Strategies For Students Small Group Work Mathematic Classes Education Essay

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Through my reading of the topics in the four E844 blocks it was clear how important the role of language and literacy plays in the successfully processes of teaching and learning. Therefore, in order to show, "deeper understanding of the nature of language and literacy in a changing communicative landscape" (Study Gide, p. 1), it was my intention in this small-scale research project to analysis different kinds of language in context. Mercer's book "Words & Minds" was a fascinating look at language data and an introduction "to language as a vehicle for collaborative thought". I hoped to draw on his ideas in my study along with Vygotsky's research on the successful ways for students to learn through peer talk and interaction. The intention was to evaluate which kinds of strategies and techniques in a mathematic classroom that would contribute to successful learning.

The analysis of small group work seemed to be an appropriate technique from one of variety of approaches to learning for me to use in my study as it often a valuable technique in ESL classes. It was hoped that a range of different types of talk similar to the three categorised by Mercer (1995) 'disputational', 'cumulative' and 'exploratory' would be identified. The recording of the group work for three activities within the classroom would give plenty of resources for text analysis. However, it soon became clear in the early part of the research that talk is just one of a number of conditions that assists learners to successfully complete a group lead task.This was also noted by my tutor in his evaluation of my proposal. This has meant that a change in the direction of my study would be needed having come to the realization that I was attempting to conduct too wide ranging a study. It was decided to focus on one particular area only - namely the 'attractiveness' of group work as an alternative to the teacher-led 'IRF' mode. The following questions, therefore, replaced the three originals and formed the basis of the study.

1. Is there an expectation that students can work effectively in groups?

2. Can small-group activities be valuable for all and particularly for ESL students?

The environment of the classroom, the time of day, the design of the set task and the social skills that support productive mathematical work with peers all play an important role in a successful outcome. Vygotsky's work that pointed out, children differ in their responsiveness to guidance and his concept of zone of proximal development would play a major role in the successful analysis of this project. It is the intention of this investigation to determine whether group work assists in providing learners with the scaffolding needed from them and their peers to successful complete a task. An analysis of the data gathered will allow teacher to determine whether group work can be a useful technique.


The study was informed by a variety of research papers and theoretical positions contained within the E844 materials and research in Open University digital library, however the underlying concepts that lead me to choose to look at the effectiveness of group work were sparked by early readings in Block 1 by the suggestions (Mattos 1999) based on Vygotskian concepts that learning should be based on 'real-life' learning situations. It was further fueled by references from two other Vygotskian concepts that were frequently mentioned throughout the course, the first regarding peer-assisted learning (Mercer 1995) that highlighted the vital importance of collaboration. Vygotsky (1978) states:

"Every function in the child's cultural development appears twice: first, on the social level, and later, on the individual level; first, between people and then inside the child. 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."

This pointed to the assumption that learning is social. What children learn through social interactions with adults and peers forms the basis for more complex thinking and understanding. Over time, these skills, learning, and thinking processes can be used independently. So by interacting with other suggests that children learn not only what to think but how to think. As suggested in my first assignment, the importance of spoken language in the processes of teaching and learning, like teacher-talk, group work can play a critical role in the student's learning and language development as the value of learning by doing and talking through the task with peers (especially for second learners where concrete experiences help make language comprehensible) can allow for effective learning to take place.

What fascinated me with this concept was that Vygotsky suggested that all learning is a product of 'socio-cultural' phenomena that is mediated by interactions with others (Berk & Winsler, 1995), or that the learner's view of the world is shaped by social interactions. If this is the case, should productive group work be an essential part to learning as the collaboration and interaction with peers would expand the student's aptitude for seeking new information. Therefore, why is group work often viewed as just a means of completing a project or task? Maybe 'group work' could be replaced by the term used by Barbara Rogoff 'guided participation' within the classroom environment. Indeed, her definition could be related to the dynamic processes that contribute to group work:

"Guided participation involves collaboration and shared understanding in routine problem-solving activities. Interaction with other people assists children in their development by guiding their participation in relevant activities, helping them adapt their understanding to new situations, structuring their problem-solving attempts, and assisting them in assuming responsibility for managing problem solving."

