Abstract
Making mathematics more inclusive is a stated aim of many curriculum documents in Australia and overseas. The achievement of the inclusive agenda is problematic to many beginning teachers struggling in the so called "survival stage" of transition into teaching. This paper discusses the learnings of a group of beginning women teachers in multi-cultural, Aboriginal and non-English speaking background classrooms. The model used is participatory action research. The paper highlights the learnings of the teachers about inclusive mathematics and presents a critical reflection about the use of action research with teachers in wide geographical locations.
 

The National Statement on Mathematics for Australian Schools (Curriculum Corporation, 1991) argues that "access to and success in school mathematics should be independent of gender, social class or ethnicity" (p. 8). It adds that "we are now beginning to understand some of our past curriculum practices in mathematics which have disadvantaged groups of students. For example, many of the contexts in which mathematical concepts were developed, applied and assessed were more likely to be central in the lives of boys than in the lives of girls. ... In a similar way the mathematics curriculum has tended to emphasise values and concerns which are more middle class, and to draw on experiences which are more relevant to children of Anglo-Celtic descent than those of Aboriginal descent and those from non-English speaking backgrounds" (p. 9). The National Council for Teachers of Mathematics (NCTM) (1989) asserts that "the social injustices of past schooling practices can no longer be tolerated. ... Mathematics has become a critical filter for employment and full participation in our society. We cannot afford to have the majority of our population mathematically illiterate. Equity has become an economic necessity" (p. 4).

In discussing the needs of students from different backgrounds who may not be achieving as well in school mathematics, the National Statement states that "sometimes such students are regarded as lacking in mathematical ability when they are actually experiencing problems with the formal language of the mathematics classroom" (p. 9). In the NCTM yearbook on equity issues and inclusive mathematics, Trentacosta and Kenny (1997) argue that "in order to create an equitable learning environment among a growing diverse student population, it is important for teachers to understand the relationship between learning mathematics and the linguistic and cultural background of the students .... Teachers who understand the interrelatedness among topics of mathematics and acquire the facility to operate using different mathematical world views can help students develop their ability to understand mathematics and to build on their own mathematical world views" (p. 5). Likewise, Frankstein (1997) demonstrates how the use of critical mathematics from the real context of the student can assist in making mathematics more equitable and accessible for the students. Other voices in the yearbook have stressed the importance of involving parents in the decision making process to increase availability of mathematics to students from underrepresented and/or underachieving backgrounds (Peressini, 1997; Strutchens, Thomas, & Perkins; 1997).
 

Women Primary Teachers of Mathematics

A recurring issue raised by the various reviews and reports (Curriculum Corporation, 1991; Department of Employment Education & Training, 1989) is that the teaching of mathematics is for many primary teachers an area of major concern. Among the reasons for the concern are inappropriate teaching and learning practices that teachers have themselves experienced in their own schooling and preservice courses, and many primary teachers have limited content backgrounds in mathematics and little interest or confidence to teach it.

These problems are more prevalent among women teachers who dominate the teaching profession in the primary and early childhood school years. Historically, the lack of content background in mathematics and science among women teachers may be accounted for by traditional perceptions of women as nurturers, and thus more suited to primary and early childhood teaching and subjects such as English, home economics and biology. These perceptions has been detrimental to women wishing to enter such fields as the physical sciences and mathematics. Although policies for change have been initiated (e.g., Clark, 1990; Kenway & Willis, 1993), and despite encouraging indications that women have moved into mathematics and the sciences (Willis, 1989), reports (e.g., Cobbin, 1995) continue to note that many women preservice teachers remain weak in mathematics, and have little interest in teaching the subject. Arguably, if the teaching of mathematics in many primary and early childhood classrooms remains problematic because of these factors we will continue to fail to address deficiencies in girls’ education and access to nontraditional subjects higher up.
 

Needs of Beginning Teachers

The early classroom experiences of beginning teachers may either inhibit or catalyse a lasting commitment to effective mathematics teaching. Successful early experiences may contribute to a positive sense of self-efficacy and hence instil confidence in the teaching of mathematics. Therefore, it is a crucial aspect of teacher professional development that we seek ways of fostering the professional growth of beginning women teachers so that they can acquire the confidence to be effective teachers of mathematics in the long term.

