Using Focus Groups to Guide Action Research in Mathematics Education

Mr Marc Jacobs, Reading University

The aim of this doctoral research is to determine how students learn mathematics successfully and what strategies work best in secondary classrooms. Mathematics classrooms and teachers’ practice were investigated through several research methods. One method was student focus group interviews to reveal students’ views of teacher practice. It is widely appreciated (Dowker, 2009; Wilson & Räsänen, 2008) that there is limited research available on effective strategies for supporting students with their learning in mathematics compared to that available for literacy. Wilson and Räsänen (2008) suggest that there are several reasons for this limited research including the cost in terms of monetary considerations and implementation, particularly with large numbers. Therefore, implementing any form of successful mathematical investigation and intervention is challenging when attempting to use a strategy that works across a modern secondary school with a diverse population of teachers and students. This paper reports on the use of focus group interviews for the purpose of obtaining data from students about their learning experiences in mathematics lessons and their views of their teachers’ practice. Teachers’ practice is fundamental to successful learning experiences and Ball (1988) acknowledges that their practice is influenced by their beliefs about teaching and learning, about their students, and about their context thereby shaping how they teach.

Keywords: mathematics, focus groups, research methods

In the past few years, focus group interviews have been used increasingly in fields other than market research, where the technique was first developed (Berg, 1995). Berg (1995:65) also notes, focus group interviews have traditionally been dismissed as part of the “vulgar world of marketing research”. However, it is a method that is increasingly being appreciated for the advantages it offers to researchers in other data collection situations (Morgan, 1993; Gibbs, 1997; Barbour & Kitzinger, 1998). During the 1990s, one begins to see what a reversal in the elitist attitude that may be that focus group interviewing belongs to the somehow vulgar realm of marketing research. Instead, social scientists have begun regarding the approach with greater respect. Sussman, Burton, Dent, Stacy and Flay (1991: 773) state that “focus group methodology is one of the most widely used qualitative research tools in the applied social sciences.” Similar arguments have been offered by Basch (1987, 1989) and by Stewart and Shamdasani (1990). Clearly, there are some advantages to the use of this data-collecting orientation in certain situations. This research aims to explore how students believe they learn mathematics successfully and what classroom strategies work best by initially drawing upon reviews of this method and then subsequently using it with a group of secondary student participants. This paper is part of a wider doctoral project entitled Intervention in Mathematics: Creating successful strategies to ensure success in Secondary Schools where focus groups were used as one of the methods of data collection.

Definition of focus groups
There are many definitions of a focus group interview and Kitzinger (2005) suggests the focus group method is an ‘ideal’ approach for examining the stories, experiences, points of view, beliefs, needs and concerns of individuals. The method is especially valuable for permitting the participants to develop their own questions and frameworks as well as to seek their own needs and concerns in their own words and on their own terms. Powell, Single and Lloyd (1996) define a focus group interview as a group of individuals selected and assembled by researchers to discuss and comment on, from personal experience, the topic that is the subject of the research. Morgan (1997) notes that a focus group (also called a focus group interview or a focus group discussion) is a form of group interviewing but it is important to distinguish between the two. Group interviewing involves interviewing a number of people at the same time and the emphasis is on questions and responses between the researcher and participants. Focus groups, however, rely on interaction within the group based on topics that are supplied by the researcher. The key characteristic, which distinguishes group interviewing from focus groups, is the insight and data produced by the interaction between participants (Morgan, 1997).
A focus group is a form of qualitative research in which a group of people is asked about their perceptions, opinions, beliefs, and attitudes towards a phenomenon. Furthermore, focus groups are a form of group interview that capitalises on communication between research participants in order to generate data. Focus groups explicitly use group interaction as part of the method (Kitzinger, 1994). This means that instead of the researcher asking each person to respond to a question in turn, people are encouraged to talk to one another by asking questions, exchanging anecdotes and commenting on each other’s experiences and points of view (Kitzinger, 1994). During the 1980s focus groups reappeared in social sciences after being absent for some time and are now commonly used in cross-cultural research in a variety of fields, such as academic, policy-related or marketing research. Malhotra (1996:171-172) remarked that “focus groups are the most important qualitative research procedure. They are so popular that many marketing research practitioners consider this technique synonymous with qualitative research.” Even though this statement refers to the mid-1980s in the USA, it still has relevance today, although the arrival of new techniques, among them online focus groups, has certainly redesigned the overall picture.

