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Utilising collaborative learning methodology in the mathematics classroom: An autoethnography

Naif Mastoor Alsulami
King Abdulaziz University, Saudi Arabia
and
Science and Mathematics Education Centre
Curtin University of Technology
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While I was trying to encourage my students (mathematics pre-service teachers) to use collaborative learning methodology (CLM) as an approach in their teaching I found that many were not interested in using this innovative approach. So, the key purpose of my research was to investigate obstacles that I had encountered when using CLM in my teaching. I made use of autoethnography as a research methodology, with 'narrative inquiry method', to carefully describe events and dilemmas that occurred in my teaching while I was using CLM. In using this research methodology my aim was to understand participants' lived experiences and to communicate educatively with my reader about what I learned for my professional practice. My narratives are intended to demonstrate the truthfulness of my study by providing satisfactory details of my experience, rather than to generalise what I have learned. In this way I am writing to enable you to decide whether what I have learned can help you meet your own goals for using CLM. To make sense of my study, you need to use your own personal beliefs to check the degree of similarity between my experience and your own.


Background

When I was studying as a mathematics pre-service teacher at a college in Jeddah (a town in Saudi Arabia), I learned various methods of teaching; one of those was cooperative learning methodology. One of my teachers was trying to implement this innovative approach but contrary to this I found there were many teachers not interested in wanting to teach by this way. I wanted to know the reason behind that, so I asked a colleague of mine about this issue. We discussed cooperative learning methodology and came to realise that this method may make a classroom very noisy and hard for a teacher to control. Using traditional teacher-centred way of teaching meant the teacher is able to keep a class quiet and in control in which students' behaviour and learning are strongly controlled by teachers.

In 2006, I was appointed to be mathematics teacher educator at Jeddah teacher's college. I was commissioned to observe pre-service teachers who were practicing in school. I found that they prefer using traditional teacher-centred way of teaching although I was encouraging them to apply different student-centred methodologies of teaching such as cooperative learning. I informed my novice teachers about the benefits of using cooperative learning and how it improves the quality of teaching and learning towards students. I explained how cooperative learning considers the appropriate way in building up a student's skills and developing those skills further. It can develop a better way a student conveys his idea or opinion towards the whole classroom. As Ballantine and Larres (2007) stated in their research, students for whom graduation is forthcoming found the cooperative learning experience valuable in terms of developing skills which will equip them for the workplace and all-time learning. However, the novice teachers were avoiding using CLM. Consequently, this issue has become bigger in my mind; most novice teachers regardless of official teachers do not use CLM in their teaching.

I learned that cooperative learning has been widely recognised as one of the most popular practices in the field of education (Holt, Chips, & Wallace, 1991). It is used widely in mathematics classrooms especially (Ding, Li, Piccolo, & Kulm, 2007). This learning has also been used in instructional procedures such as in kindergartens, high school, many subject areas and all different parts of learning and education. Cooperative learning has also been used in non traditional as well as traditional learning, after school learning and non-school educational programs (Johnson, Johnson, & Stanne, 2000). This methodology actually gives the teacher a better teaching technique, getting students to learn and understand just by using small groups and teamwork. This will allow students to get the most out of learning strategies (Kara & Venanzi, 1998).

Research questions

  1. How do I perceive the place of cooperative learning in my classroom?
  2. What are the obstacles that I encounter when I want to apply cooperative learning in my classrooms?
  3. How can I deal with the obstacles that I meet when I apply cooperative learning in my classroom?
  4. How can I persuade novice teachers to use cooperative learning?
  5. How can other teachers be encouraged to use cooperative learning in their classrooms?

Significance

The way I feel when I have my students ...
I have several students that tell me all the time ...
I wish you were my [dad] ...
I wish I could go home with you ...
[And I tell them] you know ...
When I have children ...
I want children just like you (Pennington, 2007, 98).

This methodology of teaching has many potential advantages. It contributes to creating an effective classroom learning environment of enthusiastic learners. In particular, it helps to create friendly educative relationships between teachers and their students. This is likely to lead to learners feeling free to ask questions and to participate more fully in class activities. Ideally, when the relationship is excellent learners will love their teachers and consequently love the subject taught by those teachers. Moreover, this study will -hoping - encourage me, my colleagues and other teachers to appreciate the educational value of Cooperative Learning Methodology, with a view to transforming classroom environments from teacher-centred to student-centred.

