Elizabeth Warren
Australian Catholic University

Janelle Young
Australian Catholic University

Eva deVries
Independent Schools Queensland

This paper reports on a component of a research project, Young Australian Indigenous students Literacy and Numeracy (YAILN), a longitudinal study investigating learning and teaching activities that support young Indigenous Australian students as they enter formal schooling. In Queensland, students are allowed to attend a non-compulsory year of schooling, Preparatory (Prep), if they reach the age of five years by the end of June in the year they enrol. In YAILN, one of the participating schools' preparatory intake included Indigenous students who had not reached the required age for Prep. Numeracy understandings for two of these students were tracked during their pre-prep year. The pre- and post-test numeracy results and the interview conducted at the beginning of their ‘official' preparatory year suggest that this extra year of schooling enhanced their knowledge of mathematics and has (a) put them on an even footing with students from more advantaged backgrounds as they enter Prep, and (b) given them a distinctive advantage over other Indigenous students who have not had equivalent experiences.

Introduction

Young Indigenous Australian students continue to experience difficulties at school, especially in the areas of literacy and numeracy. Results from the National Report on Schooling, National Benchmarks for reading, writing and numeracy in Years 3, 5 and 7 demonstrate a high percentage of Indigenous Australian children performing well below the benchmark (ACER, 2005; MCEETYA, 2008). The latest National Report on Schooling in Australia (MCEETYA, 2008) includes the following results for Indigenous students obtained from testing in 2006. Seventy-two per cent of Indigenous Queensland students are achieving at the benchmark for numeracy in Year 3. This is significantly below their achievement in both reading (88.5%) and writing (89.7%), and also significantly below the achievement of Indigenous students in five other states. Similar trends exist in the National Scores. While reading and writing scores have been gradually improving for Indigenous students since 1999, there has been little change in the numeracy results. The Year 5 and Year 7 numeracy results mirror the results found in Year 3.

Unjustified blame has been laid upon Indigenous students in the past, and absenteeism, disadvantaged social background and culture have all be seen as contributing factors (Bourke & Rigby, 2000). This paradigm is seen as irresponsible (Cooper, Baturo, Warren, & Doig, 2004; Matthews, Howard & Perry, 2003; Sarra, 2003). Historically, most educational efforts have aimed to assimilate Indigenous students into Euro Australian society and are based on the ideology of cultural deprivation (Prochner, 2004). Our longitudinal research project, Young Australian Indigenous students' Literacy and Numeracy (YAILN) draws on and adapts relevant mainstream research about young students' numeracy learning, and endeavours to situate these findings in local settings where Indigenous cultural practices are recognised and respected. To date, there have been few published studies on the impact of early childhood education on Indigenous students (Prochner, 2004).

Theoretical underpinnings

Briefly, the research base and design principles that underpinned the development of the Numeracy aspect of YAILN were:

• Maths ability: All children are capable of learning mathematics. Children do not have to be made ready to learn as they freely engage with informal mathematics in everyday life (Greenes, 1999).
• Role of the teachers: Play is not enough to assist learning in the early years. Children learn through play but they need adult guidance to assist them to reach their full learning potential (e.g. Balfanz, Ginsburg & Greenes, 2003; Vygotsky, 1962). As compared with other cohorts of early years students, Indigenous students gain even less from attending play-based programs (Tayler, Thorpe & Bridgstock, 2006, cited in Fleer & Rabin, 2007).
• Types of activities: Hands-on activity-based learning best helps young Indigenous students to engage with mathematics (Cooper, Baturo, Warren & Grant, 2006).
• Role of oral language: A focus on the language of mathematics fosters important language acquisition and helps students to acquire meta-cognitive abilities. This focus is even more relevant for students whose first language is not English (Pappas, Ginsburg & Jiang, 2003). Yet pathways for oral language experiences tend to be restricted in early childhood settings (Kennedy, Ridgway & Surman, 2006).
• Maths curriculum: Young students are capable of dealing with a comprehensive mathematics curriculum (Greenes, Ginsburg & Balfanz, 2004).
• Indigenous students' language: Aboriginal English reflects the culture and identity of Aboriginal people (Cronin & Diezmann, 2002) and discourses of Indigenous families often do not match that of the school (Cairney, 2003). Teachers need to create a bridge for young Indigenous students between Aboriginal English (AE) and Standard Australian English (SAE) as these students grapple with new language, new concepts and vocabulary presented for literacy and numeracy.
• Value of ‘white' mathematics: Parents of Indigenous students want their children to be bicultural and learn to live in both worlds (Partington, 1998). An understanding of ‘white' mathematics is important for two reasons: (a) many traditional industries are now calling for personnel with advanced skills in mathematics (Mullis, Martin, Gonzalez & Chrostowski, 2004), and (b) mathematics is an empowering process acting as a tool to identify power differences among socioeconomic classes (Gustein, 2003).

