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Outcomes

This final chapter of the report draws together the formatively-oriented day-to-day descriptions of the Train a Maths Tutor Program (see Chapter 3) with the summatively-oriented descriptions of the effect of the Program on the IEWs (see Chapter 4) to form conclusions with respect to training Indigenous IEWs as mathematics tutors. The chapter summarises the impact of the Program on the IEWs, their students, the community in general, and the researchers, in particular (see Section 5.1), discusses the components of the Program that enhanced and inhibited the successful training of the IEWs (see Section 5.2) and lists findings and implications (see section 5.3).

Impact of program

The Train a Maths Tutor Program had the potential to impact on the IEWs who were trained as tutors (see Section 5.1.1), the students who were tutored during and after the Program by the IEWs (see Section 5.1.2), members of Woorabinda Community (see Section 5.1.3) and the researchers who did the training (see Section 5.1.4

Impact on IEWs

The Train a Maths Tutor Program had a major impact on most of the IEWs involved as evidenced by their attendance and positive changes in all characteristics across Blocks A and B. Observers were continually impressed by the IEWs’ progress in affects, beliefs, knowledge and skill, stating how unusual it was and how much more effective the IEWs would now be. The improvement in theory and practice enhanced the IEWs’ ability to support students with difficulties in mathematics learning in terms of planning, preparation and delivery. These improvements were evident to the IEWs themselves, leading to a sense of pride in their own accomplishments and enthusiasm for future learning - both becoming hallmarks of the IEWs’ participation in the Program.

However, more detailed analysis showed that the significance of all positive changes was due to the low ratings at the beginning of the Program as well as the high ratings at the end. Most of the IEWs came to the Program lacking confidence in their own ability to do mathematics and effectively tutor students and with beliefs about mathematics, computers, and mathematics learning and teaching that were too instrumental to be effective in facilitating student understanding. Most of the IEWs also had very inadequate knowledge of 2- and 3-digit numeration and of the material, language, and computer usage that is appropriate for teaching numeration. The IEWs’ knowledge of the students and Community was insufficient to compensate for this lack of knowledge. Overall, the IEWs’ affects, beliefs, knowledge and skill at the beginning were such that would make it difficult for them to effectively tutor students in mathematics.

In general, the data in Chapter 4 showed that the Train a Maths Tutor Program met real needs in the IEWs and at the schools at which they worked. Without the training provided by Block A of the Program, the IEWs would never have been able to undertake the effective mathematics tutoring activities that teachers, administrators and observers reported (see Section 5.1.2).

Impact on students

Although no direct pre-post information was available with respect to student affect and achievement, evidence provided from observations and delayed-post interviews showed that Block A training of the IEWs appeared to have had a positive impact on Woorabinda students.

This evidence was apparent early in the Program. After observing one of the early trial sessions, two Wadja Wadja High School teachers tried to reorganise their school day so that the IEWs, as a group, could continue the same type of tutoring in their classrooms. They said that the student learning they had seen in the training session was the most positive they had experienced in a long time and felt that it would enhance their mathematics teaching.

The evidence was even stronger after the Program. The delayed-post interviews showed that administrators had observed the following in the trial sessions in the Train a Maths Tutor Program:

Kids were well behaved because they knew and liked what they were doing; enjoyed being taught by the IEWs. They liked the challenge of it, and for kids who generally didn’t succeed at school work, they liked the fact that they were able to succeed.

Kids also seemed to enjoy every part of it particularly the one-on-one teaching that they received.

The administrators argued that both the IEWs and the students had “gained confidence” and “knew what they were doing”, and that “as a result of the project, IEWs and students have a better understanding of one another and how IEWs can assist students”. One argued that the IEWs were now more successful at working with students because they were “more confident and prepared to have a go”. They said that the opportunities had “not just been in the area of maths but in all curriculum areas” and that they would like the IEWs to “gain experience with teaching a bigger group and share material with all in the class”.

The teachers also supported this position. One teacher described the changes in her IEW’s practice as “completely different”. Before the program, her IEW had tended to sit in the back of the classroom working with the students only when directed to do so. As a result of the Program, the IEW had become a more active participant in the classroom, wandering amongst the students and offering assistance without having to be directed to do so. She felt that her IEW was now more confident and knowledgeable in how to tutor students.

The strongest support for the IEWs’ impact on student performance came from the Primary School. In previous years, no students from this school had escaped the Year 2 Diagnostic Net. However, in 2004, six students had passed. The credit for this was being given to the support provided to the teachers by IEWs in Years 1 and 2, IEWs who had successfully completed the Train a Maths Tutor Program.

