Forming Homogeneous, Heterogeneous and Mixed Groups of Learners

Forming Homogeneous, Heterogeneous and Mixed Groups of Learners Agoritsa Gogoulou, Evangelia Gouli, George Boas, Evgenia Liakou, and Maria Grigoriadou Department of Informatics & Telecommunications, University of Athens, Panepistimiopolis, GR 15784 Athens, Greece rgog@di.uoa.gr, lilag@di.uoa.gr, geboas@gmail.com, liakoujenny@gmail.com, gregor@di.uoa.gr Abstract. The formation of groups based on learners personality and performance attributes is a challending goal in the area of collaborative learning environments. In this paper, a tool for group formation, referred to as OmadoGenesis, is presented in terms of the algorithms implemented and its functionality. The OmadoGenesis tool accommodates learners characteristics in the formation of pure homogenous, pure heterogeneous or mixed groups, that is groups that satisfy heterogeneity for a specific learners characteristic and homogeneity for another characteristic. 1 Introduction Collaborative learning describes a situation in which particular forms of interaction among people are expected to take place, which would trigger learning mechanisms. However, there is no guarantee that the expected interactions will actually occur [3]. Hence, a general concern is to develop ways to increase the probability that some types of interaction occur. One way to do this is to set up initial conditions related, among others, to the group size and the selection of group members [3]. To this end, group formation, that is the identification of those learners belonging to one specific group, is considered very important [2]. Various practices may be used for the assignment of learners into groups. Random assignment helps mix up learners but do not directly address the problems caused by social dynamics. Learner-formed groups almost guarantee that a person will be comfortable with his/her group, but such groups are often based on friendships. Other practices are based on the ability or performance level of each learner; usually instructors form groups taking into account learners performance to a pre-test. Researchers in the area [1], [8] emphasize the importance of personality attributes (personal and social characteristics) in group composition. They suggest that in addition to performance level, attributes such as gender, ethnic background, motivations, attitudes, interests, and personality (argumentative, extrovert, introvert, etc.), should be given due attention in the process of forming groups. It is also observed that although homogeneous groups are better at achieving specific aims, when learners with different abilities, experience, interests and personalities are combined (heterogeneous groups), they out-perform homogeneous groups in a broader range of tasks [8], [9]. In a manual environment (with paper-and-pencil), a great deal of time and effort may be needed in the formation, especially of heterogeneous, groups. This is because, the numbers and combinations of performance level and values of personality attributes to be considered may be too many to handle and manage. Also, the problem may be more difficult, when the interest focuses on the formation of mixed groups, i.e. groups that satisfy heterogeneity for a specific learners characteristic and homogeneity for another characteristic. Research efforts attempt to develop computer-based tools that support the automatic forming of groups based on learners characteristics. The system developed by Yang et al. [10] is an attempt to group similar learners according to their preferences and learning behaviours. The system uses a multi-agent mechanism to manage and organize learners and learner groups. Inaba et al. [7] incorporated the grouping and constructed a collaborative learning support system that detects appropriate situations for a learner to join in a learning group. Graf and Bekele [6] propose a mathematical model that addresses the group formation problem through the mapping of both performance and personality attributes into a learner vector space. Their tool supports the formation of heterogeneous groups and uses an Ant Colony Optimization algorithm for maximizing the heterogeneity of the groups. In: P.Brusilovsky, M. Grigoriadou, K. Papanikolaou (Eds.): Proceedings of Workshop on Personalisation in E-Learning Environments at Individual and Group Level, 11th International Conference on User Modeling, 2007, pp. 33-40