(Rogoff 1995:93)

The final concept is that of the zone of proximal development which describes the distribution of a child's mental development along stages. Vygotsky described it as, "the distance between the actual development level as determined by independent problem solving and the level of potential development as determined by independent problem solving and the level of potential development as determined through problem solving under adult guidance or in collaboration with more capable peers". This could describe parents of children, who frame or simplify a child's immediate world in such a way as to facilitate learning as mediators. So as teachers we could do this by setting up carefully framed group activities for students to explore within their present level knowledge and experience. In the mathematic class, do we present these situations or are the lessons meaningful? Would group work helped to make maths achieve this goal?

Maybe the reason for this reluctancy is the fear of group work going wrong as teacher we like to be 'in control' of our learners. Frey et al suggests that even if we recognize that group learning is vital for our students, simply placing them in groups and giving them a task does not mean learning or mastery is soon to follow. She adds that conditions must be right.

In the ESL classroom, group work seems frequent activity as it could be argued that group work is one of the major collaborative learning processes within the class that are part of the gradual release of responsibility model where the teacher moves from assuming "all the responsibility for performing a task . . . to a situation in which the students assume all of the responsibility" (Duke & Pearson, 2002, p. 211).

In a typical ESL classroom group work is one technique regularly used to provide opportunities for exploratory talk that is content-focused allowing students to test ideas and talk their way into understanding. It also provides specific language features to be practiced in a less threatening purposeful context.

For three years, I worked as both a maths and ESL teacher for Key Stage 3 students following the National Curriculum in an international school environment. The classes were made up of a range of ESL students at different levels of English, a variety of techniques where used; group work was one of these as it allowed better English language users to model and scaffold language choice for the weaker students and provide an opportunity for me to observe an individual student's use of language or to work closely with a group of student who might need scaffolding. However, group activities in maths set even if made up of ESL students would rather prove successful.

This year, I have taken on a slightly different role as a language support teacher of maths but maintained the role as a Language B (ESL) teacher. My ESL students are spread between the two maths groups that I support at the lower end of the ability groups in the class; the specialist maths teacher takes the majority of the role of teaching. My role is to assist the students who are unable to understand the content due to language. The opportunity to observe the lesson in this matter provides with a unique way of undertaking a study in an environment where the students are familiar with the researcher. The original idea was to study classroom talk at the beginning of the lesson looking at the IRF exchange between the teacher and students. However, after consultation with the teachers, it was suggested that a student centred study would be more beneficial. I still hoped to base my research on a study of classroom talk and it was Mercer's chapter entitled 'Development through dialogue' in the book 'Words & Minds' along with his research 'Socio-cultural approach: talk and learning' that provided me with the idea to carry out research by looking at the role group plays in increased metacognition and metalinguistic awareness through talk focused on thinking, strategies and language in context


As stated above, my research focus has been heavily influenced by the teaching roles that I have taken up at my place of work, British International School, which is in Phuket over the last three years. As a language specialist for teaching second language in an international school where the medium of instruction is English, there are always plenty of opportunities to observe teaches through the in-class support programmes that have been set up at our school. My main role is to assist ESL students in understanding the concepts of the lesson and to scaffold their learning. In addition to that I differentiate materials and occasionally plan small group activities.

The groups that I choose for my research was from the Year 7 (MYP1) cohort that uses the International Baccalaureate Middle Years Programme (MYP) style method of teaching. The school has recently been granted IB MYP candidate status which means the school is in a period of curriculum change of teaching practices and assessments in order to follow the IB MYP guideline to be granted full MYP status. The classes were made of a range of different nationalities and abilities in English. The maths' groups were divided into four sets based on their maths ability. All groups had ESL students and native speakers of English. However, the low set generally had students who had only studied English for between 6 months to a year. On request from the maths teacher support is provided for language or special needs. This takes various forms in the classroom from individual support to whole class team teaching.


