URL: https://revista.inicc-peru.edu.pe/index.php/delectus

DOI: https://doi.org/10.36996/delectus

Email: publicaciones.iniccperu@gmail.com

Vol. 4 No. 1 (2021): January-June [Edit closure: 01/01/2021]

RECEIVED: 12/08/2020 | ACCEPTED: 23/12/2020 | PUBLISHED: 01/01/2021

**Suggested quote (APA, seventh edition) **

Luna Santos, J. C. (2021). Collaborative learning in the teaching of mathematics at the undergraduate level. *Delectus*, *4*(1), 129-138. https://doi.org/10.36996/delectus.v4i1.71

CONTINENTAL UNIVERSITY, Peru

jlunas@continental.edu.pe

Today, collaborative learning is a key factor in the development of Mathematics teaching and its study intervenes in the progress of educational quality. Therefore, our study aims to analyze how collaborative learning is employed in the teaching of mathematics through the solution of exercises and the use of strategies. We made a conceptual approach from different authors that help to evidence the importance it has, in the social organization in the classroom establishing a positive interdependence. The information allowed me to conclude that, as a strategy in Mathematics at an undergraduate level, it increases the academic productivity of the students. However, it needs to be developed as a strategy in universities, and if it were complemented with the use of ICTs it would generate a very beneficial learning.

Collaborative learning is a technique that promotes the study of students, which is based on the work of small associations of students who come together in classes, with the purpose of developing their skills, coordinate between them; using dialogue, where their views are respected, makes use of learning levels that are integrated to enrich their understanding. It is a pedagogical tactic whose purpose is to encourage and structure intersubjectivity through the relationship of students where they form work teams, whose purpose is to learn in the classroom, this interaction makes that by working together they can improve their learning and personal development (Rivero & Suárez, 2017). For many centuries it was spoken about the great privileges and benefits that the grouping of university students in the classroom has to develop academic aspects called tasks, through this technique we can observe improvements in their learning in a significant way (Ramirez, 2017) With the application of the Collaborative Learning as a teaching strategy, it is sought to propitiate changes in the model of teaching and learning, from one centered in the teacher to a model centered in the student, in order to develop roles and responsibilities in both and help the purpose of the achievements understanding this as a cognitive, procedural, and attitudinal process (Rivadeneira-Silva, 2017), they would no longer be net recipients of the information transmitted by their teachers and would instead become "people who participate in the process of their learning" (Danker, 2015). For this, it is sought that the collaborative teaching be used in the solution of the exercises in an analytical way, helping to eliminate the rejection of this exact science, at the same time that it helps to satisfy the requirements of the UNESCO about the development and learning of the exact sciences.

It is not a coincidence that for many years the doubts that students have when facing academic problems in science, when they solve mathematical exercises in universities, constitute a great problem. This is how we ask ourselves: How is collaborative learning used in the study of mathematics at an undergraduate level? How does collaborative learning contribute to the study of mathematics at an undergraduate level in the cognitive and procedural aspects? For this reason, we ask ourselves either because they do not know the topics, they do not have a solid base of the subject matter, or because their teachers have not known how to motivate them since their school training. This problem has been increasing over the years, and to date has not been able to be solved, despite the fact that alternative solutions are being sought. In view of this perspective, we present some alternatives to be developed, such as strategies for the stimulation of dialogue using nomenclatures, listening to the other, and procedural reciprocal evaluation.

In the face of this challenge, we tried to renew and innovate, using learning strategies. For the application, we made use of collaborative learning that seeks in all cases, that students learn in a group way, they are socially integrated so that it is easier for them to assimilate knowledge and use it being a proposal of a high scope for learning in education. In the educational sector during the last periods of time, in every year that passes the methodological strategies are innovated according to the eventualities presented in the classroom. The aim is to improve our educational system by using a collaborative strategy where the main protagonist is the student. This strategy tries to turn the students into active participants of their own knowledge and that is why the collaborative study is conveniently used in the process of their study. In addition, it tries to change the rejection of mathematics, motivating students to accept it. Trying to understand the problem and look for alternative solutions.