Our work attempts to contribute in the field by proposing a tool, referred to as OmadoGenesis that can be used for the formation of homogeneous, heterogeneous and mixed groups based on learners characteristics. The tool implements three algorithms: one for pure homogeneous groups (Homo-A), one for pure heterogeneous groups (Hete-A) and a third one based on the concept of genetic algorithms for homogeneous, heterogeneous and mixed groups. Also, the tool enables the random assignment of learners into groups and the assignment by the instructor on the basis of his/her preferences or learners demands. Moreover, the tool provides a number of facilities to the instructor such as the selection of the desired learners characteristics, the definition of the group size (i.e. the desired number of learners in a group), the refinement of the grouping results by rearranging the learners, the setting of the algorithm s parameters, and the specification of the criterion for the determination of the moderator of each group. The paper is structured as follows. In Section 2, we give a brief description of the conceptual framework and the definitions of various terms used. Following, in Section 3, a presentation of the algorithms is given in terms of their functionality. In Section 4, we present the tool from the instructor s point of view. Finally, in Section 5, we discuss the preliminary results of the application of the algorithms with real data and conclude with our future plans. 2 Conceptual Framework and Definitions The Learner Space Model. Each learner is represented in a multidimensional space by a vector; each dimension corresponds to a learner s attribute A n (i.e. learner s personality and performance attributes such as competence level, learning style, indicator for collaborative behaviour, indicator for acting as evaluator in peer-assessment). Each attribute A n has a value X n which is represented for the learner i as X n (L i ). The vector is made up of the values X n of all attributes. That is, learner i in a n th -dimensional space is represented as L i (X 1,X 2,,X n ). The values of the attributes are mapped to numerical values. Each of the n attributes has five possible values, i.e. X n =1, 2, 3, 4, 5, where 1 corresponds to the qualitative characterization Insufficient, 2 corresponds to Rather Insufficient, 3 corresponds to Average, 4 corresponds to Rather Sufficient, and 5 corresponds to Sufficient. For example, in a 3-dimensional space, the representation L 10 (2,3,5) means that learner with i=10 has values X 1 =2, X 2 =3 and X 3 =5 for the attributes A 1, A 2, A 3 respectively. Group. A group i of k learners is represented as G i =G(L 1,L 2, L k ). For example, G 1 = G(L 1,L 2,L 3,L 4 ) is the first group composed of the four (k=4) learners L 1, L 2, L 3 and L 4. Homogeneity. In a group G i with k learners, homogeneity with respect to an attribute A n exists when learners have similar values of the attribute considered, that is X n (L 1 )= X n (L 2 )= = X n (L k ). Difference. Difference (D n (L i, L j )) is defined as the distance between the values X n of the attribute A n of two learners (L i and L j ), that is D n (L i, L j )=abs{x n (L i )-X n (L j )}, e.g. if L 1 (1,3,5) and L 2 (2,4,1), then D 2 (L 2, L 1 )=abs{x 2 (L 2 )-X 2 (L 1 )}=abs(4-3)=1. Heterogeneity. A group of k learners G(L 1,L 2,,L k ), is heterogeneous with respect to the attribute A n, when D n (L j, L j-1 ) >= T, where (i) 2<=j<=k, (ii) the values of attribute A n are sorted such as X n (L 1 )<X n (L 2 )< <X n (L k ) and (iii) T is the threshold, which is defined as the lowest desirable possible value of the difference between the values X n of the attribute A n. Matrix-Hete used for the construction of heterogeneous groups in Hete-A algorithm. A Matrix-Hete of n attributes (where n=1, 2, 3) is defined as a n-dimensional array Matrix- Hete[5x5x5], where each element Matrix-Hete[i, j, z] (i, j, z =1,2,3,4,5) represents the number of learners that X 1 (L i )=i, X 2 (L i )=j, X 3 (L i )=z and contains a reference to an one-dimensional array that holds the identities (ids) of all learners L i that X 1 (L i )=i, X 2 (L i )=j and X 3 (L i )=z. In the Matrix-Hete, the parameter ideal distance is defined, which refers to the distance between the cells of the array when there are more than one cells having the same (highest) value. Criteria for group formation. The group formation process complies with the following criteria: each learner belongs only to one group, only one member is specified as the moderator of the group, if there are N learners to be segregated in q groups of k learners, then q=n/k if (N mod k=0 or N mod k=1) or q=n/k+1 if (N mod k>1).