First year teachers enter the teaching profession with varying levels of skills, content knowledge, and pedagogical knowledge. Because of the lack of employment opportunities, many apply for, or are posted to isolated schools or schools with students who are culturally unfamiliar to the teachers. While first year teachers are attempting to overcome difficulties faced in the new school environment, Veenman (1984) suggests that these teachers "need both pedagogical assistance and psychological support." Katz (1972) describes four stages of teacher development: survival, consolidation, renewal and maturity. It is suggested that the first two stages characterise the first two or three years of teaching. The survival stage is distinguished by self interest and self concern, for instance, getting through the day and planning for a short period of time. In the consolidation stage, concerns move beyond self, and towards children.

Fuller (1969) describes three major phases in teacher development: pre-teaching, characterised by non concerns phase; early teaching phase, characterised by concerns for self; and a late teaching phase, characterised by concerns for pupils. This model was revised by Fuller and Bown (1975) to three stages of concerns of an inservice teacher’s development. The stages were characterised by concerns for survival, the teaching situation (e.g., content, methods, materials), and pupils (e.g., students’ learning and emotional needs). Other models have been reported in the literature, for example, Vonk (1983) and Burden (1980). Common to all of these models is the initial survival stage.

The study reported here is part of the Enhancing the immersion of beginning women teachers into Mathematics and Science Teaching through participatory Action Research networks (EMSTAR) project, a collaborative participatory action research (PAR) among nine first-year women teachers and university researchers. For the university staff, one of the main aims of the project was to investigate the support needed to enhance the transition of teachers from their university course into the profession, and the use of action research for facilitating such transition. For the participating teachers, the project allowed them to collaborate with each other and the university staff to deal with specific aspects of their teaching of mathematics in their schools. The focus of this paper is on the learnings of one group of three teachers and an academic investigating problems and issues in inclusive mathematics. Other papers consider the findings from the action research cells investigating issues in assessment (Suhrbier, Moman, Fitzgerald, & Ginns, 1997) and catering for the gifted and talented (Watters, Andrews, Henderson, & Everett, 1997).
 

Action research in Education

Atweh and Heirdsfield (1998) have identified several approaches to cater for the needs and support for beginning teachers. The methodology adopted in this project was PAR. Kemmis and Wilkinson (1998) discussed the following characteristics of PAR. First it is a social activity in that "it deliberately explores the relationship between the realms of the individual and the social." It recognises that "no individuation is possible without socialization, and no socialization is possible without individuation" (Habermas, 1992, p. 26). PAR is also participatory in that "it engages people in examining their knowledge (understandings, skills and values) and interpretive categories (the ways they interpret themselves and their action in the social and material world)." It is also participatory in the sense that people can only do action research "on" themselves - individually or collectively. It is not research done "on" others. PAR is also collaborative in that "[a]ction researchers aim to work together in reconstructing their social interactions by reconstructing the acts that constitute them. It is a research done "with" others. PAR is emancipatory in that "it aims to help people recover, and unshackle themselves from the constraints of irrational, unproductive, unjust, and unsatisfying social structures which limit their self-development and self-determination." PAR is also critical in that "[i]t is a process in which people deliberately set out to contest and to reconstitute irrational, unproductive (or inefficient), unjust, and/or unsatisfying (alienating) ways of interpreting and describing their world (language/discourses), ways of working (work), and ways of relating to others (power)." Finally PAR is recursive (reflexive, dialectical) in that "it aims to help people to investigate reality in order to change it (Fals Borda, 1979), and to change reality in order to investigate it ... It is a process of learning by doing - and learning with others by changing the ways they interact in a shared social world."
 

Participants

The teachers participating in this group were three beginning women primary teachers who came from a four year BEd course at the Queensland University of Technology. During their final year in their course, these teachers had participated in a study on Women Trainee Teachers in Mathematics (Atweh & Burnett, 1997; Atweh, Kyle, & Burnett, 1996). The teachers were joined by a university lecturer who facilitated the project supported by one research assistant, and an experienced teacher and author, as a critical friend, who has worked in Aboriginal contexts.
 

Procedures

In 1996, the three teachers were interviewed during the last year of their preservice course regarding their life histories in studying mathematics and their teacher preparation course. Special attention was given to the perceptions of these teachers about their confidence in the content of mathematics and in their ability to teaching it in the primary school. At the end of the year the teachers met to discuss issues related to action research and to plan the overall structure of the project for 1997.

The main activities of the project were conducted in 1997. At the conclusion of the first school term in April, the participants finalised the decision on the specific areas on which they would concentrate in their action research. Because of the great geographical distance between the participants, the main proposed means of communication among the participants were teleconferencing and email.

