Why have we humans been so successful as a species. We are not strong like tiger, big like elephants, protectively coloured like lizards, or swift like gazelles. We are intelligent, but an intelligent human alone in the forest would not survive for long. What has really made us such successful animals is our ability to apply our intelligence to cooperating with others to accomplish group goals (Schmuck 1985)
Groupwork is an effective technique for achieving certain kinds of intellectual and social learning goals. It is a superior technique for conceptual learning, for creative problem solving, and for increasing oral language proficiency. Socially, it will improve intergroup relations by increasing trust and friendliness. It will teach students skills for working in groups that can be transferred to many student and adult work situations. Groupwork is also a strategy for solving two common classroom problems: keeping students involved with their work, and managing instruction for students with a wide range of academic skills (Cohen, Elizabeth G. 1994)
Theoretical approaches to group work
When discussing the theoretical approaches that underpin the use of group work in the classroom, I will attribute the majority of my focus to the history and development of the constructivist approach. Constructivism describes a learner-centered environment where knowledge and the making of knowledge is interactive, inductive, and collaborative, where multiple perspectives are represented, and where questions are valued (Brooks&Brooks,1993).
Let me introduce the background and theory of social learning theory. Constructivist teaching is based on the belief that learning occurs when the learner constructs his or her own knowledge and understanding. Learning is an active process that means that the learner must actively participate in the process. Learning does not occur when the learner passively receives information. Learners are the makers of meaning and knowledge, not simply the receivers (Nahalka, 2003). Constructivism recognises that as teachers, it is important to provide pupils with a personal and challenging experience and to ensure that collaboration between a partnership or a group arises. This interaction is instrumental in allowing pupils to desert individual ideas and concepts, or modifies their ideas in the light of the new experience. In this sense the teacher is of central importance and is seen to facilitate numerous roles within the mathematics classroom environment such as the enabler, catalyst and challenger (Ollerenshaw and Ritchie, 1995).
'The teacher's role is not merely to convey to students information about mathematics. One of the teacher's primary responsibilities is to facilitate profound cognitive restructuring and conceptual reorganizations.' (Cobb, 1988: 89)
The most outspoken pioneer of a constructivist approach to teaching has been Ernst von Glasersfeld, whose 'radical constructivism' still is at the center of the debate. Elaborating on the works of Jean Piaget that knowledge is purely subjective, von Glasersfeld has particularly focused on individual self-regulation and the building of conceptual structures through reflection and abstraction. According to von Glasersfeld, authentic learning depends on seeing a problem as 'one's own problem', as an obstacle that obstructs one's progress toward a goal (Von Glasersfeld's, 1989)
'Constructivism is a theory of knowledge with roots in philosophy, psychology cybernetics. It asserts two main principles whose application has far reaching consequences for the study of cognitive development and learning, as well as for the practice of teaching, psychotherapy and interpersonal management in general. The two principles are: knowledge is not passively received but actively built up by the cognising subject; the function of cognition is adaptive and serves the organisation of the experimental world, not the discovery of ontological reality.'
(von Glasersfeld, 1989 quoted from Jaworski, 1994: 15-16)
He argues that knowledge is not passively received but actively built up by the cognizing subject and that people develop their individual view of the world alone.
On the other side of the spectrum far removed from this individualistic approach would be the theory of social constructivism. This emphasizes the role of culture and context in developing personal and shared interpretations and understanding of reality. This was famously adopted by Lev Vygotsky in the early twentieth century. He observed that;
"Every function in the child's cultural development appears twice: first, on the social level, and later, on the individual level; first, between people (interpsychological) and then inside the child (intrapsychological). This applies equally to voluntary attention, to logical memory, and to the formation of concepts. All the higher functions originate as actual relationships between individuals." (Vygotsky, 1978: pg 57)
Thus according to Vygotsky, social interaction is a fundamental aspect of successful cognitive and intellectual growth. A concept is first presented to a child socially, either by a parent, peer or teacher, later to appear inside the child through the process of internalisation.( ) He places great emphasis on dialogue and other interaction between the learners. One of the key elements of Vygotsky's work was the development of the concept of a zone of proximal development (ZPD). Vygotsky defined this zone as
'the distance between the actual development level as determined by independent problem solving and the level of potential development as determined through problem solving under adult guidance with peer collaboration with more capable peers' (Vygotsky, 1978 : p.86). In other words, a student is able to perform certain tasks better under adult guidance or with peer collaboration. Further work on socio-learning was carried out by Bruner throughout the 20th century. His major theme is that learning is an active process in which learners construct new ideas based upon their current and pre-existing knowledge. According to Bruner (1966) learning does not take place in isolation; it is not a spontaneous act. Learning needs stimulus, context and structure. Bandura stresses the importance of the social nature of learning. He points out that human lives are not lived in isolation (Royer, 2004).