Group Quality. The formation of a group may take into account more than one attributes and may follow for each attribute either homogeneity or heterogeneity. Therefore, the quality of group G i, consisting of k learners with respect to attribute A n, that is QG i (A n ), where 0 <= QG i (A n ) <= 4 (the range of possible values of the attributes is 1 to 5; thus, the maximum quality value 4 results from the difference between the highest and the lowest attribute value), is defined as follows: In case of homogeneity, QG i (A n )= 4 (max{x n (L 1 ), X n (L 2 ), X n (L k )} min{x n (L 1 ), X n (L 2 ), X n (L k )}) In case of heterogeneity, The quality of group G i is defined as k QG i (A n ) = = j 2 min{x n (L j) - X n(lj - 1),1} QG i = QG i( An), where n is the number of attributes considered for the formation of group G i n Solution Quality. The total quality QS of a solution is the sum of the qualities of all groups in the solution, i.e. q QS = QGi, where q is the number of all groups in the solution and 0 <=QS<= 4*n*q (4 is i= 1 the maximum quality value of group G i and n is the number of attributes) The Group Quality and the Solution Quality have been defined and used in the context of the genetic algorithm. However, they are also used in the context of Homo-A and Hete-A algorithm in order to have an indication of the quality of the produced solution. Moreover, they can be used as a quality measure for comparing the solutions produced by the available algorithms. 3 Developing the Algorithms Initially, our efforts focused on the construction of pure homogeneous or heterogeneous groups, therefore we developed two different algorithms (Homo-A and Hete-A), each one devoted to each case respectively. Following, having as an objective to cover also the case of mixed groups, we turned our efforts to the genetic algorithms as this category of algorithms are very flexible and allow the instructor to modify each time the definition of quality (see Group Quality in Section 2) for composing different groups of learners. The Genetic Algorithm (GA), presented in the following, is based on the principles of genetic algorithms but was adapted in order to be applied in all three cases (homogeneity, heterogeneity and mixed). Homogeneous Algorithm (Homo-A). The Homogeneous algorithm (Homo-A) is proposed by the tool only if homogeneity has been set for the selected learners attributes (up to three attributes can be selected). Homo-A uses clusters in order to create groups of learners and is based on the functional principles of k-means algorithm. The algorithm works as follows: consider that q groups of k learners will be created. A learner L i (X 1,X 2, X n ) corresponds to a point (X 1,X 2, X n ), where 1<=X 1 <=5,, 1<=X n <=5. At first, the q centers of the q clusters are chosen at random. In other words, q points (X 1,X 2,,X n ) are considered to be the centers of the q groups. Then, for each center the k closest points (learners) are chosen and moved into the group that the center belongs to. The proximity between points is calculated using Euclidean distance. In the next step, after the creation of the groups, a new center is calculated. Generally, for k learners per group with n attributes L 1 (X 1,X 2,,X n ),., L k (X 1,X 2,,X n ), the center is calculated as follows : k k X 1 ( Li) Xn( Li) i=1 i=1 Center = (,, ) n n The previous steps are repeated until there are no changes in the centers of the groups.

