# Automatic Group Organization for Collaborative Learning Applying Genetic Algorithm Techniques and the Big Five Model

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Foundations

#### 2.1. The “Big Five” Model

#### 2.2. Work and Collaborative Learning

#### 2.3. Genetic Algorithms

## 3. Related Works

## 4. Proposed Approach

#### 4.1. Big Five Inventory (BFI)

#### 4.2. Algorithm for Group Formation

#### 4.2.1. Student Representation

#### 4.2.2. Individual Representation

#### 4.2.3. Fitness Measure

^{i}, these averages (IM) are represented as follows:

^{1}= 0.048 and D

^{2}= 0.380 are obtained.

_{2}and at the same time heterogeneous for C

_{1}and C

_{3}. According to (7) and (8), we obtain:

_{2}and inter-heterogeneous for C

_{1}and C

_{3}than Individual 1; with this distribution, all groups of Individual 2 more accurately reflect similarity and variability with the whole set of students (TM), when simultaneously seeking homogeneity for C

_{2}and heterogeneity for C

_{1}and C

_{3}.

#### 4.2.4. Initial Population and Evolution

#### 4.2.5. Search Complexity and Algorithm Performance

^{43}possible combinations (applying (24)), which makes finding the best solution from an exhaustive search not very feasible in many cases. Hence the usefulness of the proposed method.

_{c}) and the mutation probability (p

_{m}), values of each of the parameters were simulated in the ranges suggested by the literature [50,51], and others slightly outside of them, selecting the set with the best results. A high crossover probability allows greater exploration of the solution space, reducing the possibility of establishing a false optimum; but if the probability is very high, it causes a great investment in computation time in the exploration of unpromising regions of the solution space. As for the mutation probability, if it is very low, some genes that could have been produced are never tested; if it is too high, there will be much random disturbance, the children would begin to lose their parental likeness.

_{c}= 0.4 and p

_{m}= 0.01.

#### 4.3. Empirical Design

_{0}: the means of the grades obtained by the students in the topic of the collaborative activity are equal (null hypothesis); H

_{1}: the means of the grades obtained by the students in the topic of the collaborative activity are different (research hypothesis). It is a quasi-experiment since the study groups (described below) were already formed before the experimentation, they were intact groups (the reason why they arose and the way they were formed have nothing to do with the experiment, it is a task that corresponds to the registration and academic control University office for each new academic period) [55]. This is a common situation in educational contexts, as teachers must evaluate the efficacy of their teaching methods, but pure experiments in these contexts are seldom politically, administratively, or ethically feasible [56].

_{1}and G

_{2}groups were the experimental groups and G

_{3}and G

_{4}were the control groups in each course. In addition, X was the experimental treatment that consisted of forming the required groups using the proposed approach, carrying out a collaborative learning activity during work sessions scheduled. In the control groups, to which the experimental treatment was not applied, the groups required for the collaborative activity, which was the same as for the experimental ones, were formed by students’ preference.

_{1}, O

_{2}, O

_{3}, and O

_{4}, were the pre-tests applied at the beginning of the experiment, both for the experimental and control groups, seeking to guarantee in some way the initial equivalence of the groups, which in turn guarantees the internal validity of the experiment. The pre-tests consisted of the individual response to the same questionnaire (for each of the courses), related to the topics of the collaborative activity.

_{5}, O

_{6}, O

_{7}, and O

_{8}were the post-tests applied at the end of the experiment for both experimental and control groups, seeking to determine the implication of the experimental treatment. The post-tests consisted of individual responses to the same pre-test questionnaire (for each of the courses), related to the topics of collaborative activity.

_{1}consisted of 22 students from the Computer Programming course—Group 1 of the second semester of Electronic Engineering, who were applied the experimental treatment X and the post-test O

_{5}. The control group G

_{3}consisted of 17 students from the Computer Programming course—Group 2, from the same semester and academic period, and who were not experimentally treated, but the O

_{7}post-test was applied. The second experimental group G

_{2}consisted of 24 students from the Graphic Programming course—Group 1 of the tenth semester of Systems Engineering, for whom the experimental treatment X and the post-test O

_{6}were applied. The control group G

_{4}consisted of 19 students from the Graphic Programming course—Group 2, from the same semester and academic period, and who were not experimentally treated, but the O

_{8}post-test was applied. As mentioned above, all groups were given pre-tests O

_{1}, O

_{2}, O

_{3}, and O

_{4}, seeking to guarantee the initial equivalence of the groups in each of the courses.

## 5. Results

_{0}: the means of the grades obtained by the students in the pre-test are similar; H

_{1}: the means of the grades obtained by the students in the pre-test are different.

