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Chapter 2 - Research design

The project’s methodology was qualitative, interpretive and case study, with observations, interviews (individual and group), discussions (reflections) and gathering of artefacts as the main sources of data, with a focus on understanding the project in terms of the IEWs, and with each tutor (and the Train a Maths Tutor Program itself) as a case. The methodology also had aspects of:

1. action research or action learning for both the trainers (improving their training) and the IEWs (improving their tutoring); and
2. teaching or design experiment where the training was seen as a trial of ideas that would later be modified and refined as a package for others.

The activity of the project and the analyses of the data were hermeneutic, that is contingent, emergent and cumulative.

This chapter covers the four aspects of design: participants, procedure, instruments and analysis.

Participants

The participants in the Train a Maths Tutor Program comprised the tutors (IEWs,) researcher-trainers, Wadja Wadja High School students, observers (critical friends, visiting scholars and teachers), and research assistants.

Tutors

The tutors were the IEWs from Wadja Wadja High School (AISQ) and Woorabinda State School (EQ). Eleven IEWs attended all or part of Block A of the Program – four of the five possible IEWs from the high school and all seven of the IEWs from the primary school whose teachers allowed them attend. (Though encouraged by the principals, attendance was voluntary and also dependent on the teachers’ agreeing to release their IEW, a situation that was not possible for some teachers for all or part of the Program.)

Eight IEWs attended Block B of the Program – one from the high school (new to the school and community) and seven from the primary school. For a variety of reasons, not all IEWs were able to attend each off-computer training and trialling session. (See Chapter 3.)

Students

The students who acted as trainees for the Train a Maths Tutor Program, Block A, were drawn from Years 8 and 9 at Wadja Wadja High School, and from Year 10 when there was an insufficient number of Years 8 and 9 students (mainly Thursdays). A small cohort (3) of these students acted as trainees for all six trialling days of the Block A program. With respect to Block B, there were very few students at the school in November to act as trainees for the computer activities.

Trainers

Block A. The trainers were Dr Annette Baturo and Professor Tom Cooper from the School of Mathematics, Science and Technology Education (MSTE), QUT, and Ms Eva DeVries, Project Officer (Numeracy), AISQ. Dr Baturo undertook training and trialling across the 4-week block, Professor Cooper undertook training and trialling across two weeks, whilst Ms DeVries assisted for 4 days.

Block B. Dr Baturo also undertook the computer training and was assisted by Professor Cooper, Ms Lorrie Maher, Ms Sandra Berry, and Ms Kylie Thompson. Kylie also ensured that the computer laboratory was functional throughout the training, and video-taped all training and curriculum development sessions.

Critical friends

Ms Lorrie Maher, ex AISQ, was a nominated Critical Friend for the Innovative Projects Initiative. Lorrie observed and helped prepare and administer some activities in Block A (Week 3) and Block B, and attended the Graduation Ceremony in Week 4 (at the end of Block A).

Professor Miriam Amit is the Head of the Center for Science and Technology Education at Ben-Gurion University of the Negev in Israel. Before this, she was Chief Superintendent, Department of Mathematics, in charge of the teaching of mathematics within the Israeli Ministry of Education. Because of her extensive work with Bedouin students in Israel, the researchers invited Miriam to QUT to compare and contrast Indigenous mathematics teaching and learning in Queensland and Israel. In this capacity, Miriam acted as critical friend during week 4 of the training program and attended the Graduation Ceremony.

Visiting scholar

Ms Sandra Berry is a PhD student at Purdue University in Indiana, Lafayette, US. Her research interest is in the field of professional development with traditional elementary and middle school mathematics classrooms. She was in Brisbane to compare professional development models in Queensland with those in the United States, and asked if she might attend the final training week in Woorabinda to add to her experience. Sandra acted as observer and critical friend during Block B training.

Teacher observers

The Years 8 and 9 teachers observed the Block A trials when able (i.e., when all of their students were involved in the trials). This meant, in practice, that one teacher observed all the trials whilst the other observed the Thursday trials only. As well, the Deputy Principal of Wadja Wadja High School observed the trialling sessions in Week 4 of Block A. No trials were undertaken in Block B.