The origins and history of focus group research
The first use of group interviews was in the 1920s by social scientists Emory Bogardus and Walter Thurstone who used it to develop survey instruments. The methodology is mainly attributed to Bogardus who in 1926 described focus groups in his social psychological research to develop the social distance scale (see Wilkinson 1998). During World War II Robert Merton and Paul Lazarsfeld used group interviews to assist the allied forces in the development of propaganda materials, training manuals and to understand social issues. In the 1950s, focus groups became commonplace among marketers to understand customers while social scientists continued to prefer formal survey research. Sociologist Robert Merton worked with colleagues on the effectiveness of focus group in the years following World War II and the group (Merton, Fiske & Kendall) later wrote a seminal text entitled The Focused Interview: A manual of problems and procedures which was published in 1956. Of particular interest in the post-World War II era was the study of mass-mediated ‘propaganda’. The term focus group replaced group interview as the name of this technique. Over the last twenty years, there has been a steadily increasing interest in establishing qualitative research’s place in the academy which has resulted in the growing use of focus groups, especially in social sciences.
In the 1980s focus groups re-emerged as a distinct research method in the social sciences (Conradson, 2005). Kamberelis and Dimitriadis (2005) state that focus groups have been popular and used extensively in several disciplines. Many social scientists and other professionals have found this qualitative approach very useful. Political scientists, for example, employed focus groups to examine the public perceptions of political candidates and their opinions on particular political issues (Madriz, 2003; Gaiser, 2008). During President Ronald Reagan’s administration in the 1980s, focus groups were adopted to learn about the perceptions of relations between the United States and the Soviet Union and their citizens (Stewart, Shamdasani & Rook, 2007). Focus groups were also used by the New Labour government from the early 1990s to early 2000s in the UK to examine British opinions about health spending, education policy and military action. The aim was to explore ‘a better understanding of the multiple and sometimes conflicting perspectives held by the public on particular issues’ (Conradson, 2005:130). The use of focus groups has been established over a period of time so their value to researchers for uncovering significant information is of interest.

Advantages of focus groups
Focus groups are valuable when you want to consider not only people’s personal accounts of reality but also the way they negotiate these accounts with others, therefore showing divergence or convergence between their views. Cambridge and McCarthy (2001) describe a focus group interview as a group dynamic that can help build confidence, safe environments that are not threatening or intimidating and peer support and validation, enabling all people, regardless of perceived competence, to contribute to research discussions. Focus groups appear to be of value for all members of society and this success was evidenced by Fraser and Fraser (2001) whose research engaged participants with communication difficulties. Focus groups require both individual contributions and group dynamics and they found that with participants with communication difficulties groups smaller than the six-ten usually recommended were better and that the addition of an interpreter familiar with the participants’ communication was also important.
Moreover, Fraser and Fraser (2001) found that participants’ ability to interact with others in a group was more important to success than their various types of communication challenges such as the ability to produce more than a few words, reliance on Makaton sign language, or even repetitive language. They concluded that ‘focus groups are a very good method for some people with learning disabilities in some situations but not in others; it is important to be able to distinguish this before setting up the group’ (Fraser & Fraser, 2001:225). So, there are clearly some limitations that need to be considered before the method is developed as a data collection instrument.