YAILN is now in its second year. The students who participated in our first year were all from the preparatory classrooms, a non-compulsory year of schooling prior to Year 1 in Queensland. Prep classes are conducted five days a week and children stay all day. Participants must be aged five by 30 June in the year they start Prep. At the completion of the first year of YAILN our results indicated that, although Indigenous Australian students scored significantly lower on the numeracy pre-test, intervention focussing on (a) the language of mathematics, and (b) representations that support mathematical thinking in both directed teaching and play-based contexts helped these students to bridge the gaps in their learning (Warren, Young & deVries, 2008). The particular focus of this paper is to investigate the impact of engagement with YAILN on a small cohort of Indigenous students who had not reached the official age for entry to a Prep program.

One YAILN school, with a totally Indigenous population (School D), enrolled a small cohort of children in their Prep class who had not reached the age of five by 30 June, hence the term pre-preparatory students. The class consisted of up to 18 students, many of whom did not attend school on a regular basis. Of the 18 students, we managed to consistently track nine students over the school year; five were the correct age for Prep, two were Year 1-age students, and two were pre-prep students. The focus of this paper is the two pre-prep students (Widgy and Caddy) and was guided by the following research questions:

1. How does participation in the YAILN project affect understanding of number, patterning and oral language for pre-preparatory Indigenous students?
2. How do the mathematical understandings of Indigenous pre-preparatory students compare to Indigenous prep students who had not previously engaged in numeracy activities?

Both Widgy and Caddy's families were from low socio-economic backgrounds. The literature suggests that students from low socio-economic backgrounds begin school with many disadvantages. It seems that children who bring to school early mathematical knowledge are advantaged in terms of their mathematical progress through primary school (e.g. Aubrey, Dahl & Godfrey, 2006; Young-Loveridge, Peters & Carr, 1997). A consequence is that students with little mathematical knowledge at the beginning of formal schooling remain low achievers throughout their primary years and probably beyond. Denton and West (2002) showed that low income students usually come to preschool with the same basic readiness to learn as the more advantaged students. The difference lies in how they engage with advanced concepts and skills. Results from this study indicated that 63 per cent of students from high income families and 37 per cent of students from low income families had a strong understanding of the number sequence and could read two-digit numbers, identify the ordinal position of an object and solve simple word problems by the end of kindergarten. These differences were seen to reflect the mathematical knowledge each group brought to school and, in this instance, the educational gap remained by the end of the first year of schooling.

International studies suggest that allowing disadvantaged students and students with lower educated parents to attend school at an early age has a positive effect on their literacy and numeracy scores. Leuven, Lindahl, Oosterbeek and Webbink (2004), in a Dutch study involving data from more than 16000 students reported that early learning makes subsequent learning easier. They found that increasing enrolment by one month increased the language and maths scores of students from a low socio-economic background or ethnic minorities by 0.06 standard deviation, while early enrolment did not make a difference for non-disadvantaged students.