This study seeks a diagnosis of how their academic performance is, make proposals that improve their achievement of study in college students. In addition, to restructure and innovate the academic and administrative planning of the curricula linked to the integration of the New University Act for the benefit of young university students.

One tool to consider is the collaboration, used in the classroom where dynamics are developed provoke better interactions between students and teach us to overcome academic problems, looking for the increase of a higher order learning. This study intends, that the collaborative learning is used in the school classrooms in a mandatory way since this strategy develops the value of the interpersonal relations in groups when being considered as a value for the student's formation. Likewise, this research aims to contribute to the development of university students and their training, improving their qualifications. This technique benefits the students in their environment since it promotes values such as commitment to communication, solidarity and teamwork.

In this sense, the following objective is set: to analyze how collaborative teaching is used in the study of mathematics in the cognitive and procedural aspects.

It is understood that the student benefits significantly in the teaching of Mathematics by making use of collaborative learning, since this encourages them to develop goals within the classroom, where they assume responsibilities in a group, when relating to others, respecting and accepting their points of view, exposing their criteria in an analytical and reasoned way. In addition, it is observed that students are motivated and understood with the help of their peers. When they work in groups, they receive contributions from their peers and become socialized in a more didactic and assertive way. This research also investigates how collaborative learning contributes, in the academic formation and teaching practice of students, as in qualitative research as a way to corroborate how didactic strategies were used, how direct and concrete data were obtained between the researcher and the object studied, which allowed to deepen people's interactions and their appreciations with the use of collaborative learning.

In addition, the study seeks to develop interpersonal relationships in groups by considering it as a value for the student's education. In order to design the class sessions, specific topics are included that required to solve problems where each question had a specific time and value per question, comparing in this activity the individual and group form of working, whose objective was to develop the cognitive and procedural aspects, the group interaction through the collaborative work, obtaining a conclusive result that reflected how this strategy improved their learning considerably when working in group delegating to the individual form.

Most likely, this research will make use of research on collaborative learning in an experimental way where monitored and studied individual and group samples were formed to show whether learning in mathematics is actually improved and whether students' skills are developed where the logical reasoning, the cognitive deduction is important in the development of the mathematical operations to all this it is added that they will have to face diverse situations when interrelating and that in spite of all these considerations, the result of the learning is very beneficial. In addition, it should be considered that at the moment of comparing those who used this collaborative learning with those who did not obtain the same result as those who used it in a group, they obtained better results.

According to the Tuning Latin America Project and the skills to be developed in the training of mathematicians when carrying out a study on this subject, it will allow me to analyze different methodological strategies of collaborative learning, to choose which are the most appropriate to use in the students' learning. It will also be appropriate to make a diagnosis of how the academic performance was at that time and how they were doing it, and then present proposals to improve student learning. Therefore, it is stated that collaborative learning in the study of Mathematics at the undergraduate level strategically improves student teaching.

From the experiences made, it is also clear that the synergy between the CA and the study of mathematics in the universities improves the work climate in the classroom, effectively promotes the acquisition of new skills, increases the interest of young university students in the subjects under study and obtains better academic grades.

**Collaborative learning is employed in the teaching of Mathematics at the undergraduate level**

Similarly, it is stated that the student benefits significantly in the teaching of mathematics when using collaborative learning, since this encourages them to develop actions within the classroom where they assume commitments in a group way, relating to others, respecting and accepting their points of view, exposing their criteria in an analytical and reasoned way, it is stated that the students are more motivated when they work in groups, they receive contributions from their peers, they are socialized in a more didactic and assertive way. Likewise, in order to investigate how collaborative learning contributes to the academic training and teaching practice of students, as in qualitative research, as a way to corroborate how it was used, they applied a didactic, where they obtained direct and concrete data between the researcher and the object studied, which allowed to deepen the interactions of people and their perceptions with the use of collaborative learning. In a similar way, it also mentions that when studying about the cooperative and collaborative work it shows many incidences in the study of mathematics, it is a great challenge where the resolution of workshops and the team work in group or individual form has been carried out to be able to compare using diverse techniques when proposing this topic involves capacities in the teaching of mathematics being obtained a better result when working in group collaboratively that in individual form, this way when all the students are involved it is incurred appropriately in the development of their abilities. It points out that the collaborative learning is indispensable for the educational formative character in the diverse student environments. Here it is mentioned that students in economics by forming groups to perform coursework tasks substantially complement each other and learn significantly (Yong Chang et al., 2018).