Limitations of focus groups
Like any other research method focus groups do not suit all research aims and there have been times when they were found to be inappropriate or problematic. For example, compared to individual interviews, focus groups may not be as efficient in providing maximum depth on a particular issue. A particular disadvantage of a focus group is the possibility that the members may not express their honest and personal opinions about the topic at hand (Smithson, 2008). They may be hesitant to express their thoughts, especially when their thoughts oppose the views of another participant. Smithson (2008), a researcher who uses focus groups extensively, contends that some research topics are unsuitable for focus group environments. For example, topics which are seen as too personal (such as living with HIV/AIDS, sexuality, infertility, financial status, divorce, domestic violence and abortion) may be better carried out by other methods such as individual interviews. In institutional contexts (such as the workplace or schools), people may be reluctant to express their opinions or discuss their personal experiences in front of colleagues. Hopkins (2007) and Krueger and Casey (2009) found that often focus groups are criticised for only offering a shallower understanding of an issue than those obtained from individual interviews. In a focus group discussion, personal information and experiences may not be discussed thereby reducing the natural narrative that emerges from rich discourse. An example of this is Hopkins’ (2007) qualitative research project about the life and times of young Muslim men living in Scotland which showed that they revealed personal experiences of racism during individual interviews far more than they did in focus group discussions.
The fact that focus groups are driven by the researcher’s interests can also be a source of weakness. What may be of intense interest to the researcher may be a non-issue to the participants. However, the fact that the researcher creates and directs the groups makes them distinctly less naturalistic than participant observation so there is always some residual uncertainty (Morgan 1996) about the accuracy of what the participants say. In particular, there is a very real concern that the researcher, in the name of maintaining the interview’s focus, will influence the group’s interactions. This problem is hardly unique to focus groups because the researcher influences all but the most unobtrusive social science methods. In reality, there is no hard evidence that the focus group researcher’s impact on the data is any greater than the researcher’s impact in participant observation or individual interviewing. Indeed, the dyadic nature of individual interviewing would seem to create at least as many opportunities for researcher influence.
The concerns for focus groups include both a tendency toward conformity, in which some participants withhold things that they might say in private, and a tendency toward ‘polarization’ in which some participants express more extreme views in a group than in private (Sussman, Burton, Dent, et al., 1991). It is clear, however, that for some types of participants discussing some types of topics the presence of a group will affect what they say and how they say it. This is an inevitable aspect of focus groups that should be considered as a potential source of weakness for any given research project. Morgan (1988) states that the researcher, or moderator as they are often termed, has less control over the data produced than in either quantitative studies or one-to-one interviewing. The researcher has to allow participants to talk to each other, ask questions and express doubts and opinions while having very little control over the interaction other than generally keeping participants focused on the topic. By its nature focus group research is open-ended and cannot be entirely predetermined.
On a practical note, focus groups can be also difficult to assemble. It may not be easy to get a representative sample and focus groups may discourage certain people from participating, for example, those who are not very articulate or confident, and those who have communication problems or special needs. The method of focus group discussion may also discourage some people from trusting others with sensitive or personal information. In such cases, personal interviews or the use of workbooks alongside focus groups may be a more suitable approach. Finally, focus groups are not fully confidential or anonymous, because the material is shared with the others in the group (Morgan 1997) and this has ethical implications that need to be considered when developing a methodological approach.

Types of focus groups
There are different formations of focus groups and this section explores those types. Traditional Focus Groups are more straightforward, question-oriented groups. Usually, there is a ‘warm-up’ then the concept, idea, situation or product is presented to the group for their reaction. A neutral moderator who probes for issues of interest and follows up on interesting or relevant comments made by the participants’ guides this process. The key factors to successful traditional groups include clearly defined research issues, an experienced moderator who understands the issues at hand and decisions to be made; and diligent recruiting (Morgan, 1984).
Projective Focus Groups bear a resemblance to traditional focus group discussions in that they are an informal, subtly structured conversation on a specific subject lead by a neutral moderator. They differ in the methods used to explore thoughts and feelings about the subject, and in the emotional depth that can be reached using these methods. Projective Groups rely more on indirect questioning and strongly emphasize the interpretation of group input. Some of the techniques that may be used in Projective Focus Groups include collage-building, brand personification, guided journey and pictorial symbols (Morgan, 1984). Projective Focus Groups are used extensively in exploring brand image and the development of creative concepts for products, services and advertising. A few of the questions addressed in Projective Focus Groups have included: Is this the right name for the product? What feelings are evoked by our brand? What mood should our advertising and collateral material invoke? I have used the traditional focus group interview as I wanted to hear what students think – literally. There is nothing more powerful than hearing first-hand what students have to say about how they learn mathematics.

