Cooperative Learning and Attitude to Mathematics

Definition of Cooperative Learning

Cooperation means working together to achieve some goals. In such kind of cooperative learning persons try to get results which are advantageous for both they themselves and other group of members. In this learning small groups are used by giving some instructions where students work together and increase their as well as each other’s learning. On the basis of teacher’s instructions class members are arranged in small groups. The group members understand the assignmnets and then they complete it successfully (Johnson & Johnson, 2009, Para 1). All group members are benefitted from each other’s efforts which are called mutual benefit; it is the goal of cooperative learning. It is recognized here that all group members have common fate and one’s performance is mutually based upon either of one’s own actions or his colleague’s actions. They feel proud and equally celebrate when a group member is appreciated for his achievements. Cooperative learning indicates that group members’ goal achievements have positive interdependence. Students get the idea that they can achieve goals only if the other students in their groups achieve goals. A team member’s success depends on both his own efforts as well as his team members efforts who contribute in knowledge, skills and resources. It is not necessary that even a single member in the group will be having all the information, skills and resources required for any particular presentation (Johnson & Johnson, 2009, Para 1).

Cooperation signifies mainly small groups of students working together but collaboration may happen in both small and large groups (Cooperative Learning, n.d., 2009, Para 1).

Cooperation is basically working together to achieve common goals. Within cooperative activities individuals look for outcomes that are useful to all members of the group. Cooperative learning is an instructional methodology in with which students are divided in groups so as to increase their own as well as their group learning and knowledge. A sense of cooperation and positive interdependence helps the group member to achieve the desired goal (Johnson & Johnson, 2009.Para 1).

Background about Cooperative Learning

Studies have shown the advantages of cooperative learning over competition. Researches also support individualized learning in variety of learning tasks.If we compare cooperative learning efforts with competition or individualized work, they show higher group or individual achievements, more new ideas and solution to problems and high quality reasoning strategies. Also the students those who work in groups are generally highly motivated, intellectually curious, caring for others and psychologically fit. But at the same time it is not said that competition and individual works should not be encouraged. For example, competition is suitable when there can be only one winner like sports events etc and individualistic efforts are considerable in such situations where the goal is personally beneficial and does not affect others’ goals (Johnson & Johnson, 2009, Para 2).

Why Cooperative Learning should be used

Students’ learning goals should be structured to support cooperative, competitive or individualistic efforts (Johnson & Johnson, 2009, Para 2). Cooperative situations are opposite to competitive situations. In competitive situations, students work against each other to achieve goals where such goals can be accomplished by one or two students. Competitive situations have negative interdependence for achieving goals. Here students’ perception is this that they can achieve their goals if the other students in the class fail to accomplish their goals. Due to this situation students either work hard to do better than their classmates or they take it easy by believing that they cannot do better than their classmates (Johnson & Johnson, 2009, Para 2). Individualistic situation shows an individual student’s performance better than his classmates. In this situation, students work alone to achieve goals. They are analyzed on the basis of criteria. They have their independent goal achievements. The students’ perception is here that their learning goals are not related to other students. It results focusing on self interest and personal success. It ignores the success and failure of others (Johnson & Johnson, 2009, Para 2).

Researches have been made on cooperative, competitive and individualistic efforts (Johnson & Johnson, 2009, Para 3).

The first study was done in 1898 and since then approximately 600 experimental studies and about 100 correlation studies have been conducted (Johnson & Johnson, 2009, Para 3). Various studied results have three major categories: positive relationships, achievements and psychological health. Researches have shown that cooperation if compared with competitive and individualistic efforts has higher achievement and productivity. It is more supportive and caring. It has greater psychological health and self esteem.. As cooperation has lots of positive effects, it becomes the most precious learning technique (Johnson & Johnson, 2009, Para 3).

Elements of Cooperative Learning

Cooperative learning involves students’ participation in group learning. The participation of every student in the group is understood important. The students are appreciated for their individual as well as collective efforts. Merely, grouping of students does not establish cooperative learning relationship; It should be properly managed by teachers (Agashe, 2000, Para 3 & 4).

