Influence of Collaborative Group Work on Students' Attitude towards Mathematics.
The paper investigates the effect of Collaborative Group Work (CGW) on students' attitude towards mathematics at elementary level in Pakistan. It documents the results of two case studies. Evidence was collected over one teaching term in an academic year in a usual classroom context in the form of observations, audio and video recordings, interviews, questionnaires and field notes. The purpose was to collect the data in classroom conditions that were as normal as possible. The paper is part of larger study so only questionnaire and interview data were taken for this as an evidence of the shift of students' attitude developed during intervention. The analysis of the attitudes to mathematics of students at the start, during and at the end of the teaching programme shows a positive change in students' attitudes over the period of the intervention.
Key Words: Attitude; Belief; Emotion; Collaborative Group Work; Collaborative learning
A large number of studies are conducted on attitude towards mathematics but studies like teaching experiment focusing on a change in students' attitude towards mathematics are rare in the mathematics education. The purpose of this study is to explore the influence of the intervention throughout whole teaching term on students' attitude towards mathematics. The attitudes of students influence their level of engagement and learning (Eagly and Chaiken, 2005) but attitudes are not fixed. A potential benefit of Collaborative Group Work (CGW) is that attitudes are affected positively, which will inform engagements and learning. For that reason, the students' attitudes are monitored in the study for detecting change. They "can be seen as constantly in the process of being recreated and renegotiated by those who hold them - attitudes can change" (Moreira and Noss, 1995, p. 157).
During CGW, the students' subjective and objective knowledge influence each other and can change their attitudes about mathematics either in a positive or negative way. Such change has influence on their engagement and learning. One of the challenges in this kind of research is to define the construct; what is attitude?
What is attitude?
Zan and Di Martino (2007, p. 621) state that despite a large number of studies about attitudes, there is no clear definition of the construct itself. They provide three definitions; a simple, a bi-dimensional and a multidimensional, which are given below:
1. A "simple' definition of attitude, that describes it as the positive or negative degree of affect associated with a certain subject. According to this point of view the attitude toward mathematics is just a positive or negative emotional disposition toward mathematics (McLeod, 1992; Haladyna, Shaughnessy and Shaughnessy, 1983).
2. A multidimensional definition, which recognizes three components in the attitude: emotional response, beliefs regarding the subject, behaviour related to the subject. From this point of view, an individual's attitude toward mathematics is defined in a more complex way by the emotions that he/she associates with mathematics (which, however, have a positive or negative value), by the individual's beliefs towards mathematics, and by how he/she behaves (Hart, 1989).
3. A bi-dimensional definition, in which behaviours do not appear explicitly (Daskalogianni and Simpson, 2000): attitude toward mathematics is therefore seen as the pattern of beliefs and emotions associated with mathematics
The researchers preferred neither the simple nor the multidimensional definitions of attitudes. The simple definition only tells about the "positive emotional disposition' or "negative emotional disposition' of an individual. This ignores the role of beliefs, which seem to be important to attitude (Eagly and Chaiken, 2005). Another reason for not considering the simple definition is an issue of measurement. For example, if one says mathematics is a good subject, it shows he/she has positive views about mathematics. However in most attitude measuring questionnaires, the items used are positive but could be related to different constructs as shown in the Table1.
Table 1. Items related to different constructs
Items used in Questionnaire###Related to###'Positive' generally means
I like maths###Emotion###Perceived as pleasurable
Maths is useful###Beliefs###Shared by the experts
I always do homework in maths###Behaviour###Successful
The three "positive' items in Table 1 create confusion whether "positive' related to emotion, beliefs, or behaviour when we use in any attitudes questionnaire. Actually, three meanings are overlapping. Zan and Di Martino(2007, p. 160) argue that:
The differences in the use of the adjective "positive' not only imply different choices of assessment /measurement instruments: it also triggers a different formulation of the research problem to be dealt with. For example, the problem of identifying how to push a "positive attitude', typically encountered in this field of research, requires a completely different approach depending on whether the positive attitude refers only to the emotional component or it refers to a particular pattern of beliefs and emotions, to be assumed as a model.