Heterogeneous Algorithm (Hete-A). The Heterogeneous algorithm (Hete-A) is proposed by the tool only if heterogeneity has been set for all the selected learners attributes (up to three attributes can be selected). Hete-A is based on the Matrix-Hete. Fig. 1 presents a two-dimension Matrix- Hete for 90 learners; one dimension corresponds to attribute A 1 and the second one to attribute A 2. Each cell C[i,j] of the matrix where i, j =1,2,3,4,5, has a value denoting the number of learners having the values i and j for A 1 and A 2 attributes respectively, e.g. the cell C[3,5] with value 4 denotes that there are 4 learners (L 1, L 25, L 33 and L 82 ) having the value of 3 for attribute A 1 and the value of 5 for attribute A 2. A2 5 4 8 4 9 12 3 3 8 22 2 5 8 8 1 2 1 L 1 L 25 L 33 L 82 0 1 2 3 4 5 A1 Fig. 1. Matrix-Hete for two learners attributes A1 and A2 The algorithm works as follows: consider that q groups of k learners will be created. In the first step, the cell with the highest value is chosen. One learner from this cell is randomly chosen and put into a group. When the learner is chosen then the value of the cell is decreased by one and the learner is subtracted from the array. The line and the column that this value belongs to are excluded. This procedure is repeated till k learners are put into the group. The whole process is repeated from the beginning (using each time the updated cell values of Matrix-Hete) till all learners are run out. If there are more than one cells that have the same highest value (e.g. the cells having the value 8 in Fig. 1) then the parameter ideal distance is used to choose the right cell. More specifically, the Euclidean distance is calculated between the cell having the highest value in the previous step and the cells having the same highest value specified in the current step. The cell that has distance (from the previous specified cell) closer to the ideal distance is chosen. It may happen that the current group cannot be completed although there are still free learners because a learner cannot be chosen as all lines and columns have been excluded. In this case all lines and columns are recovered with their updated values and the process is repeated till the group is complete or there are no more free learners. In case that the Matrix-Hete is one-dimensional then the only difference is that only a column is excluded. In the example of Fig. 1, assume that groups of three members have to be formed. The cell having the value of 22 is the first one chosen and one of the 22 learners is randomly selected. The corresponding line and column are excluded and the cell with the next highest value is chosen, that is the cell having the value of 9. One of the 9 learners is randomly selected and put into the group. Afterwards, as there are three cells with the same highest value (value of 8), the distance of these cells from the last specified cell (having the value of 9) is calculated. The cell that has distance closer to the ideal distance (ideal distance=2) is chosen, that is cell C[4,2]. One of these 8 learners is randomly selected and put as the third member in the group. Since the first group has been formed, the Matrix-Hete is updated with the new cell values and the whole process starts from the beginning in order to form the remaining 29 groups. Genetic Algorithm (GA). Genetic algorithms are inspired by Darwin's theory about evolution. The evolution starts from a population (generation) of randomly selected solutions. Solutions from one population are taken and modified through the genetic operators of crossover and mutation to form a new population. The new population is expected to be better than the old one. The selection of some solutions (parents) to form new solutions (offspring) is based on their quality (fitness), which is calculated by a fitness function. The more suitable the solutions are the more chances

they have to reproduce new solutions. This process is repeated until some condition (e.g. number of generations or improvement of the best solution) is satisfied. The Genetic Algorithm (GA), implemented in the OmadoGenesis tool, can be applied for the construction of homogeneous, heterogeneous or mixed groups. The GA is defined by the following set of parameters: (i) Number of Generations: number of times that the population evolves, (ii) Population: number of solutions in one generation, (iii) Transport to New Generation: number of best solutions of one generation that pass to the next generation without the genetic operation of crossover and mutation (elitism), (iv) Mutation Possibility: (random) number which specifies if parts of the solutions of the worst groups will change, after the genetic operation of crossover, and (v) Avoidance of Marginal Values: it concerns only heterogeneity and means that D n (L i, L j ) < 4, e.g. group G(L i,l j ) is not a desirable one, where X n (L i )=1 and X n (L j )=5, as D n (L i, L j ) = 4. The procedure of GA is as follows: - STEP 1. The first generation is created by composing random groups of k