Uses of focus groups
Morgan and Kreuger (1993) state that the main purpose of focus group research is to draw upon respondents’ attitudes, feelings, beliefs, experiences and reactions in a way in which would not be feasible using other methods such as observation, one-to-one interviewing, or questionnaire surveys. These attitudes, feelings and beliefs may be partially independent of a group or its social setting but are more likely to be revealed via the social gathering and the interaction which being in a focus group entails. Compared to individual interviews, which aim to obtain individual attitudes, beliefs and feelings, focus groups elicit a multiplicity of views and emotional processes within a group context. The individual interview is easier for the researcher to control than a focus group in which participants may take the initiative. Compared to observation, a focus group enables the researcher to gain a larger amount of information in a shorter period of time (Morgan & Kreuger, 1993). Observational methods tend to depend on waiting for things to happen, whereas the researcher follows an interview guide in a focus group. In this sense, focus groups are not natural but organised events. Morgan and Kreuger (1993) suggest that the method is particularly useful when there are power differences between the participants and decision-makers or professionals, when the everyday use of language and culture of particular groups is of interest, and when one wants to explore the degree of consensus on a given topic.

Ethical issues
According to Homan (1991), ethical considerations for focus groups are the same as for most other methods of social research. For example, when selecting and involving participants, researchers must ensure that full information about the purpose and uses of participants’ contributions is given. Being honest and keeping participants informed about the expectations of the group and topic, and not pressuring participants to speak is ethical practice. At the outset, moderators will need to clarify that each participant’s contributions will be shared with the others in the group as well as with the moderator. Participants need to be encouraged to keep confidential what they hear during the meeting and researchers have the responsibility to anonymise data from the group.

The Research Study

a) Selecting participants
Miles and Huberman (1994) explain that most focus groups rely on purposive sampling with researchers selecting participants on the project and on the potential contributions of participants. Alternatively, participants can be randomly selected from a larger group that should be able to give insight into the topic. For example, if someone wanted to know more about a particular religious congregation purposive sampling, such as obtaining a church membership listing and randomly selecting parishioners to participate, would be an efficacious approach (Patton, 1990).
This action research project has a wider population of 240 students in Year Seven (2013-2014) but the focus group interviews included 10 participants selected anonymously; one child from each of ten mathematics sets was selected to form two focus groups of five. The members of a focus group were invited because they are known to have experience from a particular context which in this case was secondary mathematics classrooms.

b) Structure
Researchers such as Kitzinger and Barbour (1990), Lindlof (1995), Kreuger (1998), Green and Hart (1999) and Brown (1999) disagree about the practicable number of participants for a successful focus group. Many experienced moderators prefer a group ranging from eight to twelve suggesting further that the group should consist of four to twelve if the group is homogeneous and six to twelve if heterogeneous. A balance between the need to have sufficient participants for a lively discussion and the unwieldy milieu of a large group is the goal of the researcher.

c) The role of the moderator
The moderator’s management of the focus group can determine the success or otherwise of the method regardless of the context. Morgan (1998) describes the moderator as the person who has the task of leading the focus group. This leadership or management involves:
a) setting the scene;
b) explaining the purpose of the focus group;
c) introducing participants to the topics for discussion;
d) keeping the group on time;
e) focused on the topics;
f) encouraging participation from all the group members; and,
g) ensuring that all the key issues are addressed (Morgan, 1998).
It is useful to have a note-taker recording all discussions so the moderator can give all their attention to the group. The notion of conducting a focus group interview effectively includes an assumption that the interview will be facilitated. The moderator had assumed most of the practical roles concerned with the planning of the physical environment of the interview room and the organisation of equipment and refreshments. The moderator also took responsibility for the welcoming of participants on the day and therefore began the process of setting participants at their ease and opening up channels of communication. According to Kitzinger (1995:299) the moderator ‘leads’ the focus group, their role is only to keep the discussion on track and should not influence the opinions of the group, this has been referred to as “structured eavesdropping”.
During the start of proceedings of the focus group, the moderator’s first question is critical in breaking the ice. After each participant has said something it becomes easier to make further contributions and feel that their opinion is valued. With the use of focus groups in this research, it was particularly important to avoid domination by any particular participant, making sure that everybody had their say and enabling some level of consistent data collection between focus groups. This study worked with young teenagers and it became apparent that the moderator’s role was to ensure that all children felt their ideas were valued and that no one child dominated the discussion.
d) Running the Focus Groups
Two focus groups were held as part of the initial data collection period of this study. I undertook the role of the moderator and my supervisor took the role of the assistant who was responsible for the audio recording of the event and note-taking during the discussions to capture non-verbal signals and nuances. There were five participants in each of the two focus groups which were conducted during the students’ regular mathematics lesson time in a quiet library space on their campus.