The reason for not preferring the multidimensional definition is that it can again create confusion between beliefs and behaviour as a third construct that this "positive' attitude is because of beliefs or behaviours. The practical constraints on the study meant that the researchers could only study effect through questionnaire and interviews, and trying to access behaviour through verbal responses creates confusion between beliefs and behaviour. For that reason, researchers considered the bi-dimensional definition, which deals with two dimensions: beliefs and emotion.
Beliefs: The researchers consider beliefs as the personal thinking from which individuals make decisions about the actions they undertake. Beliefs represent one dimension to analyse the students' attitudes towards mathematics because it is assumed that beliefs develop the attitudes of the students. Beliefs are a form of knowledge and knowledge is situated and socially constructed and beliefs of people are made with their social life (De Abreu, Bishop, and Pompeu Jr, 1997). Students have beliefs, which are developed from different communities of practice (Op't Eynde, Corte and Verschaffel, 2003). An individual's beliefs are the results of different social interactions.
Emotions: "The emotions are socially organised phenomena which are constituted in discourse, shaped by relations of power, and implicated in constructing social identity" (Evans, Morgan and Tsatsaroni, 2006, p. 209). During CGW, emotion arises during the interaction of students, shaped by their personal experiences related to social interaction and pedagogic and other practices in which they participate (Evans, et al., 2006). Emotions are taken as a second dimension that reveals the on-going behaviours of the students during intervention.
This subsection presents three principles adopted from Moreira and Noss (1995) to be used as action guidelines in this study. Moreira are Noss (1995) treat attitude as dynamic.
Principle 1: Attitudes can be understood only as the history of attitudes
This principle says that to understand the character of students' attitudes towards mathematics, it is necessary to consider how these attitudes are formed. The focus here is that attitudes are learned and are continually evolving as a result of different experiences. It is not claimed that all the experiences contributing to students attitudes should be brought to light, but that an attempt should be made to uncover some of the factors that might explain the attitudes that students' developed in their previous classroom practices.
Principle 2: Attitude change can be understood only as the history of change
This principle argues that the study of attitude change should not limit itself to acknowledging that change did or did not occur. For example, in attempting to document eventual changes in students' attitudes towards mathematics associated with the classroom environment, it is important to try to understand the trajectories followed by the participating students. We will take an approach to the study of attitude change that takes into account not only the outcomes of the intervention but also consider how and why any change takes place.
Principle 3: Context is a main agent
This third principle says that context is an important factor, which influences students' attitudes. It is the place where students get the new ideas, feelings and experiences, specifically the classroom context which acts as a catalyst for developing students' beliefs.
For this research, the researchers utilized the case study method in which the focus does not lie on individuals, but on the social and cultural phenomenon of student- student interaction that the individuals perform during collaborative group work (CGW). In this study, evidence was collected in two schools (the Light Campus and the new school) over one teaching term in the academic year in a usual classroom context in the form of observations, audio and video recordings, interviews, and questionnaire and field notes. Classes were videotaped with one camera. The questionnaire and interview data were taken as evidence of the shift of students' positive attitude developed during this intervention. The qualitative data, generated from the transcription of interviews, were classified into categories. Quantitative data derived from structured questionnaire were analyzed by applying statistical tools (percentages, frequencies, and means).
The focus was to provide a general view of students' attitude towards mathematics and how it changed through the interaction. Semi structured interviews were conducted before, during and after the intervention. The purpose was to analyze the change in attitudes of students if any because of intervention. The developed questionnaire contains a set of 27 items, which have been adopted and modified from earlier research. The questionnaire consists of several attitudes scales developed in accordance with the Likert scale of four points, strongly disagree to strongly agree. The instrument was given to the experts in mathematics education for validation. All the respondents participating in the study were required to choose the answer that reflects their own views. This questionnaire was given to the students to answer twice; before and after the intervention, and differences between their responses are used to measure the attitudes changes of the students.
