fig. 1 shows a student’s construction of a model that is comprised of two patterns, the red and the green. The red pattern (made of a building block of 2 tiles) is repeated horizontally 5 times. In an effort to make the model general and animate it, the student specifies that the green pattern (made of a building block of 5 tiles) is repeated ‘one more time’ than the red building block. To achieve this, the student creates a variable called ‘gaps’ to represent the number of gaps in the model. In order to color the model, the student has to specify algebraic expressions that represent the number of tiles in each pattern and subsequently define the model rule that represents the total number of tiles in the model. It is evident that the same model can be constructed in different ways, leading to different model rules. The description of the task and the classroom culture encourages students to construct structurally different models.
Subsequently, a collaborative task encourages students to discuss the correctness
and equivalence (or not) of their derived rules. It challenges students to read,
deconstruct and match their rule with their own model as well as with their partner's
model. In previous work we have established the benefit of these collaborative tasks
in that they provide students with opportunities to reflect on their interaction with the
system and develop strategies that allow them to justify the correctness and
equivalence of their rules [
As students are working individually at the beginning, the analytic tools of eXpresser look for landmarks, i.e. significant points that demonstrate important information about a student. One situation that might occur is that Student A achieves the landmark of creating a “general rule.” The analytic tools of eXpresser recognize and report this event to the analysis channel in the Metafora framework. The Metafora analysis agent recognizes that Student B has not yet reached this landmark. The LASAD tool reports any sharing of models over the analysis channel as well, so the system can recognize that the two students have not discussed this model. Thus, we have a situation where Student A has reached an understanding that could be helpful if shared with Student B. If the system took no action, Student B might struggle a bit in doing her own generalization, or Students A and B could potentially discuss their findings and share knowledge on their own. However, if Student B continues to struggle, and Student A doesn’t communicate her model with Student B, the system could suggest to Student A that she share her work with Student B and they discuss. Additionally, or alternatively, this information can be conveyed to the teacher who can take appropriate decisions.
Here we see some of the pedagogical benefits of linking the individual workspace
with a group discussion space. Rather than relying entirely on automated feedback
from within the microworld, we can exploit the advantages of collaboration to
encourage students to help each other. Similar tactics for encouraging students to help
one another have been suggested in prior work on the Rashi project where the system
used an expert knowledge base to recognize differences between student knowledge
and would then elicit conversation about these differences [
The Metafora analysis agent then monitors indicators (the lower level events such
as messages sent and statements created in the argument space) logged from the
LASAD tool to the analysis channel of the Metafora framework. When the analysis
agent recognizes that the model has been shared, and that a sufficient amount of
conversation has occurred, the system suggests to Student B that she re-visit her
model with the aim of reaching this landmark with her own solution. As the analysis
system for LASAD matures for this specific application, LASAD itself could offer
landmarks, such as recognition that the students have “shared knowledge”, or
“reached agreement”. This is a challenge to be addressed, and can refer to earlier
work in the ARGUNAUT project in which graph and text matching techniques were
used to identify certain critical exchanges between students [
Finally, after some time passes in which both students are moving between discussion and microworld environments, the analysis agent in the eXpresser system reports that student B has created her own general model, attaining the same landmark as originally attained by student A. Since the analysis agent is now aware that both students have achieved the landmark “general rule”, the system refers both students to the discussion environment (if they are not both there), and prompts them to discuss questions like “How are your models different?”, or “Convince each other that your models are correct?”. Fig. 2 shows an example of the discussion that follows in LASAD. Both students provide arguments that, in their opinion, justify the correctness of their rule. However, in Student A’s opinion, Student’s B argument (Box 4) does not explain clearly why the rule is correct. Having been challenged, Student B provides a further explanation (Box 12) that demonstrates a better understanding of the microworld affordances and a growing appreciation of some algebraic concepts (e.g. by writing “even if the number changes the rule is always correct”).