_{1}with the control group G

_{3}of the Computer Programming course, a p-value of 0.589 was obtained. As this value is greater than 0.05, the alternative hypothesis (H

_{1}) is rejected in favour of the null hypothesis (H

_{0}), with a confidence level of 95%, that is, that the means of the grades obtained by the students in the pre-test are similar.

_{2}with the control group G

_{4}of the Graphic Programming course, a p-value of 0.607 was obtained. As this value is greater than 0.05, the alternative hypothesis (H

_{1}) is rejected in favour of the null hypothesis (H

_{0}), with a confidence level of 95%, that is, that the means of the grades obtained by the students in the pre-test are similar.

_{0}: the means of the grades obtained by the students in the post-test are similar; H

_{1}: the means of the grades obtained by the students in the post-test are different.

_{1}with the control group G

_{3}of the Computer Programming course, a p-value of 0.029 was obtained. As this value is less than 0.05, the null hypothesis (H

_{0}) is rejected in favour of the alternative hypothesis (H

_{1}), with a confidence level of 95%, that is, that the means of the grades obtained by the students in the post-test are different, with a difference of 0.6545 in favour of G

_{1}. According to the classification made by Cohen [58], the effect size of the experimental treatment (g) with a value of 0.729 is considered as medium, approaching large, which implies that there is a significant difference between the results of the experimental group versus the control group not due to chance.

_{2}with the control group G

_{4}of the Graphic Programming course, a p-value of 0.039 was obtained. As this value is less than 0.05, the null hypothesis (H

_{0}) is rejected in favour of the alternative hypothesis (H

_{1}), with a confidence level of 95%, that is, that the means of the grades obtained by the students in the post-test are different, with a difference of 0.4311 in favour of G

_{2}. According to the classification made by Cohen [58], the effect size of the experimental treatment (g) with a value of 0.579 is considered as medium, which implies that there is a moderate difference between the results of the experimental group versus the control group that is not due to chance.

_{0}: the means of the grades obtained by the students in the post-test and the pre-test are similar; H

_{1}: the means of the marks obtained by the students in the post-test and the pre-test are different.

_{0}) is rejected in favour of the alternative hypothesis (H

_{1}), with a confidence level of 95%, that is, the means of the grades obtained by the students in the post-test and the pre-test are different. According to the classification made by Cohen [58], the effect size of the experimental treatment (g) with values (in all cases) greater than 0.8 is considered large, which implies that there is a very significant difference between the results of the post-tests and pre-tests that are not due to chance. In addition, these results indicate that there is an improvement on the part of the students in the domain of the specific topics in each course, independent of the group formation strategy that is used, which is more evident in the experimental groups than in the control ones.

