Cálculo de parámetros para evaluar la aptitud de la tierra

Sampling is a crucial aspect of research and it is important to carefully determine the population of interest and assess the suitability of the chosen sampling strategy so as to ensure research design rigour. As this was a mixed methods study, two forms of sampling featured, namely, two-stage random sampling and stratified purposive sampling. In both the quantitative and qualitative phases of the study, samples were chosen from the adjacent countries of Ireland and Northern Ireland. The decision to include samples from these particular countries was made due to the fact that Northern Ireland was the top performing European country in fourth class mathematics in TIMSS 2011, whereas Ireland, the country in which I live myself,

Chapter 3: Methodology 77 ranked considerably lower. A comparison of teachers and teaching practices in both countries, both quantitatively and qualitatively, offered nuanced insights, which provided rich, detailed answers to my research questions. As well as this, conducting research in these two countries answered the call for more research on the link between classroom interactions and student achievement in different countries (Cadima et al., 2010). Practically, I am familiar with the education systems in both countries, which ensured that I understood the phenomenon under investigation (Silverman, 2004).

With respect to the quantitative phase of the study, it was important that an unbiased sample of the population was included in the research design, so as to allow for generalisation (Muijs, 2011). TIMSS 2011 employed “rigorous school and classroom sampling techniques” (TIMSS & PIRLS International Study Centre, 2011, p1), which included two-stage random sampling and national sampling plans that were implemented by National Research Coordinators and TIMSS sampling experts. In Ireland, a nationally representative sample of 151 schools and 220 teachers took part in the TIMSS 2011 study, and a total of 4560 students completed the TIMSS assessment. The large sample means that “the data are likely to be an accurate reflection of the achievements, attitudes and environment of Fourth class students” (Eivers and Clerkin, 2012, p6). Similarly, in Northern Ireland 136 schools and 184 teachers took part in the TIMSS 2011 study, and a total of 3571 students were assessed (Sturman et al., 2012). Statistically, the large samples for Ireland and Northern Ireland reduced “the extent to which noise of error variance influences observations” (Tolmie et al., 2011, p55) and, as such, provided a more dependable picture of effects with decreased possibility of type I and type II statistical errors (Muijs, 2011).

The qualitative phase of the study involved a smaller sample of just 11 interviewees. This smaller sample is typical of the number of informants included in qualitative research, as it allows for greater depth to be achieved within the data (Hitchcock and Hughes, 1995). Although the sample was small, it was nonetheless important to engage in a transparent sampling strategy. Stratified purposive sampling was employed in the second phase of this study and this is a common feature of qualitative research (Cohen et al., 2011). This non-random form of sampling allowed me to strategically choose research participants from subgroups of interest (Bryman, 2012), which was important, as I wanted to integrate the quantitative TIMSS 2011 data with the qualitative interviews conducted in 2015, insofar as was possible (Day et al., 2008). It was not possible to select teachers who had taken part in TIMSS 2011 for reasons of anonymity; therefore, research participants were selected instead from categories of schools that mirrored the categories used in TIMSS 2011. This sampling strategy is typical in sequential mixed methods research, where one sample precedes and influences another (Teddlie and Tashakkori, 2009). For example, the TIMSS 2011 school questionnaire categorised schools into five areas including urban, suburban, medium size city or large town, small town or village, and remote rural (5B, schools questionnaire). Schools with populations that were highly disadvantaged, highly affluent and with high numbers of English as an Additional Language (EAL) status children were also categorised. In addition, fourth class was the primary school grade level studied. Hence, I selected fourth class teachers who worked in schools that fell within each of the aforementioned categories as research participants for the qualitative phase of the study. This is depicted in Table 3.6. While the use of stratified purposive sampling in this manner allowed for integration of the qualitative and quantitative phases of the study, it also ensured the inclusion of teachers working within a variety of school settings in the study, which takes

Chapter 3: Methodology 79 cognisance of Campbell et al.’s (2004) assertion that context matters for teacher effectiveness.

Table 3.6 below summarises the details of the eleven interviewee participants of this study and also provides information on their schools’ size and the TIMSS categories that the schools would fall under if the schools had been involved in TIMSS 2011. Pseudonyms are used to ensure interviewee anonymity.

Table 3.6 Interviewee and school details

Interviewee School Identifier Code School Location (TIMSS Classification) School Population (TIMSS Classification) Years of Experience Maths Major School Student Number (Approx.) Years teaching Fourth Class or Primary 6 Finola Ireland,

School A Suburban Highly Affluent 11 Yes 250 1 Alison Ireland,

School B

Medium Size City/Large

Town

High EAL 9 No 400 3 (non - consecutive) Una Ireland, School C Urban Highly Disadvantaged 5 Yes + Master’s 400 1 Patricia Ireland, School D Small Town/Village 23 No 230 4 (2 consecutive) Ciara Ireland,

School E Remote Rural 12 No 12

4 (composite class setting) Phyll _{School F} Ireland, _Town/Village Small 9 No 350 _consecutive) 3 (non - Majella N. Ireland, School A Small Town/Village Highly Disadvantaged 16 No 250 6 consecutive Gareth N. Ireland,

School B Remote Rural 16 Yes 190

9 (consecutive

blocks) Geraldine N. Ireland, _{School C} Suburban Highly Affluent 25 Yes 350

5 consecutive (20 years in P7) Michael N. Ireland, School D Small Town/Village 5 No 190 3 (2 consecutive) Dervla N. Ireland, School E Medium Size City/Large Town 22 No 420 16 (consecutive blocks)

Although a sample size of six teachers in Ireland and Northern Ireland was posited at the outset, the final sample size was six teachers in Ireland and five teachers in Northern Ireland. The sixth interview in Northern Ireland was cancelled by the participant due to unforeseen circumstances. While over twenty schools were contacted in June 2015 in order to secure a replacement interview, these attempts were not successful. However, this was not considered to be a significant limitation, as data saturation had been achieved prior to this point and the variability of themes had become stagnant (Bryman, 2012). The sixth interview in Ireland confirmed the researcher’s assumption regarding data saturation, as it did not reveal any new themes.