According to the definition of attitudes used in this study, attitude consists of two dimensions: beliefs and emotions. The pre- and post-intervention interviews and questionnaire data are used mostly to explore the change in students' beliefs. The interviews conducted during the intervention are used mostly to investigate students' emotions. The results are presented in two ways through (1) the attitude questionnaire; and (2) the interviews for each category. Possible analysis, interpretation and indication about the data are explained. The researchers did not use the original names of the school and participants.
Questionnaire and interview content
The questionnaire and interview had questions in three categories: (i) beliefs about mathematics as a subject; (ii) beliefs about mathematics as learning (understanding); and (iii) beliefs about social context. These categories are developed to view the students' attitudes towards mathematics and attitude changes in different settings for this study based on the emotions and beliefs that the students have. First category is emotional responses to mathematics as a subject, which are likely to affect the nature of their interaction with it. Second category deals with the issue of students' learning, what they think and feel about how they learn, others learning and what type of behaviour can be effective for learning. Third category refers to the students' views, feelings and perceptions about parents and others outside the school and also of the classroom norms and group work in mathematics because grouping is a significant part of the social context of the classroom.
This category is important because collaborative learning is encouraged in mathematics is not used in Pakistan where this study is located. Asking about group learning can give insight into how students' attitudes change towards mathematics. These three categories are not, however, mutually exclusive or exhaustive. The three categories questions were included in the questionnaire. There are 11 positive and 16 negative items in total. These items are changed into one direction in analysis.
The interpretation of scores
Responses of the students are interpreted against the four point Likert scale ranging from 1- 4 with the direction of negative items reversed so that a low score specifies tendency of negative attitude and high score identifies a positive attitude for example with strong agreement with a positive item being scored as 4 but strong agreement with a negative item being scored as 1. For the sake of extraction of meaning from the data, I used the following criteria. I admit that there is no statistical ground for these boundaries. It is a kind of arbitrary common sense scale.
- The students have a very negative attitude, if the mean score is between 1 and 1.50
- The students have a fairly negative attitude, if the mean score is between 1.51 and 2.50
- The students have a fairly positive attitude, if the mean score is between 2.51 and 3.50
- The students have a very positive attitude, if the mean score is between 3.51 to 4.00.
A computer analysis was conducted to provide simple descriptive statistics of the students' responses. It provided the means and standard deviation of each item before and after the intervention. The results are shown in Table 2. The "negative' items 2, 5, 6, 7, 8, 9, 12, 14, 15, 18, 19, 20, 23, 26, 11, 24 have a low score if students agreed with them, all the other items have a low score if students disagreed with them.
The descriptive statistics provide general information about each category.
They also support the comparison of students' attitude before and after the intervention.
Figure 1 shows that, after intervention, the respondents' beliefs changed in favour a positive view of mathematics as a subject. The overall mean score changed from fairly negative to fairly positive (1.90 to 3.14). This increasing trend was observed for every statement in this category. However, the increase in the mean value of each statement ranged from 0.38 to 2.08. The qualitative data presented subsequently also substantiate the above trend. In the new school three students were interviewed before the interview and four after and their responses are transcribed and translated. The results of interview analysis exposed that Abdul likes mathematics because of group work and considers it an interesting way of doing mathematics. He likes and is enjoying mathematics more than before "Yes; I like it and enjoying more than before". Larab and Mehak both do not like mathematics at the beginning of the intervention.
Table 2. Descriptive statistics before and after intervention
1###Mathematics is an interesting subject.###2.00###1.15###3.38###1.04
2###Mathematics is a difficult and complicated subject.###1.62###0.87###2.69###1.38
3###Mathematics is mostly about methods for getting the###2.08###1.12###2.54###0.97
4###Mathematics is largely concerned with word problems.###2.69###1.11###3.08###0.86
5###In mathematics something is either right or it's wrong.###1.62###0.65###3.00###1.00
6###Mathematics has one solution so by practice I memorize it.###1.46###0.88###3.54###0.88
7###Mathematics is a boring subject.###1.69###1.32###3.38###1.04
8###I have trouble in understanding.###2.08###1.04###3.54###0.97
Cumulative Mean (Beliefs about mathematics as subject)###1.90###-###3.14###-
9###Mathematics problems can be done correctly in only one###1.77###1.30###3.54###0.66
2###The best way to do well in mathematics is to remember###1.46###0.78###2.92###1.12
###all the formulas.
