Journal of Instructional Science and Technology ISSN: 1324-0781 Editors-in-Chief: Olugbemiro JEGEDE (jegede@ouhk.edu.hk) and Som NAIDU (s.naidu@meu.unimelb.edu.au)

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Volume 1 No 3, May 1996
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Some Outcomes of Learning Through Teleconferencing

by

Joan Robson
Australian Catholic University
Signadou Campus
PO Box 256
Dickson ACT 2602

Abstract | Introduction | Methodology, Method and Sampling | Literature Review | Findings | Discussion of Findings | Conclusion | Acknowledgments | References | Author |

Abstract

A recent study investigates the outcomes of learning when secondary students study mathematics using teleconferencing as a component of a distance education course. Results indicate that the attitudes towards the subject and towards the learning environment provided are positive and that the learning outcomes are comparable to those of students studying in a traditional classroom.

Introduction

An overview of uses of electronic technology in the education of students at primary, secondary and tertiary levels, living in remote areas in Australia (Robson, Routcliffe and Fitzgerald, 1991) highlighted two important facts. Firstly, electronic technologies are rapidly being introduced to make up for the perceived deficiencies of non-contiguous teaching and secondly, many teaching strategies associated with the new technology are transported directly from the traditional classroom. It became apparent that there is an urgent need for research into the relationship between the 'virtual' classroom and fundamental educational principles and into the use of electronic technologies to maximize the effectiveness of such an education (Robson, Routcliffe and Fitzgerald, 1991: 38). Subsequently extensive material was collected by the author during 1993 on one particular use of technology, namely teleconferencing, for detailed analysis with the hope of highlighting appropriate teaching strategies for use in distance education at the secondary school level (Robson, 1996). It is these data which form the basis for the material used in this study. They allow examination of, not only the teaching strategies but, the teaching and learning experience involved in the use of teleconferencing in secondary mathematics education.

Mathematics is a core subject in the Australian school curriculum and is taught at all levels of school education in most states and territories. Modern mathematics has shifted from computational skills towards an understanding of these skills and their applications and contains content considered essential to equip students to take their place in the contemporary world.

If student numbers in small rural schools preclude the formation of regular mathematics classes then amalgamation into distance education classes is an alternative. The 'class' comprises the students in say Year 11 mathematics, in all the small schools and a teacher. All are physically located in their own schools. A group of such individual rural schools is called a 'cluster' and technology can be used to support such distance education classes. However, the worth of such education is often questioned by educators and the community alike, and it is important to examine the impact and the effectiveness of technology in facilitating student learning in such a situation. The aim of this study is to demonstrate that using teleconferencing in teaching mathematics by distance education gives the students access to an effective learning environment.

Results from this study should allow both students and parents to make informed decisions regarding the educational options available to the student. Information on the effectiveness of courses conducted using this technology will also be important for schools when planning to extend their curriculum offerings, not only in the core subjects but in specialist areas such as languages (Department of Education, 1989a: 7). Lessons learned from the mathematics classes can be applied to other courses taught by teleconferencing. These models may refer to curriculum design, pedagogy, assessment or clientele. Such information may influence the format of the lessons, the physical arrangements of equipment, rooms and buildings of the school or the choice of technology. Decisions made in small schools impact on, not only the students and teachers, but also on the local community through common use of facilities, economic and social input from students and staff and the traditional role of a school in a rural area. The seven Australian Departments of Education which offer courses by distance education (Robson, Routcliffe and Fitzgerald, 1991) will want to optimize the facilities they provide for isolated students with respect to balancing costs against access to a wider curriculum. To this end they share the goals of exchanging information and developing a national approach as emphasized in reports such as The Australian Education Council's Creating a national framework for educational delivery (1991: 14 & 35). It is anticipated that illuminative evaluation will facilitate theory-building and ultimately decision making at this level.