Cooperative learning includes lots of methods for organizing and conducting classroom instructions Almost any teacher can use cooperative learning according to his philosophies and practices (Agashe, 2000, Para 5). There are lots of forms or techniques for Cooperative learning. But these techniques are most effective when they have a careful use of some specific elements. The important elements of Cooperative learning are as follows which are well studied (Agashe, 2000, Para 5):

Following are some specific conditions where cooperative efforts could be more productive than competitive and individual efforts (Agashe, 2000, Para 6):

• Clearly thought positive interdependence
• Considerable face to face interaction
• Clear perception of individual accountability as well as personal responsibility to achieve the group’s goals.
• Frequent use of the relevant interpersonal and small group skills
• Regular analysis of the performance of the group for checking its future effectiveness

There are some more elements of Cooperative Learning which show that under some specific conditions cooperative efforts could be more productive than competitive and individualistic efforts. Such conditions are (Cooperative Learning, n.d., Para 4):

Positive Interdependence: it is liking sinking and swimming together (Cooperative Learning, n.d., Para 5):

• Every group member’s efforts are required for the success of the group.
• Every group member has a unique contribution in his responsibilities.

Face to Face Interaction: it is about promoting each other’s success (Cooperative Learning, n.d., Para 6):

• Explaining verbally the ways of solving problems
• Conveying one’s knowledge to other group member
• Analyzing understanding
• Discussing concepts which are learned
• Combining present and past learning

Individual and Group accountability (Cooperative Learning, n.d., Para 7):

• Try to keep the size of the group small. As smaller is the group as bigger will be the individual accountability.
• Assigning every student a test (Cooperative Learning, n.d., Para 7)
• Examining students randomly and orally so they present their groups’ work to the teacher or the whole class (Cooperative Learning, n.d., Para 7).
• Observing each group and analyzing each member’s contribution to the group’s work.
• Giving responsibility of the role of checker to one student in each group who will explain the rational basic group answers. Adaptability.
• Making students teach what they learnt from someone else.

Interpersonal and Small Group Skills: It includes some social skills which must be taught to the students(Cooperative Learning, n.d., Para 8):

• Decision-Making
• Trust-Building
• Communication
• Leadership
• Conflict management skills

Group Processing (Cooperative Learning, n.d., Para 9):

• The members of the group discuss their achievements of the goals and maintain successful working relationship.
• Describing which actions of the members are helpful and which are not.
• Deciding the behaviors what to continue and what to change.

Function of Cooperative Learning Center

The Cooperative Learning Center is a Research and Training Center, which focuses on students’ interaction with each other. Approximately 800 studies have been done to analyze the issue of student to student interaction and learning (Johnson & Johnson, 2009, Para 1).

Background: Johnson & Johnson (2009, Para 2) mention that from the past 20 years the Cooperative Learning Center has been the part of the College of Education at the University of Minnesota. The Office of Special Education, Department of Education, Department of Defense, Office of Naval Research and the National Science Foundation have funded the center (Johnson & Johnson, 2009, Para 2). The center is concentrating on making classrooms more cooperative places and the teaching of cooperative skills like communication, leadership, trust building, decision making etc. (Johnson & Johnson, 2009, Para 2).

Research and Training: The center has conducted almost 80 research studies on cooperation and learning. Throughout not only Canada and the US, the training of teachers has been conducted but also it has been done in Germany, England, New Zealand, Panama, Singapore and Hungary (Johnson & Johnson, 2009, Para 3).

Training Institutes: The center supports lots of training centers located in North America, Texas, Washington, Colorado, Florida, South Carolina and Montreal (Johnson & Johnson, 2009, Para 4).

Staff: David and Roger Johnson are the main part of this center. The other faculty includes Karl Smith who is professor of Engineering and Edythe Johnson (Johnson & Johnson, 2009, Para 5).Many teachers are trained in Cooperative Learning who have got Leadership Training and are teaching Cooperative learning in their own areas (Johnson & Johnson, 2009, Para 5).

Visitors: Lots of people from the US visit this center and stop for the information or spend many months in study (Johnson & Johnson, 2009, Para 6).