The research stance that was taken was that of ethical research. Parental permission was required as students participating in the research were under 18 years old. A parental permission letter was sent out before data was collected (Appendix III).

Those involved in providing information either qualitative or quantitative, were informed of the intention for its use and given the opportunity to decline its inclusion. No names were revealed and participant confidentiality was maintained at all times. The analysis was necessitate the students concerned participating in activities solely for the requirements of the research; rather, the study was part of the regular classroom routine where students were exposed to active discuss within the classroom environment. The participation in this study did not pose a risk greater than a regular school day if parents decided not to let their child participate, the decision did not affect the student's grades or role in the classroom. The student was able to opt to drop out of the study at any time. Any recorded dialogue or transcripts were stored in a locked cabinet in my office. All recorded dialogue was deleted when the report was completed.


As the research was primarily based on reporting on use of group work experience amongst teachers and their students, rather than the original proposal of recording the student dialogue in groups, I wanted to have the opportunity to collect as much data before the school finished their academic year. I also wanted to make the most of the resources available:

time available to liaise with colleagues during meetings or lesson planning sessions within the mathematic department;

observation time within the class setting when providing in-class support;

meeting with students during library and private study when permitted;

the use of recording and report writing technologies such as personal computer, mp3 recorder, internet based surveys;

The data collected was both qualitative and quantitative. It was divided into two categories:

informal notes and the opinions' of the teachers;

questionnaires, formal interviews taken after group activities;

It was important for me use a variety of different forms data as suggested in the Research methods in Education Handbook, which suggests that 'adopting more than one method is often advantageous' (p 184). In addition to that, I plan to use a similar method of research as Rojas-Drummond who discussed 'the guided participation, discourse and construction of knowledge in Mexican classrooms' of primary student which as she points out 'greatly influenced by socio-cultural perspective'. However, instead of analyzing the interaction of the student-teacher the data looked at the successes of group work compared to other activities in a classroom setting.

It was important for me at the start of the study to provide the individuals involved as much as time needed for them to understand the rationale behind my research. The first task was to discuss with the maths teachers the feasibility of the study. At the earlier stages of the discussions three general factors were felt that were needed to be considered before moving students into groups;

the expectation that their students could work effectively in groups without prior tuition in cooperative learning skills;

the need to know their class as individuals;

the need to know their strengths and weaknesses;

Therefore, the start of my study was delayed by two weeks to spend more time in the classes selected. During this period of time, the students were collecting data of their measurements (height, weight, size of feet) for class comparisons of individuals. A simple consent form was produced for classmates to sign before they could collect data from their classmates. Setting out this mini-study proved to be extremely invaluable when I eventually explained to the students about my study.

Over a week the questionnaire (Appendix 1) was handed out to teacher and then returned. A short informal interview was scheduled for each individual teacher to discuss the data on the questionnaire. This provided an opportunity for them to elaborate and reflect on their responses to Q8 'In your opinion list the positive or negative sides of using group work to complete a maths task in class.' Their responses were recorded in written forms. During this time draft versions of the three planned activities (Appendix V) were discussed which provided me with the first feedback to adapt them to the student's ability, experience and interest. One further session was arranged for the purpose of collaborating with the classroom teacher in order for the activities to be with current with the unit of work and scope & sequences of the lessons. The main objective at this time was for all classes to do the same formative and summative assessment tasks so the comparison of different spoken texts for the same task with different level of maths and English ability would be possible.

As the school approached half-term, I met with each class to explain the reason for my study and why the students needed to get their parents to sign the permission form (Appendix III) before collecting data. As mentioned before, the fact that the students had a similar activity meant there were few concerns. The student's questionnaire (Appendix II) was also handed out so it would be completed once the parents had signed the form and the students had returned from their break. I prepared three versions of parents permission form in Thai, Korean and Japanese which were distributed on request.

The response of forms returned was 100%. In order for the results to be collected, I set up a web based survey response (Lime Survey). Each individual class was booked into the ICT Labs, questionnaires were returned and students inputted their response via the Lime Survey. Answers to the questionnaire from all teachers and students have been reproduced as Appendix IV.