e) Conducting and Observing the Focus Group
The moderator and assistant sought to provide a friendly introductory environment which was established as the students arrived at the library. The moderator introduced himself and his assistant. Thanks, were extended to the students for attending and the purpose of the meeting was explained. The conventions of the group discussions were outlined together with reassurances about guarantees of confidentiality. Any initial anxieties or questions about the proceedings were invited. Each participant was asked to introduce themselves before the questions were addressed. The focus groups went smoothly and generated a great deal of data within the allocated timeframes.
Moderator intervention was mainly restricted to prompts, probes and moving the discussion on when a particular issue had been exhausted. An example of moving them on to the next topic was when one of the participants could not think of a time he had a ‘good learning experience’; I told him that I would give him time to think and that I would come back to him. He then told us about a ‘good learning experience’. There was no domination in the group. The assistant moderator contributed or intervened in the discussion and sat at the main table to support the clarity of the Student contributions and to witness the discussion. Once the formal proceedings were brought to a close, participants were once again thanked for their contributions to the focus group.

Focus group research raises a number of ethical issues. We were particularly concerned to ensure confidentiality in and after the discussions. To this end no questions probed for any personal or sensitive information. Anonymity remains paramount and pseudonym use ensures that participants cannot be identified in any publications. Data from tapes and transcripts of the interviews are retained by the researcher and all data stored on university computers.

Analysis of the data
There are a variety of methods of analysing data for focus groups (see Johnson & Christensen, 2004). The audio recordings were transcribed and the data together with the notes were discussed with the researcher’s supervisor. The discussions on a number of topics revealed the high level of detail which focus groups can engender as a result of the group interaction. For example, in the first focus group discussion on the topic of ‘how maths should be taught at secondary school,’ this led to a lively debate in which the students were very open about their own views and experiences. An example of this was, all the participants in the focus group wanted to express their views that maths should be interactive, fun and hands-on. Any reservations that we had that students would be reluctant to open up in front of their peers on such a sensitive issue were not borne out.
Although it might be expected that participants would be guarded concerning their knowledge around maths teaching, they revealed that they felt trapped and teachers are unable to relinquish textbook teaching. The participants were therefore particularly interested in hearing the experiences of their peers as they were all taught by different teachers. The students reflected upon the use of textbooks as the primary resource, in most lessons and they reflected on how they felt in using textbooks on a daily basis, four times a week. It is commonly assumed that textbooks (with accompanying teacher guides) are one of the main sources for the content covered and the pedagogical styles used in classrooms. It is not surprising, then, that considerable attention has focussed on textbooks, including the economic and political circumstances of their production (Apple, 1986 and 1992), their linguistic features (Castell et al, 1989) and their sociological features (Dowling, 1996). Students in this study were put in sets for mathematics during their first year in secondary school according to their results in national curriculum tests. Once in those sets, they followed the same national curriculum but from different starting points and with different endpoints in mind. Textbooks reflected this way of organising students so that in any year group, a particular textbook scheme might have different textbooks aimed at different sets of students. Teachers used textbooks regularly, and almost all that use in lesson times was for students to practice exercises selected by the teacher following from teacher explanation of a particular skill or technique. Listening to the students and their concerns regarding the use of textbooks and their need for more ‘hands-on’ activities, gave me sufficient information to enact change in the mathematics classrooms as part of the Action Research for this project.