In May, 1997, the participants had their first one hour teleconference. During the meeting, the participants briefly discussed their experiences in their respective schools as well as agreed on some of the processes for conducting the project. General issues such as the need for establishing good contact with parents and for making the context of activities relevant to the student background were discussed. The participants agreed to write situational analyses of their schools stressing the specific problems they were encountering. These were to be distributed to each other for discussion in future meetings. The possibility of writing a paper on the project for presentation at national educational conference was met with support by the participants. The participants agreed that this paper should be written collaboratively and not by the university staff on behalf of the teachers.

The second telephone conference was held in August. The discussion on the situational analysis could not proceed since not all participants had received each others papers. It was agreed to have another meeting within a week where each of the situational analyses would be discussed in turn and each participant would attempt to provide some critical comments and suggestions on each other's situational analysis. Further planning for the writing of this paper was done at this meeting. The concepts of critical mathematics were discussed and some examples given. Likewise the principles of "culturally relevant context" vs "individually meaningful context" were discussed. In terms of planning action research projects within the school, the meeting discussed the need for projects to start very small - rather than attempting to change the whole classroom context. It was suggested that participants should concentrate on a small manageable aspect over which they have control in changing. The next meeting occurred a week later where the situational analyses were discussed.

One of the final activities of the group in 1997 consisted of writing the conference paper. The participating teachers were asked to submit their reflections on the first year of teaching and their reflection on the project. The intention was that these would be distributed to each other and further meetings would be devoted to compilation of the individual stories toward the writing of a cohesive paper. This could not happen due to delays in submissions of the final reports from the teachers. Christensen and Atweh (1998) have discussed in detail the problematics of collaborative writing in action research projects. The authors have identified different processes used for development of writing. This paper was written by the university research team members based on material supplied by the participating teachers.

The Three Teachers

Lisa's career choice of primary teaching was perhaps by elimination rather than deliberate planning. She felt rather confident in certain areas in mathematics such as operations and measurement, while she was least confident in algebra and fractions. Similarly, Lisa expressed some lack of confidence towards teaching mathematics, because in her mind "you can not afford to make a mistake in mathematics, because the kids will pick it up - once they have learnt something wrongly, it is very difficult to unlearn it." In her first year of teaching, Lisa was appointed to a remote Aboriginal community in the Northern Territory, about 300 km northeast of Katherine. Many students missed a large portion of the school year because families move toward the out-stations in the dry season. Kriol is the spoken language outside school by all students. However, at the community’s request, the school's focus is learning to speak, read and write English. Lisa taught a multi-age group consisting of grades 3 and 4, covering a wide range of educational achievement levels.

Gabrielle also "fell into" general primary school teaching, with her initial preference being special education. She considered herself rather confident in mathematics in general, though not confident enough to teach it at a secondary level. However, Gabrielle was not as confident about teaching mathematics. In her first year of teaching, she was appointed to a regional primary school about 500 km north of Alice Springs. The school of 420 students had a mixed student population, consisting of Asian, Europeans from various national origins and Aboriginal students. She taught a combined class of years 4 and 5. However, in mathematics she took the grade 5 students only. Students were streamed in mathematics classes based on ability. There were no Aboriginal students in the upper stream class.

Janette worked full time for three years before deciding to pursue a teaching career. Of the three teachers, Janette is the only one who studied Mathematics I (a medium level mathematics course in Queensland) at senior high school. She did this because of the perceived opportunity that this subject would provide in selecting university options, even though she lost interest in the subject by Year 11 when it became "too scientific" and not applicable to real life. Like Gabrielle and Lisa, Janette was also disillusioned by the lack of support from her mathematics teachers who seemed to devote more attention to the high achieving students. She did indicate however, that she was confident that her mathematical background was sufficient for teaching primary school mathematics. Janette taught Year 5 in an independent school, which primarily caters for students with a non-English speaking background.
 

Problems Identified by the Teachers

Through their involvement in the project the teachers have had several opportunities to reflect on the difficulties that they faced in teaching mathematics in their diverse contexts. In her situational analysis, Lisa identified several factors hindering inclusive mathematics. Lisa was aware that the world view of traditional Aboriginals may be incompatible with aspects of Western mathematics. She wrote: "The teacher is confronted continually with Aboriginal world view of these concepts which are vastly different from and more complex than non-Aboriginal concept of time, measurement and space." Further, the day to day experiences of students in isolated areas is quite different from those of urban students "as [their] mathematics usage is usually only necessary for purchasing goods at the store, ... money is the only mathematics concept that is used frequently. Usually mental computation of adding or subtracting money is a strong point [with many of these students]". Further, language difficulty compounded these factors. She wrote: " As English speakers, we have a variety of words that may describe one mathematics concepts, for example, the concept of addition [i.e.,] add, how much all together, plus, etc. For Aboriginal children [whose first language is not English] they find it difficult to learn all the different language varieties for the concept of addition".