Future Directions: Recent work of the center has focused mainly on moving from cooperative classrooms to cooperative schools and systems (Johnson & Johnson, 2009, Para 7). Johnson & Johnson (2009,Para 7) mention that the main focus is on books and Active Learning that is Cooperation in the College classroom which analyzes the use of Cooperative Learning in adult settings.. Johnson & Johnson (2009, Para 7) mention that the Conflict Resolution Material in the Cooperative Skills area is being focused for dealing with violence in schools.. The Creative Controversy material is being used to focus on provoking more intellectual conflict in classrooms (Johnson & Johnson, 2009, Para 7).

The current projects of the center may assist schools in Eastern Europe to promote cooperative learning and to help the next generation (Johnson & Johnson, 2009, Para 8).

Teacher’s role in Cooperative Learning

Foyle and Lyman (1988) discuss some basic steps which are must for implementing cooperative learning activities successfully (Foyle & Lyman, 1988, Para 10):

• The teaching contents are identified and criteria for excellence are determined by the teacher.
• The most useful cooperative learning technique is recognized where the teacher determine the group size.
• Students are allocated to groups.
• The classroom is organized to make group interaction possible.
• Group processes are reviewed to make sure that the groups run smoothly (Foyle & Lyman, 1988, Para 10).
• The teacher helps in developing expectations for group learning and they make sure that students understand the purpose of the learning. The students are given a time line for all the activities (Foyle & Lyman, 1988, Para 10).
• The teacher presents appropriate material on the basis of techniques whatever he chooses (Foyle & Lyman, 1988, Para 10).

The teacher observes the activities of the students and assists and clarifies the things to the students. The teacher analyzes the group skills and makes problem solving technique possible when it is necessary.

All the results acquired by the students are evaluated. Evaluation of the students should be based on their performance or their verbal responses to the questions. There is no need to use paper and pencil.

For their successful performance the groups are given rewards. Either the teacher can praise verbally, or they can get recognition in the class news letter or the school’s bulletin board. This is for those groups who have high achieving rewards (Foyle & Lyman, 1988, Para 10):

• As Cooperative Leaning Lesson Plan Considerations: Cooperative Learning presents challenging environment and it brings major changes from teacher fronted instructions, for that reason it raises new issues which the teachers need to consider. Using Cooperative learning does not mean that teacher fronted mode should be dropped out; it basically focuses mixing many modes of learning. There are some issues mentioned below which are faced by L2 teachers when they think to adopt cooperative learning technique (Jacobs, n.d., Para 21).
• Difficulty Level: the difficulty level of any activities could be the biggest drawback in the success of cooperative learning techniques. In the beginning the activities should be easier which the students can do comfortably and confidently in the groups. So basically the process should be sequential: giving the students easy tasks, clarifying the procedures, providing examples and observing the groups so anytime the teacher can help whenever the students need it (Jacobs, n.d., Para 22).
• Sponge Activities: It generally happens that some group may finish before other groups. The teacher may be ready for this situation and be prepared with some extra activities to cover extra time. It is similar to that when a sponge can soak extra water (Jacobs, n.d., Para 23). The extra time can be used in doing homework, reading, helping other individuals or groups who have not finished prior to them, comparing answers with others who have finished and doing tasks like Question and Answers Pairs (Jacobs, n.d., Para 23).
• Groups that do not get along: Cooperative learning groups are chosen by the teacher to encourage heterogeneity. In such cases the students may be uncomfortable in their new group where they work with those group mates with whom they may not be familiar before or they know them they do not like them. So they may not get along with each other (Jacobs, n.d., Para 24). The teacher can explain the students the importance of heterogeneity, encouraging team building activities, promoting trust and also helping students get to know each other. The teacher can also teach collaborative skills (Jacobs, n.d., Para 24).
• Noise Level: Some teachers are concerned about the noise level and they worry that it is higher during cooperative learning activities. Some ideas which can be applied here to solve this problem are first try to include good noise, organizing the room in that way where students can sit close together, instructing students to monitor the sound level and use of writing instead of speaking which can also control noise level (Jacobs, n.d., Para 25).
• Use of the L2: The students generally want to apply L1 when they are working in the groups. The teachers can motivate them to use L2 and they should also explain them the appropriate constitution of L2. Here the students need language support like dictionaries, pre task examples (Jacobs, n.d., Para 26).