The research methodology
Autoethnography is an autobiographical genre of writing and research that displays multiple layers of consciousness connecting the personal to the cultural. (Ellis & Bochner, 2000, p. 739)

In this study an autoethnographic inquiry was be used to answer the study questions. By entering deeply into critical moments of my lived experience this approach enabled me to understand critically and imaginatively my experience as a teacher educator. I used narrative as a key genre for representing my autoethnographic inquiry. Autoethnography has been used recently for qualitative inquiry (Reed-Danahay, as cited in Pennington, 2007), in particular for writing stories that connect the autobiographical and personal to the cultural and social (Ellis, as cited in Bailey, 2008). Autoethnography provides a way of doing something meaningful for myself and the world, especially in the context of my professional work as a teacher educator. Autoethnographic texts appear in a variety of forms - short stories, poetry, fiction, novels, photographic essays, personal essays, journals, fragmented and layered writing, and social science prose (Ellis & Bochner, 2000, p. 739).

Ontology and epistemology

This study was referenced by two paradigms, interpretivism and postmodernism. Interpretivist paradigm embraces many social perspectives. Because the social world is created by the interactions of individuals, interpretivism does not view a society as a fixed structure. There are many different stories of events. Teachers, students and others have different views to interpret events. The researcher in this paradigm seeks to understand the meaning behind these events (Burton & Bartlett, 2005).

In these paradigms, there is no one right beginning or ending. There is no one conclusion that I have to arrive at. My conclusion may be another beginning. Through that, I demonstrated how my classroom seems with CLM. And showing how my students work with this methodology of teaching. Also, I endeavoured to understand the extent of obstacles that impede me from using CLM and how I dealt with them.

My ontological position in this inquiry is that reality is multiple. There is no one objective reality. The "reality" in this study is that there is multiple perceiving of using CLM in the classroom. And the multiple realities relate to the teachers' perceptions of their experiences when they are applying CLM. Teachers seemed to find teaching by CLM more difficult than teaching by teacher-centred way. The knowledge is personal, subjective and unique. I was always concerned to be a good teacher and learners could enjoy in mathematics class by using different approaches of teaching rather than standing in the front of the class, talking a lot and writing many notes on the board for learners to copy. Move the class from boring class to effective one, move the subject from crisp subject to enjoyable one.

The research method

I used personal experience methods and storytelling as 'mixed methods' in this study. I used narrative inquiry to investigate key aspects of my experience in daily life in my classroom. In reflexive experiences, the researcher's personal experience becomes important primarily in how it reflects the life of an individual. Reflexive autoethnography starts with the experience of the researcher and includes confessional tales wherein the researcher's experience of conducting the study becomes a major focus of the investigation (Ellis & Bochner, 2000). 'Stories that create the effect of reality, showing characters embedded in the complexities of lived moments of struggle, resisting the intrusions of chaos, disconnection, fragmentation, marginalisation, and incoherence, trying to preserve or restore the continuity and coherence of life's unity in the face of unexpected blows of fate that call one's meanings and values into question' (Ellis & Bochner, 2000, p. 744).

Theoretical referent

In this study I considered constructivism as the main theoretical referent, as described in the following section.

Constructivism

We construct our understanding through our experiences, and the character of our experience is influenced profoundly by our cognitive lenses (Confrey, 1990, p. 108).

Cooperative learning has a major role in constructive cognitive development (Piaget, as cited in Kumar, 1996). "Constructivist learning theory predicts that knowledge encoded from data by learners themselves will be more flexible, transferable, and useful than knowledge encoded for them by experts and transmitted to them by an instructor" (Cobb, 1999, p.15). The major theme of constructivism is that "learning involves a sequence of mental operations that result in constructions of meaning for experiences, and the subsequent storage of those meanings" (White, 1998, p. 61). All operations as White mentioned are depending on what the learners already know and their previous knowledge. Hence, students learn by actively making their own meanings rather than by passively receiving information.

Cooperative learning methods can give students a chance to present and discuss together their previous knowledge Thereby, new learning happens when students make connections between what they previously thought and new knowledge. Then, when students see the connections between their previous knowledge and new knowledge, the new knowledge will become more meaningful to them (Learning and Teaching Unit, 2004). Thus, different meanings from the same information may be constructed by different learners (White, 1998).