## 6. Conclusions and Further Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Moreno-Guerrero, A.-J.; Rondón García, M.; Martínez Heredia, N.; Rodríguez-García, A.-M. Collaborative Learning Based on Harry Potter for Learning Geometric Figures in the Subject of Mathematics. Mathematics
**2020**, 8, 369. [Google Scholar] [CrossRef] [Green Version] - Cárdenas, M.L.B.; Malagón, L. The Formation of Study Groups: Experiences in the Outset of a Permanent English Teacher Development Program. Signum Estud. da Ling.
**2007**, 10, 73–93. [Google Scholar] [CrossRef] [Green Version] - Barkley, E.F.; Major, C.H.; Cross, K.P. Collaborative Learning Techniques: A Handbook for College Faculty, 2nd ed.; Jossey-Bass: San Francisco, CA, USA, 2014; ISBN 9781118761557. [Google Scholar]
- Lin, Y.-S.; Chang, Y.-C.; Chu, C.-P. Novel Approach to Facilitating Tradeoff Multi-Objective Grouping Optimization. IEEE Trans. Learn. Technol.
**2016**, 9, 107–119. [Google Scholar] [CrossRef] - Bekele, R. Computer-Assisted Learner Group Formation Based on Personality Traits; University of Hamburg: Hamburg, Germany, 2005. [Google Scholar]
- Costaguta, R.; Menini, M.D.L.Á. An Assistant Agent for Group Formation in CSCL Based on Student Learning Styles. In Proceedings of the 7th Euro American Conference on Telematics and Information Systems—EATIS ’14; ACM Press: Valparaiso, Chile, 2014; pp. 1–4. [Google Scholar]
- Lescano, G.; Costaguta, R.; Amandi, A. Genetic Algorithm for Automatic Group Formation Considering Student’s Learning Styles. In Proceedings of the 8th Euro American Conference on Telematics and Information Systems (EATIS); IEEE: Cartagena, Colombia, 2016; pp. 1–8. [Google Scholar]
- Wang, D.-Y.; Lin, S.S.J.; Sun, C.-T. DIANA: A Computer-Supported Heterogeneous Grouping System for Teachers to Conduct Successful Small Learning Groups. Comput. Human Behav.
**2007**, 23, 1997–2010. [Google Scholar] [CrossRef] - Wichmann, A.; Hecking, T.; Elson, M.; Christmann, N.; Herrmann, T.; Hoppe, H.U. Group Formation for Small-Group Learning. In Proceedings of the 12th International Symposium on Open Collaboration; ACM: Berlin, Germany, 2016; pp. 1–4. [Google Scholar]
- Manske, S.; Hoppe, H.U. Managing Knowledge Diversity: Towards Automatic Semantic Group Formation. In Proceedings of the 17th International Conference on Advanced Learning Technologies (ICALT), Timisoara, Romania, 3–7 July 2017; IEEE: Timisoara, Romania, 2017; pp. 330–332. [Google Scholar]
- Zheng, Z.; Pinkwart, N. A Discrete Particle Swarm Optimization Approach to Compose Heterogeneous Learning Groups. In Proceedings of the 14th International Conference on Advanced Learning Technologies, Athens, Greece, 7–10 July 2014; IEEE: Athens, Greece, 2014; pp. 49–51. [Google Scholar]
- Amarasinghe, I.; Hernandez-Leo, D.; Jonsson, A. Intelligent Group Formation in Computer Supported Collaborative Learning Scripts. In Proceedings of the 17th International Conference on Advanced Learning Technologies (ICALT), Timisoara, Romania, 3–7 July 2017; IEEE: Timisoara, Romania, 2017; pp. 201–203. [Google Scholar]
- Sadeghi, H.; Kardan, A.A. Toward Effective Group Formation in Computer-Supported Collaborative Learning. Interact. Learn. Environ.
**2016**, 24, 382–395. [Google Scholar] [CrossRef] - Lykourentzou, I.; Antoniou, A.; Naudet, Y.; Dow, S.P. Personality Matters. In Proceedings of the 19th ACM Conference on Computer-Supported Cooperative Work & Social Computing; ACM: San Francisco, CA, USA, 2016; pp. 260–273. [Google Scholar]
- Duque Reis, R.C. Formação de Grupos Em Ambientes Cscl Utilizando Traços de Personalidade Associados Às Teorias de Aprendizagem Colaborativa; Universidade de São Paulo: São Carlos, Brazil, 2019. [Google Scholar]
- Battur, S.; Patil, M.S.; Desai, P.; Vijayalakshmi, M.; Raikar, M.M.; Hegde, P.; Joshi, G.H. Enhancing the Students Project with Team Based Learning Approach: A Case Study. In Proceedings of the 4th International Conference on MOOCs, Innovation and Technology in Education (MITE); IEEE: Madurai, India, 2016; pp. 275–280. [Google Scholar]
- Borges, S.; Mizoguchi, R.; Bittencourt, I.I.; Isotani, S. Group Formation in CSCL: A Review of the State of the Art. In Higher Education for All. From Challenges to Novel Technology-Enhanced Solutions. HEFA 2017. Communications in Computer and Information Science; Cristea, A.I., Bittencourt, I.I., Lima, F., Eds.; Springer: Cham, Switzerland, 2018; Volume 832, pp. 71–88. ISBN 9783319979335. [Google Scholar]