3###I think that practising a lot is the best way to learn###2.46###1.20###3.77###0.60
14###I have to remember all the steps.###1.92###1.26###3.54###0.78
15###Some people are good at mathematics and some just are###1.08###0.28###2.31###1.11
16###Teachers of mathematics teach well.###2.54###1.33###3.46###1.13
17###I accept challenge to solve the difficult sums.###2.08###1.44###2.92###1.12
18###I have a trouble to understand how teachers teach in the###2.31###1.38###2.77###1.36
19###Mathematics is not for everyone.###2.31###1.38###2.69###1.32
20###I make many errors in mathematics.###2.08###1.26###3.00###1.15
21###Hard work can increase mathematical ability.###2.46###1.05###3.31###0.95
23###To solve mathematics problems I have to be taught the###1.62###0.87###2.77###1.17
###right way to do it, or I can't do anything.
25###Real mathematics problems can be solved by common###2.23###1.17###3.46###0.97
###sense instead of the maths rules, I learn in school.
26###I will never be good at mathematics.###1.92###1.32###3.23###0.83
Cumulative Mean (Beliefs about mathematics learning)###2.02###-###3.12###-
10###I wish we did more work in groups.###2.62###1.33###3.62###0.87
11###I like to solve mathematics sums alone.###1.38###0.65###3.69###0.85
22###I like to work with others on problems.###2.46###1.20###3.85###0.38
24###It is better to work alone than group work in###1.77###0.83###3.46###0.88
27###Its better to work in a group than on your own.###2.46###1.05###3.62###0.65
###Cumulative Mean (Beliefs about social context)###2.14###-###3.65###-
Beliefs about mathematics as subject
Interviewer: Do you like mathematics? Larab: No
Mehak: Shaking her head, (No) [no good gestures appeared on her face] Interviewer: Why do you not like it?
Larab: Hum... there are many difficult problems.
Interviewer: What is the subject of mathematics like?
Larab: There are some problems of addition and subtraction, ascending and descending etc.
Mehak: (smiles and feels a bit shy), I do not know... difficult... yes it is difficult subject.
But a shift of their attitude was noted at the end of intervention when they described their feelings "mathematics is an interesting subject".Larab told the reason of liking that, "he is working with his friend Abdul"; and Mehak told that "teachers are teaching well". She wished to work with her friend Hala.
In the light campus, before the intervention, three of the students said that they do not like mathematics, and believe that it is a difficult and boring subject with long solutions that are difficult to remember. On the other hand, Rida said she liked mathematics although she did not express beliefs about it. At the end of intervention, when the same question "do you like mathematics" was asked again Rida replied, "I like it very much and like from my childhood" because "answers of mathematical questions are not long like Urdu, and English, I like it more now because we work in groups". A shift observed in the attitudes of some of the other students who had not liked mathematics before the intervention. Mahnoor however, continued to feel that mathematics is a difficult subject.
Beliefs about mathematics learning
Figure 2 shows that, after intervention, the respondents' beliefs changed in favour of a positive view of mathematics learning (understanding). The overall mean score changed fairly negative to very positive (2.14 to 3.65). Again this increasing trend was observed for every statement in this category. The increase in the mean value of each statement ranged from 1.00 to 1.69.
In the new school, two interviewees Abdul and Mehak think that everyone cannot learn mathematics. But the opinion of Larab is different from them he associated everyone's learning with hard work even before the beginning of the intervention.
Interviewer: Can every student learn math if they try hard enough?
