CLASSROOM MANAGEMENT IN MATHEMATICS CLASSROOMS

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CHAPTER 3 RESEARCH DESIGN AND METHODOLOGY

INTRODUCTION

There are various research methods which may be utilised in a research study; the choice of a research method for this study was driven by the research questions, and instruments to be used in order to resolve the problem under study (Johnson & Onwuegbuzie 2004). The main research question of this investigation was to explore how effective classroom management of Mathematics relate to the improvement of Mathematics education. The challenges and opinions of Mathematics HODs and other educator participants were explored. From the main research question, a number of sub-research questions transpired and were formulated as:
1 What are the challenges faced by educators in Mathematics classrooms?
2 What are the functions of classroom management in Mathematics classrooms?
3 Which classroom managerial skills can be applied to enhance performance in Mathematics?
4 Is educators’ knowledge sufficient to provide and manage Mathematical instruction?
5 Which elements should be included in a model for effective classroom management?
Qualitative research was employed to provide answers to the research questions. The application of research methods in this study are highlighted under the following headings: research design and methodology, data collection methods, data analysis and interpretation, ethical considerations, rigour of the study, and conclusion.

RESEARCH DESIGN AND METHODOLOGY

Research design

Burns and Grove (2003, p. 195) define a research design as “a blueprint of conducting a study with maximum control over factors that may interfere with the validity of the findings”. Similarly, Parahoo (1997, p. 142) describes a research design as ‘a plan that describes how, when and where data  are to be collected and analysed.’ Furthermore, Polit, Beck and Hungler (2001, p. 167) define a research design as ‘the researcher’s overall for answering the research question or testing the research hypothesis. The description of the research design posits that a given research design should explain the whole outline which is meant to answer research questions. The design methodologies of qualitative research are particularly robust when it comes to social validity, culminating in the involvement of participants (Kozleski 2017).
The aim of this part of the research study was to understand the educators’ perspectives on the place and role of effective classroom management in the improvement of Mathematics education in Gauteng province. The researcher was conscious of the fact that research findings may not be generalised to a larger population (Creswell 2011). In addition, the researcher was also conscious of the fact that learners who attend the participating schools are from different economic backgrounds. In some schools, the Government introduced a feeding scheme whereby learners are given food as a basic human need and this is done to enable learners focus and put more attention on school activities. Additionally, learners from disadvantaged homes usually need to be treated in accordance with their living conditions in cases where they have for example not done their homework properly because they might not have access to some materials such as calculators or Mathematical sets.
A qualitative research design was selected for this study. The reasons for selecting this design was that it was viewed as the best approach to obtain detailed and first-hand information as experienced by educators. As such, the research design was best to suit the research study with the focus on the place and role of effective classroom management in Mathematics classrooms.
Lichtman (2010) describes qualitative research as research in which a researcher gathers, organises and interprets first-hand self-collected data through interviews and/or observations in natural and social settings. Furthermore, Burns and Grove (2003, p. 19) describe a qualitative approach as ‘a systematic and subjective approach used to describe life experiences and situations to give meaning.’ The notion is supported by Jin and Bridges (2016) who describe qualitative research as one which aims to capture the complexities and subtleties of human thoughts and behaviours by understanding the phenomenon of participants’ interests.
Qualitative research focuses on the experiences of people as well as stressing the uniqueness of the individual (Parahoo 1997). Similarly, Holloway and Wheeler (2002, p. 30) refer to qualitative research as “a form of social enquiry that focuses on the way people interpret and make sense of their experience and the world in which they live”. Kozleski (2017, p. 22) observes that ‘qualitative methods make important contributions to achieving social validity.’ In addition, Kozleski (2017), further expressed that qualitative research methods offer feedback loops that can provide information in enough depth and frequency that may enable school practitioners to shift, tune, and transform their practice in an attempt to improve learning through thick and rich descriptions of a given phenomenon.
Most qualitative research studies begin with an observation of an event or phenomenon under study. In this way, qualitative studies offer the opportunity to provide subtle details that outline a presenting problem (Ponterotto 2005). Literature reveals qualitative research as an approach that targets an audience’s range of behaviour and the perceptions that drive it with reference to specific topics or issues. Kozleski (2017) explains that qualitative research is vital for an educational research study as it is empirical, stemming from experience and/or observation since it is capable of producing knowledge about perspectives, settings, and techniques thereby involving the systematic use of specific research skills and tools. Qualitative research studies therefore tend to utilise in-depth studies of individuals and small groups of people to guide and support the construction of hypotheses (Krauss 2005).
From another angle, qualitative research provides insights into the problem or helps to develop ideas or hypotheses for potential quantitative research (Kozleski, 2017). Furthermore, Kozleski (2017) alludes to the fact that qualitative research is also used to uncover trends in thought and opinions, and dives deeper into the problem. This enables exploration of how Mathematics educators were managing their teaching and learning settings and how this in turn affects Mathematics education.
Several unique aspects of qualitative research have been identified that contribute to rich, insightful results, one of which is synergy among participants as they build on each other’s comments and ideas (Flemming 2014). As such, this research study employed the qualitative approach to
explore the behaviour, perspectives, experiences, opinions and feelings of the targeted group of Mathematics educators and Mathematics HODs as 55
related parties in education. This was carried out in a qualitative manner through exploring the role that effective classroom management has in the improvement of Mathematics in Gauteng province.