Similarly, it was considered that this study seeks to develop interpersonal relationships in groups by considering them as a central value for education. In this way, the collaborative learning strengthens the critical thinking in the teaching of mathematics, the work in groups is so effective that it promotes the increase of abilities in the students in their university environment teaching them to live together and to relate in spite of the divergences of characters that are presented in the work by grouping, promoting their adaptation towards objectives and ends that are beneficial in the resolution of problems. He mentions that this research on virtual courses at Minuto de Dios University made use of observation logs and questionnaires applied to students. Therefore, it shows that these students grouped in teams, using different learning methods obtain better academic results, greater integration and the objectives set are met considerably (Guerra Santana et al., 2019).

This strategy when used improves and complements considerably the assimilation of knowledge when solving problems in the classroom, we must also consider the use of ICT that strengthens their learning obtaining very optimal results that favor learning and motivates them to learn more every day. In accordance with what was done by the State Distance University (UNED) of Costa Rica, a survey was applied to two groups of students, each concerning two virtual courses where collaborative learning was used as tools with open and closed questions. Finally, the students responded that they prefer the collaborative work, because it complements their knowledge when interacting between classmates and if they use the virtual tools their learning becomes more effective, in this case it will depend on the learning style that the teacher assumes, on the way he motivates the class, on the tools he uses, in order to make the university students learn in the best way, being able to verify that the collaborative learning contributes to the teaching of Mathematics.

Furthermore, when presenting the questionnaires with a set of problems classified by topics developed and with characteristics to be able to solve them at the university level, many felt doubts for their resolution when they solved them individually, but when they integrated in group and used as a strategy in the collaborative learning, they were academically strengthened to such an extent that they were motivated to investigate and learn to exchange opinions, to learn from others to unify ideas and to obtain as a result a significant learning that made them learn together so they could improve their grade.

This study mentions that Panamanian university students participated where the instrument called questionnaire and an observation sheet were applied to them. Likewise, the students demonstrated to be able to solve problems, to accommodate and structure the mathematical data, as well as to promote themselves and to exhibit a dynamic intervention in the growth of the educational activities of the class. According to the research about collaborative learning in an experimental way, individual and group samples were monitored and studied to know if learning in mathematics is really improved and if students' skills are developed in a memoristic and procedural way when using calculus and algorithms in mathematics, considering also to challenge problematic situations derived from personal relationships with the result that collaborative learning is very beneficial and advantageous with respect to those who did not use this strategy (Morales-Maure et al., 2018).

**Collaborative learning contributes to the teaching of mathematics in the cognitive and procedural aspects as it is affirmed in an analogous way**

Similarly, with what is mentioned we know that if the collaborative learning is complemented with the Flipped Classroom, this tool contributes significantly to solve and assimilate knowledge in university students especially in solving mathematical problems, even allows them to deliver quality academic work and a relatively orderly and precise resolution consult computer media and analyze video tutorials on the specific topic. Improving considerably and actively participating in the academic work. Similarly, the social cultural exchange and exchange of ideas, will encourage learning, supports us such assertion Vygotsky's theory of learning. Furthermore, it is assumed that collaborative study with the Fllipped Classroom has much more sense of learning and is better coordinated than that developed by the inverted class (Sánchez-Cruzado et al., 2018). In the same way we agree with the expressed in that it is of much necessity to give a significant value to the session of learning developed in the university classroom where the interactions and experiences that are generated in this context are significant, essential in the learning where the use of the technologies jointly with the employment of the collaborative learning complements that the student assimilates the knowledge integrally.