learners. A solution is the set of groups generated. The quality of each group G i (QG i ) and the quality of each solution (QS) are calculated. - STEP 2. In order to create the next generations (parameter Number of Generations), a number (parameter Transport to New Generation) of the best solutions is transferred to the new generation. Then, two solutions are chosen with the roulette wheel selection method (an imaginary roulette wheel is used so that each candidate solution represents a pocket on the wheel). The better the quality of a solution (the bigger the pocket on the wheel), the bigger the possibility of the solution to be chosen for reproduction. From the two solutions, two offspring are created using crossover and mutation operations and the one with the best quality is chosen and is passed to the next generation. - STEP 3. The procedure of STEP 2 is repeated until the required number of solutions in a generation is created, that is until the number of solutions in a generation is equal to Population Transport to New Generation. In the context of the OmadoGenesis tool, a graphical representation of the GA is offered and the instructor has the possibility to terminate the GA at any time s/he wishes and the best solution (with the highest QS) that has been found at this time is provided as the final solution. In the current implementation, the fitness function supports groups consisting of up to four members (as we are interesting in such size of groups) but it can be easily adjusted to support any group size. The mutation and crossover are the most important operations of the GA. The aim of mutation is to prevent solutions in population falling into a local optimum of the problem. More specifically, if N is the number of all learners then, the following are repeated N times for all the solutions: A random number p is produced. If p is smaller than the parameter mutation possibility then two more random integer numbers are produced which take values from 0 to N. These two random numbers are used to select two learners of the solution. If these two learners belong to groups with poorer quality than the quality of the best group of the solution then the exchange is done. This means that the first learner is moved to the group of the second learner and the second learner moves to the group of the first learner. Otherwise, there is no exchange. Regarding crossover operation, there are many crossover techniques used in genetic algorithms such as one point crossover, two point crossover etc. Instead of using these techniques, in our development, we created a new technique in which the measure of the quality of each group (QG i ) is used in order to create the offspring. More specifically, the procedure of crossover follows the steps described below: - STEP 1. The groups in each solution are classified in an ascending order, according to the quality of each group (QG i ). As a result, there are two solutions in which the first group of each solution has the worst quality and the last group has the best quality. - STEP 2. The second step starts from the best group of the second solution and continues for each group of this solution. For each learner of the candidate target group (i.e. the group that is examined in order to be placed in the offspring), the group in which this learner belongs to the first solution is found and the quality of this group is examined. If all learners of the candidate target group (in the second solution) belong to groups in the first solution with worse quality than the quality of the candidate target group, then the candidate target group is added to the offspring. - STEP 3. All groups from the first solution that were not influenced in the previous step (i.e. consisting of learners that were not added in the offspring) are added in the offspring.

- STEP 4. All the remained learners from the first solution belonging to groups that were influenced in the second step are added in the offspring according to their order in the first solution. These learners are assigned to groups following their sequential order. - STEP 5. The second offspring is created in the same way as the first one with the difference that the second step starts from the first solution and ends to the second solution and STEPS 3 and 4 refer to the second solution. For example, let us assume that homogeneity has been selected for attribute A 1 and the groups may consist of three learners. The two solutions A and B, presented in Table 1, are consisted of 5 groups (Column G i ). The column QG i represents the quality of each group. The crossover operation works as follows: The groups in each solution are classified in an ascending order according to their quality. The first candidate target group is the group of the second solution with the best quality, that is group G 5 =(L 10,L 6,L 12 ) of solution B. Learners with ids 10, 6, 12 are searched in the groups of solution A. Every learner of G 5 of solution B belongs to groups in solution A with worse quality than QG 5, so G 5 of B is