 Research methodology

The research methodology consists of the sampling procedure and data collection methods.

 Sampling procedure

Johnson and Christensen (2013) emphasise the importance of using suitable sampling procedures when selecting participants to ensure the selection of a portion from the population as a representative of that population or universe. The researcher ensured that the sample selected was comprised of participants who are knowledgeable in the Mathematics subject and whose experience in managing their own Mathematics classes would provide dependable answers to the main research question.
According to Wyse (2011), in qualitative research the sample size is typically small. The researcher in this case focused on four schools in Gauteng province. Respondents were selected to fulfil a given quota. As such, the respondents had to be 24 participants consisting of Mathematics HODs and educators. In order to align the research to a qualitative approach, sampling procedures that are of qualitative nature were utilised. The researcher thus made use of purposive and convenience sampling. The researcher collected data from a total of 24 participants involving four Mathematics HODs and 20 Mathematics educators. The following table 3,1 indicates the educator qualifications.
Purposive sampling
Parahoo (1997, p. 232) describes purposive sampling as ‘a method of sampling where the researcher deliberately chooses who to include in the study based on their ability to provide necessary data.’ In support, Jacqueline and Barriors (2006) affirm that purposive sampling uses information-rich participants. This means that purposive sampling enabled the researcher to get reliable data as participants were expected to be knowledgeable. In addition, the researcher concentrated her effort to produce better quality research which is based on better instruments (Mashabela 2010).
Holloway and Wheeler (2002) assert that sample size does not influence the importance or quality of the study and note that there are no guidelines in determining sample size in qualitative research. Qualitative researchers do not normally know the number of people in the research beforehand; the sample may change in size and type during research. Sampling goes on until saturation has been achieved, in other words, until no new information is generated (Holloway and Wheeler 2002).
The researcher purposively selected participants from four schools in the Gauteng province to participate in the research. The schools purposively selected were from different locations in terms of socio-economic conditions. The researcher intended to explore the Mathematics views regardless of the location as long as it was a secondary school in Gauteng province. As such, out of the four schools selected, two schools are located in underprivileged area, the other one in a medium density while the fourth school is in a more privileged location. Purposive sampling was employed to enable feasibility in terms of getting information reform Mathematics HODs and educators regardless of age, experience or qualifications. De Vos, (2002, p. 207) describes purposive sampling as “a procedure based entirely on the judgement of the researcher.” He adds that a sample is composed of elements that contain the most characteristics representative or typical attributes of the population, in this case Mathematics educators (De Vos, 2002, p. 207).
In this research study the researcher specifically utilised a smaller group to enable capturing of lived experiences and participants’ interpretations of classroom management. The focus was on a single phenomenon which sought to explore the place and role of effective classroom management for the improvement of Mathematics education.
Challenges in utilising purposive sampling unfolded as the selection of a small size sample did not specifically resemble the population as assumed in quantitative research. Some Mathematics educators were regarded as suitable for inclusion as participants even though they were only qualified as Mathematical Literacy trained educators. This selection is in line with Parker (2010) who spelled out the educator qualification in South Africa as ranging from a teacher certificate, diploma certificate to bachelor degrees. This range of qualifications explain the level of speciality and not the subject speciality. Furthermore, research findings as shown in table 3.1 indicate that only four participants have 2 years or less experience as teachers. The researcher thus felt confident that the group of educators selected were suitable to be interviewed for this research study although there are probably not enough Mathematically qualified educators in some Gauteng High schools.