- Jung, C. Psychological Types; Taylor & Francis Ltd.: London, UK, 2017; ISBN 9781138687424. [Google Scholar]
- Keirsey, D. Please Understand Me II: Temperament, Character, Intelligence; Prometheus Nemesis Book Company: Carlsbad, CA, USA, 2006; ISBN 9781885705020. [Google Scholar]
- McCrae, R.R.; Allik, J. The Five-Factor Model of Personality Across Cultures; Springer: Boston, MA, USA, 2002; ISBN 9780306473555. [Google Scholar]
- Torrin, K. A Guide to Myers-Briggs Type Indicator (MBTI), Including Its Background, Concepts, Applications, and More; Webster’s Digital Services: New York, NY, USA, 2012; ISBN 9781276177030. [Google Scholar]
- Aguilar, R.A.; De Antonio, A.; Imbert, R. Searching Pancho’s Soul: An Intelligent Virtual Agent for Human Teams. In Proceedings of the Electronics, Robotics and Automotive Mechanics Conference (CERMA 2007), Morelos, Mexico, 25–28 September 2007; IEEE: Morelos, Mexico, 25 September 2007; pp. 568–571. [Google Scholar]
- Soto, C.J.; Kronauer, A.; Liang, J.K. Five-Factor Model of Personality. In The Encyclopedia of Adulthood and Aging; Krauss Whitbourne, S., Ed.; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2015; pp. 1–5. ISBN 9781118528921. [Google Scholar]
- John, O.P.; Naumann, L.P.; Soto, C.J. Paradigm shift to the integrative Big Five trait taxonomy: History, measurement, and conceptual issues. In Handbook of Personality: Theory and Research; John, O.P., Robins, R.W., Pervin, L.A., Eds.; The Guilford Press: New York, NY, USA, 2008; pp. 114–158. ISBN 9781606237380. [Google Scholar]
- Sleep, C.E.; Lynam, D.R.; Miller, J.D. A Comparison of the Validity of Very Brief Measures of the Big Five/Five-Factor Model of Personality. Assessment
**2020**, 28, 739–758. [Google Scholar] [CrossRef] [PubMed] - Maldonado Pérez, M. El Trabajo Colaborativo En El Aula Universitaria. Laurus Rev. Educ.
**2007**, 13, 263–278. [Google Scholar] - Chaljub Hasbún, J.M. Trabajo Colaborativo Como Estrategia de Enseñanza En La Universidad/Collaborative Work as a Teaching Strategy in the University. Cuad. Pedagog. Univ.
**2015**, 11, 64–71. [Google Scholar] [CrossRef] - Johnson, D.W.; Johnson, R.T.; Johnson Holubec, E. The New Circles of Learning: Cooperation in the Classroom and School; ASCD: Alexandria, VI, USA, 1994; ISBN 9780871202277. [Google Scholar]
- Revelo-Sánchez, O.; Collazos-Ordóñez, C.A.; Jiménez-Toledo, J.A. El Trabajo Colaborativo Como Estrategia Didáctica Para La Enseñanza/Aprendizaje de La Programación: Una Revisión Sistemática de Literatura. TecnoLógicas
**2018**, 21, 115–134. [Google Scholar] [CrossRef] [Green Version] - Holland, J.H. Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence; MIT University Press: Cambridge, MA, USA, 1992; ISBN 9780262275552. [Google Scholar]
- Wang, R.; Sato, Y.; Liu, S. Mutated Specification-Based Test Data Generation with a Genetic Algorithm. Mathematics
**2021**, 9, 331. [Google Scholar] [CrossRef] - Díaz, D.; Valledor, P.; Ena, B.; Iglesias, M.; Menéndez, C. Improved Method for Parallelization of Evolutionary Metaheuristics. Mathematics
**2020**, 8, 1476. [Google Scholar] [CrossRef] - Goldberg, D.E. Genetic Algorithms; Pearson Education: New York, NY, USA, 2006; ISBN 9788177588293. [Google Scholar]
- Alba, E.; Dorronsoro, B. Solving the Vehicle Routing Problem by Using Cellular Genetic Algorithms. In Evolutionary Computation in Combinatorial Optimization. EvoCOP 2004. Lecture Notes in Computer Science; Gottlieb, J., Raidl, G.R., Eds.; Springer: Berlin, Germany, 2004; Volume 3004, pp. 11–20. ISBN 9783540213673. [Google Scholar]
- Asadzadeh, L. A Local Search Genetic Algorithm for the Job Shop Scheduling Problem with Intelligent Agents. Comput. Ind. Eng.