Following are some more points which can tell about a teacher’s role in cooperative learning (Chamberlin-Quinlisk, n.d., P.9):

• Teacher creates balance between being strict and caring.
• He clarifies expectations and develop mutual respect
• A teacher can be a role model for the students in his behavior so the students can believe.
• A teacher should be responsible for whatever he does.
• He also must realize that teaching is not an easy job.
• He must respect culture, language and families.
• The students should be given choices and their decisions should be respected.
• The teacher should focus on every student to give them same attention and care.
• The students actions should be monitored regularly and carefully.

Benefit of Cooperative learning

Cooperative learning is very advantageous at every level of academic achievements. In Cooperative Learning the teams which have low achieving students can also perform remarkably where the contribution of every student to the group is remarkable. They can experience success. All the students can develop their understanding of ideas by explaining them to other students of their group (Foyle & Lyman, 1988, Para 7).

Cooperative learning can be called the type of instructional strategies where students are kept in mixed ability groups in which students perform for common academic goal. According to researchers this kind of learning has become more advantageous as in this type of learning students’ individual differences and styles as well as multiple intelligences are studied (Ray, 2008, Para 2).

The effects of cooperative learning may be vague and it is not necessary that they can be evaluated perfectly. Still the studies have shown that cooperative learning is a better way to support academic achievements than traditional instructions (Ray, 2008, Para 3). It is found that cooperative learning is beneficial in reading comprehension and mathematics and also to increase understanding in Science. Cooperative learning has become highly popular in the education society (Ray, 2008, Para 3).

The major benefit of cooperative learning is it increases students’ motivation through their group mates support. They become the part of the learning team and can gain success by working well with others. Students learn the material deeply and become creative to convince their teacher that they have learned the material perfectly (Foyle & Lyman, 1988, Para 6).

Foyle & Lyman (1988, Para 8) discuss that the well-constructed cooperative learning tasks consist of positive interdependence on others and individual responsibility. The students should be perfect in interpersonal skills for performing successfully in a cooperative learning team. These skills are required for the group to complete its tasks (Foyle & Lyman, 1988, Para 8).

Foyle & Lyman (1988, Para 8) state that Cooperative learning is also beneficial for different ethnic background students to improve their reciprocal relationship. For older students, teaching stress upon competition and individual learning. For older students, teaching stress upon competition and individual learning. The students are given cooperative tasks and learning is evaluated individually but the rewards are given according to group’s performance (Foyle & Lyman, 1988, Para 9).Cooperative learning promotes the skills which are needed for group participation. It lay the foundation for later school success (Foyle & Lyman, 1988, Para 9).

Cooperative Groups

“Work together’, ‘Cooperate’ and ‘be a team’ are not sufficient defined directives for creating cooperative efforts among group members (Cooperative Learning, n.d., Para 4). It is not necessary that all groups are cooperative. To make students work cooperatively requires understanding of the components (Johnson & Johnson, 2009, Para 4).

When working in a group, the students are directed to stay on a task by being responsible and they are also told to contribute equally. To smoothen the progress of group work, the students are expected to (Cooperative Group Responsibilities, n.d., Para 1):

• Take turns for sharing
• Use buddy when working in groups
• Listen to each other by showing gestures like eyes on speaker, nodding, asking questions etc.
• Encourage each other
• Help each other
• Have responsibility where everyone works
• Talk about problems. In case the problem is not solved, raise hands and ask teacher.

To make students responsible team members the following jobs have been created where the students themselves decide the role of every team member (Cooperative Group Responsibilities, n.d., Para 2):

• Captain: This member focuses upon the organization of the group. He starts the project quickly and directs every member what to do.
• Monitor: this member keeps the record of time and checks the necessities of the group. If the captain is not doing his task properly, the monitor is the person who can remind the caption about his responsibilities.
• Recorder: this member checks if the group has all the required information. He takes notes. He is careful about original work and discourages plagiarism.
• Reporter: This member does the reporting of the group’s achievements. After getting the final product from the group, he checks if the job is done on time and well (Cooperative Group Responsibilities, n.d., Para 2).

A teacher has to master the essential components of cooperation. These are positive interdependence, face to face interaction, individual and group accountability, interpersonal and small group skill and group processing (Johnson & Johnson, 2009, Para 5).

The first and foremost element in the cooperative learning is positive interdependence (Johnson & Johnson, 2009, Para 6). Each member of the group has to make a unique contribution and he should be indispensable. Nobody in the group should be an excess baggage or a parasite. It should be a symbiotic relationship (Johnson & Johnson, 2009, Para 6).