Impact on the community

Block A of the Program had a significant positive impact on the Community. This was evident in the graduation ceremony held at the end of Block A. This ceremony became a major event in the town. Many elders and Community members attended as did external dignitaries in Indigenous Affairs. All applauded the success of the IEWs. One Elder commented that her generation was not educated past Year 4 and that she “never thought she’d see the day when people of her community would have the opportunity to undertake a university program”. She and others indicated their pride in the IEWs’ achievement. Another elder said that the ceremony was wonderful because there was “no shame”.

This positive impact on the Community was important for the Program because it increased the potential for similar training programs to be supported in the future.

Although successful, Block B did not have the same effect as Block A. Being only one week long and having very little trialling with students meant that Block B was not of sufficient duration and did not have the community presence to attract the attention of many Woorabinda Community members (an application of the duration principle – see Section 3.1). This lack of attention and no graduation ceremony (or other form of end of training celebration) meant that Block B had little impact outside of the IEWs, particularly on the community in general.

There were indications that the affiliation of the trainers (university lecturers) and the positioning of the learning space (not at a school) had a positive effect on community impact. Some Community members came to see the Program as a University course. As described earlier, one member stated “I never thought I’d see the day when Woorabinda people would be doing University courses”.

Finally, the principle of group cohesion seemed to be important to Community impact. The IEWs in Block A became an identifiable group which, over time, the Community came to support.

Impact on the trainers

The successful experience with the IEWs in the Train a Maths Tutor Program had a strong impact on the trainers/researchers. Previous projects at Woorabinda had focused on teacher development and student performance. This project was different in that it focused on training IEWs rather than teachers and had the potential to provide a resource that would remain in the Community.

Over the duration of the Program, a feeling of camaraderie grew between the IEWs and the trainers. As a result, the trainers became more widely accepted in the Community which led to new collaborations being formed between the trainers and Community organisations (e.g., training in budgeting for parents and youth)

The IEWs’ positive reaction to the training as evidenced through their excellent attendance, their thirst for, and enjoyment of, learning, their obvious pride in their accomplishment, their support for each other and the trainers, made this the most rewarding research project ever undertaken by the researchers.

Program success

The successful outcomes of the Program may be thought of in terms of the effectiveness of tutoring skill, the continued attendance over four weeks, Community recognition, and the IEWs’ wishes to do further training. This section considers each principle in terms of its effects on success (see Section 5.2.1) and synthesises their contribution to the Program’s success in tutoring, attendance, Community recognition, and further training (see Section 5.2.2).

Effect of principles

Figure 17. Principles embedded in the Train a Maths Tutor Program

The three areas under which the principles were organised were: Mathematics and Pedagogy, Professional Development, and Social (see Figure 17). The effect of the Principles in each of these areas will be discussed in turn in this section.

Mathematics and pedagogy principles

All of the associated principles, namely, abstract mathematics, kinaesthetic learning, and language, impacted positively and directly on the success of the Program in terms of tutoring skill. They also impacted, albeit indirectly) on continued attendance and Community recognition. This resulted in a direct impact on future learning (see Figure 18).

Abstract mathematics

As the discussion in Chapter 3 showed, the first week was crucial to the Program’s success. In this week, there were no trials with students; rather, the focus was on the IEWs’ experiencing Number. The IEWs explored the structure of the number system through looking at: (1) how the system counts (e.g. through games such as Snakes and Ladders and experiencing number on hundreds boards), (2) how it is based on position and place value (e.g., through using the common materials used in teaching students such as Place Value Charts and Bundling straws), (3) how it represents single quantities (e.g., through number lines), and (4) how it is multiplicative in the way adjacent positions are related. The discussion extended to abstract understandings; an alternative base-5 number system (see Section 3.2) based on “Fee, Fie, Foe, Fum” was constructed. The possible relationships between Western number system and body parts (e.g. fingers) were discussed.

The unrelenting extension of all discussions to abstract forms of mathematics appeared to be taken by the IEWs to mean that they were being taken seriously and given the “real mathematics of the white people”. They reacted to this by an enthusiasm to learn that amazed all observers and has been extensively described in Section 5.1. It was evident to these same observers that the success of the first week and the subsequent success of the Program was due to the learning and teaching focusing on abstract mathematics. The Principle directly affected tutoring skill and indirectly contributed to continued attendance over four weeks and desire to do further training.