Abdul: No; every student cannot learn mathematics but ... (after thinking some time) if one works hard then he can learn.
Mehak: (After thinking sometimes says)... No
When these three students were again interviewed after the intervention, they all have the feelings that everyone can learn, if he/she works hard.
Interviewer: Can every student learn mathematics if they try hard enough?
Abdul: No; every student cannot learn mathematics but ... (after thinking some time he says) if one works hard, he can learn.
Larab: Yes, every student can learn mathematics, if he works hard
Mehak: One of my friends cannot learn because she does not work hard and do not study at home.
Interviewer: Do you think everyone learns mathematics in the same way?
Abdul: We learn mathematics in different ways. Teacher solves the sum on the board by her own way... and when you give us problems to solve in the group, then we solve them in different ways but answer is same.
Larab: No in different way, we solve the problems from many ways ... we are solving multiplication sum in more than one way.
Before the intervention, they all think that everyone learns mathematics in the same way, for example, Mehak said, "we copy the solution of problem from the board when teacher solve on it". This shows that they have to memorize the method to solve the other similar parts.
Interviewer: Do you think everyone learns math in the same way?
Abdul: If all the problems are of same nature then they can be solved in the same way, for example there are addition problems, one is different from other... if there are two different questions ... their answer cannot be same; answer of one problems can be different from other problem.
Mehak: Every one learns in the same way. Yes, what teacher tells in the class.
After having group experiences during intervention their beliefs appeared to have changed and they think now that students learn in different ways and an advantage is that if one member forgets one method then he/she can use the other method. Abu- Baker took admission late in the school term therefore he could not be interviewed at the beginning of intervention, but he participated in some episodes in place of a member of the focus group when one of them was absent. In his interview, he replied sometime I used different methods "when teacher teaches I use one method when you (researcher) teach I use different methods'.
In the Light School, before the intervention, Rida believed that everyone can learn mathematics because it is an easy subject. Mahnoor and Arbab also agree with Rida and give more emphasis to work hard for learning. However, Ammad's belief is different from the other interviewed students. He thinks that "everyone cannot learn mathematics".
Before intervention, all the interviewees except Rida believe that they learn by the one method that the teacher adopts in the class. They remember the teacher's method and solve the problems by using this method. However, Rida says "sometimes I use different and sometime I use the same method". When the same questions were asked again after the intervention a shift of students' attitude was noticed, which evidences that CGW affected the students' beliefs about learning. Almost all interviewees replied that everyone can learn mathematics and that students learn by different ways. Arbab, however, gave an example from the class, saying that Ammad is not good at mathematics but "He can learn if he works hard. He can understand mathematics. If he only works and do not involved in useless talk within group then he can learn".
Beliefs about social context
Figure 3 shows that, after intervention, the respondents' beliefs changed in favour of a positive view of social context. The overall mean score changed from fairly negative to fairly positive (2.02 to 3.12). This increasing trend was once more observed for every statement in this category. However, the increase in the mean value of each statement ranged from 0.38 to 1.77. In the right school before the intervention, when it was asked; "do you want to work alone or with others", the answer of all three students was almost the same that they wanted to work alone.
Interviewer: Is maths something you can do with other students, or do you always have to do it by yourself?
Abdul: I do mathematics alone. Larab: I do myself.
Interviewer: Has your teacher do group work in maths?
Abdul: No, No; they are not
Interviewer: Do you learn maths best by working alone or working with a partner or group?
Larab: I like to work alone
Mehak: I learn alone... or I like to learn with my friend Hala.
Interviewer: Do you like group work?
One possible reason might be that they were not aware of group work. Their teacher did not do group work in their classes, according to the interviewee Abdul. After the intervention, a very clear change in the students' beliefs could be observed.
Most of the students share that they like group work. The common reason before the intervention, Arbab, Mahnoor and Ammad said they like to work individually. Arbab said she wants to assist the students who will be sitting next to her seat, but she does not say how she can help her. The students' responses show that teachers do not offer group work in their classes. Some of the students were not aware of group work, for example, Ammad consider working in group to mean to do previous work.