Other factors were identified by Gabrielle. First there are difficulties related to the teacher. She wrote that she had the "[t]endency to teach as I was taught: [being] teacher directed and prescriptive. I feel that I understand how mathematics should be taught but because my [own] schooling is so embedded in my way of thinking, I find it difficult to change." Similarly, there are certain problems with the mindset of the students. "Most students see mathematics as an isolated subject area and don't understand the connections with the real world or the language used". Other difficulties arose because of the time limitation available for a beginning teacher to master a variety of tasks. She wrote "I have so much to plan all the time and other school wide commitments that I find I have little time to spend on re-reading university notes or other professional development materials". Other contextual factors she identified related to the rigid structured of the school timetable and curriculum plans that did not allow her flexibility to dwell on the content that has not been mastered well by the students.

Lastly, Janette identified the diverse background of her students as a major problem that she had to deal with. Within her class there were "7 children with behavioural problems; 2 visually impaired and 1 with a speech impairment. Nearly all of these children are from Arab countries, and have English as a Second Language; ... 2 of these children have been in Australia for less then 1.5 years". As a beginning teacher, one of the main problems she faced was to cater for the diverse needs. She wrote: "The ability levels within the children are diverse, therefore I need to acquire good management routines and techniques to cater for more children within the classroom. [For example], one child in particular is unable to communicate effectively and I find it very difficult to help her when I have so many other children within the classroom who are also in need". Further it was difficult for the teacher to "create an interesting curriculum for all ... children [who] have different interests, backgrounds and educational history". Finally the lack of adequate school facilities such as playground, power, place for books and bags, and classroom space, create a difficult work environment for classroom management. Within this context, student behaviour was a very serious problem identified by Janette. Lack of parental support and the existence of "family feuds" between some students compounded the problems within the school.
 

Learnings about Inclusive Mathematics

There is varied evidence that throughout the first year of teaching, and through their involvement in the project, the teachers have been able to develop significant learnings towards inclusive mathematics. Lisa concluded that "making mathematics more inclusive in not an easy task". She realised that learning about and from the student background of the students is a "first and vital step". She related how toward the end of the year she was able to "get acceptance both from the community and the children". She also demonstrated an ability to be critical of curriculum material that are available within the school. In trialing one curriculum series developed specially for Aboriginal students she reflected how inappropriate it was because it "was so basic. It underestimated how much previous knowledge these children have." She concluded:

Finally, Janette has been able to identify the social context of first year teaching as needing to change to achieve the inclusive mathematics. She wrote "None of my previous practical teaching experience gave me the appropriate skills to deal with a high concentration of multi-cultural, non-English speaking students. I believe that some additional training and/or support should have been afforded during my first year of teaching, and also on an ongoing basis." In discussing the preparation of teachers to work in such contexts she suggested that the university preservice courses had not adequately prepared her for being a first year teacher.

 
All three teachers were quite aware of the great gap between their cultural background and that of the particular school context that they found themselves in during their first year of teaching. The Aboriginal background of the students at Lisa's school, the multicultural background of the school at Gabrielle's school, and the non-English speaking background at Janette's school have presented great challenge to the three teachers to make mathematics more meaningful to the students and for finding a pedagogy that is culturally appropriate. The discussions at the teleconferences often expressed these concerns. Has the project assisted them in dealing with these concerns?

At the conclusion of the first year of the project, Lisa talked about gradually becoming accepted by the school's parent community. This was discussed during the project meetings. Rightly, she concluded that the process to make mathematics more inclusive is "not an easy task". Arguably, it is a much more difficult task for a beginning teacher who herself is being enculturated into the dominant school culture and often lacks confidence and experience. Further, in her reflection on teaching and learning of mathematics she re-discovered lessons that she has learnt from university lectures of how to teach mathematics through emphasis on mathematical language and using techniques such as big book and learning cards. These seemed to have helped her teaching; however, their cultural relevance is not directly clear.

Similarly, Gabrielle was self critical of her own approach to the teaching of mathematics that is based on her own experience in being taught mathematics and of the practices of streaming that her school used that were counter to her beliefs about inclusive mathematics. As a new teacher, she showed signs of overcoming these limitations. Yet, at the end of the year, she concludes that overall her practices were still not catering for the students' specific needs.