One's picture of the world is not static; our conceptions can and do change (Confrey, 1990, p. 108).
Consequently, it is extraordinarily important to know that students have knowledge and ideas when they come to the classroom. Within a constructivist perspective, students enter classrooms not as "blank slates" but with previous knowledge ("Learning and Teaching Unit", 2004). Similarly as mentioned by Tytler (2002b) that when students come into class, they are not empty; they bring with them their intuitive conceptions. In many cases these conceptions are useful knowledge and a teacher can use them and build on them. If a teacher does not care about what students have as their knowledge, students may reject the new idea or at least will not throw out their previous ideas. They will keep it in their mind to use it in some other cases.

There is evidence to suggest that students do not abandon their intuitive conceptions once they learn to operate with a new conception, but carry them alongside, to be used in situations where the new conception has not yet learnt to be used. Thus, as teachers we should recognise the richness and variability students' ideas, and find ways to challenge and to make use of them (Tytler, 2002b).

When we as teachers recognise students' previous experience and knowledge, it can assist us to develop expectations of our students' learning. It can also assist us to identify whether resources of additional learning are needed for some students. Besides that, when we recognise and build on their prior knowledge and experience of the students, we actually send a message that we have taken time to understand where the students are coming from. This has clear implications for the motivation and morale of students. Moreover, when we also encourage students to examine themselves and what they already know, we help them to become more active learners and this could be by implementing cooperative learning as is mentioned before (Learning and Teaching Unit, 2004).

"Constructivist teaching approaches have mostly emphasised the importance of monitoring students' views, to bring them into the open for discussion and evaluation in the light of evidence" (Tytler, 2002a, p. 30). Cooperative learning plays a major role to applying these approaches and students can discuss freely and show their own intuitive concepts amongst their groups in the classroom.

New vision of teaching mathematics

Classroom photo 1

In this section, I describe extensively my own experience of using CLM. Also, I clarify the dilemmas that I came across while using CLM and how I dealt with them. This section also involves the participants' experiences who used CLM in their professional practice. All these and writing this section narratively and asking some critical questions and supporting my experience with some quotes from literature review are in attempting to stimulate mathematics teachers to employ CLM in their teaching.

July 2004

In primary school in my city "Jeddah" and after I took my time table from the manager and while I am walking toward my classroom and before entering the class ... There are some reflections ... Ideas ... Thoughts ... Questions come to my mind.

How are students looking to mathematics teachers? ... Do they like mathematics class? ... How are their experiences with mathematics teachers and mathematics class? ... There are many questions coming to my mind ... I arrive to the class ... My heart is beating strongly ... This is the first time for me to be a teacher ... I take deep and long breath ... I knock the door ... I enter the classroom.

Naif:Salam[1] students (who are in grade five).
Students:Salam teacher.
Naif:How are you doing?
Students: Quite good.
Naif:Do you know the subject that I am gonna teach you?
Students:No teacher.
Naif:Ok. Have a guess.
Students:Sport ... art ... religion ... geography ...
Naif:Oh no, no one says mathematics. Ok ... Fine ... I hope you enjoy this subject ... I am gonna teach you mathematics ...

The class becomes hushed.

One day ... I ask myself why my students are not active in my class ... Why they are not happy ... I think there is a problem ... There is something wrong. Finally, I decide to use different methods of teaching that I have learnt in teacher's college. Cooperative learning methodology (CLM) is one of them ... Why do I not try it? ... Why do I not shift the way of teaching? ... Especially since there is evidence suggesting that using cooperative learning can make the classroom and students work and think more effectively, and for students to be generally interdependent because it prepares students for more and more interaction in the classroom (Holt et al., 1991) ... So, let me try ...

Next day...

I enter the classroom ... I divide the class into seven groups ... Each group consists of five students. The number of groups is quite big but it is ok. I start ... after a few minutes ... The class is noisy and the students are very active ... They are talking a lot and loudly ... I try to keep them quiet but unfortunately I fail to do that ... The students are so enthusiastic ... they are thirty five students. This is the first time they sit together and they are free to talk and discuss. As a result, students forgot that they are in the class ... The time is up. I struggle to manage the class in terms of the time and control. I do not finish what I have planned to do. It is a hard class.