Rida's response at the start of the intervention was found to be different from the other students, as she already likes group work, just a few days into the intervention the reason she mentioned was to give and receive help by their group mates in the case of a difficult situation. After the intervention, a clear change of attitudes of the students was noticed, for example students saying that they are learning more in groups and they like mathematics more than before. In response to the question: "why do teachers not do group work"? Rida replies that teachers in their school are very strict. "We cannot say a single word in front of them". This is evidence of a typical behaviour of the teacher with the students in a teacher centered classroom before the intervention.
Another student Mahnoor does not like group work when one student tries to dominate in the group or claims that I did it individually or "I will solve my part". She states, there should be no collaboration if such type of students' behaviour appeared in groups. She responded against this question; "should teacher give worksheet each student in a group or one sheet for each group" that one sheet should be given to each group member when individual work is required but for collaborative work one worksheet should be given for each group, not individual in a group was that "they can get the help from one another working together". Abu-Baker replied if I am working with my friend, I can ask him again and again, and this also suggests that students feel more comfortable working in groups with friends.
Analysis of interview of three students during intervention
Dania is a bright student in the class, and she says in her interview that she did not like group work before the beginning of intervention. She says she had changed her mind after one month saying that sometimes I like and sometime I do not like. The reasons that she shared for when she does not like group work are: if there is a noise in the group; all are saying something but nobody bothers with other's proposals; participants do not try to understand each other's opinion; then she says, I preferred to work alone. She said that definitely group work is better but it is best work when there is discipline within the group. When it was asked what do you mean by discipline? She replied when students listen to each other and do not say unnecessary things.
Another student Neha in the middle of intervention expressed her beliefs in the interview; she likes group work because she thinks during group work she can get assistance from their partner and understand more as compared to working individually.
She proposed that when any member of the group failed to understand any point then they should consult the teacher for assistance. In the response to the question, what type of partner do you like? She said she wished to sit with Dania and Rida because they are her friends. She considers them brighter students in the class. She believes that all the students in the class are not bright. She spoke about Hammad and Ammad who are not academically good in the class. It shows the students' role as evaluator of each other in the classroom and knows their mates behaviour. She does not want to work with Hammad and Ammad because they had disturbed her and she cannot concentrate on her work. However, she believes that they can learn, if one teaches them. She suggested that "they can learn from Ms Rabia's (class teacher) way of teaching, who is very strict with them and works with them by holding their pens. If you will adopt such an approach then Hammad and Ammad can work and understand mathematics".
This interview shows that Rida responded differently when same question; "do you like to work individually"? was again asked in the middle of intervention as she responds, "now I do not like to work individually". She states, in case of illness I cannot work within group therefore in this situation I like to work individually. One possibility of this response might be that she believes that during group work participants have to share their views, speak and participate so she is a little reluctant about working in groups during illness. Another reason of working individually she mentioned was when students are making noise then she feels disturbance and cannot concentrate on her work then she wished to work individually. This implies that teacher should be very careful about the participant's personal need and group work norms, to ensure that participants work on task smoothly.
From the comparison of before and after intervention questionnaire data, it is clear that the students' beliefs about all three categories: mathematics as subject, understanding and social context had changed positively during the intervention. The results indicate that collaborative group work increased positive attitudes towards mathematics. This may be because when students work in groups they feel that they can depend on others for help and therefore increase their confidence in solving mathematics problems. This may indirectly change their attitudes towards mathematics. However, this idea was not revealed in the questionnaire. It is necessary to turn to the interviews.
The interviews from selected students before, during and after the intervention will be used to explore the findings from the questionnaire. The questionnaire and interviews together explain the shift of attitude. Overall students response during the semi structured interviews were much shorter, less reflective and demonstrated, less understanding of the pedagogical process at the start of intervention than middle and post intervention. In addition in the end students seemed more enthusiastic working in groups than before.