With two clear conflicting ideologies between an individualistic (subjective) and a socio cultural (inter subjective) approach, it beckons the question which theory you adopt. The focus on the answer to such a question has led to the structuring and enhancement of the field. Jaworski (1994) indicates that in today's modern society there tends to be a movement from a radical to a social view and draws comparison with the move from a Piagetian to a Vygotskian view of learning (Jaworski, 1994: 25).
Although Cobb made an influential case for coordinating socio cultural and cognitive constructivist perspectives, proposing
"that the adoption of one perspective or another should be justified in terms of its potential to address issues whose resolution might contribute to the improvement of students' education" (Cobb, 1994, p.18).
In conclusion a teacher should make a decision on what approach to adopt, based on how it would best fit their students.
Teaching within a group
David and Roger Johnson (1975) identified many of the conditions necessary for successful group work. They defined cooperative learning as an "instructional arrangement" than allows two to six students the opportunity to work together on a shared task in order to construct their knowledge. They mentioned five principles for making the arrangement successful- positive interdependence, face-to-face interaction, individual and group accountability, interpersonal and small-group skills and group processing. Courtas (2007) suggests that constructive talk is the most essential ingredients of a good lesson. Teachers know that talk is vital to engage the students in their learning and talk can transform relationships in the classroom. It is not easy for the teacher to organise a lesson that is based on constructive talking. Not only cognitive impact of talk on learning that is important.
"The psychological and social impact of talk can have a particularly dramatic impact on pupil motivation, particularly in challenging classrooms, because talk boots children's self-esteem and helps to establish relationships based on respect. It is structured effectively, talk can help the teacher relax and bring the fun and pleasure back into any classroom."
(V. Courtas (2007) Constructive Talk in Challenging Classrooms, Routledge p66.)
The idea is that if students talk and start from what they already know about a subject, they feel more involved and less anxious. If a teacher can provide a wide variety of well-organized talk, with the emphasis on group achievement, allows pupils to show the teacher what they know (A.Pritchard,J.Woollard2010).
As mentioned above, in the constructivist classroom, students work primarily in groups. When it works well group work is the most organic form of learning (M. Neamen, M. Strong 2001).Group work allows for children to learn from each other, question each other.
"Small group learning can have an enormous impact on pupil self-confidence as the pupils realise that both their own experience and their existing knowledge are valuable in assimilating new ideas. Group work thus changes and improves relationships in the classroom and helps pupils to understand that learning is a collaborative process." (V. Courtas (2007) Constructive Talk in Challenging Classrooms p.54)
Cooperative learning, which is a teaching approach with small mixed groups, is composed of methods and techniques depending upon the group success and the awarding of this success. It has many definitions. In the article "Education consumer Guide", Cooperative learning is a successful teaching strategy in which small teams, each with students of different levels of ability, use a variety of learning activities to improve their understanding of a subject. Each member of a team is responsible not only for learning what is taught but also for helping teammates learn, thus creating an atmosphere of achievement. Students work through the assignment until all group members successfully understand and complete it. According to Slavin ( 1988) cooperative learning covers learning methods in which students work in small groups ( generally 4-6 students) and group success is awarded in different ways. However, according to (Christison, 1990) cooperative learning is a classroom learning approach which is used to increase motivation and retention, to help students to develop positive thoughts about themselves and their friends , to develop students ability to solve problems and think critically and to help the student on cooperative skills.
