Data Analysis

The literature provided a typology of techniques available for analysing data for mixed methods studies (Onwuegbuzie et al., 2007b; Johnson and Turner, 2003; Teddlie and Tashakkori, 2009). Waysman et al. (1997:236) warns that

researchers still lack ‘clear operative guidelines’ for blending mixed methods evaluations and that great care should be taken not to misinterpret the findings. Ivankova et al. (2009:18) claims the priority of the quantitative or qualitative data is determined by the study purpose and the research questions asked in a study. Recently Heyvaert (2013:323) argues that a critical appraisal framework for the evaluation of the methodological quality of mixed methods studies is overdue.

A mixed analysis matrix involving mixed methods consists of a number of analysis types generating a general typology (Onwuegbuzie et al., 2007b:8). The authors discuss what they describe as the fundamental principle of mixed analysis. They describe this principle as one that involves the use of

quantitative and qualitative techniques that are used either concurrently or sequentially (Onwuegbuzie, 2007b:5). Johnson and Turner (2003:298) provide a matrix of data collection strategies for mixed methods research. This matrix was adapted by Teddlie and Tashakkori(2009:207) who emphasised its use with mixed methods research. They describe the two basic mixed method data collection strategies for use with MM studies. The authors describe these as Within-strategy and Between-strategies data collection strategies. The within- strategy involves gathering quantitative and qualitative data using the same data collection strategy (Teddlie and Tashakkori, 2009:18). The between- strategies mixed methods data collection is referred to quantitative and qualitative data that use more than one data collection strategy. Between strategies mixed methods may be associated with sequential designs and as this design had already been chosen for this study (Section 3.4.3.1 above) it was considered appropriate for use as a data collection strategy for this study.

Quantitative Data Analysis:

SPSS software was used to analyse the data collected on all of the research questions from the MRBQ survey instrument. The results of the statistical tests are described in detail and illustrated in Chapter 4.

In this study the internal consistency of the four factors of Mathematics Related Beliefs Scale (MRBQ) were tested using Cronbach’s Alpha. This measured the internal consistency among the items of the scale and was useful for

establishing reliability in multi-item scales (Cohen, 2007, Tavakol, 2011). Tavakol goes on to say that alpha is a property of the scores on a test from a sample group of individuals and hence alpha should be measured each time the test is administered.

Related t-tests were chosen as an appropriate measurement of analysis of the data. The tests were carried out on the total scores for each of the factors. These tests were considered to be appropriate as each student produced a pair of scores from the survey MRBQ Scale, one score from before the intervention and one after the intervention was completed. The rationale for calculating the t- tests was to see if there was any change in the scores on any of the four factors

from before to after the intervention. Means are calculated to see if they differ a little or a lot (Field, 2005:286).

Independent t-tests were carried out to see if there was a difference between the intervention group and the control classes on students’ beliefs about the teacher’s role, their competence in mathematics, relevance of mathematics to their lives and mathematics as an inaccessible subject.

Analysis of Variance (ANOVA) was then chosen as the appropriate method of analysis. Use of the Anova test was to determine how the students’ beliefs fared from before to after the intervention in the classroom. A two-way Analysis of Variance (ANOVA) was used to test for differences between the four classes of students and/or differences in gender.

Focus Groups and individual interviews Data Analyses:

The data collected from the focus groups and individual interviews were analysed separately. The data from the focus groups was analysed using two types of analysis as this is thought to strengthen the trustworthiness of the findings. Onwuegbuzie et al. (2009b:25) used a 2-dimensional matrix indicating analytical techniques as a function of approach (Quan. v Qual.) and analysis emphasis ( case v variable). Case oriented techniques include Constant comparison analysis, Keywords-in-Context, Classical Content Analysis, Text mining, Member Checking, Micro-interlocutor analysis (Onwuegbuzie, 2009:25). Constant comparison analysis is commonly used to analsyse qualitative data (Onwuegbuzie, 2009; Teddlie and Tashakkori, 2009; Angell and Townsend, 2011). Constant comparison analysis and micro-interlocutor analysis are both considered to be suitable for qualitative phases of a mixed methods study (Onwuegbuzie et al., 2009b:25). Member checking was considered for use with this study to confirm the information interpreted from the focus group data. However, it was not possible to use that method as some of the individuals in the focus groups were no longer present in the school.

a. Constant comparison analysis (Leech et al., 2007:565) which has been termed coding and

b. Micro-interlocutor analysis that attempts to assess the level of consensus in answers given in the focus groups (Owuegbuzie et al., 2009:7).

