Grouping Partners for Cooperative Learning Using ...

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Procedia Engineering 00 (2011) 000–000 Procedia Engineering 29 (2012) 3888 – 3893

Procedia Engineering www.elsevier.com/locate/procedia

2012 International Workshop on Information and Electronics Engineering (IWIEE)

Grouping Partners for Cooperative Learning Using Genetic Algorithm and Social Network Analysis Rong-Chang Chena,*, Shih-Ying Chenb, Jyun-You Fanb and Yen-Ting Chena a Department of Logistics Engineering and Management, National Taichung Institute of Technology Department of Computer Science and Information Engineering, National Taichung Institute of Technology No 129, Sec. 3, Sanmin Rd. Taichung, Taiwan 404

b

Abstract This paper employs a novel approach which is based on genetic algorithm (GA) and social network analysis to grouping partners for cooperative learning in the classroom. A social network analysis tool, i.e., sociometry, is used to measure social status of students. Subsequently, GA is used to optimize the grouping subject to the constraints of heterogeneous grades, social status, and gender in different levels. The results from GA are illustrated in the sociogram generated by a sociometry tool. Results show that the proposed approach can optimize the grouping well.

© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Harbin University of Science and Technology

Open access under CC BY-NC-ND license.

Keywords: grouping; genetic algorithm; social network analysis; cooperative learning

1. Introduction To enhance the learning performance of students, teachers need to employ techniques that can effectively help students in the classroom. Among useful techniques, cooperative learning [1-7] is one of the most popular ones. Cooperative learning is an approach to organizing classroom activities into academic and social learning experiences. The positive outcomes include: academic gains, improved race relations and increased personal and social development [1]. Tsay and Brady reported that students who fully participated in group activities, exhibited collaborative behaviours, provided constructive feedback and cooperated with their group had a higher likelihood of receiving higher test scores and course grades at the end of the semester [2]. In addition, cooperative learning is an active pedagogy that fosters higher

1877-7058 © 2011 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. doi:10.1016/j.proeng.2012.01.589

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Rong-Chang Chen et al. / Procedia Engineering (2012) 3888 – 3893 Author name / Procedia Engineering 00 29 (2011) 000–000

academic achievement [2]. Consequently, to enhance learning performance of students, cooperative learning can be well utilized. In implementing cooperative learning, one of the critical processes is organizing groups. When organizing groups, the most popular methods include random grouping, selected-by-teacher, and selectedby-students-themselves [7]. Each method shows its pros and cons. A common disadvantage for the above methods is that they cannot find global optimization solutions. To get the global optimization grouping, one can make use of the relational network of the students. A typical network is illustrated in Fig. 1. As we can see from the figure, the network is so complicated that it is hard to find best grouping by intuition. Thus, an effective approach is needed.

Fig. 1. A schematic diagram of relational network.

Many other factors may influence the success of cooperative learning. One important factor that has been advocated is heterogeneous grouping. Previous studies suggest that the most effective cooperative work groups include a mixture of students in terms of ability, gender, and ethnic background [5, 7]. As the number of students and groups become large, the grouping becomes a complex problem. Moreover, if some constraints are imposed, it is very hard to solve this kind of problems. A method that can obtain an optimal solution but takes lots of computation time seems to be impractical. Instead, algorithms that can find feasible solutions in shorter computation time are more suitable. Among the best suitable algorithms is the genetic algorithm (GA) [8-16], which has been successfully applied to many complex problems. In this paper, we employ a novel approach that can find hidden information behind students. In addition, the grouping can be generated heterogeneously. Firstly, students’ preferences are collected by an index system where a one stands for the first choice, two for the second choice, and so on up to a preassigned maximum number of preferences. Then the data are aggregated and a combined sociometry [1718] and genetic algorithm approach is used to organize groups. The rest of this paper is organized as follows. In Section 2, the grouping problem is briefly introduced. In Section 3, the problem is described and the analysis is presented. Results and discussion are presented in Section 4. Finally, conclusions are drawn in Section 5. 2. The Grouping Problem The grouping problem is to optimally assign s students to g groups with n students in each group. Let S = {1, 2, …, s} be a set of students, G = {1, 2, …, g} be a set of groups, P = {1, 2, …, n-1} be a set of a student’s group-mates , C = {1, 2, …, c} be a set of choices, Q = {1, 2, …, nq} be a set of grade levels, R = {1, 2, …, nr} be a set of social status levels, and T = {1, 2, …, nt} be a set of genders. Students can list a number of preferred classmates with whom they would like to learn cooperatively by an index system that a “1” stands for the first choice, “2” for the second choice, and the like, up to a pre-assigned maximum