The LASAD analysis agent can analyze this discussion of differences and
correctness, looking for patterns such as “lack of consensus”. Again, here we see the
benefit of combined systems, knowing that both students have reached the landmark
(creating a “general” rule) allows the system to predict that they should reach
consensus on the correctness of each model. We also see the major challenges offered
by such a task, in recognizing a lack of consensus. The LASAD feedback agent
employs rule-based pattern recognition using information such as the types of boxes
used (e.g. claim, argument, explanation) and linkage between them, as well as limited
text analysis (keywords, etc.) in an attempt to recognize patterns of argumentation.
Once user data has been collected, this work can be extended using proven
machinelearning techniques applied to similar discussion environments [
We now discuss our initial ideas on creating a system that can handle the abovementioned situation in a generic manner, working also in the context of different challenges, with different kinds of microworlds, and potentially different types of discussion environments, in a standardized manner. In this way, we describe how the analysis agent for the overall Metafora system can recognize and take action to create the scenario described above.
First, the intelligent analysis components of the separate tools must share information, in particular analysis and abstraction of student actions, which allows for unified analysis of the integrated learning system. The systems remain highly separated, with each individual tool running from its own server. The over-arching Metafora system maintains multiple communication channels for the interaction between tools: an analysis channel where tools’ analysis components can report indicators and landmarks; and a command channel, where the system can instruct tools to display specific states or offer feedback to a specific end-user. The server logs and analyzes data coming in from the analysis channel, and provides commands to the tools based on this analysis.
Each tool reports processed information about the current users to the Metafora system (indicators and landmarks), and receives feedback information from the system to be presented to a user or a group of users. The challenge for the analysis agent on the Metafora server is to decide what is relevant information for the given task and tools. In the example above, we see that one relevant piece of information from the microworld is the generation of a landmark, in this case the accomplishment of the high-level task "creating a general rule”. The discussion environment can provide other pertinent pieces of information by generating indicators of student activity: in this case indicators showing discussion of the artifacts involved in this landmark (e.g. references to the “general rule” model that have been shared in discussion). Considering the generated landmark, we can allow it to act as a phase judgment consisting of three phases, as presented in Table 1. Here we see that the landmark defined by the microworld helps define when and how the system encourages students to use the discussion tool. We propose that the combined analysis of individual activities (individual students’ actions in a microworld) and collaborative activities (discussion of the microworld activities between students) can lead to productive intelligent support. The information provided by individual components can be used to define phases of work and recognize opportunities for productive collaboration. One major challenge of employing the approach described here is to generalize beyond the specific use case above. We have offered insight for a specific scenario between two tools and two users. Table 1 is the beginnings of a generic way of considering the state of individual tools in a more global way by the Metafora system. Future work includes scaling this type of support over multiple tools, in particular, to encompass different microworlds, and larger groups of students. Another major challenge, related to the first, is defining an abstraction layer that is able to capture and represent a variety of indicators and landmarks. Furthermore, such an abstraction layer must represent the connections between landmarks. For instance, in the example provided, there is a need for the landmark achieved by Student A to be linked to the need of a similar landmark for Student B.
With this effort, we also suggest a path that fellow researchers might follow in
attempting to introduce collaborative activities into their current systems, or combine
current systems to create collaborative workspaces. We suggest that single-user
environments can be integrated with collaborative workspaces by adding small
components to communicate student state information with external systems. We also
demonstrate how current intelligent feedback agents can be integrated and extended to
work with information across multiple tools by using simple message passing with a
common language and data format. Such an approach can offer a solid foundation for
taking many currently independent and specialized tools and creating a collaborative
workspace that can offer holistic, intelligent support to students. Furthermore, such an
approach can provide useful information to teachers and support them in their efforts
to help students. Future work includes defining and implementing a teacher interface
and interaction that will allow teachers to access and respond to such information,
building off of previous similar efforts in the Argunaut and MiGen projects [