The time-line of the study

Data collection for the study was conducted during the period 2007 to 2008. The pilot study conducted in 2007 helped guide the design of the classroom study conducted in

87 2008, but no data from the pilot study was used directly in this thesis. A time-line of the study is presented in Table 3.2.

Table 3.2.

The Time-line of the Study

Date Event

April – Sept. 2007 Literature survey and study design

September 2007 Informal approach to the all-boys school for pilot study

October 2007 Social Science Human Ethics Committee formally approved study (Appendix B.2)

November 2007 Tasmanian Department of Education formally approved study (Appendix B.4)

December 2007 Pilot study conducted at the all-boys school

March 2008 Formal invitation to the two schools to participate in the study May 2008 Consent to participate in study

June – Ju1y 2008 Classroom data collection stage September 2008 Detailed study data collection

October 2008 Colleague teacher interviews and sample size follow-up test 3.2.6 The sample of participants

Five criteria were used to select the class cohort: (a) students had sufficient background mathematical skills and knowledge to allow the sample size model to be potentially accessible; (b) time and flexibility existed within the mathematics course; (c) the class had access to a set of computers; (d) school, colleague teachers, and students were supportive; and (e) students had the potential to benefit from the opportunity.

The most junior level of school – Year 9 – at which the topic of explicitly determining sample size could be conducted, was determined by the mathematical concepts involved. The large population sample size model (Section 2.4.13) required calculating surds and the reciprocal of surds, and these topics are not considered until early high school. The most senior school level where the study could be conducted – Year 10 – was determined by the flexibility within the existing mathematics course; at senior high school Years 11 and 12 students are preparing for formal tertiary entrance examinations, so schools and teachers were reluctant to offer access for a study that did not address the existing mathematics curriculum. Students who were likely to benefit most from the opportunity presented by the study had demonstrated ability and motivation to study mathematics, such as might be demonstrated by enrolment in an elective advanced mathematics class.

88 The study was conducted with two Year 9 extended mathematics class at two single- gender government funded high schools in metropolitan Hobart. Although the student group was an extended mathematics class, the students had self-selected to enrol in the mathematics course, and both colleague teachers believed the group was of mixed ability. The students were 14 or 15 years old. Twenty-one male and 35 female students were enrolled in the classes. Two female students were international exchange students and did not have English as their first language, so their work samples were not included in the analysis.

The students who participated in the detailed study had also participated in the classroom study. The colleague teacher was asked to select and approach prospective participants using the general criteria that the students approached should offer a range of abilities, likely to engage in the work and produce meaningful data, be moderately motivated, willing to place their work under greater scrutiny, and be willing to use the Captivate screen capture software. The students were not representative of the classes, but the students did offer a range of perspectives. Students were paid a modest gratuity of A$20 and a movie pass in recognition of their contribution to the study. The research items used in the detailed study are presented in Section 3.7.

The colleague teachers, one female and one male, were the two senior mathematics teachers at their schools. Both were career teachers in their early fifties with thirty years professional experience, teaching in rural and metropolitan schools across the full range of student ability and interest. Most significantly, both teachers had had several years experience teaching senior mathematics at the Tasmanian college level Year 11 and 12, and this was thought important because it provided a longitudinal sense of the curriculum and allowed teachers to see the topic and concepts within the broader mathematics curriculum. The colleague teachers supported the project, and were always in attendance, observing the research study, offering suggestions, and supporting the study by participating in classroom discussion and offering support with behavioural management issues on the rare occasions issues occurred. The colleague teachers were invited to participate in the refinement of the teaching unit and training, but both declined citing other professional teaching commitments.

89 3.2.7 The research settings

An all-boys and an all-girls government school in Hobart participated in the study. The two schools were formally invited to participate via the school principals, who referred the invitation to the head mathematics teachers.

General indicators of each school’s culture included a high level of compliance with the school’s uniform policy and a low level of graffiti on school property. Enrolment in the all-girls school was eagerly sought with student entry restricted by residency in the immediate area, or by sibling or maternal relationship. The students were drawn from a middle-class socio-economic group. In 2010 on the Index of Community Socio- Educational Advantage [ICSEA] the all-boys school was rated at 984 and the all-girls school was rated at 993, which is marginally below the mean score of 1000 for Australian schools (Australian Curriculum, Assessment and Reporting Authority [ACARA], n.d.).

The physical environment is a factor in teaching and learning. The research study was conducted in the schools’ computer laboratories. The researcher used Fathom as a teaching aid with a data projector that projected the image of the computer screen onto a screen at the front of the classroom. Interactive whiteboards were not available. The computer laboratory in the all-girls school was used intensively and setting-up was done in the few minutes between classes, and this frequently disrupted the start of the lesson. The equipment in the all-girls school was not reliable and this also disrupted the class. In the all-boys school the computer system was largely trouble-free.

In the classroom study students used Department of Education personal computers running Windows 97-2003 operating system and Fathom Version 2. Fathom was installed on each computer in the computer laboratory, students were assigned to individual computers, and the computers were adjacent to each other. Students were able to work independently or collaboratively if they wished.

Students accessed pre-prepared Fathom work files from the school’s computer system, and students submitted work electronically using a shared drive using a filename based on their personal identity code (Section 3.2.13); this was an unfamiliar practice and students needed support initially to use the directory system. In the post-study assessment students submitted work as a hard-copy. Students’ electronic work samples were copied as a class set to a flash drive and saved to a secure drive at the university.

90 The detailed study was conducted in an office in the School of Education, University of Tasmania. Students attended, in pairs and at a pre-arranged time, during the school term vacation some six weeks after the conclusion of the classroom study. Students sat side- by-side, which allowed students to view each other’s work, in an environment akin to a small classroom. The digital audio recorder provided a record of the workshop.

3.2.8 Summary of data collection instruments