I go back to my home ... I sit down on a sofa that is in my room ... I ask myself what happened with me. Is it a bad way to teach? ... There were many obstacles ... I think I will not do it again ... forget it ... at that time I heard sound inside my heart call me ... no... no ... please Naif do not think like that ... do not be pessimistic ... think about your students ... your students were so happy ... they found that mathematics class was very interesting ... you have achieved what you want in changing students' ideas about mathematics such as it is a dry subject ... you made comfortable classroom and suitable environment for students to study ... do not drop that down ... please continue ...it is normal to encounter some dilemmas but do not make them reduce your insistence of changing ... a good teacher who attempts to deal and overcome on the dilemmas not who gives up ... no surrender ... students were joyful and very active ... some said we want that again ... yeah that was right ... let me try again ... but before that, I will see what is wrong and obstacles to deal with them ... first, the noise ... second, miscontrol the class ... third, time management ... these were the major obstacles ...

Next week...

Today I have learnt from the mistakes which occurred in my first experience with CLM. After explaining to my students what is going to happen ... I divide my students into groups of five... You should know that dividing students into groups usually means that I act a bit like a social director at a vacation resort or summer camp (Bruffee, 1993).

I wade in to help them rearrange their chairs ... I separate groups to minimise noise from other conversations ... I encourage group members to draw close enough together (knee to knee and eye to eye) to hear one another over the din and to make the group more likely to cohere ... I ask them to introduce themselves and decide on a recorder (a member of the group who is gonna take notes on the group's discussion and report on the consensus the group has reached when the work is over) and a reader and so on ... I give the students a sheet with a task and instructions on it ... I ask each group at some point ... How much more time do you think you will need ... And while students are at work, I am keeping time and conserve it ...

The length of time that students spend on a task depends on the complexity of the task and on how accustomed students are to working together (Bruffee, 1993).

Abruptly...

The door is knocked on ... I open the door ... Hi deputy manager ...

Deputy Manager:Naif, what do you do? What is going on in the class? Why are students in this situation? ... Students are in groups.
Naif:I use collaborative learning method as a new way of my teaching.
Deputy Manager:Collaborative learning way??!! Teach the students the subject ... Do not waste your time.
Naif:(angry voice) what do you say? I do not waste my time. I teach my students by using different way. I just want to change and transform the way of my teaching ... I want my students to enjoy while they are learning mathematics ... I do not want my students feel that mathematics is a dry subject and mathematics class is a boring class ... I do not want my students to learn mathematics as I have learnt ... I want to change ... I want to transform my teaching method. Sorry, I have class now and my students are waiting for me ... If you want, I will talk to you after this class.
Deputy Manager:(surprised) Ok ... Ok ... Please come to my office ...

Classroom photo 2

I come back to my class ... I continue with my students ... I talk to this group ... I ask that group ... I encourage this group ... And when most groups have completed the task, I ask the recorder in each group to report to the class as a whole and write out the results on the blackboard ... I referee the plenary discussion in which the class as a whole analyses, compares and synthesises the groups' decisions, negotiating toward an acceptable consensus. I compare the class's consensus with the current consensus in the knowledge that I represent.

The time is up ... The class finishes ... Salam students ... Salam Teacher.

To the office...

I am walking to the office of deputy manager ... I arrive at the office ... I knock on the door ... I enter the office ...
Deputy Manager:Hi Naif, welcome ... Please takes a seat.
Naif:Thank you ... I sit down on a chair in front of him.
Deputy Manager:Naif, Let me ask you about what you have done in your class. What is that?
Naif:I used a different way of teaching which is called CLM. It is a situation in which two or more students learn or attempt to learn something together (Dillenbourg, 1999). Students work together to achieve a goal.
Deputy Manager:But you must teach students the subject. Students do not know the new topics. How can they learn?
Naif: What do you mean by saying "teach students"? If you think that I need to give them the knowledge, I think we have different perspectives. Knowledge is not something that I can give to my students. It is something that they construct in their mind. And when you said "students do not know the new topics", you are right but they can build on what they have of knowledge to make sense of the new topics. I do not think that they come to the class with empty mind.
The interacting with others stimulates the construction of knowledge through the negotiation of different opinions, meanings and knowledge (Munneke & Andriessen, 2000, p. 2).
Deputy Manager:Yeah, you are right, but I think you need to tell them the information which is in the curriculum.
Naif:Ok. This is another issue in which we have, as I think, different perspectives of seeing the curriculum.
Deputy Manager:Really?! How do you see the curriculum?
Changing what teachers do implies changing what they think knowledge is. (Bruffee, 1993, p. 98)
Naif:In the previous lessons, I was dealing with curriculum as an "object". I see the curriculum just as content. I give and transmit the knowledge to my students while they just receive the facts. In this technical interest, I am just controller of the class in which I control the students' behaviour.
Also, when I determine to do some activities in my class, I do not give my students the opportunity to apply these activities in their own ways. I decide the way of implementation. Unfortunately, by this view I reduce my students' skills and also I disempowered their thinking. This technical interest does not mean anything to me. It is much like traditional ways of teaching in which the knowledge transmits from the teacher's head to students' and the curriculum must be taught and tested. There is no communication between me and my students. I send the fact and they receive it. There is no room for reflection. They should accept it and memorise it.