Research assistants

Three research assistants (Ms Kylie Thompson, Ms Shani Doig, and Ms Gillian Farrington) were also involved, at various times, in the project. Kylie and Shani undertook many of the interviews, videotaped the training and trialling sessions, and observed the proceedings. Gillian undertook the administrative activities related to travel and to payment claim forms.

Kylie set up the advertising of the project (see brochure in Appendix A) and travelled with the Wadja Wadja Community Liaison Officers to obtain parent/guardian consent forms for the students who would be involved in the trialling component of the Program, and to invite parents to participate in the project. Kylie also oversaw the various activities related to the Graduation Ceremony at the end of Block A and made the cake for the Ceremony (see Appendix B for pictures).

Procedures

Procedures for the Program covered timetable, training/trialling focus, daily schedules and learning spaces.

Timetable

The Program comprised a 4-week block (Block A – Concrete Training) and a 1-week block (Block B – Computer Training), with the training and trialling aspects of the Program contingent and contiguous. Table 3 provides an overview of the timetable which was planned in conjunction with the IEWs.

Table 3: Train a maths tutor program: timetable, activities, training personnel

Note. Ms Lorrie Maher, Critical Friend, observed the procedures in Block A (Week 3) and Block B, and attended the Graduation Ceremony. Professor Miriam Amit (Israel), visiting expert in indigenous education in Israel, observed the activities in Block A, Week 4. Ms Sandra Berry (US), visiting PhD student who is expert in teacher professional development, observed the activities in Block B.

The reflections at the end of the trialling days focused on the effectiveness of the IEWs’ tutoring. The interviews at the end of Week 1 focused on each IEW’s background while the group interview at the end of Week 4 discussed the IEWs’ reflections on the four weeks of training.

Training/trialling focus

The initial training plan was to dedicate the second week to 2-digit numbers and the remaining two weeks to 3-digit numbers. However, Week 2 revealed the IEWs’ paucity of understanding of the patterns embedded in 2-digit numbers which lead to an understanding of seriation (1 more/less and 10 more/less10 less) and the numeration processes, namely, identifying, representing, counting, comparing/ordering, regrouping and approximating (see Section 3.3). Therefore, two weeks were devoted to establishing the foundations of numeration processes, leaving just one week to facilitate transfer of knowledge to 3-digit numbers. As a result, training did not extend to the use of virtual materials which is an important aspect of teaching 2- and 3-digit numeration. Therefore, training in virtual mathematics activities was planned for later in the year but the time within the last school term meant that one week only could be devoted to the use of technology in teaching. Table 4 provides the focus of each training and/or trialling session for Blocks A and B. The trialling activities are provided in Appendix A, Interim Report.

Table 4: Train a maths tutor program: Training and trialling schedule of activities for Blocks A and B

Note. * Calculators were used to abstract the symbolic mathematics embedded in the processes; ** 3-digit numbers included only if students understood the preceding 2-digit activity.

Daily schedules

Tables 4 and 5 provide the daily schedules for the Block A training and trialling components respectively of the Train a Maths Tutor Program. Table 7 provides the daily schedules for the Block B computer training and activity development components of the Train a Maths Tutor Program.

Table 5: Daily schedule of activities for Block A training of the Train a Maths Tutor Program

Table 6: Daily schedule of activities for Block A trialling of the Train a Maths Tutor Program

Note. *The morning teas became a vehicle for informal reflection and for “hearing the voice” of the IEWs. Much of the feedback that resulted in changes to the Program was given during these informal times. (See Chapter 3.)

Table 7: Daily schedule of activities for the Block B training component of the Train a Maths Tutor Program

Learning spaces

To facilitate long-term benefits for the Community, the project was designed to use learning spaces that would make the Program more visual to the Community. To this end, community venues were used as the learning sites for the IEWs. For example, the training took place in the Community Skill Share building, trialling took place in the Community high School and morning tea reflection and sharing took place in the Community Hall which was a casual meeting place for the people within the community.

Instruments

The instruments consisted of:

1. planned interviews with IEWs (pre and post), external observers (post), and teachers and administrators of the IEWs (delayed post);
2. observations of the training and trialling sessions;
3. ad hoc discussions with participants (particularly reflecting on trials); and
4. collection of artefacts (e.g., training materials, photographs of IEWs’ activities, IEWs’ and students’ work, computer programs).