In the responses, most of the students spoke of the advantages of small group learning. However, the students' interviews do provide some insight into the benefits of using small group learning in school mathematics. The semi-structured interviews revealed a strongly positive evaluation of the impact of the intervention, in both of the schools in which it was implemented. In particular, the interviews revealed heightened functions of talk amongst participating students, and of the importance of improving children's communication skills as a means of ensuring their successful participation in the classes.
Streitlien, Wiik and Brekke as cited in Kislenko, Grevholm, and Lepik (2005) in their study found that the students who showed a positive attitude towards mathematics on average, performed better in mathematics than their fellow students. Therefore, it seems that a positive attitude towards mathematics leads in general to greater motivation to learn. On the other hand, "... research certainly suggests caution against over optimism in assuming a very direct relation between attitude and achievement" (Cockcroft and Halliday, 1982, p. 61). Nevertheless, a more positive attitude to mathematics is generally accepted to be worthwhile and the results of this study convinced me that CGW can have a positive effect on students' attitudes toward mathematics. The descriptive statistic in section 3.3 provides evidence that the attitude of the students towards mathematics at the end of the intervention was much more positive than at the beginning.
The overall mean score changed from fairly negative to fairly or very positive. Students tended to believe that mathematics is a useful subject and by working hard everyone can learn mathematics. Students also found mathematics to be an interesting subject rather than boring. This increasing trend was observed for every statement in three categories of the questionnaire. To that extent the results of this study showed the influence of the intervention on the cognitive development of students (Breiteig, Grevholm, and Kislenko, 2005). The results of this study are consistent with the conclusions from other researches such as Gillies (2004) and Walmsley (2003), who found students' attitudes were positive after they had been working in cooperative groups. Gillies (2004) suggested teachers can encourage a positive attitude towards learning by adopting a non-traditional pedagogical approach such as CGW in their classes.
According to Schoenfeld (1985) one's views about mathematics make a beliefs system that is dynamic and changeable. Students during CGW shared their experiences and beliefs and they possibly restructured their system continuously (Breiteig, et al., 2005). Students before the intervention mostly believed that mathematics was boring and they did not like it. Some of them even had the view that "everyone cannot learn mathematics'. It is unfortunate that schools have not been able to arrange teaching in such a way that students find mathematics challenging and fascinating (Breiteig, et al., 2005). In Pakistani schools, there is emphasis on rote learning of rules and the procedure of solution in mathematics in a teacher centered classroom. The students before the intervention tended to believe that mathematics is a difficult subject, with long solution problems that are difficult to remember.
The analysis shows that CGW gave the opportunity to the students to share and reflect on their ideas and to evaluate themselves, which leads to the improvement of mathematical discussion. CGW offered the opportunity to express new ideas, feelings and experiences to the other members within a group. The students believed that they were enjoying mathematics more. The beliefs are developed when working together and students accepted beliefs from one another (Walmsley, 2003). As Moreira and Noss (1995) say, attitudes are learned and are continuously evolving because of different experiences. The analysis indicates that mostly students started to like and enjoy the mathematics later on in the intervention. The common reason might be that they started to think about and understand mathematics instead of treating it as rote learning and this change could be because of the changing context, where they got opportunities to share ideas, challenge each other and justify their hypotheses.
Moreira and Noss (1995) also link attitude change with the classroom environment, and this study provided the opportunity to the students to experience a different classroom environment, which contained the whole history of their collaboration, and this is important for understanding the trajectories followed by the participating students. Overall, the collaborative context helps to encourage students to participate more in task completion. It is noted that students learn the art of collaboration with each other over time and the change in attitude that occurred in this study is evidence of the potential value of CGW. The results also show a positive change in the attitude of the students towards mathematics. At the start of the intervention, the attitude was generally negative, but in the end it was fairly positive or very positive. In a nutshell, CGW affected the students' attitudes towards mathematics positively.
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|Author:||Qaisar, Shahzada; Dilshad, Muhammad; Butt, Intzar Hussain|
|Publication:||Journal of Educational Research|
|Date:||Jun 30, 2015|
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