The second element of cooperative learning is interaction preferably face to face (Johnson & Johnson, 2009, Para 7). Students should work together by sharing resources helping, supporting and appreciating each other efforts Johnson & Johnson, 2009, Para 7). The students should work face to face exchange their ideas and the things learned. A group discussion where exchange of ideas takes place is an important ingredient. It helps in solving problems and understanding the interpersonal subject and the other group member also (Johnson & Johnson, 2009, Para 7).

Johnson & Johnson (2009, Para 8) state that the third basic element of cooperative learning is individual and group accountability while the group must be accountable for achieving its goal each member must be accountable for contributing his/her share of work. Individual accountability required to know which group member needs more support to encouragement in learning. This will promote individual competency (Johnson & Johnson, 2009, Para 8).

Johnson & Johnson (2009, Para 9) discuss that the fourth basic element of cooperative learning is to teaching students the required interpersonal and small group skills. Johnson & Johnson (2009, Para 9) mention that in cooperative learning students must also learn skills like leadership, decision making, communication and conflict management skills to manage team work successfully. It helps in personality development of students alongside academic learning (Johnson & Johnson, 2009, Para 9).

Group processing is the fifth basic element of cooperative learning (Johnson & Johnson, 2009, Para 10). Individual member and their behavior is assessed in the light of successful achievement of goals. Improvements are prescribed based on the findings and careful analysis of the working of the group (Johnson & Johnson, 2009, Para 10).

Application of Cooperative Learning in the Classroom

A study was done through a project which was designed for Kindergarten students to develop the essential skills for working cooperatively as a group to complete a project. The students were broken groups and they had their individual role in completing the project and every group had job responsibility to make the project successful. Here the groups had to work interdependently (Ryall, 2005, Para 14).

Implementation: The teacher read to the class, taking them as a whole group, the story of Arthur Makes the Team. The story told about how Arthur and his friends worked together cooperatively. After the story was read, the teacher asked them questions on the basis of story and working cooperatively (Ryall, 2005, Para 15).

Now the teacher would then suggest that the class would come up with its own ideas about working cooperatively. The motive was that each child would try its best to make the project successful. The students were told that this project would be successful only then when every child would work together and would be caring for each other (Ryall, 2005, Para 16).

Class Activities that use Cooperative Learning

Following are some classroom activities where cooperative learning is used. Most of them are created by Dr. Spencer Kagan and his associates (Cooperative Learning, n.d., Para 8):

• Jigsaw: Five students make a group and each group is given a unique material to learn and then to teach his group members After doing practice of material, the students teach each other (Cooperative Learning, n.d., Para 9).
• Think-Pair-Share: It has a three step cooperative structure (Cooperative Learning, n.d., Para 10). In the first step, the students silently think about the question which is asked by their teacher. In the second step, they exchange thoughts. In the third step they share their responses with the group (Cooperative Learning, n.d., Para 10).
• Three Step Interview: The team’s member choses their partners.in the first step individuals ask tehir partners questions.in the second step partners have different role and in the final step, members share their partner’s response with the whole group (Cooperative Learning, n.d., Para 11).
• Round Robin Brain Storming: Class is divided into small groups of 4-6 people with one person chosen as the recorder (Cooperative Learning, n.d., Para 12). When the question is asked, the students are given time to think about answers Cooperative Learning, n.d., Para 12). After that the members of the team share responses. The duty of the recorder is to note down the answers of their members of the group (Cooperative Learning, n.d., Para 12).
• Three minute review: In this activity the teacher stop any time while giving lecture and give three minutes to review it (Cooperative Learning, n.d., Para 12). He can ask questions or answer questions (Cooperative Learning, n.d., Para 12).
• Team Pair Solo: In this activity the students do problems first as a team, then with a partner and then of their own Cooperative Learning, n.d., Para 13).Here students can do more things with help instead of doing it alone (Cooperative Learning, n.d., Para 13).
• Partners: There are four teams in the class. Half of the team is given an assignment to be perfect in teaching the other half (Cooperative Learning, n.d., Para 14). Partners learn to work with other partners. Tema also analyze their learning and teaching to improve the process (Cooperative Learning, n.d., Para 14).