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integer value, c. For i  S, k  P, define cik as the preference given by student i to being grouped with his/her partner k. If partner k is the first choice of student i, cik is equal to 1, the second choice, cik is equal to 2, and the like. If student i has not selected his/her partner k in the list of preferences, then cik is assigned a relatively large penalty value B. Similarly, cki is defined. The mathematical formulation, hence, can be expressed as:

     

™Š‡”‡

and ziq, zir, and zit are 1 if student i belongs to grade level q, social status level r, or gender t, respectively. The objective is to minimize the total scoring value, as shown in Eq. (1). As for the scoring function f(.), a popular function used is the squared function [16]. Eq. (2) requires that each student is assigned exactly one group. Eq. (3) ensures that one group has n students. 3. The Approach A questionnaire is designed to collect the preferences of the students. After aggregating the preferences, a sociometric tool is employed to draw the sociogram and find the social indices. If the remainder of s/n = a ≠ 0, n-a dummy students will be added and n will be changed to n+1 per group. Otherwise, GA is directly employed to solve the grouping problem. In this paper, we employ one of the most popular social network analysis tools, sociometry, to measure the social status of students. Sociometry was developed by Moreno in 1934. It is a quantitative approach for measuring social relationships [18]. Sociometric explorations disclose the hidden structures behind group members such as the alliances, the subgroups, the hidden beliefs, and more. One of Moreno's

 

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contributions to sociometry was the development of the sociogram. It is a systematic method that graphically represents individuals as points/nodes and the relationships between them as lines/arcs [17]. A mutual choice (MC) refers to the situation that individuals choose each other. One-way choice refers to individuals who choose someone but the choice is not reciprocated. Some indices are often used to indicate the social status of individuals. Among the most popular indices, the ISSS (Index of Sociometric Status Score) is employed in this study. To consider the mutual choices between members, ISSS is defined as [8]:

where NTC, NTR, NMC and NMR represent the numbers of total choices by others, the total rejects by others, mutual choices, and mutual rejections, respectively. c is the allowed maximum number of choices that a student can make. The value of is in the range [-1, 1]. A higher value of indicates that a student is more popular within a group. The encoding of a chromosome is illustrated in Fig. 2. Since there are s students, the number of genes is equal to s. Each gene is assigned a number which stands for a student. As illustrated in Fig. 2, the values of the genes are, in order, 15, 6, 2, 10, …, and 4. If n = 3, i.e., a group has three individuals, then student 15, student 6, and student 2 are at the same group, and the like. 15

6

2

10

3

7

11

23

…

4

Fig. 2. Representation of chromosome.

The initial solutions are generated using the random method. The Roulette wheel method [11-12] is employed to select fitter individuals. In addition, the swap method is employed to mutate. Two genes are randomly selected and their values are changed each other. The swap method has the advantage of no duplicated values. Since a student is assigned exactly one group, the values in the genes should be different. A simple elitism strategy is employed to preserve the best chromosome in every generation. The best chromosome of each generation is duplicated to the next generation. This strategy assures that the best chromosome of each generation will be at least equal to the best chromosome of the previous generation. The termination condition in this paper is the generation number defined by the user. The calculation will repeat until the number of generation reaches the pre-assigned value. Once the termination condition is satisfied the solution is displayed. 4. Results and Discussion The grouping program was developed using Microsoft Visual Basic .NET 4.0. The program was performed on an AMD Turion 64 x 2 TL-58 1.90 GHz CPU and with 1.87 GB RAM. To evaluate the effectiveness of the proposed approach, a real dataset from a class of undergraduate students was tested. The number of students is 60. Each case was tested ten trials. For multiple trials, we designate the best result of all trials as OPT and their average value as AVG. To validate the GA program, some tests were made. The results from GA were compared with those from branch and bound (B&B), which can obtain optimal solutions. The results show that the GA



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program can obtain optimal solutions that are the same as those from B&B, indicating that the GA program is correct. Table 1. Comparison of results between Branch and Bound and GA (c= 6). B&B

GA

s

n

Fitness value

Runtime (min)

OPT

AVG

Average runtime (min)

6

2

41

0.4

41

41

0.06

6

3

155

0.4

155

158

0.07

8

2

65

0.6

65

67

0.09

8

4

592

0.6

592

593

0.10

10

2

67

3.48

67

68

0.10

The grouping result is shown in Fig. 3. A heterogeneous can be obtained effectively if the penalty value (B2) of violating the required constraint is set to be greatly larger than the penalty value (B1) outside the list of preferences.

