Sample Composition

The school in which the study was undertaken is designated Disadvantaged within the DEIS scheme (Delivering Equality of Opportunity in Schools) in Ireland. The school had six separate years ranging from first year to sixth year. The students’ age ranges are from 12-18 years. In the first three years the students study for the Junior Certificate in Education at the end of which they take a state examination. These students were aged between 12-15 years. The

second year students were chosen, as participants for this study, by the author for the following reasons:

1. The students in second year were aged 13 -14 years old. Younger students were considered to be more suitable participants for the study for two reasons. The beliefs held by the younger students about mathematics and its teaching and learning may be less entrenched and hence may be more open to change. Students at age 12, irrespective of gender or nationality were a half a point more positive than students at age 15 in their beliefs about learning mathematics (Andrews et al., 2007:214).

2. Changes were being introduced countrywide in Ireland to the teaching of mathematics at the time. Project Maths, as the new curriculum has been called, is a substantial curriculum innovation in second-level mathematics (N.C.C.A., 2008). The second year students were not to be included in the implementation of these changes until 2013, after the fieldwork had been completed. In attempting to measure changes in students’ beliefs over a period of time for this study it was considered that introducing additional variables such as involvement in Project Maths might make it more difficult to assess outcomes from this study, so this ruled out the use of other year groups.

The second year students were divided into classes as follows:

Table 3

Classes Number of Participants

Class 1 27

Class 2 27

Class 3 17

Class 4 10

Total 81

Of the 81 second-year students in the school 78 took part in this study. The breakdown of the classes by gender was as follows:

The students attending the school, in the main, had transferred from five or six local primary schools. The year group was divided into classes on the basis of the standardized Drumcondra mathematics and literacy tests of achievement (Drumcondra, 2010). This test gave an indication of the standards achieved by students in mathematics in the primary school. However, in a small number of these schools, the primary syllabus was not completely covered making these scores somewhat unreliable. Class lists of students were routinely adjusted in the school after achievement in the December school tests at the end of term one in first year secondary were examined. The December scores arose from school-based tests designed by teachers and completed prior to Christmas. The scores achieved in the Drumcondra tests did still provide an overall picture of the sample group taking part in this study in comparison to the national scores at the time. The tests were given to students in March 2009 prior to their entry to the school. Student scores (some students were absent) from the mathematics test are indicated in the table below:

All students were expected to study the ordinary level mathematics course for the school year in which the study was undertaken, the second year of the Junior Certificate cycle. Within this framework school management expected a minimum of one class to undertake the higher-level mathematics course, two groups were expected to undertake the ordinary level course and the small class four would follow the foundation level course Junior Certificate course. Outcomes from the Drumcondra mathematics test for the participants in this study indicated that 82.1% of the participants in this study lay within the 0th - 60th percentile nationwide and 3.9% in the 60-100th percentile. Comparing these figures from the table above with national statistics from Table 6 below on

percentages of candidates studying each of the available levels for examination indicate differences.

The percentages given for the participants studying each level in the table above indicates those placed in these second year classes by management policies. The number of participants given in Table 6, who actually did sit the higher level papers in June 2012, was lower than those given. The sample was

of lower ability than the national average, as shown above. The lower

proportion of those actually taking the higher level suggests that the work was challenging for those participants.

The school would seem to be generally well-respected by local communities with full enrollment for the past number of years and a waiting list in operation. Parents had a number of schools to choose from in the area including 3 mixed community schools, 2 single sex girls schools, 2 single sex boys schools. The school operated a strict first come first served policy in enrolling students for the academic year.

All of the classes were studying the Junior Certificate Ordinary Level syllabus, although at different paces for the academic year. Class 1 was expected to complete the ordinary level syllabus over the course of the year, Class 2 a large part of the syllabus, Class 3 was expected to make adequate progress with the content and Class 4 was expected to make slow progress. Entry expectations, on entering secondary on the level of mathematics that would be studied, by students and their parents were most often ordinary level standard. This was based on the author’s long experience of teaching these students. A number of topics from the syllabus were chosen for study at the beginning of an academic year at the teacher planning meetings. Within these general guidelines

individual teachers were free to plan their own individual teaching periods. Class 1 was chosen to be the experimental class for this study as it was reasonably sized and it had been allocated to the researcher’s teaching timetable for that academic year. The remaining three classes formed the control classes for this study.