Similarly, he also mentions that the use of ICT develops skills and abilities in students, is an alternative to help university students who have problems with learning mathematics because it helps them to interact in an organized way learning and exchanging information in the area of science, in this way, it seeks to complement the knowledge provided by teachers and improve their learning. It mentions that it is a problem the academic grades of the students in the Mathematics course where they have a high percentage of failure, they fail the course and others opt for desertion. Therefore, we have chosen as a proposal the use of collaborative teaching and the use of ICT, with educational improvements for the development of the course in the classroom and to enhance the skills of students where it provides them with greater autonomy, willingness and cooperative work. In order to better understand one of the phases developed by the author is to choose technological resources where data are integrated and managed causing the interaction, where it is observed that teaching and motivation in the solution of mathematical problems in the form of questionnaires (Montes en al., 2018).

In the same way if we take as a starting point the pedagogical factor, which influences the academic productivity of the students according to the questionnaire that served as information, being constituted as one of the obtained variables the time of dedication to the study, the way and the type of used strategy, being the proposal in our investigation the most recommended. The results that are reported, in the academic productivity of the engineering students of FUAC, in the course of the first three semesters of their professional academic formation are progressive when strategies that help the learning are used.

Similarly, it also mentions us, about the academic performance in the study of Mathematics at university level, the problems that it presents and the proposal of offering an innovative way of teaching, originating that the students learn using strategies, where the acquired knowledge should be used in the development of the academic tasks, being evident advances in the cognitive and procedural aspects, constituting itself as an academic success (Camacho et al., 2017). According to the relationship between collaborative learning used in virtual courses and the various ways of teaching students in university training have been taken with great importance over the years in virtual environments. Where the strategy used at a given time becomes a social interaction through which students and teachers relate to each other, significantly strengthening learning.

According to this research on virtual courses at Minuto de Dios University, it made use of observation logs, and questionnaires applied to students. Therefore, it shows us that these students grouped in teams, using different learning methods obtain better academic results, greater integration and the objectives set are met considerably, where they demonstrate their capabilities and skills using it in problem solving.

Similarly it mentions that the collaborative learning strengthens the critical thinking in the teaching of mathematics, the work in groups is so effective that it promotes the development of capacities in the students in their university environment, teaching them to live together and to relate in spite of the divergences of characters that are presented in the work by grouping, promoting their adaptation towards objectives and ends that are beneficial in the resolution of problems (Arenas, 2017).

The collaborative methodology used by the social networks is suggested to be used since it develops in the university students abilities and skills in the solution of mathematical exercises, independent of the gender. Therefore, students show a high level of satisfaction towards the strategy because, in such an abstract area, it allows them to improve their learning levels, being accessible for different activities. The use of this proposal was valued and recognized by parents as a very positive way of teaching. In a similar way, they tell us that the strategies used in teaching and learning are very powerful for the solution of problems in mathematics. Furthermore, that the use of ICT and social networks add considerably, creating environments that are conducive to learning for participating students in this context.In the same way, it makes known how collaborative learning is beneficially employed in mathematics knowing that they use a symbolic, representative and interpretative language also called technical vocabulary, necessary to decipher symbols, scientific notations, besides it should propose the development of mathematical competences as a purpose of their teaching (Cruz et al., 2017).

According to the author who proposes an active methodology that encourages students to work as a team and to participate actively in the classroom. Promoting at all times the work of the group to achieve greater achievement of skills in students when solving math exercises recognizing that it promotes an environment of effectiveness to seek a good climate in the classroom, promotes active listening in the classroom whose motto is: " share and support each other" in the development of teamwork and that the effort deployed has as a goal the delivery of academic work better written and supplemented, likewise comments that in this research students benefit from collaborative learning considerably, where it makes known that the strategy used by the teacher, will determine learning in solving problems in mathematics in college students and that these are significant for them. In other words, it also mentions that they present independent and dependent variables that support the proposal that is presented as a hypothesis of the research that is indicated when making use of didactic strategies to improve the process of study in the teaching of Mathematics, obtaining the expected results measured by means of indicators developed and verifying that it is beneficial for university students (Torres, 2018).