Kinaesthetic learning

To facilitate abstract mathematics knowledge, the instructional strategies focused on developing mental models from kinaesthetic activities linked with informal and formal language. Kinaesthetic learning was enabled by whole body activities (e.g., acting out mathematics situations), the manipulation of concrete materials (e.g., place value charts and MAB) and was based on the IEWs’ visualising mental models of the number system and the number processes (e.g., seriation – adding and subtracting 1s, 10s and 100s). The literature provides evidence that Indigenous learners learn better with kinaesthetic and visual activities (see Section 1.4.) This was found to be the case for the IEWs in this Program where kinaesthetic learning was successful in promoting abstract mathematics and mathematics pedagogy. As such, like abstract mathematics, it directly affected tutoring skill and indirectly contributed to continued attendance and further training

Language

The role of formal and informal language in mathematics learning is well-documented in the literature, particularly when learning is not in the learner’s home language (see Section 1.4).Because the Standard English of the mathematics classroom is neither the IEWs’ or students’ home language, a strong focus on developing a wide repertoire of informal and formal mathematics language was an effective support for the IEWs’ mathematics learning and tutoring skill, thus directly affecting tutoring skill and indirectly affecting attendance and future learning.

Professional development principles

The Professional Development Principles, namely, training in tandem with trialling, just-in-time support, reflecting and sharing, and duration, provided the framework for the Program and, as such, impacted indirectly on all aspects of the success of the Program (see Figure 18).

Training in tandem with trialling

The train-trial cycles were an essential component of the Program and a major direct influence on the success of the Program in terms of effective tutoring skill. They also provided an authentic motivation for the IEWs to learn both mathematics and pedagogy and an authentic focus for revision of the work covered in the training day, As described in Section 3.3, the IEWs’ success in the trials reinforced the relevance and practicality of the training sessions and provided the basis for the growing sense of pride that underpinned the positive changes in affects and beliefs (see Section 4.2) and the continued attendance of the students. The train-trial cycles also served to increase group cohesion and to develop a common identity within the group and indirectly affected Community recognition and desire for further training.

Just-in-time support

The success of the train-trial cycles required support that was tailored to the IEWs’ needs and available when needed. The low ratings assigned to their initial affects, beliefs, knowledge and skills (see Chapter 4) indicated fragility of the IEWs with respect to learning and teaching mathematics. It was essential that their first tutoring sessions were successful. Thus, the trainers designed the training-trialling cycle so that there was continuous just-in-time support. This was a crucial component in enhancing the success of the Program in terms of effective tutoring skill and continued attendance and underpinned Community recognition and future training.

Reflection

Reflection took place immediately after the trialling sessions and often continued into morning tea. It also took place on the next day during the training sessions. Public reflection was a novel activity for many of the IEWs and, hence, they tended to be reactive (not proactive) in the reflection sessions, talking to a greater extent about the students’ performance than their own performance. Positive comments from the trainers and observers concerning tutoring skills appeared to be more important to the IEWs than comments from each other. The reflection sessions during morning tea tended to be more oriented on social rather than on “professional” matters and, as such, developed and reaffirmed group cohesion. Therefore, the impact of reflection on the success of the Train a Maths Tutor Program tended to be oriented towards both tutoring skill and continued attendance, although there was also some impact on Community recognition and future learning.

Duration

The duration of Block A was very important to the effectiveness of the Program in terms of effective tutoring skill, continued attendance, and Community recognition. Although another week of training would have more fully established the IEWs’ knowledge of 3-digit numbers, four weeks was the correct balance between the learning needs of the IEWs and the difficulties schools had in releasing them. The one week of Block B was sufficient to develop embryonic expertise with PowerPoint and Excel applications to construct virtual mathematics activities, and certainly whetted the appetite of the iEWs for further training.

Social principles

The Social Principles, namely, success, group cohesion, identity, and learning space, impacted positively and directly on continued attendance, Community recognition and the desire for further training (see Figure 18).

Success

Ensuring that the IEWs’ experienced immediate success in the training and trialling sessions was an important component of the Program as it promoted the motivation and confidence to trial their new knowledge as well as contributed to group cohesion. Without experiencing immediate success, the IEWs would probably not have continued to attend, to grow in confidence and knowledge or to desire further training, and to be recognise by the Community as something special in their midst.

Group cohesion

Although the IEWs came from the same small community, they worked in different schools and had limited experience, if any, of learning together as a cohort. Initially, they were nervous about publicly exposing their mathematics difficulties, particularly in front of “white” trainers whom they perceived as experts in the field. Group cohesion (amongst the IEWs and between the IEWs and the trainers) grew across the Program, no small feat considering the initial differences, and resulted in mutual trust, the removal of shame and the development of a group willingness to try new ideas. A cohesion grew, so did group identity both in terms of how the IEWs were viewed by themselves and the Community. Thus, group cohesion impacted on the success of the Program in terms of continued attendance, Community recognition and the desire for further training.