Data collected from the individual interviews was analysed using the same methods as used with the focus groups above. In both the focus groups and individual interviews constant comparison analysis was undertaken inductively with the codes emerging from the data (Leech et al., 2007:565).The data

collected from focus groups acted as a follow-up that might assist in interpreting the survey results (Morgan, 1996:135). Explicit comparisons of survey and focus group results shows the biggest difference found between the methods was the ability of the focus groups to produce more in-depth information (Morgan, 1996:137).

3.9.1 Conclusion

This study used a quasi-experimental sequential explanatory mixed methods design. It attempted to measure the change in students’ beliefs about

mathematics and its teaching and learning after a classroom intervention was carried out in the classroom. Decisions made on the design of this study were influenced by the current literature at the time the study was implemented. The study was predominately quantitative with a qualitative approach included to extend and enhance the findings. The quantitative data collected used a psychometrically tested survey instrument and was analyzed using statistical methods. The qualitative data consisted of focus groups and individual interviews.

Chapter 4) Results

The purpose of this study was to measure changes in students’ beliefs about mathematics and its teaching and learning following a classroom intervention. This chapter presents the results of this study. The quantitative and qualitative data collected in this study were separately analysed and the results are reported below. The results from the quantitative and qualitative data are then combined. A discussion of the results is in the conclusions chapter (Chapter 5) that follows.

Research on the analysis stage of the mixed methods research process is a very undeveloped area in the literature according to Onwuegbuzie et al., (2009b:15) who advise that extra care is needed when combining

interpretations stemming from quantitative and qualitative data findings. However, an agreed comprehensive framework for mixed data analysis does seem to be developing in the literature currently. The framework used with the data from this present study was chosen as being in keeping with the current literature.

This chapter is therefore structured as follows: 1) Analysis of the quantitative results:

Descriptive statistics were used to summarise the data. As previously stated in Chapter 3, the fully mixed sequential dominant status design was the chosen design for this study, with the quantitative approach being dominant. The study’s focus was on changes in students’ beliefs about their teacher’s role, about their personal competence, about the relevance of mathematics and about mathematics as an inaccessible subject after the intervention had been completed, all factors of the MRBQ scale. The analysis first provides an

overview with calculations on these factors on all participants (experimental and control) in the study combined together. The statistical tests in this study were used to analyse separately the two sets of scores (i.e. before and after the classroom intervention) from the MRBQ questionnaire. Statistical tests carried out included related (paired) t-tests and independent t-tests and ANOVA. The aim was to discover whether there was a quantitative relationship between the

classroom intervention and changes, if any, to students’ belief scores for these factors of the scale.

(2) Analysis of the qualitative results:

The data collected from the focus groups and individual interviews were analysed separately and the results are recorded below. The constant comparison analysis tool was used to analyse the focus groups and the individual interviews (Onwuegbuzie, 2009:27). As mentioned previously in Chapter 3 a second line of analysis, that of the focus group interviews, was informed by the micro-interlocuter (MIC) approach: this was intended to reveal the level of consensus and dissention in the data from the focus groups

(Onwuegbuzie et al., 2009:10). The MIC approach was valuable because consensus can otherwise go unnoticed. This approach was chosen to provide confidence that the interpretations of the data were properly made. The opportunity to return to the students for member checking was not available. If this had been possible, it would have informed further discussion about the extent to which the interpretations made from the data collected were valid. Appendix B contains data from the interviews and results of analyses carried out on them.

The reports below, of all of the outcomes, have each been divided into three sections that matched the four research questions on the factors belonging to the MRBQ scale. The different sections are:

a) Constant comparison analysis of the focus group data b) Micro-interlocuter analysis of the focus group data

c) Constant comparison analysis of the individual interviews data

3. Comparison and Contrast: The final section combines the outcomes from