According to that the collaborative learning benefits in the learning of the Mathematics to the university students if they use suitable strategies are mentioned: the gamification that is to say the use of games in context of different nature those who have common elements like the mechanics, the dynamics and the motivational ones the second strategy is the learning based on games that refers to the use of the games in suitable environments and oriented to the educational formation, whose intention is to use a part of its time in educational purposes, this way the student learns to develop in the classroom respecting the norms of interactivity and feedback. Likewise, he comments that the handling of the ICT by the students nowadays plays a main role in the study of mathematics, by using this instrument, all this improves innovatively their learning. Finally, it also mentions about the procedural aspects that we must approach for the learning of mathematics as it is the development and knowledge of new technologies many times in form of interactive games that encourage and improve the learning of the students in groups (Zabala-Vargas, 2020).

It is confirmed that, by using collaborative learning as a strategy in the teaching of Mathematics at the undergraduate level, it strategically improves the teaching of students.

It is also confirmed that the use of collaborative learning as a strategy in the teaching of Mathematics and that, as it develops, in the cognitive and procedural aspects in students, it significantly strengthens their learning.

Our proposal for the future is to use collaborative learning in the teaching of Mathematics at the undergraduate level in a strategic and mandatory way, complementing it with teacher training to use new digital technologies, all this will contribute to the improvement of their learning in the undergraduate student.

Arenas, C. (2017)**. ***Los estilos de aprendizaje y su relación con el aprendizaje colaborativo en cursos virtuales [Learning styles and their relationship to collaborative learning in virtual courses].* [Master's Thesis, Technological University of Monterrey]. Institutional Repository. https://repositorio.tec.mx/bitstream/handle/11285/622384/TESIS%20RITEC.pdf?sequence=1&isAllowed=y

Cruz, I., Puentes, A., & Cabero, J. (2017)**. **The use of social networks for the teaching of mathematics. *Espacios Journal, *38(55). https://idus.us.es/bitstream/handle/11441/67242/a17v38n55p31.pdf?sequence=1%20&isAllowed=y__ __

Danker, B. (2015). Using Flipped Classroom Approach to Explore Deep Learning in Large Classrooms. *Journal of Education, 3*(1), 171-186. https://files.eric.ed.gov/fulltext/EJ1100618.pdf

Díaz, L., Sarmiento, H., & Rodríguez, D. (2017). Relación entre el Rendimiento Académico en Matemáticas y los Estilos de Aprendizaje de los Estudiantes de la Fundación Universidad Autónoma de Colombia [Relationship between Academic Performance in Mathematics and the Learning Styles of the Students of the Foundation of the Autonomous University of Colombia]. *Revista de Estilos de Aprendizaje [Journal of Learning Styles]*, *10*(20), 34- 62. http://revistaestilosdeaprendizaje.com/article/download/1056/1770/

Guerra, M., Rodríguez, J., & Rodríguez, A. (2019). Aprendizaje colaborativo: experiencia innovadora en el alumnado universitario [Collaborative learning: innovative experience in university students]. *Revista de estudios y experiencias en educación [Journal of studies and experiences in education]*, *18*(36), 269-281. https://scielo.conicyt.cl/pdf/rexe/v18n36/0718-5162-rexe-18-36-269.pdf__ __

Montes, R., Escobar, M., y Cadavid, G. (2018). Uso de herramientas tecnológicas en el desarrollo de un curso de Matemáticas 1 en la Universidad Tecnológica de Pereira [Use of technological tools in the development of a Mathematics 1 course at the Technological University of Pereira]. *Revista entre Ciencia e Ingeniería [Magazine between Science and Engineering],* 12(23), 66-71. http://www.scielo.org.co/pdf/ecei/v12n23/1909-8367-ecei-12-23-00066.pdf