Method

In its first year, YAILN was a collaboration between researchers and teachers in five schools in North Queensland. The design of the project was a multi-tiered teaching experiment with the seven preparatory teachers participating in professional dialogue/learning with the researchers on four occasions throughout the school year. On each occasion, all of the teachers were released from their classrooms to participate in a day of professional learning. Subsequent to these days, the researchers visited all participating classrooms to continue professional dialogue and help teachers to trial activities and new resources. Discussions during these visits focused on both mathematics and literacy learning in the early years. From a mathematical perspective the focus of the dialogue was three fold: (a) the role of mathematics language in assisting young students to engage in mathematical thinking; (b) representations and activities that support mathematical learning in the early years with an emphasis on the language associated with these activities; and (c) how this learning underpins higher levels of mathematical understanding.

Figure 1. Typical activities utilised in Phase 1

The second phase of classroom activities involved students using mathematical language and understanding representations in contexts that involved number. Figure 2 illustrates some typical number activities.

Figure 2. Mapping language onto number contexts

The repeating number pattern on the Grid in Figure 2 can eventually be mapped onto the pattern of '3's.

Data gathering techniques and procedures

Queensland is one of the largest states in Australia, and all schools in the study were a two-hour plane flight away from the researchers' home town, so it was difficult to visit the school sites on a regular basis. Thus, the data tended to be gathered in one-week blocks, with the researchers visiting the sites five times during the year. Data-gathering had four components: pre- and post-tests, student portfolios, classroom observations, and teacher interviews. In total, 120 preparatory students participated in YAILN. All pre- and post-tests were conducted in a one-on-one assessment interview. Because of the intensity of the data collection—with each assessment interview taking up to one hour, 30 minutes for numeracy and 30 minutes for literacy—only 48 students participated in both the pre- and post-numeracy tests. This purposely selected sample consisted of all the Indigenous students and a selection of Australian students and students from other cultures representative of a range of abilities. The pre-assessment interview (pre-test) occurred two months after the start of the school year. The pre- and post-tests and teacher interviews occurred in March and November. Insights into the first research question, How does participation in the YAILN project affect understanding of number, patterning and oral language for pre-preparatory Indigenous students?, were provided by the results of the tests administered in the pre- and post-assessment interview.

In order to answer the second research question, How do the mathematical understandings of Indigenous pre-preparatory students compare to Indigenous prep students who had not previously engaged in numeracy activities?, a short interview was conducted with Jo, Widgy, Sussi and Fran at the beginning of the Prep year. Sussi and Fran were young Indigenous girls who had not attended a pre-preparatory year of school. All four students came from similar home backgrounds. The results of a pre-test interview conducted at the start of YAILN Preparatory year indicated that Indigenous students at school D had limited understanding of concepts about Western number systems on school entry (see Table 2), a trend confirmed by School D's Prep teacher. Jo had attended pre preparatory at School D, but enrolled midyear and hence did not complete the pre-test for numeracy. Unfortunately, Caddy was absent in the week the interviews occurred. The aim of the interviews was to gauge how Widgy's and Jo's understanding of mathematics compared with two students who had not attended a pre-preparatory year of school. This interview focused on their understanding of the number 5 and was conducted by the students' preparatory teacher, who was also Widgy's and Jo's pre-prep teacher.

Pre- and post-tests results

The pre- and post-assessment interview consisted of three tests, one for number, one for patterning, and an oral language test. All the tests were developed by the researchers. The number test, School Entry Number Assessment (SENA), consisted of an interview with three main sections: number recognition, counting, and early addition and subtraction. This was based on the Mathematics component of School Entry Assessment (SEA), a tool designed by the New Zealand Government. Originally the context was a shop and assessments about students learning were made as students played a shopping game. SENA extended the types of questions asked, the way they were asked, and modified the context and materials for Australian Indigenous students. The context of a shop was replaced by objects that were considered to be in most of these Indigenous students' homes; for example, leaves, clothes pegs, and hair clips. Before the interviews, the interviewer spent time interacting with the students in their classroom. Time was also allowed for the children to play with the objects before testing began. Students were encouraged to talk about their play, with the interviewer asking questions such as ‘Do you have this at home?', ‘Do you know what we call this?' All these actions were believed to help students to feel confident about answering the questions. The interview consisted of three main sections: number recognition, counting, and early addition and subtraction.