The main aim of cooperative learning is to increase both their own and their friends learning to the top level and not to encourage competition. Competition fosters a win-lose situation where superior students reap all rewards and recognition while low-achieving students reap none. In contrast everyone benefits from a cooperative learning environment. "Students help each other and in doing so build a supportive community which raises the performance level of each member" (Kagan 1986). "This in turn leads to higher self esteem in all students (Webb 1982)". Each member of the group should help all the other members to learn. (Reeve, 1996) believes there are Psychosocial Benefits to be gain when students work together. According to him we must consider the increased comfort and enjoyment that students have when pleasurable social interaction is incorporated into their learning experience. In order to carry out cooperative learning successfully, the group must have a purpose, and all the students in the group should undertake responsibility to achieve the aim of the group. In this approach, students should combine their own efforts with those of their friends in the group because the essence of this approach is "either we swim together or we sink together". No matter what his/her success level is, every student should believe that he does what he can to contribute to the success of the group. Every group member should be aware of the concept of commitment of aim and commitment of success. "In this method, the group members should be in face to face interaction. This interaction is obtain by helping each other, giving feedback, relying on each other, discussing and encouraging each other" ( Johnson and
Johnson, 1989). For communication and social skills, students should be taught the required small group skills and interpersonal skills. Such as leadership, decision making, trustworthiness, communicating and resolving conflict skills. If these skills are not present in the student, cooperative study cannot be achieved. Also, no matter what level the students' ability and competence levels are, their contributions to the group should be appreciated. Students should be given the opportunity to show themselves at the subject they are good at. Slavin(1992) emphasizes that "Students will learn from one another because in their discussions of the content, cognitive conflicts will arise, inadequate reasoning will be exposed, disequilibrium will occur, and higher quality understandings will emerge". To conclude
"When students participate in engaging learning activities in well-designed, supportive cooperative groups, their affective filters are not blocking the flow of information. When you plan your group so that each member's strengths have authentic importance to the ultimate success of the group's activity, you have created a situation where individual learning styles, skills, and talents are valued, and students shine in their own way and learn from each other in the areas where they are not an expert. They call on each other's guidance to solve compelling problems and develop their interpersonal skills by communicating their ideas to partners". (Toga & Thompson, 2003)
How should a group be grouped
Gender, Group Composition, and Mathematics
'The benefits to learning of working in groups have been known for some time' (Edwards & Jones,2003: 135), with numerous educators (e.g. Koehler, 1990; Lou et al., 1996) acknowledging that attainment within mathematics may be influenced by the classroom organisation. Lou et al. (1996)reveals that the variety of students within the classroom 'means that teachers face difficultpedagogical decisions if students are to learn effectively and enjoyably' (Lou et al., 1996: 423).Peterson (1988) conducted a study into the development of higher-order mathematics, andrecommended 'teaching approaches which analyse children's thinking and place greater emphasis on problem-solving and more active learning, including work in small cooperative peer groups' (Jaworski, 1994: 9).In addition, Peterson (1988) emphasised classroom processes such as:a)a focus on meaning and understanding mathematics and on the learning task;b)encouragement of student autonomy, independence, self-direction and persistence inlearning; andc)teaching of higher-order cognitive processes and strategies.(Peterson, 1988 quoted from Jaworski, 1994: 9)Wilkinson and Fung (2002) examined 'the extent to which the grouping of students within classes affects their learning processes and outcomes' (Wilkinson & Fung, 2002: 426), and presents the argument that 'learning is socially constructed during interaction and activity with others, so there is interdependence of social and individual processes in the co-construction of knowledge' (Wilkinson & Fung, 2002: 426).