**2015**, 85, 376–383. [Google Scholar] [CrossRef] - Pongcharoen, P.; Hicks, C.; Braiden, P.M.; Stewardson, D.J. Determining Optimum Genetic Algorithm Parameters for Scheduling the Manufacturing and Assembly of Complex Products. Int. J. Prod. Econ.
**2002**, 78, 311–322. [Google Scholar] [CrossRef] - Rezoug, A.; Bader-El-Den, M.; Boughaci, D. Guided Genetic Algorithm for the Multidimensional Knapsack Problem. Memetic Comput.
**2018**, 10, 29–42. [Google Scholar] [CrossRef] [Green Version] - Vaishnav, P.; Choudhary, N.; Jain, K. Traveling Salesman Problem Using Genetic Algorithm: A Survey. Int. J. Sci. Res. Comput. Sci. Eng. Inf. Technol.
**2017**, 2, 105–108. [Google Scholar] - Zhang, W.; Lu, J.; Zhang, H.; Wang, C.; Gen, M. Fast Multi-Objective Hybrid Evolutionary Algorithm for Flow Shop Scheduling Problem. In Proceedings of the Tenth International Conference on Management Science and Engineering Management. Advances in Intelligent Systems and Computing; Xu, J., Hajiyev, A., Nickel, S., Gen, M., Eds.; Springer: Baku, Azerbaijan, 2016; pp. 383–392. [Google Scholar]
- Ani, Z.C.; Yasin, A.; Husin, M.Z.; Hamid, Z.A. A Method for Group Formation Using Genetic Algorithm. Int. J. Comput. Sci. Eng.
**2010**, 2, 3060–3064. [Google Scholar] - Deleón, A.F.; Gómez, S.; Moreno, J. Uso de Tests de Aptitud y Algoritmos Genéticos Para La Conformación de Grupos En Ambientes Colaborativos de Aprendizaje. Av. Sist. Inf.
**2009**, 6, 165–172. [Google Scholar] - Amara, S.; Macedo, J.; Bendella, F.; Santos, A. Group Formation in Mobile Computer Supported Collaborative Learning Contexts: A Systematic Literature Review. Educ. Technol. Soc.
**2016**, 19, 258–273. [Google Scholar] - Odo, C.; Masthoff, J.; Beacham, N.; Alhathli, M. Affective State for Learning Activities Selection. In Proceedings of the Intelligent Mentoring Systems Workshop Associated with the 19th International Conference on Artificial Intelligence in Education, AIED 2018, London, UK, 27 June 2018; pp. 1–10. [Google Scholar]
- Cruz, W.M.; Isotani, S. Group Formation Algorithms in Collaborative Learning Contexts: A Systematic Mapping of the Literature. In Collaboration and Technology. CRIWG 2014. Lecture Notes in Computer Science; Baloian, N., Burstein, F., Ogata, H., Santoro, F., Zurita, G., Eds.; Springer: Cham, Switzerland, 2014; Volume 8658, pp. 199–214. ISBN 9783319101651. [Google Scholar]
- John, O.P.; Robins, R.W.; Pervin, L.A. Handbook of Personality, 3rd ed.; The Guilford Press: New York, NY, USA, 2008; ISBN 9781593858360. [Google Scholar]
- Benet-Martínez, V.; John, O.P. Los Cinco Grandes across Cultures and Ethnic Groups: Multitrait-Multimethod Analyses of the Big Five in Spanish and English. J. Pers. Soc. Psychol.
**1998**, 75, 729–750. [Google Scholar] [CrossRef] - Moreno, J.; Rivera, J.C.; Ceballos, Y.F. Agrupamiento Homogéneo de Elementos Con Múltiples Atributos Mediante Algoritmos Genéticos. DYNA
**2011**, 78, 246–254. [Google Scholar] - Han, J.; Kamber, M. Data Mining: Concepts and Techniques, 2nd ed.; Elsevier Inc.: San Francisco, CA, USA, 2006; ISBN 9780080475585. [Google Scholar]
- Conradie, W.; Goranko, V. Logic and Discrete Mathematics: A Concise Introduction; John Wiley & Sons, Ltd.: Hoboken, NJ, USA, 2015; ISBN 9781118751275. [Google Scholar]
- Kramer, O. Evolutionary Self-Adaptation: A Survey of Operators and Strategy Parameters. Evol. Intell.
**2010**, 3, 51–65. [Google Scholar] [CrossRef] - Mirjalili, S. Genetic Algorithm. In Evolutionary Algorithms and Neural Networks. Studies in Computational Intelligence; Springer: Cham, Switzerland, 2018; pp. 43–55. ISBN 9783319930251. [Google Scholar]
- Reza Hejazi, S.; Saghafian, S. Flowshop-Scheduling Problems with Makespan Criterion: A Review. Int. J. Prod. Res.
**2005**, 43, 2895–2929. [Google Scholar] [CrossRef] - Araujo, L.; Cervigón, C. Algoritmos Evolutivos: Un Enfoque Práctico; Alfaomega Grupo Editor: Ciudad de México, México, 2009; ISBN 9786077686293. [Google Scholar]
- Revelo-Sánchez, O.; Collazos, C.A.; Solano, A.F.; Fardoun, H. Diseño Colaborativo Basado En ThinkLets Como Apoyo a La Enseñanza de La Programación. Rev. Colomb. Comput.
**2020**, 21, 22–33. [Google Scholar] [CrossRef] - Kirk, R.E. Experimental Design—Procedures for the Behavioral Sciences, 4th ed.; SAGE Publications, Inc.: Los Angeles, CA, USA, 2013; ISBN 9781412974455. [Google Scholar]
- Duzhin, F.; Gustafsson, A. Machine Learning-Based App for Self-Evaluation of Teacher-Specific Instructional Style and Tools. Educ. Sci.
**2018**, 8, 7. [Google Scholar] [CrossRef] [Green Version] - Ledesma, R.; Macbeth, G.; Cortada De Kohan, N. Tamaño Del Efecto: Revisión Teórica y Aplicaciones Con El Sistema Estadístico ViSta. Rev. Latinoam. Psicol.
**2008**, 40, 425–439. [Google Scholar] - Cohen, J. Statistical Power Analysis for the Behavioral Sciences, 2nd ed.; Lawrence Erlbaum Associates: New York, NY, USA, 1988; ISBN 9780805802832. [Google Scholar]