But in the lesson which you came to me, I see the curriculum as a "subject" not as an "object". There are interactions between me - as teacher - and my students. I am not giving them the knowledge only, but I aim to achieve understanding and sense-making. My students gain access to the facts by the understanding of meaning. I also connect and communicate with my students in sense-making activities. We share our ideas, thoughts and feelings. I am interested in developing my students' thinking skills and their skills in judgment-making. So, I am interpreter not controller.

Deputy Manager:Your ideas are very nice. Naif, how is your impression?
Naif:If you are in the classroom right now, you will see the answer all around you. As students, in mathematics classroom with CLM, they can find it easy to talk to their colleagues ... to ask ... to participate ... to join in activities.

As I teacher, after I applied this method I found a lot of things. Student became happy in the class. They interacted effectively. They became like the class even some of them still suffered from the subject. They became love me, indeed. You should know that when the relationship between students and their teacher is excellent, they will love their teacher and consequently love the subject. And there are teachers who really look to their students as their children. Improving the relationship could be achieved by using CLM. By the way, I remembered a story. Can I share it with you?

Deputy Manager:Yes, please.
Naif:At the last year of my study at teachers' college, we as pre-service teachers have to visit some schools to see how official teachers teach. One of my cousins is the manager of a school and he is always talking with me about a particular mathematics teacher. He always commends and praises him. This teacher, in spite of his age, is very active. He could build mathematics laboratory in his school campus. He designed the building to be appropriate for teachers who use CLM. I saw this building; it is really a great effort. This building contains many tools that mathematics teachers need to use to simplify mathematics concepts to students. The main thing in this building is that students sit as groups. All tables are designed in a circle shape. I met this teacher and I discussed with him some issues about mathematics. And when we talked about the relationship between a teacher and students, he asked me this question: How do you feel when one student comes to you and says to you: you are the best teacher. Then he commented: I found this greatly encourages me and gives me as much pleasure as awards from the Minister. The Minister does not know me; he just signs the certificate due to someone who recommends him to give me a certificate. No balance between these.
Deputy Manager:You have a very good perspective and I will encourage you to accomplish your ideas. Naif, can you tell me your targets?
Naif:I would like to promote mathematics subject from pure subject to im/pure[2] subject at least if I cannot promote it to impure subject. Also, I feel like to change the class from boring class to effective class. By using CLM, I think I will be able to kill the routine of the way of teaching. In addition, I want to move the technique of teaching from teacher-centred to student-centred. I agree with the ideas of Zakaria and Iksan (2007) that cooperative learning can represent a shift in educational paradigm from teacher-centred approach to a more student-centred learning in small group (p. 37). Furthermore, I want to focus on the process of teaching (how to teach), not just on the products and outcomes (what I teach). I want to involve my students in teaching. I will attempt to investigate and classify the linguistic act as constitutive of collaborative learning (Aggarwal, 2000).
Deputy Manager:Naif, you seem confident. But, this way is not easy to be implemented. It needs hard effort. Thanks Naif very much. You have changed my ideas about teaching. Good luck.
Naif: You are welcome and I also want to thank you for this chance.

At the end of the semester...

Deputy Manager:Naif, I asked the students; who is teacher that you love. They said: Mathematics teacher; Naif. I am so happy to hear that. Mathematics teachers often are dislikeable.