Once, the students' questionnaires' had been collated, I interviewed two students from each of the classes. This gave me the opportunity to target specific areas of views regarding the use of group work within their maths classes.

The interviews were eventually the primary means through which I gathered important facts and accounts of the students' group work experiences. The constructed comments for these sessions from both teachers and students proved to be saving grace for me regarding this study.

Once the interviews were completed, scheduled times were arranged for the group work activities to take place and be recorded. The class was prepared for the first activity 'Solving Picture Equations' and one of the groups in the class was selected to be recorded. The response was quite surprising as the group completed the task with little or no dialogue. A similar situation happened in next class so Activity one was abandoned as a task. For the remaining classes,

Activity two 'colouring Africa' or activity three 'maths without speaking' were used. There was some success with both of these activities when the group was not being recorded. However, when the recorder was recording most students remained silent in group. After a few more attempts, I took the decision to abandon the recording of the activities and concentrate on the success of the types of activities planned.

In order for this to be achieved feedback sessions were arranged and notes taken of the students positive and negative responses were noted down in my research diary which would provide me with practical insights as a researcher.

The intention to use a research diary throughout the study to make notes on any observations, comments or attitudes that relate to my research helped me to salvage the failure of the recording allowing me to reflect and re-evaluate my original research.


After data recorded in the questionnaire and interview, the teachers who were part of the research had used group work in their classrooms before and they were aware that carefully designed group activities and strong individual effort are necessary, but not sufficient, to guarantee a successfully activity. However, few had used this activity regularly in the class routines.

The teachers remained in fairly high regard for use of group work from data collected from interviews. Here represents a broad spread positive and negative of opinions using group work within the daily routine of teaching mathematics.

Positive Comments

the use of discussion helps learning of vocabulary and how to use it

it reinforces concepts learnt previously

encourages reflection

stronger students are able to explain to weaker student which helps both to enhance understanding

useful to assess knowledge level of class as a whole

develops language, communication and social skills

students can share ideas and different approaches to the solution of the task;

Negative Comments

sometimes hard to know who is doing the work

difficult to give individuals assessment grades for group tasks

some students in this group 'opt out' of discussion which may be due to language or lack of social skills

groups can be difficult to on task - slow to start, easily distracted

some strong personalities can be very dominating;

The most worrying trend in the survey was the frequency of the use of group week in the regular week's programme which showed a 'rare' use of this learning enhanced activities. Teachers identify in their face-to-face interviews that their students needed to develop their social skills that supported productive mathematical work. In order for them, there is a need for students to be set guidelines that makes them aware of their rights and responsibilities during small group work. When I inquired about the type of guideline, there was no clear 'ground rules' set out for teachers. This was not just unique in the maths department but across the whole of the secondary school. However, the same cannot be said of the primary school where signs similar to 'our ground rules for talk' (Words & Minds p 161-162) are posted in each classrooms.


We have agreed to: share ideas, give reasons, question ideas, consider, agree, involve everybody, everybody accepts responsibility;


We share our ideas and listen to each other

We talk one at a time

We respect each other's opinions

We give reasons to explain our ideas

If we disagree we ask why'?

We try to agree in the end

What is interesting to note is the negative opinions were similar to rules that some of the students break. Here's just a sample of the comments made by the students;

Negative comments

There too make talking not about the activity we need to do

If someone doesn't know the answer then they will copy and not understand how to do it.