Group Size
Wilkinson and Fung (2002) reveal that few studies have 'examined systematically the relationship between group size and learning outcomes' (Wilkinson & Fung, 2002: 436), however, although individual study findings appear varied, there appears to be a negative correlation between group size and learning outcomes. Levine and Moreland (1990) concluded that: 'as a group grows larger, it also changes in other ways, generally for the worse. People who belong to larger groups are less satisfied, participate less often, and are less likely to cooperate with one another.' (Levine & Moreland, 1990: 593)
Vygotsky placed great emphasise on social interaction and communication being perquisites for learning, with the 'developmental process deeply rooted in the links between individual and socialhistory' (Vygotsky, 1978: 30). Therefore, this relationship between group size and learningoutcomes seems to be of central importance in relation to the implementation of socialconstructivism as a theory about knowledge and learning within the mathematics classroom. Numerous educators (Barnes & Todd, 1977; Kagan, 1988; Cohen, 1994; Lou et al., 1996; Wilkinson& Fung, 2002) report the optimal size group for learning and achievement consists of four members, however, Wilkinson et al. (2002) acknowledge that 'evidence on students' interaction and learning in groups of different sizes is equivocal' (Wilkinson & Fung, 2002: 437). Lou et al. (1996) reports that 'pairs achieved significantly more than students in ungrouped classes' (Lou et al., 1996: 448), as interaction was a perquisite for learning (Wilkinson & Fung, 2002), however, the limitation of pairs is that 'if the task is a challenging one requiring academic and other creative abilities, there is a strong chance that some pairs will not have adequate resources to complete the task' (Cohen, 1994: 73).Cohen (1994), and Wilkinson et al. (2002) reveal that groups consisting of three members often results in two members forming a 'coalition' and subsequently ignoring questions, concepts, and ideas proposed by the third member. Barnes and Todd (1977), and Cohen (1994) report that groups consisting of five members results in members remaining silent, rather than participating. Finally, Lou et al. (1996) argues that groups of six to ten members 'did not learn significantly more than students from ungrouped classes' (Lou et al., 1996: 448), thus negating the theoretically purposed benefits of social constructivism. Lou et al. (1996) meta-analysis concludes that: 'there are small but positive effects of placing students in groups within the classroom for learning. On average students placed in small groups achieved more, held more positive attitudes, and reported higher general self-concept than students in non grouped classes.' (Lou et al., 1996: 446)At this point, the assignment will progress and investigate the hypothesis that the difference in learning styles of boys and girls influences mathematics learning and achievement in groups of different gender composition; that the intra psychological difference between males and femalesinfluences the interpsychological construction of knowledge and cognitive development inmathematics, as defined by Vygotsky (1978).
Why use cooperative learning?
When examining the research comparing students learning cooperatively, competitively, and individualistically,
the results from the interaction patterns indicates that students learn more effectively when they work cooperatively. The data suggest that Students achieve more in cooperative interaction than in competitive or individualistic interaction. With several colleagues, research studies compared cooperation, competition and individualistic learning (122 studies from 1924 to 1980). The results indicated that cooperation seems to be much more powerful in producing achievement than the other interaction patterns. The study indicates also that students are more positive about school, subject areas, and teachers or professors when they are structured to work cooperatively. Students are also more positive about each other when they learn cooperatively than when they learn alone, competitively, or individualistically regardless of differences in ability. Another benefit of this strategy are that Students are more effective interpersonally as a result of working cooperatively than when they work alone, competitively or individualistically. Students with cooperative experiences are more able to take the perspective of others, are more positive about taking part in controversy, have better developed interaction skills, and have a more positive expectation about working with others than students from competitive or individualistic settings.
According to Johnsons and Johnsons, he made a great and matchless contribution in the field of cooperative learning. "Cooperative learning is doubtlessly a great way of learning. It is a great field of research and study as well". Cooperative learning encourages students
to work in groups and teams. The core aim of this group or team is to achieve a specific task. Groups are created at beginning of the semester, for some specific semester activity, or for any other collaborative purpose. The teacher needs to make sure that students benefit from face-to-face interaction. The teacher must monitor each group. Monitoring means to check continuously. "Monitoring has four stages: preparing for observing the learning groups, observing to assess the quality of cooperative efforts in the learning groups, intervening when necessary, and having students assess the quality of their own individual participation in the learning groups to encourage self-monitoring" (Johnson, Johnson & Holubec, 1998).