Spanish Big Five Inventory | ||||

Las siguientes expresiones le describen a usted con más o menos precisión. Por ejemplo, ¿está de acuerdo en que usted es alguien “chistoso, a quien le gusta bromear”? Por favor escoja un número para cada una de las siguientes expresiones, indicando así hasta qué punto está de acuerdo o en desacuerdo en cómo le describe a usted. | ||||

Muy en desacuerdo 1 | Ligeramente en desacuerdo 2 | Ni de acuerdo ni en desacuerdo 3 | Ligeramente de acuerdo 4 | Muy de acuerdo 5 |

Me veo a mi mismo-a como alguien que… | ||||

___ 1. es bien hablador ___ 2. tiende a ser criticón ___ 3. es minucioso en el trabajo ___ 4. es depresivo, melancólico ___ 5. es original, se le ocurren ideas nuevas ___ 6. es reservado ___ 7. es generoso y ayuda a los demás ___ 8. puede a veces ser algo descuidado ___ 9. es calmado, controla bien el estrés ___ 10. tiene intereses muy diversos ___ 11. está lleno de energía ___ 12. prefiere trabajos que son rutinarios ___ 13. inicia disputas con los demás ___ 14. es un trabajador cumplidor, digno de confianza ___ 15. con frecuencia se pone tenso ___ 16. tiende a ser callado ___ 17. valora lo artístico, lo estético ___ 18. tiende a ser desorganizado ___ 19. es emocionalmente estable, difícil de alterar ___ 20. tiene una imaginación activa ___ 21. persevera hasta terminar el trabajo ___ 22. es a veces mal educado con los demás | ___ 23. es inventivo ___ 24. es generalmente confiado ___ 25. tiende a ser flojo, vago ___ 26. se preocupa mucho por las cosas ___ 27. es a veces tímido, inhibido ___ 28. es indulgente, no le cuesta perdonar ___ 29. hace las cosas de manera eficiente ___ 30. es temperamental, de humor cambiante ___ 31. es ingenioso, analítico ___ 32. irradia entusiasmo ___ 33. es a veces frío y distante ___ 34. hace planes y los sigue cuidadosamente ___ 35. mantiene la calma en situaciones difíciles ___ 36. le gusta reflexionar, jugar con las ideas ___ 37. es considerado y amable con casi todo el mundo ___ 38. se pone nervioso con facilidad ___ 39. es educado en arte, música, o literatura ___ 40. es asertivo, no teme expresar lo que quiere ___ 41. le gusta cooperar con los demás ___ 42. se distrae con facilidad ___ 43. es extrovertido, sociable ___ 44. tiene pocos intereses artísticos | |||

Por favor, compruebe que ha escrito un número delante de cada frase. | ||||

English Big Five Inventory | ||||

Here are a number of characteristics that may or may not apply to you. For example, do you agree that you are someone who likes to spend time with others? Please choose a number for each statement to indicate the extent to which you agree or disagree with that statement. | ||||

Disagree strongly 1 | Disagree a little 2 | Neither agree nor disagree 3 | Agree a little 4 | Agree strongly 5 |

I see myself as someone who… | ||||

___ 1. is talkative. ___ 2. tends to find fault with others. ___ 3. does a thorough job. ___ 4. is depressed, blue. ___ 5. is original, comes up with new ideas. ___ 6. is reserved. ___ 7. is helpful and unselfish with others. ___ 8. can be somewhat careless. ___ 9. is relaxed, handles stress well. ___ 10. is curious about many different things. ___ 11. is full of energy. ___ 12. starts quarrels with others. ___ 13. is a reliable worker. ___ 14. can be tense. ___ 15. is ingenious, a deep thinker. ___ 16. generates a lot of enthusiasm. ___ 17. has a forgiving nature. ___ 18. tends to be disorganized. ___ 19. worries a lot. ___ 20. has an active imagination. ___ 21. tends to be quiet. ___ 22. is generally trusting. | ___ 23. tends to be lazy. ___ 24. is emotionally stable, not easily upset. ___ 25. is inventive. ___ 26. has an assertive personality. ___ 27. can be cold and aloof. ___ 28. perseveres until the task is finished. ___ 29. can be moody. ___ 30. values artistic, aesthetic experiences. ___ 31. is sometimes shy, inhibited. ___ 32. is considerate and kind to almost everyone. ___ 33. does things efficiently. ___ 34. remains calm in tense situations. ___ 35. prefers work that is routine. ___ 36. is outgoing, sociable. ___ 37. is sometimes rude to others. ___ 38. makes plans and follows through with them. ___ 39. gets nervous easily. ___ 40. likes to reflect, play with ideas. ___ 41. has few artistic interests. ___ 42. likes to cooperate with others. ___ 43. is easily distracted. ___ 44. is sophisticated in art, music, or literature. | |||