Some insight is given into the effectiveness of the technology in mathematics education by a detailed examination of a class using teleconferencing as one component of the standard mathematics course. This study examines the students' attitudes towards the discipline of mathematics itself and searches for ways in which the teleconference component aids or abets the formation of positive attitudes towards the subject. Linked to this are the students' attitudes towards using the technology as a tool in learning mathematics. This leads to a comparison with the students' preferred learning styles to investigate whether the technology used is compatible with these learning styles. This will be distinct from learning about technology through using technology. The in-depth examination of their understanding will sample the knowledge skills that the students have acquired through learning via this medium of teleconferencing.

Mathematics was chosen for scrutiny as it is a discipline which is heavily dependent on visual communication. With such communication restricted to textbooks, facsimile machines and oral descriptions of diagrams, the teacher is limited to regular audio and contrived visual and kinesthetic teaching strategies. This situation should emphasize any deficiencies in teaching or learning through teleconferencing. For this same reason, the trigonometry section of the course was selected to investigate learning outcomes, this being an area in which visualization is vital.

It is important not to make comparisons with an imaginary stylized mathematics class. Squires and Sinclair (1993: 36) point out the pitfalls in using an 'urban school' as the benchmark for measures of educational worth. Mathematics classes vary according to the age, socio-economic status, sex and background of the students as well as the characteristics of the teacher, the school support in terms of time allowance and the resources. Long (1992: 54) found that the number of uncontrolled variables, in the comparative study of on-campus and off-campus students, make it difficult to generalize about the effects of different forms of study. In the Australian context, the geographic distances, economic situation and isolation are other significant variables, while Granholm (1973: 6) points to the myriad of personal, external and other elements which affect the comparison of results. He argues that a 'fuller investigation of the possibilities within the various modes of instruction' is more valuable than comparisons of efficiency. Consideration of the psychological and physical environment in which the students and teacher work is necessary for analyzing the interdependence of the learning and teaching and for relating the organization and practices of instruction with the immediate and long-term responses of the students. In spite of the unique nature of each of the small classes communicating through teleconferencing, one such New South Wales mathematics class was monitored in detail over eight months. The diverse nature of the schools concerned, each with its own school ethos and infrastructure, precludes simplified generalizations. However, analysis of the data collected in this case study should determine, whether or not, the use of teleconferencing results in desirable outcomes, in this particular instance. A positive result will not enable a generalization to this effect, but will support the hypotheses of Granholm (1973) and Childs (1965) that learning through distance education is at least as good as that through conventional teaching. A negative result would support the findings of Long (1992) that there is a difference between the results of on-campus and off-campus students.

Methodology, Method and Sampling

This study uses the interpretative methodology to investigate student outcomes as they use teleconferencing. This approach would seem to be appropriate to use in the investigation of a single class where technology is being used to make societal links simulating those usually found in a traditional classroom. Care is taken not to introduce a value element in the interpretation of the findings. However, bearing in mind that the interpretative approach should point to action or change, it is important to note that at this point in time, in the development of the initiatives, there is opportunity for the institutions and schools involved to modify and change.

The goals of this teleconferencing program are both general and specific.

General.

• to provide for the intellectual development of the students
• to equip students to take their place in society
• to form the basis of a future career

Specific.

• to increase access to an education for rural students
• to increase access to a wider range of electives
• to encourage increased retention rates in Years 11 and 12.

(NSW Teachers Federation, 1993)

The technology used was chosen in the design stage of the pilot program in 1989 (Department of Education, 1989a). Currently it is being used to fulfil the planners' ideas so outcomes can be compared with the above general and specific goals.