My experience with using CLM maybe in such way is similar to your experience. I really enjoyed using this method. However, using this method requires double effort. There were some obstacles that I came cross such as miscontrolling the class, mismanaging the time and students' noise. Teacher who would like to change his/her way of teaching needs to deal with any dilemma that he/she may meet, not to run away. Teachers should know that they might find difficulty to use CLM. However, they should know as well that many obstacles will disappear little by little. The biggest dilemma that I ran into is the noisy. However, this issue is not danger as we think. It is normal issue because students find chance to talk in which they were not allowed to speak. However, after I explain the method and apply it again and again, students understand the targets and the strategy of the method. Moreover, I did competition among the groups in which quiet group will win award. Consequently, this matter became easy one. Anyway, classroom noise is largely a matter of expectation and is partly a matter of room size and sound-absorbing materials (Bruffee, 1993).

Other issues of dilemmas (miscontrolling the class and mismanaging the class' time) are also big matter but I want to say that it just in the first experiment. These also are linked with the noise's matter in which teacher spend much time to minimise the noise and that leads him/her to lose the class's time and its management. All these issues will not exist over time. Finally, before you start implementing the method, no matter what approach to CLM or system that you use, you need to understand its strategy and how to apply. I found that many teachers do not understand its strategy. Also, you should clarify aims for cooperative learning lessons to your students because they must clearly understand the procedures and rules that will be involved in the lesson (Arends, 2004).

Students' perspective

I was a student ... You are/were a student ... We can show an image of traditional mathematics classroom ... As well the image of mathematics classroom with cooperative learning. I wrote two verses from students' perspective for the two different images of the classroom.
The image of an indigenous mathematics classroom:
I sit down on my chair,
I look to my teacher,
I look to the board,
I write the answer,
I do not know who sits in front of me ... near me ... behind me,
I do not know who are in my class,
I have no friends,
I feel alone,
So on ... So forth.

We sit down on our chairs,
We look to our teacher,
We look to the board,
We write down the answer,
We do not know who sits in front of us ... near us ... behind us,
We do not know who are in our class,
We have no friends,
We feel alone,
So on ... So forth.

I do not like that ... I do not like this class ... I do not like this subject ... I do not like the teacher. I hate mathematics.
Mathematics teachers are as boring as what they are teaching.

The image of a modern world mathematics classroom:
I help other and other helps me,
I ask other and other asks me,
I talk to other and other talks to me,
I learn from other and other learns from me,
So on ... So forth.

We assist each other,
We ask each other,
We have a word to each other,
We gain knowledge from each other,
So on ... So forth.

Each and every one aids each other,
Each and every one asks each other,
Each and every one speaks to each other,
Each and every one is taught from each other,
So on ... So forth.

Students are joyful ... Groups are joyful ... Teachers are joyful

As we can see, the difference between the two images is very clear. Students seem like the modern image of the classroom. They clarify some reasons. First, they say: each and every one aids each other(in modern classroom); they are unavoidably interdependent. The skills of interdependence are important because we need it in our real life. Students need these skills of when they go to work in the real world. I very much agree with Bruffe (1993) when he said these skills can be improved by cooperative learning. Moreover, we should know that the first element of cooperative learning is "positive interdependence" in which team members are obliged to rely on one another to achieve the goal. If any member of the group fails to do his/her part, everyone on the group will suffer consequences (Johnson, Johnson, & Smith, 1998).

Secondly, they say: each and every one speaks to each other (in modern classroom); students not only need knowledge but also communication skills, problem solving skills, creative and critical thinking skills (Zakaria & Iksan, 2007). These skills of communication and others maybe are too hard to be achieved in classrooms which do not allow students to talk (indigenous classroom).

Thirdly, they say: we do not know who sits in front of us ... near us ... behind us, we do not know who is in our class, we have no friends, we feel alone (in traditional classroom), but in cooperative learning classroom the matter is different in which students are able to know their classmates point-blank owing to interactive activities. Researchers have found that after participating in cooperative learning activities, students' attitudes towards their classmates improve significantly (Kara & Venanzi, 1998).

Fourthly, they say: each and every one asks each other (in modern classroom). So, students can have the answers of their questions straight away by their own colleagues rather than waiting for the teacher's attention. Since the average class size is about 30 students to one teacher, getting sufficient attention and response from the teacher can be both a frustrating and time consuming process for the student. But when students are actively interacting with one another, they can have more time to learn and spend less time waiting (Kara & Venanzi, 1998).

Finally, they say: each and every one is taught from each other (in a cooperative learning class). There should be no doubt that, students' language is easier than teachers'. Therefore, students can explain difficult ideas to one another by translating the teacher's language or directions into a more understandable 'kid' language (Kara, 1998).