The Patterning test consisted of 11 questions. Students were asked to copy, continue and complete repeating patterns and to identify the repeating part in each. Research suggests that an understanding of these key concepts impacts on the application of numerical strategies in the later years of schooling (Papic, 2007). BOEHM, the third test, is a commercially produced standardised oral language test. In this test students were presented with three pictures. A typical question was ‘Point to the picture where the cake is in the middle of the tray'.

Figure 3 presents samples of typical questions from SENA and the Patterning test.

The results of a pre- and post-test, an interview conducted with 48 students selected from five prep school settings (average age 4 years and 11 months), indicated that, although the Indigenous Australian students (n=14) scored significantly lower on the pre-test, after one year of school there was no significant difference in their scores as compared with the whole cohort (Warren, Young and deVries, in press). For both the Patterning test and Oral Language tests, while there was no significant difference in the pre-test results and the post-test results for Indigenous Australian students and non Indigenous students, both groups exhibited significant improvement in both areas by the completion of the first year of the project.

The effect of participating in pre-prep for Widgy and Ceddy

The total possible scores for the three tests were, SENA (28); Patterning (11) and Oral language (50). Table 1 presents the pre- and post-means and standard deviations for the whole sample of 48 students. Fourteen students were Indigenous and 34 students were from non Indigenous backgrounds.

Table 1. Mean scores and standard deviations for all students (n =48)

A Wilcoxon Signed Rank Test was performed to ascertain if there were any significant differences between the students' pre- and post-test scores for the three tests. The Wilcoxon Signed Rank Test revealed a significant difference between the students' pre and post test scores for SENA (Z= 5.82, p=.000), Patterning (Z=5.92, p=.000) and Boehm (Z=5.91, p=.000). School D, the school that both Widgy and Caddy attend, is one of the participating schools in YAILN. Pre- and post-test scores for the three tests were obtained for nine of the students from the preparatory class at School D. Table 2 presents the mean scores and standard deviations for each test.

Table 2. Mean scores and standard deviations for School D (n=9)

The Wilcoxon Signed Rank Test revealed a significant difference between the students' pre- and post-test scores for SENA (Z=2.67, p=.000), Patterning (Z=2.68, p=.000) and Boehm (Z=2.55, p=.000). Table 3 presents the mean scores and standard deviations for Widgy and Caddy for the three tests.

Table 3. Pre- and post-test scores for Widgy and Caddy

Widgy and Caddy's pre- and post-test scores indicated a marked improvement in their understanding of number, patterning and oral language after their participation in a pre-prep program.

Widgy and Caddy's scores, as compared with their cohort and the whole sample indicated that this improvement was similar to the trends exhibited in their cohort and the whole sample. While Widgy and Caddy's post-scores for SENA were below the average scores of their cohort and the whole sample, both post-scores were within 1 standard deviation from the mean post-scores. Widgy was also below the mean score for the cohort and the whole sample for patterning and Boehm, but she still exhibited significant improvement in both scores. Caddy's post-patterning score was above the mean patterning score for his cohort and the mean score for the whole group. His post-Boehm score was above the mean score for his cohort and just below the mean score for the whole group. These results would suggest that attending the pre-preparatory year of schooling did make a significant impact on both of these students' understanding of number concepts, patterning and oral language.

It should be noted that Widgy and Caddy's post-test scores were also above the mean scores for the whole sample pre-test scores. This suggests that they now have a very strong foundation on which to build their mathematical understanding as they formally participate in the prep year of schooling. The next section presents the data relating to the second research question, how do these understandings compare to Indigenous students who had not attended pre-prep?

Comparing students who attended pre-prep with students who did not attend

The interview consisted of five main components: One-to-one counting to five; conversation of five; Subitising to five; counting on and counting back from five and creating stories about five (e.g., two and three make five). The preparatory guidelines for Queensland schools (QSA, 2006) indicate that students should know all about five by the end of prep, hence the choice of the number five. Figure 2 presents a selection of activities used in this phase of the research.