The students in this study are in the penultimate year of their secondary schooling. Although they are not adults in the sense of tertiary students, it is worth considering Burge's six components involved in implementation of a new program at tertiary level (1989: 49) and applying these components to the implementation of this project and they would seem to apply to the mathematics teleconference course being considered. The first component involves the individual student's academic ability and motivation. Examination of learning outcomes would elucidate the value of the project with respect to the student's capacity. Also weighing up family and community support in providing access to education for the students could expose barriers. The second component, choice, is the responsibility of the Department of Education and the school with its curriculum offerings, and the teacher in its implementation. In this case the course is the same as that taught face-to-face throughout the state, but the implementation of the course is the role of the teacher. Therefore, the learning environment that the course and teacher offer is a consideration - importantly, the structure of the lessons and the flexibility of the teaching medium. The third involves the relationship between teacher, associate teacher and the student and the role of the course in the student's world. In addressing this component, the power control and interaction within the lesson interaction can illuminate this relationship. The fourth component, diversity of learning styles, implies diversity of teaching styles. This is a consideration in any classroom, but gains prominence in distance education because of the limitations geographic separation places on possible teaching strategies. Smaller class sizes are usually a compromise made to address this situation of dispersed students. Determination of the students' preferred learning styles is a starting point in considering the diversity of learning styles of the students and the range of teaching strategies which the teacher must use. The fifth component of support mechanisms embraces textbooks, library, counselling and school support of the student's social and academic well-being. The support that all the participants see as essential for the success of the project can enlighten an evaluation of the course. The sixth component is related to the first in that it involves the degree of academic and motivational development of the student. This emphasizes the importance of determining the learning outcomes in terms of the knowledge, processes and attitudes towards mathematics.

Burge points to fruitful areas of scrutiny. The relationship between the students' preferred learning styles, the learning environment which the technology supports and the resultant attitude of the students towards learning are part of the fourth point. Her first and sixth points are considered in learning outcomes. In this present study, the 'outcomes' of the learning - both the attitude of the students towards the area of knowledge and the learning environment together with their understanding of the topic are considered. Providing context for these is the nature of the course itself as part of the regular Higher School Certificate curriculum and the support mechanisms available. The data were collected over a period of eight months from February 1993 to October 1993. A skills survey is used to compile data on learning outcomes. Personal diaries, interviews and questionnaires were used to collect data on attitudes. Thus the framework for the determination of the effectiveness of the use of teleconferencing in teaching and learning in this case is based on these components, but adjusted to be in harmony with this particular situation of upper secondary students studying mathematics using a major teleconferencing component. Some of the goals of the National statement on mathematics in Australian schools which are strategic in this situation of remote teaching are:

As a result of learning mathematics in school all students should:

• gain pleasure from mathematics and appreciate its fascination and power;
• acquire ... mathematical knowledge;
• develop skills in presenting and interpreting mathematical arguments;
• communicate mathematically to a range of audiences.

(Curriculum Corporation, 1991: 15)

The first three goals are concerned with the attitudes and outcomes of the learning.

Attitude Outcomes
The visits in February 1993 aimed to establish contact and to determine the initial student profiles in mathematics and the technology. The teacher and students were interviewed and diaries distributed. Throughout the research both students and the teacher were asked to keep personal diaries for the recording of their perceptions and reflections. The diary is not used directly for research but is designed to focus the attention of the participants on aspects of the teleconferencing lessons and was used when completing the questionnaires. Putting distance education and teleconferencing in perspective for the students, hopefully aids in reflection on their practice. At each stage both students and teachers completed questionnaires and participated in interviews that focused on their experiences of this style of teaching and learning, self-evaluation and support mechanisms. The associate teachers at each school also completed questionnaires. School records were searched to give an overall view of the enrolment patterns in the course to highlight attendance and continuation as indicators of attitude. All this information has been used to investigate student attitudes towards mathematics itself and towards learning mathematics by teleconferencing. Linked with this is the need for students to feel that school work will help them achieve their life goals.

Attitudes Towards Learning Mathematics
The importance of student attitudes towards mathematics is highlighted in the National statement on mathematics in Australian schools where it is argued that given the impossibility of identifying which knowledge and skills are necessary to prepare students to take their place in the world, a better approach is to develop in the students, a positive attitude towards their involvement in mathematics (Curriculum Corporation, 1991: 12). In order to control variables and minimize the effect of negative attitudes towards mathematics, such as disinterest or fear, the teacher should be an experienced and competent mathematics teacher. The teacher who conducts the class is such a teacher. This should minimize the formation of negative attitudes towards mathematics due to dislike of the teacher or the teaching methods.

This study searches for changes resulting from participation in this distance education program. It also searches for reasons behind the students' decision to continue the study of mathematics at the Years 11 and 12 levels. Effective teaching would be expected to result in a more mature attitude towards mathematics, so this is also investigated.