Participants' experiences

You have seen how my experience with CLM was and my students' view. However, do other teachers who may use CLM in their teaching encounter obstacles? To answer like these questions, I asked some teachers about those questions. You need to know that there are many teachers using the method in their teaching. Each teacher has slightly different experience of others while the obstacles generally are the same. The major difficulty is miscontrolling the class. This difficulty occurs when teachers mismanage the time as a result of an attempt to reduce the noise. So, when you use this teaching method, it is important to have a few rules and routines that govern your students talk and movement, keep a lesson moving smoothly and maintain a general level of good behaviour in your classroom. The rules will allow you to deal quickly and firmly with misbehaviour of student when it occurs (Arends, 2004). Consequently, your classroom will be under control.

Now, let me show you two experiences of teaching by using CLM. Actually, I asked two mathematics teachers in my country to write their experiences with CLM but unfortunately they did not do that. I found that, as a limitation of doing this study. However, two Malaysian teachers were willing to participate with me. Osama is a chemistry teacher educator and Muna is a biology teacher educator. At this time, I think I am lucky because my study has involved different nationality and different subjects. This issue may help you again to rethink about CLM. I think it is very good to you when you realise that the obstacles that you may encounter, they come across other teachers as well in another country.

Osama said:

During my school time, I admit I never know what CLM really is. Maybe I did know cooperative in terms of value to present people who cooperate with each other to complete particular tasks. At that time, most of my teacher only use traditional way teaching which all of us familiar with; lecture style. Furthermore, there is no reason why I should know about CLM. It is all about teacher job.

I was introduced to this methodology during third semester of my undergraduate. Even though the CLM lectured not too depth, but I think I started to like the basic concept of this methodology. After I had completed my degree in education, I have the opportunity to implement what I have learned in my teaching. For your information, one of the teaching methods I often apply was CLM.

The context of my experience with CLM was a year seven (Age 16-17) at Secondary school in Malaysia. In every chemistry class for example, I allocated 15 minutes for class activity which I called it 'engagement stages'. In this stage, I divided students into 5 groups. Each group consisted about 4 to 5 members. After all the students have taken place and ready to start, I projected the task on the LCD projector. Usually the task will ask the students to discuss or to find solution for particular questions. The questions considered to have medium difficulty where needed them to communicate, calculate and present their answer on 'mahjong' paper. Do you know what mahjong paper, Naif? In my country, mahjong paper is known as large size paper which usually used to present something.

During this activity, I will let them to determine their own role in group. Maybe some of them will try to find related concepts in revision books, while other tried to extract the questions in their own word. Nevertheless, I also saw some of them also pretend to make discussion, but they actually not.

From my observation, I can conclude there are three types of students who participate in group activity. The first group was passive students who actively participate in their group but lack of communication. This kind of students usually acts as group writer. The second group is ordinary students who often take roles in discussion and problem solving. Any decision made by this group will be recorded by group writer in 'mahjong' paper. Lastly, is students who consider have good presentation skill and like to talk in front of audiences. This student often takes role as group presenter. In this activity, I prefer to consider myself a facilitator rather than as teacher. Along the activity, I will go to each group if they need my consultation. Quite often, students tried to abuse this opportunity to get the answer from me. Luckily, I not fell into their trap.

Finally, each group will present their product in the class. Each group will be given five minutes to explain what they had done in their discussion. During this time, audience able to raise any question if they think the answers were ambiguous. It then will be responded by the presenter or by any of the responsible group member. I can say it interesting situation where the class seem alive with all the debate and argument, yet, the class still in good control.

Even though this activity created positive learning experiences upon students, but there were several obstacles that I had to be aware. Firstly, the debate and argument among students often drag time away from the allocated period. This situation let them always late to enter next subject class. Secondly, I admit, I could not entertain every student. This brought me to pay less attention to passive students. Finally, sometime the product presented by the students not reach the require standard as I expected. In this case I was not sure either my instructions were the cause or only about the students not gave their best in this activity.

Muna said:

From my experience as a teacher educator who teach pre-service teachers and the subject was teaching strategies (the unit that introduce the pre-service secondary science teacher with various teaching strategies). I found that cooperative learning is very helpful to educate the students to work together. In real life, we need to socialise with other to survive. Same condition goes to human; therefore classroom is artificial space to engage the students with this social skill.