 Convenience sampling

Petersen and Warbuton (2010) interpret convenience sampling as a method of choosing participants based on how easily available, they are. The main advantage of using convenience sampling was that it reduced financial and time challenges. As noted in Chapter 2, the researcher used Mathematics educators in Gauteng Province urban area where she resides and works. Data was conveniently collected locally without travelling long distances.
The following criteria were utilised to conveniently select participants:
1 Participants had to be available, free and willing to participate.
2 Participants had to be Mathematics high school educators regardless of gender, age or ethnicity.
3 Participants had to be working in Gauteng province.
4 Participants were to read and understand the participant information sheet and sign consent forms before any data was collected. 61
5 One Mathematics HOD as the supervisor of all Mathematics educators per participating school had to be interviewed face-to-face.
6 Five Mathematics educators per school were to participate in a focus group discussion as they were understood to have experience in managing Mathematics classrooms.
The researcher had to bear in mind Punch’s (2009) observation that when utilising convenience sampling, the credibility of information attained during the research project could be questioned. As such, the researcher combined purposive and convenience sampling as an attempt to enhance credibility. However, one HOD failed to avail herself for the interview. Appointments were not easy to arrange. The researcher had to visit some participating schools several times in an attempt to secure and finalise appointments.
The findings therefore portray that a variety of data collection methods were employed as discussed in the next paragraph.

 Data collection methods

Data collection is an important aspect of any research study. Unsuitable data collection methods can lead to invalid results (O’Leary 2004). The choice of data collection instruments is therefore critical. Qualitative data collection methods vary. The researcher utilised individual face to face semi-structured interviews, focus group discussions and limited observations for this investigation. The utilisation of multiple data collection instruments was meant to enhance trustworthiness and dependability of the research findings.
 Interviews
An interview is a methodical data collection instrument that involves the interaction of two or more people with a common interest, thereby gaining knowledge or acquiring answers to the problem under study in a formal or non-formal setting as described by some writers (Kajornboon 2000). Cohen, Manion and Morrison (2000, p. 267) comment that ‘the interview is not simply concerned with collecting data about life but it is life itself, in that its human embeddedness is inescapable.’ In this research study, interviews involved conversations whereby the researcher and the Mathematics HODs could pay attention to each other with a common view of answering research questions. Interviews can be structured, semi-structured or unstructured. In this study, the researcher selected semi-structured interviewing as the most appropriate to address the research questions. Some of the interview questions were similar to those of the focus group discussion. The utilisation of similar questions was meant to compare and validate responses from the focus group discussions which took place before interviews.
Memduhoğlu (2016) describes the semi-structured interview method as a data collection instrument where research questions are outlined and the roots of the research problem is explored by providing interviewees with semi-flexibility. Semi-structured interviews enable participants to express their views freely, giving the researcher opportunity to understand the participant’s views and feelings, while at the same time enabling probing when necessary. Furthermore, semi-structured interviews allow researchers to flexibly collect personalised data by using both open-ended and closed-ended questions (Merriam & Tisdell 2015). An interview guide consisting of a list of questions was used by the researcher in order to remain focused on the main research questions (Gray 2004). The guiding questions which were utilised by the researcher are listed in Appendix F.

CHAPTER 1 ORIENTATION
1.1 INTRODUCTION
1.2 BACKGROUND
1.3 STATEMENT OF THE PROBLEM AND RESEARCH QUESTIONS
1.4 AIMS AND OBJECTIVES OF THE STUDY
1.5 SIGNIFICANCE OF STUDY
1.6 RESEARCH DESIGN AND METHODOLOGY
1.7 RATIONAL AND MOTIVATION FOR STUDY
1.8 RIGOUR OF STUDY
1.9 ETHICAL CONSIDERATIONSDITTO
1.10 DEFINITION OF CONCEPTS
1.11 OUTLINE OF CHAPTERS
1.12 CONCLUSION
CHAPTER 2 LITERATURE STUDY: CLASSROOM MANAGEMENT IN MATHEMATICS CLASSROOMS
2.1 INTRODUCTION
2.2 BACKGROUND AND CONTEXT
2.3 CLASSROOM MANAGEMENT STYLES
2.4 THE FUNCTIONING OF EFFECTIVE CLASSROOM MANAGEMENT IN SCHOOLS
2.5 CONCLUSION
CHAPTER 3 RESEARCH DESIGN AND METHODOLOGY
3.1 INTRODUCTION
3.2 RESEARCH DESIGN AND METHODOLOGY
3.3 ETHICAL CONSIDERATIONS
3.4 RIGOUR OF THE STUDY
3.5 CONCLUSION
CHAPTER 4 RESEARCH FINDINGS: PRESENTATION AND DISCUSSION
4.1 INTRODUCTION
4.2 INFORMATION ABOUT PARTICIPANTS
4.3 REALISATION OF THE ETHICAL MEASURES
4.4 RESEARCH FINDINGS
4.5 CONCLUSION
CHAPTER 5 SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
5.1 INTRODUCTION
5.2 CONCLUSIONS IN TERMS OF RESEARCH QUESTIONS
5.3 RECOMMENDATIONS
5.4 DELIMITATION AND LIMITATIONS OF THE STUDY
5.5 FUTURE RESEARCH
5.6 CONCLUSION
LIST OF REFERENCES
LIST OF APPENDICES
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