Attitudes Towards Learning Using Teleconferencing
Teaching and learning are also determined by the students' attitude to the learning environment (Barnes and Owens, 1992: 2). Students undertook an ACER standardized learning preference scale test to provide evidence concerning the appropriateness or otherwise of the distance education learning environment provided. Examination of the class on three occasions at the beginning, middle and end of the academic year provided the opportunity to show developing confidence with the technology on the part of both the teacher and the students.

Learning Outcomes
Students' understanding in mathematics has been investigated using classroom tests and researcher designed tasks. These tasks gather data on students' recognition, application and synthesis of particular mathematics concepts in a variety of problem solving situations pertaining to trigonometry. The learning that the students have demonstrated has been categorized according to the outcome statements in A national statement on mathematics for Australian schools (Curriculum Corporation, 1991). A list of these outcome statements is in Table 1. For informal comparison, a traditional city class also undertook these tasks.

Table 1: Selected outcome statements from Curriculum Corporation, (1991),
A national statement on mathematics for Australian schools, Carlton, Australian Education Council.

Sampling
The cluster of small rural schools chosen for consideration is one of a small, but growing, number in Australia using teleconferencing to supplement a distance education course. It is the larger of two such clusters in New South Wales and so enables the examination of a viable class studying one specific subject. In 1993 this cluster had been established for three years and so the support structures were already in place and it was moving from the trial stage and becoming an established part of the educational program of the schools within the cluster. The cluster of seven schools caters for students from properties or small towns within a region of approximately 30,000 square kilometres. The schools are connected via a teleconference link using the normal telephone lines and a bridge. Students within each small school can hear and speak with the teacher and with the rest of the class. Students in this program are in verbal contact daily with their peers in the other schools as part of the 'virtual' classroom as well as students within their own school surroundings. From this cluster the Year 11, 2 unit Mathematics class, was selected to be monitored. The teacher works from one school with some of the students - the other students are alone or in pairs at four other schools. These schools are between two and three hundred kilometres from the teacher's school. Following Linke et al. (1984), cost and effort are not considered in this study nor is the intrinsic value of the New South Wales Higher School Certificate 2 Unit Mathematics course appraised.

The structure of the course is determined by both the Higher School Certificate examination and the need for internal assessment marks. The course content and textbook have been determined by the Department of School Education and school respectively thus minimizing variability through teacher course design. However, in mathematics, as in all other areas of schooling, there has been a general move towards allowing and encouraging individuals to take more control of their own learning (Mousley and Rice, 1990: 185). It is important to determine whether introducing teleconferencing into mathematics education alters this scenario and whether the changes which are made to mathematics education when taught in the distance education mode affect the perceived worth of the subject.

Literature Review

Much of the research literature relevant to this study focuses on distance education, technology and mathematics at the tertiary level. However, as the students in the study are of a similar age and at the post-compulsory stage of their studies, this research is pertinent to the question of the effectiveness or otherwise of teleconferencing in mathematics education at the upper secondary level. But the differences between upper secondary and tertiary students must be acknowledged.

Distance education. Small schools in remote parts of the Australia often have difficulty in servicing a specialist subject such as mathematics (Department of Education, 1989a: 1). The Department of Employment, Education and Training (DEET) paper A fair chance for all suggests that lower school retention rates and restricted curriculum choices are factors which disadvantage students in rural areas in participation and success in higher education (DEET, 1990). One type of education proposed by Departments of Education to provide teachers for these remote students is distance education. Keegan among others (1990: 32) regards distance education as one of several forms of education - each with their own characteristics and there is enough support for this view in the research literature that for the purposes of this study, distance education is considered as a discipline in its own right. Educators speculate about the relationship between traditional and distance education at all levels of education and numerous studies have been carried out to compare the learning outcomes of students studying by each mode (Calvert, 1995: 1). The majority of these have been at tertiary level with most of these studies finding a greater drop-out rate for off-campus students and varying results of comparative learning outcomes for the two groups.