While Janette did not address the meaning of inclusive mathematics in her reflection, her overall discussion of the failure of the pre-service program in preparing her for such a job seemed to imply that she too had misgivings about her achievement in that area.

Does this mean the aims of the teachers at the beginning of the year with regard to learning about making mathematics more inclusive have failed? We do not think so. It is clear that the three teacher had shown a great ability in becoming reflective about the difficulties in their classrooms - and one of the main reasons being the cultural background of the student, and more importantly the difference between the culture of the teacher and that of the school. Identifying the problem is the first (and important) step toward its solutions. Arguably, as first year teachers having to develop the many survival skills in the new culture of the school, perhaps the skills needed to make mathematics more inclusive have to take a second priority. However, as we argue below, this project has assisted the beginning teachers to develop concerns and learnings beyond the mere "survival stage" discussed above.
 

Learning about transition

In becoming involved with this project we were interested in learning about the problems that teachers face in the transition from the university to the workplace. The experiences of these three teachers, although not typical of all beginning teachers, are not unique. The support that teachers are supposed to have is not always available in schools. Smaller schools, more isolated schools and less affluent schools often do not have programs in place to induct the beginning teacher into the profession. All three teachers indicated that the most valuable thing about the project was the chance to discuss their concerns with others in somewhat similar situations. This made the sense of isolation felt by the teachers a little less acute. Veenman (1984) argued that beginning teachers need psychological as well as pedagogical support. All three teachers identified the gain in confidence as a major outcome of their involvement in this project.

As discussed above, the first year of teaching has often been described as a survival year with major concern of the teacher is about the self. It is true that during many of the initial deliberations in this project the teachers were expressing their needs for teaching strategies and resources to use with students constructed as "weak" in mathematical knowledge and motivation. It also could be argued that elements of their final reflections also reflect the deficit model in describing the type of students that communities that they have. Yet, within these reflections are also elements of becoming critical in raising general questions about their practices and context.

 
Learning about action research as professional development

Traditionally, there has been somewhat of a demarcation between the responsibilities of the university and that of the employer in the professional development of teachers. Universities are often seen as responsible for the initial training that ceased at graduation. Induction programs are often seen as the responsibility of the employer. The funding arrangements for universities and the school sectors are consistent with this division of responsibilities. However, this does not mean that the two stages of professional development need necessarily be separated. This project is an example where funding from both sectors (the University internal research grants and the Queensland Broad of Teacher Registration) has allowed people from the university to work with school teachers in this important stage. However, the point that we want to stress here is that the involvement of the university in the provision of support during this transition period is useful in connecting what has been learnt during pre-service training with what is happening in the school. This leads to lessening the divide between the "ivory tower" and the "real world" and increasing the nexus between theory and practice.

In many ways the experience in this project has been uncommon for action research projects. I have not been involved in action research projects that consisted of people isolated by huge geographical distance. One of the basic components of participatory action research is the collaboration and negotiation among participants to develop a shared understanding of and change the practice under consideration. This has been difficult to achieve in the project. The project used teleconferencing as a means of direct communication with the participants. Due to the high cost of this medium, only few and short meetings were possible. Further, the limitations of email communication included lack of availability of personal email for the teachers, unreliable telephone lines for communicating with some isolated cites and lack of experience with email culture on the part of the teachers. However, this geographic isolation is the precise reason why this type of activity is important. Perhaps the combination of mentoring and action research into a community of learnings is useful.

Participatory action research aims at empowering participants. Has this project achieved this aim? Undoubtedly, the three teachers have found that their involvement in the project of some use to them. It allowed them to reflect on their practice and gain confidence in meeting the demands of teaching mathematics in a multicultural context. It also helped them feel less isolated in their practice. Their experiences and learning from the project have varied as portrayed in their statements above. We believe that their involvement in the project has been an enriching experience for the teachers. However, we would hesitate to use the term empowerment to describe the outcome for the teachers. Perhaps this is an aim that requires time. As one of the teachers has indicated that "next year if this project continues we may learn more from it."

Our involvement in the project has highlighted to me once again, the problems arising from the increasing demands that the university and the workplace are placing on the lives of teachers and academics. For all participants, the involvement in this project was in addition to an already busy schedule with many competing responsibilities. Often it was difficult to arrange meetings, communication was slow and feedback delayed. Little time was available for reflection on practice. Arguably for academics, as well as teachers, empowerment would include the ability to take control of one’s time and setting one’s own priorities.