The interviews were extremely short—(approximately three minutes' duration) and were conducted with four students; Jo and Widgy (both had attended pre-prep) and Sussi and Fran (neither had attended pre-prep). All four students are presently in the prep year at School D. All interviews were video-taped.

Table 4 presents a summary of the results for the four students.

Table 4. Results comparing pre prep Indigenous students with Indigenous students who have not attended pre prep

There was a clear distinction between the two groups' understanding of the number five. Jo was successful on all aspects of the interview. She could answer all questions about five, and throughout the interview did not use counting to aid her in her responses. Widgy initially had to count the number of objects the interviewer presented, but as the interview progressed, switched into discussions about five which did not require her to count the objects. Sussi could not consistently count to five. She had the numbers to three under control, but experienced difficulties with four and five. Fran could not consistently count to five. Both Jo and Widgy clearly understood the questions asked, especially the language of mathematics associated with the questions. The interview was conducted by the students' preparatory teacher, who was also Widgy and Jo's pre-prep teacher.

Discussion and conclusions

Given that this paper shares the results of two Indigenous students who attended a pre-preparatory year, it is difficult to draw conclusions for the whole Indigenous community. For these two students the results clearly demonstrate that their attendance at school prior to the preparatory year assisted them in obtaining a better understanding of important Western mathematical concepts. The results also suggest that their understandings at the beginning of their preparatory years are equivalent to the understandings held by many students from non-Indigenous backgrounds as they begin school.

The results begin to confirm the theoretical underpinnings of the YAILN project. The role of oral language in developing mathematical understanding especially for students whose first language is not English cannot be underestimated. As indicated by the results of the interview conducted at the beginning of the second year of the project, the students who had participated in pre-prep not only possessed a better understanding of numbers to five, but also the associated Western mathematical language used to access this understanding. Pappas et al. (2003) believe a focus on the language of mathematics fosters important language acquisition and helps students acquire meta-cognitive abilities. This research begins to confirm this finding.

For these Indigenous students, it appeared that direct teaching together with play-based opportunities were also important in learning mathematics at an early age. The results of the SENA component of the pre-test for number and the interview results for the two Indigenous students who had not attended pre-prep indicated that Indigenous students begin school with little knowledge about Western numbers. Most did not know the names of the numbers, nor could they meaningfully count to five. We are suggesting that this is not the type of knowledge that emerges solely from play-based situations. Adult guidance is needed (Greenes, 1999) and this is especially important for Indigenous students (Tayler et al., 2006).

Both of the Indigenous students reported in this paper are from a low socio-economic background, and allowing these students to attend school early certainly had a positive effect on their early numeracy understandings (Leuven et al., 2004). Their pre-test results suggest that they brought to school a paucity of mathematical knowledge, especially knowledge related to understanding Western mathematics. Aubrey et al. (2006) claim that students with little Western mathematical knowledge at the beginning of formal schooling remain low achievers throughout their primary experience. The results of this research suggest that attendance in a pre-prep year of school may be an effective way to address this gap. Widgy and Caddy are now on an equal footing with other students as they begin their prep year. Both students remain part of our longitudinal study. Denton and West (2002) hypothesise that early learning makes subsequent learning easier, but this is yet to be fully tested. Our initial conversations with the prep teacher and the distinctions between these students' understanding of five as compared with students who had not attended a pre-prep year, suggest that the hypothesis may indeed be correct.

In alignment with our theoretical underpinnings we are suggesting that the ratio of pre-prep to prep students should be low. Children can discover only so much through play. As the prep students learn, they are in a position to assist pre-prep students to higher levels of understanding and helping pre-prep students to reach their learning potential (Balfanz et al., 2003). We propose that learning from older peers, along with explicit teacher-directed learning, all within a play-based environment, provide the most effective context for pre-prep Indigenous students for developing early numeracy understandings.

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