Interviews

The pre-interviews, held in the first week of the Program and undertaken with individuals, were semi-structured. They covered the background of the IEWs – their education, their life in Woorabinda, their beliefs about their capacity as an IEW, and their role as an aide to the teachers. The IEWs’ responses were audiotaped.

The post-interviews held in the last week were of three types. The first were brief semi-structured interviews with the IEWs and covered their  perceptions of the Program and its effect on them. These interviews were audiotaped. The second was a semi-structured group interview with the IEWs and covered their reflections about the effectiveness of the Train a Maths Tutor Program and their feelings at the beginning and end of the Program. This interview was videotaped. The third were unstructured interviews with the observers (critical friends, visiting fellows and teachers) and covered their observations and evaluations of the Program. The responses for these interviews were recorded with field notes.

The delayed-post interviews were unstructured and were held with teachers and administrators of both schools later in 2003 and in the first half of 2004. They focused on changes in the behaviour of the IEWs as they returned to their roles in the schools as IEWs.

Observations, discussions and artefacts

The training sessions and the sessions in which the IEWs trialled activities with the students were observed by many participants – other researchers, critical friends, visiting scholars, teachers from Wadja Wadja High School, and research assistants. Most of the sessions were videotaped and still pictures were taken. The researchers and research assistants kept field notes where possible; the other observers were interviewed as to what they saw.

The informal atmosphere of the training, the social occasions around morning tea, and the meetings around the community, offered opportunities for ad hoc and informal discussions between researchers and IEWs. This was particularly so during the morning teas where the IEWs were encouraged to share their experiences and to reflect on what was important in the training and the trials. Accounts of these discussions were recorded as field notes as soon as it was possible.

For Block A, activity sheets, examples of IEWs’ work, and photographs of activities, materials and board work were collected throughout the Train a Maths Tutor Program. For Block B, the files developed by the IEWs were archived and added to the collection. These formed an illuminative if incomplete record of some of the highlights of the Program.

Purpose

The pre and post interviews with the IEWs and the observations of the training and trialling sessions were to collect evidence of the growth of the IEWs’ mathematics knowledge, teaching knowledge, and confidence. The interviews with the observers, the observations of the sessions, the discussion and the artefacts provided evidence of the effectiveness of the training and the trials, as well as information on the IEWs’ growth of knowledge.

Limitation

At the beginning of the study, it was intended to gather data on the effectiveness of the trials in terms of students’ knowledge and affects with respect to mathematics – to see how the trials affected the students understanding of mathematics. However, the low and irregular attendance of students at Wadja Wadja High School made this impossible. Only three students attended the trials with any regularity; the rest came and went. Most students were not available and/or motivated for pre and post tests, and were too irregular for any conclusions to be drawn from their performance.

Thus, the evaluation of the trials was restricted to observations of the students within the trials and the perceptions of the observers and the IEWs as to students’ appreciation, enjoyment, challenge and learning with respect to the trial materials.

Analysis

The videotapes of the training and trialling sessions were collated and important sections condensed into one CD to provide one record of the 5 weeks of the Train a Maths Tutor Program. The artefacts were organised into another record of the Program. These two records were combined with the field notes of discussions with IEWs and interviews with observers to give a rich description of the 5 weeks of the Program. This description was summarised and organised to make up the content of Chapter 3 of this report.

The audiotapes of the pre- and post-interviews (individual and group) were transcribed and combined with the field notes of the delayed-post interviews to give a description of the knowledge, beliefs, affects and tutoring skill of each IEW before and after the Program. These descriptions for each IEW were triangulated with the rich descriptions of the Program (and, in particular, the comments of the observers) to give a more detailed comparison of the IEWs pre and post the Program. This information makes up the content of Chapter 4.

The pre-post comparisons and the rich description of the Program were then analysed in terms of the effectiveness of the Program for the IEWs and the students. Analyses focused on: (1) developing a checklist of categories in terms of which the tutor change (mathematics knowledge and tutoring ability and confidence) can be described and, to some extent, quantified; (2) identifying examples of student change in terms of mathematics knowledge and engagement in the trials; and (3) identifying training practices and trialling experiences that appeared to have a positive (and negative) effect on tutor and student change.

The analyses of effectiveness were used to: (1) enable models to be built that may explain the success or otherwise of the Program, and (2) facilitate the development of a package of materials to support tutor training and student trials.

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