Most Australian federal, state and territory Departments of Education are experimenting with various forms of technology to unite small groups of students with an expert teacher (Australian Education Council, 1991: 5; Snowdon, 1992: 11). In this study, the unique educational situation and the addition of some technology to modify the situation by increasing the potential for interaction, necessitates an examination of the effectiveness of this educational scenario. Jones supports critical evaluation of such new technologies:

Policy decisions are increasingly dominated by 'technological determinism'; we face the possibility of rule by technocrats. There is an increasingly fatalist conviction that the answer to every complex problem is to be found in a technological 'fix' - and the more complex the 'fix' the more likely it is to be accepted without debate. The range and scope of political argument in technically complex areas is diminished - indeed it verges on being irrelevant.
(Jones, 1983: 210)

Mathematics. One of the most highly regarded curriculum areas is mathematics with its influential tradition as a fundamental subject, dependent on much rote learning and practise of socially-valued skills. Students learn basic mathematical facts and processes, and make correctly sequenced verbal and written statements. If mathematics is taught by distance education to give more students the opportunity to learn mathematics then this raises the question of how effective is teleconferencing in teaching this much venerated subject by distance education at this stage of development of the technology. 'Part of the conventional wisdom of distance education in Australia is that it is about access and equity' (King et al., 1991: 3) and access and equity are issues in this case. It is important to establish the effectiveness of such a teaching scenario in relation to student learning if its provision is to achieve this equity (Rashid et al., 1992: 121). Fundamental to this is the notion of effectiveness in education generally. Effectiveness is a generic term which can be viewed from many angles. Linke et al. (1984: 19) relate effectiveness to 'the levels of achievement of educational goals; it involves no connotation of value and no consideration of cost in effort required for the achievement'. Effectiveness can be examined with regard to the pedagogical processes used and desirable outcomes of learning associated with a particular course. Keegan (1990: 183) focuses on the quantity, quality and status of the learning, highlighting the need for careful thought being given to the meaning of effectiveness and its relationship to the notion of quality.

Quality. The quality of education has long been a consideration. However, in recent times there have been moves worldwide to measure this quality (Organization for Economic Co-operation and Development, 1989; NBEET, 1989). This became more urgent in Australia with the production of a national survey of Australia's schooling for use in comparisons within Australia and to allow Australia to take part in international surveys (Curriculum Corporation, 1992). Consequently there are moves to provide indicators which can be used for the international comparisons but which are relevant to the Australian situation. Of the ten goals for Australian schooling, the first is to provide quality education and student learning outcomes form one part out of the five that the national report will monitor (Ainley and Fordham, 1991: 104). Consequently student learning outcomes form part of the profile of an Australian education course and are used in this study in that context.

Outcomes. The National report on schooling in Australia (Curriculum Corporation, 1992) measures educational outcomes in terms of three indicators. The first is student retention and completion. This statistical indicator enables targets to be set by government. The second indicator is continuation rates to tertiary study. This is already an objective of most secondary curricula, and DEET reports use indicators such as educational and labour market destinations (Ainley and Fordham, 1991: 107). The final measure is satisfaction with school life. There is little evidence in the literature that most of this current focus on indicators looks at education globally and not just traditional classroom education. It should be remembered that schooling in any form is not isolated and that its effectiveness is determined, in part, by many outside factors, making valid measures extremely difficult. Also, the specified student outcomes are generalizations, with the expectation that a high proportion of, but not necessarily all, students will achieve these on every occasion. Opposing all this Masters (1991: 6) asserts that in Australia presently we have no reliable performance indicators for the student outcomes. He argues that the only valid assessments currently are 'those informal, global, qualitative evaluations that teachers make as part of their day-to-day work' and that all too often comparisons are made based on criteria which are a small sub-set of these unpretentious teacher evaluations. Ainley and Fordham support this stating that 'the effectiveness of schooling cannot be explained by a small set of interrelated factors' (1991: 105). These perspectives imply that global quantitative measures of educational outcomes can provide only limited indicators of effectiveness. Keegan devises criteria, which include the quantity and quality of learning, as measures of suitability and grades a variety of distance education institutions against these. Kemmis adds our 'choices seem not to be about the usefulness of the technology (for better or worse it was designed to be useful), they are about its wise use' (1980a: 205). Part of this wise use will be its effectiveness. Holmberg (1989: 204) extends the notion of effectiveness. Although he is loathe to compare distance education with conventional education or describe it generally as effective, ineffective, good or bad, he does support the notion of applying evaluation criteria to a particular distance education situation. He considers various forms of distance education course evaluation, such as comparison with course objectives, and supports the use of a variety of these according to the particular circumstances. In searching the literature there is a plethora of perspectives on measures of effectiveness, so any attempt to evaluate effectiveness must be multi-dimensional. Therefore, in this study, student attitudes towards the teaching and learning situation is one aspect considered. The second is the learning outcomes in mathematics, but comparison of the learning outcomes of the distance education students with the learning outcomes of traditional education students is not a major area for consideration. The third aspect is the comparison of the outcomes with the goals of the program.