Morales, L., García, O., Torres, A., & Lebrija, A. (2018). Habilidades cognitivas a través de la estrategia de aprendizaje cooperativo y perfeccionamiento epistemológico en Matemática de estudiantes de primer año de Universidad [Cognitive skills through the strategy of cooperative learning and epistemological improvement in Mathematics of first-year university students]. *Revista Formación Universitaria [University Formation Magazine]*, *11*(2), 45-56. https://scielo.conicyt.cl/pdf/formuniv/v11n2/0718-5006-formuniv-11-02-00045.pdf__ __

Ramírez, S. (2017). *El aprendizaje colaborativo y su influencia en el logro del aprendizaje en el Curso de Contabilidad de Instituciones Financieras de una Universidad Pública de la Región Huánuco [Collaborative learning and its influence on learning achievement in the Financial Institutions Accounting Course at a Public University in the Huánuco Region].* [Tesis de Maestría, Universidad Peruana Cayetano Heredia] [Master's tesis, Cayetano Heredia Peruvian University]. Institutional Repository. http://repositorio.upch.edu.pe/bitstream/handle/upch/1450/Aprendizaje_RamirezRengifo_Segundo.pdf?sequence=1&isAllowed=y

Rivadeneira, E., & Silva, R. (2017). Aprendizaje Basado en la Investigación en el Trabajo Autónomo y en Equipo [Research-based Learning in Self-Employment and Teamwork]. *Scientific Electronic Journal of Management Sciences, 13 *(38), 5-16. https://www.redalyc.org/pdf/782/78253678001.pdf

Rivero, C., & Suárez C. (2017). Mobile Learning y el Aprendizaje de las Matemáticas: el caso del Proyecto Mati-Tec1 en el Perú [Mobile Learning and the Learning of Mathematics: the case of the Mati-Tec1 Project in Peru]. *Revista Tendencias Pedagógicas [Pedagogic Trends Magazine], 30*(2), 37-52. https://dialnet.unirioja.es/descarga/articulo/6164820.pdf

Sánchez, C., Sánchez, T., & Macías, J. (2018). Flipped classroom como estrategia metodológica para mejorar la competencia en trabajo grupal en didáctica de la matemática [Flipped classroom as a methodological strategy to improve competence in group work in didactics of mathematics]. *Revista Matemáticas, Educación y Sociedad [Mathematics, Education and Society Magazine]*, *1*(3), 31-43. http://mesjournal.es/ojs/index.php/mes/article/download/18/23/

Torres C. (2018). *Estrategias de gestión del docente en el aula para mejorar el aprendizaje colaborativo de los estudiantes del V ciclo de educación de la especialidad de primaria de la universidad nacional “Pedro Ruiz Gallo”, Lambayeque, 2018 [Teacher management strategies in the classroom to improve collaborative learning of students in the 5th cycle of education of the primary specialty of the national university "Pedro Ruiz Gallo", Lambayeque, 2018]*. [Tesis de Maestría, Universidad Nacional Pedro Ruiz Gallo] [Master's Thesis, Pedro Ruiz Gallo National University]. Institutional Repository. http://repositorio.unprg.edu.pe/bitstream/handle/UNPRG/7276/BC- 2103%20TORRES%20VIDARTE.pdf?sequence=1&isAllowed=y

Yong, E., Cedeño, E., Tubay, M., & Cedeño, L. (2018). Trabajo colaborativo y el aprendizaje de las matemáticas en los alumnos de Economía de la UTEQ [Collaborative work and the learning of mathematics in the students of Economics of the UTEQ]. *Revista Ciencia e Investigación [Science and Research Magazine], 3*(10), 10-15. https://revistas.utb.edu.ec/index.php/sr/article/download/271/350/

Zabala, S., Ardila, D., García, L., & Benito, B. (2020). Aprendizaje Basado en Juegos (GBL) aplicado a la enseñanza de la matemática en Educación Superior [Game Based Learning (GBL) applied to mathematics teaching in Higher Education]. Una revisión sistemática de literatura [A systematic review of literatura]. *Revista Formación universitaria [University Education Magazine]*, *13*(1), 13-26. https://scielo.conicyt.cl/pdf/formuniv/v13n1/0718-5006-formuniv-13-01-13.pdf