When the Teacher learns: 
a Model for Symmetric Adaptivity

Abstract: In this paper, we present a model for  adaptive WWW hypermedia that is helpful in the authoring phase phase since it efficiently provides a feedback to the author about the behaviour of the system towards users.
The model is symmetric since it represents users in terms of their "interest" toward information nodes in each topic and, viceversa, it models information nodes in terms of the perceived "utility" toward users in each category. In this way, adaptive behaviour can be presented toward the user but also to the author, to help him/her in the design and tuning phases of the adaptive system.
We describe the motivations and the model, then we provide some examples and details on simulations.

Keywords: user model, authoring system.

1. Introduction

It is useful for students and teachers alike, to think of an educational system as a substitute of the real world experience. In this way, many systems use paradigms well known to users as classrooms, lessons, homeworks, lectures and so on (usually with the adjective virtual) and it is now common to denote such applications as courseware.

The issue when authoring courseware is, usually, to provide interactivity to students in a natural way so that it can become a fruitful help to the learning process, rather than an obstacle. Of course, it means that adaptive courseware must be even more carefully prepared. The problem, here, is in experimenting and testing of the system. Usually, it is done by asking students questions and comparing the interactions with the system and paths followed in the hypertext [Eklund et al.(1998)].

While this can be reasonable in small case tests, it can be seen that in applications of a certain size and that run for a non negligible amount of time, analysis of the huge amount of data can be a real problem. Still, for large case applications, it becomes much more important to be able to get quick feedback from the system by synthetic information.

In this paper we present a model for adaptive systems on the World Wide Web that is meant as an authoring aid as well as a knowledge model.The model is meant to provide a unifying view to the design-experiment-evaluate authoring scheme (shown to the right) as a continuos loop where the evaluation process provides help and feedback to the system designer and author. Our model has several characteristics. We outline them here and refer the reader to the conclusions where further comments to these aspects are presented:

• The model is symmetric: while applied toward users to provide adaptivity, it is also applied to information nodes in order to measure interests by categories of users.
• The model is efficient: it allows easily recognizable patterns for a quick analysis (even automatizable) of system performances.
• The model is natural: it is a common experience for educators to learn from the students, in the same moment the lesson is taking place. Adaptive systems have always provided a personalized response to students but it is as much important to provide responses to the teacher as well.
• The model is tunable: it allows tuning parameters since courseware is deployed in a variety of situations and time spans. The responses (feedback) of the model can be given at different intervals, therefore allowing for flexible interactions.
• The model is general: it can be changed to work for different knowledge models.

2. How the model is used

In this paper we deal mainly with the issue of feedback to the author: mechanisms to adapt the presentation and the navigation based on users' profiles can be easily mutuated by the ones in [Barra et al. - 1 (1998)], [Barra et al. - 2 (1998)] and [Calabrese et al. (1998)] where, for example, mechanisms to present personalized "Top 10 choices" are shown.

3. The model

1. a set of students S=A(K, T) where students are partitioned among the K categories in S1, S2, ..., SK.
2. a set of information nodes N=A(T,K) where nodes are partitiones among the T topics in N1, N2, ..., NT.

Now, what happens when a student A is related to a node B? The main idea is the following: we want to update  student configuration and node configuration, as well, according to the suprise that is generated. Informally, if there is not surprise, we do not want to modify the configurations since the system appears to be describing the student and the node pretty much well. If there is surprise, we would like to update the student configuration, showing an unusual (given the previous configuration) interest in a certain node and, at the same time, we would like to show to the author that something unusual happened to that information node, since it  appears to be interesting to students that were not really supposed to be attracted.

The process, here, lacks the symmetry elsewhere present in the model. We do want to update student profiles as soon as possible since the following interactions should be directed by changes in student's behaviour. On the other hand, we would not like the configuration of our information node be istantaneously changed each time a student generates a surprise. In fact, nodes are accessed by many students at once and, if nodes configurations' are changed each time one student accesses the node, then other students could not be able to retrieve the page that they previously accessed by using adaptivity techniques (like links sorting, for examples) base on nodes configurations. This would easily create confusion in the learning process. Still, we want to keep track of unusual accesses since they can be useful for the author during the authoring loop process described before. Therefore, let us describe the update operation for the student's profile, first, and, then, show how to update the information node's profile.

Assume that student A with profile Prof(A)= (c , <s1,s2,..,sT>) accessed information node B with profile Prof(B)= (d, <n1,n2,..,nK>)  with surprise Surpr(A,B). Now, the configuration of student is changed only if Surpr(A,B) is greater than sd . In this case, we change the value sd with the suprise Surpr(A,B) and, then, normalize the vector so that the configuration is legal i.e. it sums up to 1. This happens each time a student accesses a node that generates surprise. The effect of surprises is time sensitive since other surprises take place and the normalization process in the vector brings "old" surprises (not reinforced by successive surprise on nodes of the same topic) to fade out.
What happens to information node B? If a surprise takes place we might specularly act in the same way as students' profiles. This has proven iselfg a successful technique for quickly reacting to users' indications, as it is done in the model presented and tested for Electronic Commerce in [Barra et al. - 1 (1998)], [Barra et al. - 2 (1998)], [Calabrese et al. (1998)].
We add to information node profiles an additional configuration vector M that will hold the surprises (when high) of interactions by users. Given an information node B, its profile is now, Prof(B) = (d, <n1,n2,..,nK>, <m1,m2,..,mK>). The additional configuration vector <m1,m2,..,mK> is called the dynamic configuration as opposed to <n1,n2,..,nK> that is the static configuration, i.e., the configuration as chosen by the author.
In this way, the author can regularly check for wrong settings of information nodes while keeping the system stable and coherent with students expectations over a short time span.
Then, given, again, that student A with profile Prof(A)= = (c , <s1,s2,..,st>) accessed the information node B with profile Prof(B) = (d, <n1,n2,..,nK>, <m1,m2,..,mK>) with surprise Surpr(A,B) we update the dynamic configuration vector of B depending whether Surpr(A,B) is greater than mc as follows: the value mc is changed to Surpr(A,B) in the dynamic configuration vector and, then, it is made legal by normalizing the sum of values to 1.
Notice that we do not change the static configuration vector and mechanisms to provide adaptive presentation or navigation to students do rely on static configuration vectors. When the author wants to check the behaviour of the system he/she can check the distance between the static and the configuration vector and use it as an efficient sign of unexpected behaviour. Of course, automatic mechanisms of warning can be easily implemented by triggering an alarm if, e.g., dynamic configurations of more than 30% of the information nodes are "far" from the original, assigned, static configuration.

4. An example

5. Simulations

Node	Simulation results
	U1=70%,   U2=20%,   U3=10%	U1=10%,   U2=20%,   U3=70%
I1
I2
I3
I4

6. Conclusions

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