Not everyone takes part

Sometimes group members don't listen to you

Talking and going off task and not concentrating

Of course problem behavior can generally be easy corrected, such as groups choosing seating arrangements that didn't inhibit interaction which proved successful in the last activity where the general feedback of completing the task was very positive. However, as Brown states "a more persistent problem, one that is endemic to student conversations about mathematics, is the inappropriate or incorrect use of mathematical language. While difficult to eliminate, its effect on group progress can be minimized if those who are sensitive to the careless use of language make a practice of requesting clarification. A communication problem with more serious consequences is that some students tend to ignore the contributions of less articulate group members, rather than probing for their meaning by asking questions. Most challenging for almost all groups is the process of finding a level and mode of discourse that meets the needs of, and encourages the contributions of all of its members." For Brown making the ground rules explicit helps to set the stage for effective interaction. She suggests that "the guidelines describe generally the kind of behaviour considered appropriate in group work in mathematics, they alert groups to some specific problems that can limit their effectiveness, and they provide a few basic strategies for coping with problems that do arise. As concrete experience shows students the value of the guidelines, the social framework suggested gradually becomes part of the classroom culture." As a result, she had seen her students accomplish more during group work, and the limited class time that she had was used more productively. The plan will be trial out the 'guidelines for doing group work" (Appendix VI) in the new academic year in the hope that there will be produced similar successes as Brown has had.


In evaluating the project, it is fairly obvious that it was severely limited by time and depth. This was mainly due my limited experience in recording data which created a huge impact on the shape and final research of this study. I had conducted 'trial runs' with my own children who are of primary school age with some astounding success. However, maybe down to peer pressure or the environment within the class it was such a different story in the secondary school class. The main purpose that was set out in my original proposal was quite clearly defined, to analysis text from dialogue which would have been an extension of research from Chapter 5 of the Student Workbook, "Socio-cultural approach: talk and learning". It would have been interesting to compare the dialogue of primary school students in Mercer's study with my own from secondary school.

It was unfortunate that due to the responses from students during the group work recording this was unable for me to be achieved. However, my failure has given insight into how unpredictable research can be.

Mercer's extensive research on talk drawing on work by Vygotsky was truly an inspiring read and of course his book 'Words & minds' which truly 'offers practical insights into how we might improve our communication skills' are skills that may often be lacking in our classrooms these days. We can easily argument the case for the use of group work in second language learning. Long et al 1995 suggests five pedagogical arguments;

1. Group work increases language practice opportunities

2. Group work improves the quality of student talk

3. Group work helps individualize instruction

4. Group work promotes a positive affective climate

5. Group work motivates learners

However, are our mathematicians in need of these skills? The fact that the groups in my research were limited to the way they 'talk mathematics' may have indicated this or is the fact that group work is rated low by the teachers in my study for its effectiveness, a major factor. I believe that as students go through primary and secondary school they are conditioned to follow as Ray states 'hidden rules' when students work with a teacher. He claims that this common 'hidden rules' have been discovered by researchers. Without references it is difficult for me to back up his claims. However, the following were true about some observations that I made too regarding teacher-student interaction in the mathematics classes that I visited;

Never interrupt a teacher when they are explaining something (even for clarification) they might think you are rude.

After the first explanation by a teacher, it is okay to ask if you don't understand but if you still don't understand after a second explanation, just nod and try and sort it out yourself or ask a friend

Perhaps, the factor that Ray points out that 'group work allows students to talk to each other in lessons instead of listening to a teacher' is certainly a novel idea. He finally adds that 'group work may take some teachers outside their normal teaching style and indeed their comfort zone.' This may be true of some teacher but surely most would encourage active forms of learning. Mercer highlights this when defining the role of teacher which he suggests are:

"Not simply as the instructor or facilitator of the learning of a large and disparate set of individuals, but rather as the potential creator of enquiry in a classroom, in which individual students can take a shared, active and reflective role in the development of their own understanding."

(Mercer 1995 Words & Minds: p161)

Mercer sums up regarding the quality of student's educational experiences as one which "to some extent at least their commitment to their own education will be affected by the extent to which what they are doing in class has continuity, a comprehensible purpose and scope for their own active participation".

(Mercer 1995 Words & Minds: p161)

On completing this research is has allowed me look at how, what and the way I teach. It has given me an insight into how students may response differently in one subject to another. It important that teachers are aware students need first to be guided in how to talk and work together in all whole of curriculum. In order students to demonstrate 'exploratory talk' which I had hoped to find in the dialogues that might be recorded if I had set up 'ground rules' for the groups. My research in this study will continue as I reach closer to a new academic, the resources that I have found through this study will used to enhance the learning and socio-cultural experience of my students.

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