Identity

Although not directly related to the IEWs’ learning outcomes, Identity was seen as being important for the IEWs’ continued attendance because of its effect on motivation, confidence and pride (and concomitant lack of shame). This was an important outcome, particularly for attendance, Community recognition and desire for further training. Requests by Indigenous leaders for Community training programs in budgeting, computing and horticulture appear to be related to the success of the Program in building identity.

Learning space

The choice of learning space appeared to be one of the most important components in enhancing the impact of the Program with respect to Community recognition (see Section 2.3.). The trainers spent considerable effort finding a suitable room outside of the schools even though a room was readily available in Wadja Wadja High School. As discussed in Section 1.4.4, the choice of learning space seemed to have the effect of distancing the group from their negative histories of schooling and placing it within a Community-approved framework of learning. Along with the abstractness of the mathematics, this one act appeared to say to the IEWs that they were special and they were not being patronised or short-changed in the Program. As discussed under Learning and Teaching Principles, this feeling of being special led to the commitment that laid the foundation of the Program’s success. The IEWs attended whenever they could, they were enthusiastic about learning, they prepared well for the trials, all of which impacted positively on affects, beliefs, knowledge and skills. Thus, the principle directly impacted on continued attendance, Community recognition, and desire to do further training.

Contributors to success

This section analyses how the Principles contributed to the successful outcomes of the Program (tutoring, attendance, recognition and further training) and identifies a consequences in terms of the design of the Program.

Effect of principles

The Principles impacted on the success of the Program both directly and indirectly. Direct impact was by providing knowledge, beliefs and affects and social situations that positively enhanced success. For example, the Principle of abstract mathematics directly contributed to effective tutoring skill. Indirect impact was through other Principles. For example, the Principle of just-in-time support was important in ensuring immediate success in the trials and this led to improved group cohesion and identity and through these principles affected continued attendance. The direct and indirect impact of the Principles is diagrammatically illustrated in Figure 18.

Figure 18. Principles leading to successful outcomes

The direct and indirect affects of Principles on the success of the Program was often complex. For example, the trialling sessions in Block A were part of an intricate interrelationship involving many principles. The trialling sessions enhanced the IEWs’ motivation and confidence because .they experienced immediate success which, in turn, was dependent on the just-in-time support and the quality of the previous day’s training. The IEWs were confident tutors because they had learnt mathematics and pedagogy knowledge which they believed was important and not “watered down”. Thus, the success of the training and trialling was, in part, based on what made the training sessions effective, namely, abstract mathematics, kinaesthetic activities, and language, and what made the IEWs feel important, namely, the use of special Community learning spaces

Thus, relationships between the Principles were often cyclical (see Figure 19), beginning from the first day of the Program. Abstract mathematics, kinaesthetic activities , language and learning spaces combined interacted with just-in-time support to give immediate success which, in turn, enhanced group cohesion and identity and led to the IEWs’ wishing to stay in the Program and receive further similar training. At the beginning, the IEWs had to be cajoled to attend the Train a Maths Tutor Program as they were fearful of the “big mathematics”. However, enjoyment of the mathematics activities (see Section 3.2) and an awareness that others were also anxious, allayed their fears, provided the impetus to continue, and facilitated knowledge of mathematical structures. As the IEWs became aware that they were doing important (not “watered down”) mathematics and experienced success, their confidence and motivation grew markedly to where they became proud to be part of the Program.

Figure 19. Cyclic model of Program development

Consequences

Analysis of the effects of the Principles gave rise to the following consequences.

Training with IEWs needs to face to face. This is a consequence of the need for kinaesthetic activities, just-in-time support and appropriate language, all of which require face-to-face delivery for effective learning.
The trainers and the IEWs need to have a strong personal relationship. A major component of the growth in affects and beliefs was the trust established between trainers and IEWs that the mathematics would be important (abstract mathematics) and would be delivered in a way that ensured learning (kinaesthetic activities and language). This mutual trust led to the trainers becoming part of the IEWs’ group cohesion and identity.
Training programs need the support of key community stake-holders. Having an off-school council-based learning spaces was important to the success of the Program. That this was possible was due to the support of key community leaders in the Council. The graduation ceremony also showed that elders supported the Program. Their support was the building blocks of the community impact that resulted from the ceremony.
The Program needs to build a strong sense of group pride to overcome the possible feelings of shame that can mar Indigenous capacities to participate in training. The lack of shame and the presence of joy and pride was so evident at the graduation ceremony that it was directly and openly commented on. One of the reasons for this lack of shame was the building of a group sense that IEWs were training to get better, in relation to their own performance not comparison with others, at helping students.