placed in the offspring. Then, the candidate target group is G 4 =(L 11,L 4,L 9 ) of B. Learners L 4 and L 9 belong to group G 5 in solution A with better quality than G 4 of B, so G 4 of B is not placed in the offspring. Then, the candidate target group is G 3 =(L 15,L 8,L 5 ) of B. All learners of G 3, belong to groups in A with worse quality than QG 3, so G 3 of solution B is placed in the offspring. Then, the candidate target group is G 2 =(L 13,L 7,L 1 ) of B. All learners of G 2 belong to groups in A with worse quality than QG 2 of B, so G 2 of B is placed in the offspring. The last candidate target group is G 1 =(L 2, L 14,L 3 ) of B. Learner L 3 belongs to group G 5 in A which has better quality than QG 1 of B, so group G 1 of B is not placed in the offspring. So far, the offspring consists only of groups from solution B. The G 5 in solution A was not influenced in the previous procedure, so it is added to the offspring. The remained learners L 11, L 2, and L 14 belong to groups in A that were influenced in the previous procedure, so they are added in the offspring according to their order in solution A and form the 5 th group of the offspring. The first offspring produced after the crossover operation is depicted in Table 2. Table 1. Example of crossover operation. Solution A Solution B G i L i A 1 QG i G i L i A 1 QG i 10 1 2 2 1 5 3 1 1 14 3 2 11 4 3 5 8 2 13 3 2 7 4 2 2 7 4 3 1 4 1 4 6 1 15 2 3 15 2 2 3 8 2 3 13 3 5 3 12 1 11 4 4 2 2 2 4 4 5 3 14 3 9 5 3 5 10 1 5 4 5 4 5 6 1 4 9 5 12 1 Table 2. The first offspring produced after the crossover operation. G i L i A 1 10 1 1 6 1 12 1 15 2 2 8 2 5 3 13 3 3 7 4 1 4 3 5 4 4 5 9 5 11 4 5 2 2 14 3 4 The OmadoGenesis Tool The development of the OmadoGenesis Tool was inspired by our research work in the context of the SCALE and the PECASSE environments [4],[5] in order to support the group formation process. The characteristics kept in the learner model of these environments (i.e. the learner id and the values X 1, X 2, X n of the attributes A 1, A 2, A n ) constitute the main source of the OmadoGenesis tool. The instructor can select the learners s/he wishes as well as the attributes to be taken into account. In the following, the instructor can assign to each of the selected attributes whether s/he prefers homogeneity or heterogeneity to be applied. In addition, the instructor can define the condition to be hold for the determination of the moderator in each group (e.g. the

moderator should have value X i > 4 in attribute A i ). Finally, s/he sets the number of the members per group. The tool, taking into account the parameters set by the instructor, proposes the most suitable algorithm to be used. That is, for the creation of pure homogeneous or heterogeneous groups proposes the Homo-A or Hete-A algorithm respectively while in case of mixed groups the tool proposes the GA. However, in the cases of homogeneous or heterogeneous groups the instructor may also select the GA. Moreover, if the instructor wishes may ignore the available algorithms and select the random construction of the groups. Upon the setting of the above attributes, the instructor may proceed to the setting of the algorithm s attributes (e.g. Number of Generations and Population for GA, ideal distance for Hete-A). After the execution of the selected algorithm, the results of the group formation are presented and the groups are denoted in alternating colors helping the instructor to identify easily the members of each group. The instructor may intervene in the results and proceed to any re-arrangements in case s/he believes that a better result can be achieved or to avoid any problems during the collaboration. Fig. 2. A screen shot of the OmadoGenesis Tool Fig. 2 presents a screen shot of the tool. The instructor has selected to form groups consisting of three learners and two attributes to be used for heterogeneity. The tool proposed the Hete-A algorithm, and the screen shot presents the results after the execution of this algorithm. The moderator of each group has also been specified. 5 Preliminary Results & Future Work The application of the algorithms with real data reveals that good solutions can be produced, that is the quality of the solutions approximates the highest value of the quality. For example, in case that 52 learners have to be grouped in groups of 4 members and two attributes A 1 and A 2 are used for the group formation. The application of the three algorithms gives the results presented in Table 3. Considering that the highest value of quality is 101 (QS= (max quality for Attribute A 1 + max quality for Attribute A 2 ) * num_of_groups= (4+4)*13=101), the produced solutions can be considered good enough. It is worthwhile mentioning that in the formation of pure homogeneous groups, the GA and the Homo-A seem to have almost the same performance while in case of heterogeneity, the Hete-A seems to produce a better solution than the GA. Also, the application of the GA for the formation of mixed groups gives a quite good solution with high quality.