I want to use the term symbiosis as a metaphor to represent the cooperative learning in my context. Symbiosis is long lasting relationship between livings organisms that bring benefit for all that involve in the interaction. As the students work together, the students share their ideas, thoughts, and argument mutually to bring benefit to each others. Each of the group members has his or her own role to complete the task. Therefore, the tasks that I design for each of the person in the group are different to each other, but each of the information is important to complete the major task that I had designed.

The teaching strategies that I plan for particular lesson sometimes did not go as I planned. I have to take into consideration that some of the students have problem to express their other while in a group. They do not see the benefit of sharing the ideas. Why we need to share the idea with the other??? Maybe this is what they thought.

In my opinion, if we want to apply cooperative learning, we need to put extra afford to control the class. Otherwise, our class will turn to upside down. To deal with this, I assigned each of the group members with different role. For example, in one group, one for them will be the leader to give order, speaker-to represent the group's voice if I ask a question, time-keeper to make sure the group work together according to the time frame given by me and the technician- their responsibility are to manage the materials that the I gave for the lesson. These roles are changed every time I have class with time. I found that, this strategy is prefect to manage my classroom.

I think there should be no doubt about the effectiveness of CLM. I think there are teachers who like to change teaching methods but they are afraid about the difficulties that may encounter them. At all events, do you think the change is easy? If you really want to change, you have to overcome any difficulties that may arise. This is the natural in the world. Change is not easy but we need it to improve our teaching. So, you need to overcome the obstacles to achieve your targets of change. All the difficulties and the obstacles are not as what we believe; they are easier than what we think. We just need to be familiar with the method. Osama said: most of my teachers use only the traditional way of teaching which all of us familiar with: lecture style. If he/you is/are involved in CLM while he/you was/were learning, he/you will find the method of cooperation as the lectures method. I think the lecture method is popular and we like it just because we are familiar with it. That is, it is not because it is the right method of teaching but because we are familiar with it. Osama said: Even though the CLM lectured not too depth, but I think I started to like the basic concept of this methodology. That is great and indicates that CLM is desired but we need to have experience with it.

There are some advantages that Osama found. For example, he said: I can say it interesting situation where the class seems alive with all the debate and argument. On the other hand, he encountered some difficulties as well. It is very good to see the weakness in your teaching, otherwise, how can you improve your teaching?!! The obstacles were mismanage the time, less pay attention to some students and the "product" was not the desired level. Then he said: I was not sure either my instructions were the cause or only about the students not gave their best in this activity. There are many evidence and researchers admit that CLM help students to gain higher academic achievement (Holt et al., 1991). Also, there are many findings of past studies of student achievement have found that cooperative learning can significantly increase the student achievement more than other methods such as competitive, individualised or hierarchical learning (Bruffee, 1993, Kara, 1998 and Johnson et al., 2000). I am sure the method was not the cause but maybe the students do not realise the method. It is very important to clarify the method before starting the lesson.

For Muna's experiment, she said: the tasks that I design for each of the person in the group are different to each other. This way will hamper the spirit of group work. This indicates that there are some teachers do not actually understand the method deeply. This misunderstanding of the method may lead to extra difficulties and may lose the advantages. As a result, students and teacher may not have found this method interesting. Therefore, Muna said: they do not see the benefit of sharing the ideas. Why we need to share the idea with the other??? Maybe this is what they thought. This is right, because they did not get the ideas together, each one did his/her task alone then they shared what they achieved. For that reason, as I mentioned before, you and your students have to be aware of the method before applying it. On the other hand, miscontrolling the class seemed the major obstacle bumped into Muna. However, Muna did not give up for the obstacles but she did some rules to control the class. That is what teacher should to do when applying CLM.

References and bibliography

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Endnotes

  1. Salam is the Islamic greeting.
  2. If there is pure subject, there is impure subject but what about the gap between them which I call im/pure subject.

Author: Naif Mastoor Alsulami is a mathematics teacher educator at Jeddah Teacher's College, King Abdulaziz University (KAU), Saudi Arabia. He is also a student at Science and Mathematics Education Centre (SMEC), Curtin University of Technology, Perth, Australia. Email: nsulami@hotmail.com

Please cite as: Alsulami, N. M. (2009). Utilising collaborative learning methodology in the mathematics classroom: An autoethnography. In Proceedings Western Australian Institute for Educational Research Forum 2009. http://www.waier.org.au/forums/2009/alsulami.html


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