Fig. 3. A heterogeneous grouping result according to grade levels (B2=1,000 and B1=100).

The influence of the number of choices c on the computation time and the number of partners outside the list of preferences is illustrated in Table 2. As the number of choices c increases, the percentage of grouping outside the list is decreased. As for computation time, the average runtime is about the same except for c = 6. The possible reason is that n = 3 and c = 6 = 2n, positively affecting computation. Table 2. The influence of the number of choices on the computation time and choices outside the list of preferences ( n = 3, B2=1,000 and B1=100).

c 5 6 7 8 9

Average runtime (min) 29.27 25.37 29.03 28.16 28.05

Outside the list of preferences (%) 78% 72% 70% 66% 60%

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5. Conclusions In this paper we have employed a novel approach which is based on genetic algorithm (GA) and social network analysis to grouping partners for cooperative learning in the classroom. The sociometry is used to measure social status of students. Afterwards, GA is used to optimize the grouping subject to some constraints including heterogeneous grades, social status, and gender in different levels. The results from GA are illustrated in the sociogram generated by a sociometry tool. Experimental results show that the combined approach can optimize the grouping well. Further studies are recommended to apply the proposed combined approach to solve other kinds of grouping problems. Acknowledgements The authors wish to express their appreciation to Mrs. Shu-Ping Suen and Tzu-Ying Lin for their help during the course of this paper. This work was supported by the National Science Council under grant number 100-2221-E-025-016. References [1] Brown H, Ciuffetelli DC. (Eds.). Foundational methods: Understanding teaching and learning. Toronto: Pearson Education; 2009, p. 508. [2] Tsay M, Brady M. A case study of cooperative learning and communication pedagogy: Does working in teams make a difference? Journal of the Scholarship of Teaching and Learning 2010;10(2):78–89. [3] Kose S, Sahin A, Ergu A, Gezer K. The effects of cooperative learning experience on eight grade students’ achievement and attitude toward science. Education 2010;131(1):169–180. [4] Lynch D. Application of online discussion and cooperative learning strategies to online and blended college courses. College Student Journal 2010;44(3):777–784. [5] Scheurell S. Virtual warrenshburg: Using cooperative learning and the internet in the social studies classroom. Social Studies 2010;101(5):194–199. [6] Aldrich H, Shimazoe J. Group work can be gratifying: Understanding and overcoming resistance to cooperative learning. College Teaching 2010;58(2):52–57. [7] Johnson D, Johnson R, Holubec E. Cooperative learning in the classroom. Alexandria. VA: Association for Supervision and Curriculum Development; 1994. [8] Chen RC. Grouping Optimization Based on Social Relationships. Mathematical Problems in Engineering 2012. [9] Falkenauer E. Genetic Algorithms and Grouping Problems, New York: Wiley; 1998. [10] Holland JH. Adaptation in Natural and Artificial Systems, Ann Arbor, MI: University of Michigan Press; 1975. [11] Mitchell M. An Introduction to Genetic Algorithms, MIT Press, Cambridge; 1996. [12] Gen M, Cheng, R. Genetic Algorithms and Engineering Optimization, Wiley, New York; 2000. [13] Coley DA. An Introduction to Genetic Algorithms for Scientists and Engineers, World Scientific, Singapore; 1999. [14] Gen M, Cheng R, Lin L. Network Models and Optimization: Multiobjective Genetic Algorithm Approach, Springer; 2008. [15] Goldberg DE. Genetic Algorithms: Search, Optimization and Machine Learning, Reading, MA: AddisonWesley; 1989. [16] Chen RC, Huang MJ, Chung RG, Hsu CJ. Allocation of Short-Term Jobs to Unemployed Citizens amid the Global Economic Downturn Using Genetic Algorithm. Expert Systems with Applications 2011;38:7537–7543. [17] Moreno JL. Who shall survive? A New Approach to Problem of Human Interrelations, Washington, D.C.: Nervous and Mental Disease Publishing Co; 1934. [18] Rubin KH, Bukowski WM, Laursen B. (Eds.). Handbook of Peer Interactions, Relationships, and Groups; 2011.

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