Please check: Did you write a number in front of each statement? |

Id | ${\mathit{C}}_{1}$ | ${\mathit{C}}_{2}$ | … | ${\mathit{C}}_{\mathit{M}}$ |
---|---|---|---|---|

1 | 70 | 0.50 | … | 25 |

2 | 20 | 0.83 | … | −10 |

⋮ | ⋮ | ⋮ | ⋮ | |

$N$ | 45 | 1.22 | … | 13 |

S_{1} | S_{2} | S_{3} | S_{4} | S_{5} | |
---|---|---|---|---|---|

G_{1} | 1 | 2 | 3 | 4 | 5 |

G_{2} | 6 | 7 | 8 | 9 | 10 |

G_{3} | 11 | 12 | 13 | 14 | 15 |

G_{4} | 16 | 17 | 18 | 19 | 20 |

Id | ${\mathit{C}}_{1}$ | ${\mathit{C}}_{2}$ | ${\mathit{C}}_{3}$ |
---|---|---|---|

1 | 0.12 | 1.00 | 0.90 |

2 | 0.97 | 0.00 | 0.30 |

3 | 0.00 | 0.64 | 0.98 |

4 | 1.00 | 0.45 | 1.00 |

5 | 0.35 | 0.07 | 0.93 |

6 | 0.59 | 0.84 | 0.00 |

Individual 1 | Individual 2 | ||||
---|---|---|---|---|---|

1 | 2 | 3 | 1 | 3 | 5 |

4 | 5 | 6 | 2 | 4 | 6 |

Individual | Group | Id | ${\mathit{C}}_{1}$ | ${\mathit{C}}_{2}$ | ${\mathit{C}}_{3}$ |
---|---|---|---|---|---|

1 | 1 | 1 | 0.120 | 1.000 | 0.900 |

2 | 0.970 | 0.000 | 0.300 | ||

3 | 0.000 | 0.640 | 0.980 | ||

$\overline{{X}_{1,C}^{1}}$ | 0.363 | 0.547 | 0.727 | ||

2 | 4 | 1.000 | 0.450 | 1.000 | |

5 | 0.350 | 0.070 | 0.930 | ||

6 | 0.590 | 0.840 | 0.000 | ||

$\overline{{X}_{2,C}^{1}}$ | 0.647 | 0.453 | 0.643 | ||

2 | 1 | 1 | 0.120 | 1.000 | 0.900 |

3 | 0.000 | 0.640 | 0.980 | ||

5 | 0.350 | 0.070 | 0.930 | ||

$\overline{{X}_{1,C}^{2}}$ | 0.157 | 0.570 | 0.937 | ||

2 | 2 | 0.970 | 0.000 | 0.300 | |

4 | 1.000 | 0.450 | 1.000 | ||

6 | 0.590 | 0.840 | 0.000 | ||

$\overline{{X}_{2,C}^{2}}$ | 0.853 | 0.430 | 0.433 |

Homogeneous Optimal Value: 0.04259 | Heterogeneous Optimal Value: 0.37947 | Mixed (Het 1,3; Hom 2) Optimal Value: 0.35975 | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

p_{c}\p_{m} | 0.001 | 0.005 | 0.01 | 0.05 | 0.1 | 0.001 | 0.005 | 0.01 | 0.05 | 0.1 | 0.001 | 0.005 | 0.01 | 0.05 | 0.1 |

0.2 | 100 | 100 | 100 | 64 | 62 | 100 | 100 | 100 | 56 | 59 | 100 | 100 | 100 | 65 | 64 |

0.3 | 100 | 100 | 100 | 70 | 63 | 100 | 100 | 100 | 59 | 59 | 100 | 100 | 100 | 59 | 61 |

0.4 | 99 | 100 | 100 | 59 | 51 | 99 | 100 | 100 | 64 | 63 | 100 | 100 | 100 | 63 | 58 |