Teaching Tips: Cooperative Learning Strategies

It is proved that cooperative learning is very effective for all types of students. It promotes learning and friendships among different groups of students. In fact as much as the diverse is the team the benefits will be higher for the students (Colorado, 2007, Para 1).

The students work in team of four. It is important to maintain classroom norms that are helpful for the students to (Colorado, 2007, Para 2):

• Stay on task
• Contribute
• Help each other
• Share
• Solve problems
• Give and accept feedback
• Encourage each other (Colorado, 2007, Para 2)

There is a simple way to start cooperative learning with pairs instead of whole teams. Two students can learn to work on activities effectively as follow (Colorado, 2007, Para 12):

• A math worksheet should be assigned and students should be asked to work in pairs
• One of the students solve the first problem though the second becomes coach
• Students change their roles for the second problem.
• After finishing the second problem they check answers with other pair (Colorado, 2007, Para 12).

After getting agreed on the answers, the both pairs are told to shake hands (Colorado, 2007, Para 12).Then they continue working in pairs on the next two problems (Colorado, 2007, Para 12).

Cooperative Learning Techniques

Cooperative learning is more detailed than group work activity. It should be applied as a classroom management system. If the students are trained to work in a group effectively, the results are very productive (Glosser, 2010, Para 1).

Following are the cooperative learning rules (Glosser, 2010, Para 6):

• Every member of each group is responsible for all work.
• In case of disagreement, form consent. So be constructive.
• Be open to other member’s ideas and always support their participation. Always make sure no one is left (Glosser, 2010, Para 6).
• The role of facilitator should be changed every day. The facilitator does not command the group instead he managed the group everyday (Glosser, 2010, Para 6).

Definition of Attitude

Attitude is an inward feeling expressed by outward behavior (Sarong, 2009, Para 1 ).Attitudes cannot be masked for long. It always shakes to come out. One’s attitude is reflected in all aspects of his life. An attitude can take a person to the soaring heights and also but at the same time make a person hit rock bottom. Attitude can be your biggest strength or biggest weakness. It is the difference between winning and losing the race of life. It also speaks about your present as well as shapes your future. A positive attitude is the difference between a winner and loser. Everybody should try to have a positive attitude for the betterment of self and the world around (Sarong, 2009, Para 1 & 2).

Can attitude be changed

A negative attitude against a person place or thing can be destructive or goal defeating. We pick up these negative attitudes because of ignorance, lack of right knowledge and environment surrounding us. For example you always hated pets especially dogs you thought of them as ferocious and filthy animal but when your parents brought a dog and you saw the affection and faithfulness shown by the dog your attitude towards pets changed (Can attitude be changed, 2010, Para 1 & 2).

Attitude can be changed by self-awareness and change in belief. A change in behavior i.e change in your outward self helps in changing your attitude. A right attitude ensures that you are not biased and you start looking things from varied point of views (Can attitude be changed, 2010, Para 3).

One can change one’s attitude by various ways (Can attitude be changed, 2010, Para 4):

1. Education and training: Education received in school colleges or office workshops help in changing your attitude. For example a good history teacher can help in changing attitude of students towards the subject which the students thought of as boring and monotonous (Can attitude be changed, 2010, Para 5).
2. Experiences: experiences mould our attitudes. A good or a bad experience changes our attitude towards anything. More the experience in life more refined a person becomes (Can attitude be changed, 2010, Para 6).

Changing attitude

As we continue living life, it becomes necessary for us to change some of our attitudes to get adjusted to changing situations (Heath, 2003, Para 1). For that reason, changing attitude requires self awareness and motivation. We should not be resistant to change but be flexible to change our attitude for betterment (Can attitude be changed, 2010, Para 8).

Attitude towards Mathematics

Mathematics is one of the most important aspect and field of learning in our lives. From a simple 2+2 to the complex calculus plays an integral part of life. Kids start learning mathematics even before they enter the school. With passage of time some develop a liking for the subject while others develop a negative attitude towards it. For those who don’t like it, it turns out to be a very difficult and boring subject (Schmidt, 2007).

The attitude towards mathematics needs to be changed and a different method of learning has to be developed. Cooperative learning is one such method.

Reference

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