Table 3. The quality of the solutions produced by the three algorithms Homogeneity in both attributes GA Homo-A Quality (QS) 96 94 Heterogeneity in both attributes GA Hete-A Quality (QS) 87 92 Homogeneity in A1 and Heterogeneity in A2 GA Quality (QS) 96 Despite the preliminary positive results, further experiments need to be carried out and examine the quality solutions with respect to the variation of the values of the attributes taken into account for the group formation. Moreover, the support of an instructor s profile facility is in our plans; the parameters set by the instructor will be kept in his/her own profile and retrieved and made available each time s/he uses the tool. Also, in the direction of helping instructors to have the most qualitative results, we plan to investigate whether results about the effectiveness of each algorithm with respect to the data used could be drawn, so that the tool proposes the most suitable algorithm and result in a group formation process with minimum or no manual intervention. Finally, experiments with real data and the participation of instructors are considered valuable in order to elicit instructors point of view regarding the usability of the tool, the effectiveness (i.e. quality) of the produced results and the degree of easiness in intervening in the results and making the desired re-arrangements. The results of this research work may help instructors and researchers in the field of collaborative education. The experimentation with various personal and social characteristics in forming groups may give an insight to factors affecting students interaction as well as students performance in different learning situations. References 1. Bradley, J. H., Herbert, F., J.: The effect of personality type on team performance. Journal of Management Development 16 (1997) 337-353 2. Daradoumis T., Guitert M., Giménez, F., Marquès, J., Lloret, T.: Supporting the Composition of Effective Virtual Groups for Collaborative Learning. In Proceedings of the International Conference on Computers in Education (ICCE 2002). IEEE Computer Society Press (2002) 332-336 3. Dillenbourg, P.: What do you mean by collaborative learning?. In: Dillenbourg P. (eds): Collaborativelearning: Cognitive and Computational Approaches. Oxford: Elsevier (1999) 1-19 4. Gogoulou, A., Gouli, E., Grigoriadou, M., Samarakou, M., Chinou, D.: A web-based educational setting supporting individualized learning, collaborative learning and assessment. Educational Technology & Society Journal (2007) (to appear) 5. Gouli, E., Gogoulou, A., Grigoriadou, M.: Supporting Self-, Peer- and Collaborative-Assessment in E- Learning: the case of the PECASSE environment. Journal of Interactive Learning Research (2007) (to appear) 6. Graf, S., Bekele, R.: Forming Heterogeneous Groups for Intelligent Collaborative Learning Systems with Ant Colony Optimization. In Proceedings of the 8 th International Conference on Intelligent Tutoring Systems (ITS 2006), Lecture Notes in Computer Science, Volume 4053/2006. Springer Berlin / Heidelberg (2006) 217-226 7. Inaba, A., Supnithi, T., Ikeda, M., Mizoguchi, R., Toyoda, J.: How Can We Form Effective Collaborative Learning Groups?. In Proceedings of the 5 th International Conference on Intelligent Tutoring Systems (ITS 2000), Lecture Notes in Computer Science, Volume 1839. Springer-Verlag London (2000) 282 291 8. Martin, E., Paredes, P.: Using learning styles for dynamic group formation in adaptive collaborative hypermedia systems. In Proceedings of the First International Workshop on Adaptive Hypermedia and Collaborative Web-based Systems (AHCW 2004) (2004) 188-198 available at http://www.ii.uam.es/ ~rcarro/ahcw04/martinparedes.pdf 9. Nijstad, B. A., De Dreu, C.: Creativity and Group innovation. Applied Psychology 51(3) (2002) 400-406 10. Yang, F., Han, P., Shen, R., Kraemer, B., Fan, X.: Cooperative Learning in Self-Organizing E-Learner Communities Based on a Multi-Agents Mechanism. In AI 2003: Advances in Artificial Intelligence, Lecture Notes in Computer Science, Volume 2903/2003. Springer Berlin / Heidelberg (2003) 490-500