0.6 | 74 | 94 | 89 | 65 | 56 | 87 | 93 | 91 | 60 | 61 | 89 | 98 | 91 | 72 | 56 |

0.8 | 61 | 67 | 49 | 50 | 52 | 61 | 59 | 53 | 58 | 43 | 66 | 59 | 52 | 51 | 49 |

**Table 8.**Results of population size and generation number simulation (time (T) in milliseconds, fitness value (F)).

G\PS | 100 | 250 | 500 | 1000 | ||||
---|---|---|---|---|---|---|---|---|

T | F | T | F | T | F | T | F | |

50 | 670 | 2.86807 | 2793 | 2.95261 | 6039 | 2.57977 | 6440 | 2.41648 |

100 | 1294 | 3.19189 | 5196 | 3.11056 | 9153 | 2.68289 | 12,071 | 2.43724 |

250 | 3413 | 3.38202 | 13,152 | 3.27827 | 16,379 | 2.80822 | 29,856 | 2.45063 |

500 | 6311 | 3.65009 | 15,166 | 3.12584 | 30,225 | 2.77663 | 57,944 | 2.52308 |

1000 | 11,553 | 4.08895 | 30,642 | 3.24229 | 57,730 | 2.89469 | 115,698 | 2.56421 |

Homogeneous | Heterogeneous | Mix (Ht123, Hm45) | ||||
---|---|---|---|---|---|---|

Students | T | F | T | F | T | F |

20 | 2384 | 0.02564 | 2837 | 1.45408 | 3425 | 0.79947 |

50 | 12,244 | 0.15691 | 12,120 | 4.09133 | 12,406 | 2.58507 |

100 | 42,644 | 0.40598 | 40,700 | 6.79100 | 40,434 | 4.15891 |

Homogeneous | Heterogeneous | Mix (Ht123, Hm45) | ||||
---|---|---|---|---|---|---|

Students | T | F | T | F | T | F |

20 | 2711 | 0.01084 | 3038 | 1.04431 | 2908 | 0.60869 |

50 | 11,065 | 0.06563 | 12,240 | 2.97906 | 12,235 | 1.93656 |

100 | 41,801 | 0.20536 | 51,146 | 4.92599 | 41,940 | 3.26345 |

Program-Course | N | Group Type | Number of Groups | Grouping Type |
---|---|---|---|---|

Electronic Engineering- Computer Programming | 22 | Experimental | 6/3–1/4 | Heterogeneous |

17 | Control | 3/3–2/4 | Students’ preference | |

Systems Engineering- Graphic Programming | 24 | Experimental | 8/3 | Homogeneous |

19 | Control | 5/3–1/4 | Students’ preference |

Group Type | Group | Pre-Test | Experimental Stimulus | Post-Test |
---|---|---|---|---|

Experimental | G_{1} | O_{1} | X | O_{5} |

G_{2} | O_{2} | X | O_{6} | |

Control | G_{3} | O_{3} | - | O_{7} |

G_{4} | O_{4} | - | O_{8} |

Course | Group | N | Tests | p |
---|---|---|---|---|

Computer Programming | Experimental (G_{1}) | 22 | O_{1}–O_{3} | 0.589 |

Control (G_{3}) | 17 | |||

Graphic Programming | Experimental (G_{2}) | 24 | O_{2}–O_{4} | 0.607 |

Control (G_{4}) | 19 |

Course | Group | N | Tests | p | g |
---|---|---|---|---|---|

Computer Programming | Experimental (G_{1}) | 22 | O_{5}–O_{7} | 0.029 | 0.729 |

Control (G_{3}) | 17 | ||||

Graphic Programming | Experimental (G_{2}) | 24 | O_{6}–O_{8} | 0.039 | 0.579 |

Control (G_{4}) | 19 |

Course | Group | N | Tests | p | g |
---|---|---|---|---|---|

Computer Programming | Experimental (G_{1}) | 22 | O_{1}–O_{5} | 0.000 | 2.860 |

Control (G_{3}) | 17 | O_{3}–O_{7} | 0.002 | 1.433 | |

Graphic Programming | Experimental (G_{2}) | 24 | O_{2}–O_{6} | 0.000 | 2.713 |

Control (G_{4}) | 19 | O_{4}–O_{8} | 0.000 | 1.735 |

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**MDPI and ACS Style**

Revelo Sánchez, O.; Collazos, C.A.; Redondo, M.A.
Automatic Group Organization for Collaborative Learning Applying Genetic Algorithm Techniques and the Big Five Model. *Mathematics* **2021**, *9*, 1578.
https://doi.org/10.3390/math9131578

**AMA Style**

Revelo Sánchez O, Collazos CA, Redondo MA.
Automatic Group Organization for Collaborative Learning Applying Genetic Algorithm Techniques and the Big Five Model. *Mathematics*. 2021; 9(13):1578.
https://doi.org/10.3390/math9131578

**Chicago/Turabian Style**

Revelo Sánchez, Oscar, César A. Collazos, and Miguel A. Redondo.
2021. "Automatic Group Organization for Collaborative Learning Applying Genetic Algorithm Techniques and the Big Five Model" *Mathematics* 9, no. 13: 1578.
https://doi.org/10.3390/math9131578