The main purpose of focus group research is to draw upon respondents’ attitudes, feelings, beliefs, experiences and reactions in a way in which would not be feasible using other methods, for example, observation, one-to-one interviewing, or questionnaire surveys. Focus groups rely on interaction within the group based on topics that are supplied by the researcher (Morgan 1997: 12). Hence the key characteristic which distinguishes focus groups is the insight and data produced by the interaction between participants. This is to ensure that participants have a specific experience of or opinion about the topic under investigation; that an explicit interview guide is used; and that the subjective experiences of participants are explored in relation to predetermined research questions. An example is when the participants were asked ‘Which class or which teacher helped you?’ and one of the participants responded:
Well, there’s, like, most of them, they’re really nice and supportive, but some lessons are, like, a bit, like, they help a few people that are, like, really struggling, but they never really help the rest of the people. Like, they focus on a few people and that’s about it. But that’s only a few. That’s, like, three classes or two. And another participant replied: Yes, most of my teachers are quite supportive in that way, but like A, some of them can be a bit focusing on some people and, like, thinking other people can do well, so it doesn’t mean they’re… It means they’re not struggling. So they, sort of, put you aside and, like, …, you’re fine, you can do it yourself, even when you’re struggling on the topic.’
Therefore, focus groups are particularly useful when there are power differences between the participants when the everyday use of language and culture of particular groups is of interest, and when one wants to explore the degree of consensus on a given topic (Morgan & Kreuger, 1993). An advantage of focus groups to clients, users, participants or consumers is that they can become a forum for change, both during the focus group meeting itself and afterwards. For example, in this research the participants were asked: ‘… to design how maths should be taught at Secondary School, how students can really learn well…’ and they replied: Like, maybe a bit more interactive lessons because, like, it’s really, like, when they’re, like, with their friends and they can learn with their friends, but then still be with someone that they hang around with and, like, and then, but still have, like… Sort of, sometimes it’s really like they could be really interactive because people… Like, textbooks, example, are a little bit boring and, like, put you off, like, you just, sort of, read that. Like, say the teachers maybe help a bit more because, like, they say I can’t really explain this to you. It’s a bit, like, it’s, kind of, annoying when they can’t really do that. Not in my test, but, like, just in general classwork. So yes. I think they should make lessons more interactive because we usually always do textbook work and when, like, you’re stuck in your seat and you’re stuck in a textbook it gets, like, really boring, so I’d like to every once in a while, like, have an interactive lesson.
A focus group is a small-group discussion guided by a trained leader. It is used to learn more about opinions on a designated topic, and then to guide future action that can bring change to an organisation (Morgan & Kreuger 1993). A main advantage of this method derives from group relations evident in the sessions. Students were encouraged to explain, challenge and share their honest views on questions asked. Listening to the ideas, opinions and experiences of others demands that we interrogate our own beliefs, and this was evident in these interviews. The reason for a significant level of candidness may derive from a move in the influence of the relationship between the researcher and participants. In focus groups, the researcher is in a marginal position and participants are amongst their peer group. This seems to make participants more willing to discuss topics openly in their own language than they would in one-to-one research environments. Here the manner was particularly useful as a means of allowing students to express their views and experiences without hindrance by the constraints inherent in one-to-one discussions with a researcher. Thus, focus groups are an effective way of ascertaining detailed views and experiences on relevant mathematical questions asked. Although the groups were guided by an agenda, they were able to ‘snowball’ their views on issues, presenting a wider context for their own position. For example, views on motivations and learning often generated a wider discussion. The advantage of this method over face-to-face interviews is that each speaker provides a platform for another to contribute, rather than responding only to a predetermined list of questions. Here participants were prepared to add to or qualify what had been said previously, providing a much more complete picture of their mathematical world.
Participants provided long, detailed narratives about their experiences in mathematics, which often revealed their views and motivations. However, the analysis of the data emerging from group interaction can also provide a rich understanding of how students learn mathematically and, on balance, I would argue that focus groups should be used more widely. From the experience so far, the method generated data of range, depth, specificity and personal context which can stand alone or complement other research methods. Ultimately, using focus groups with students in education can help close the ‘culture gap’ between researchers and the subject they seek to understand.

This paper has examined the use of focus groups as a method of understanding teachers’ practice in secondary mathematics through the interrogation of students’ ideas, beliefs and experiences. The results illustrate that a series of ongoing focus groups should provide a valuable longitudinal viewpoint. Although focus groups seem to have been used seldom in educational research, the results of the groups reported here illustrate the contribution that this method can make as a method to provide a picture of the views and experiences of students in a secondary school.

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