Reflection. One of the national goals for schooling is to bring students to the point where they become independent learners, so in considering the effectiveness of a program, it is of interest to investigate the steps taken to encourage responsibility for their own learning among the students (Burge, 1989: 48). This leads Nunan (1990) to propose that one of the first steps in independent learning is to advocate that learners reflect on what they have learned. Candy, Harri-Augstein and Thomas (1985) refer to commentary on the learning process, personal support of the student's reflection and bench marks for students to evaluate their learning competence. This is reflection as part of the learning process of a student within a course. The provision of the opportunity for such reflection would normally be considered in the evaluation of a course.

On a more global scale is the opportunity to reflect on current classroom practices enabling both students and teacher to examine the education and educational processes used. Kemmis (1980a) supports such a model of 'self-reflection in a critical community'. Kemmis (1980b) sees 'evaluation as the process of marshalling information and arguments which enables interested individuals and groups to participate in the critical debate (the process of self-direction) about a program.' The evaluator must make the community of the program, a community of inquirers. Such a self-reflective approach is usually going on informally and can be disciplined, utilized and extended by evaluators easing communication between groups. Building self-reflection into an investigation then would have the effect of enriching the students' learning experiences as well as using their reflections in the evaluation of the effectiveness of the program.

Evidence of effectiveness. Most government documents view distance education as an attempt to simulate a face-to-face teaching situation. Holmberg (1989: 93) argues that it is tradition and negative prejudices which place the worth of face-to-face teaching above that of non-contiguous forms of study in achieving educational goals. In the cognitive and psychomotor domains he cites Granholm (1973: 6) as evidence that students learn mathematics 'at least as well' by distance education as by conventional methods and Childs who notes that there are,

no studies of achievement which show that [they] do less well than do classroom students, a number which show that they do as well, and a number which show that they do better.
(Childs, 1965: 81)

In neither of these cases is strong evidence cited to support the claims. Kaeley (1988; 1989), however, in a systematic survey, found that when entire populations of distance education and traditional groups were matched, the traditional groups achieved better in post-secondary mathematics. However, when students are paired by ability then such differences disappeared. The implication of this then, is that while students studying by distance education are weaker academically than on-campus students, the mode of instruction itself does not lead to a big difference in the learning of the students. Long (1992: 55) opposes this view in that he found that in the initial year at the tertiary level, even taking all variables into consideration, that 'there is still some evidence of marginally higher failure rates for off-campus students'. Some of the variables he considers are the nature of the courses, the different withdrawal rates for on-campus and off-campus students, the different universities, inequities in the administrative procedures and the range of student backgrounds. Other variables which he discounts as having little effect are age, sex, non-English speaking background and employment. However, he also concludes that 'academic performance of off-campus students ... more closely approximates that of on-campus students when both groups are not in the initial year of enrolment'. Thus any comparison between the learning outcomes of the two forms of education should take place late in the program between groups of students with similar mathematical backgrounds, following similar courses and being taught by comparably capable teachers.

Evaluation of a program can take many forms. One of these is to consider the outcomes of a program to reveal the level of achievement of the goals of the program. Hewton (1991: 1) in searching for indicators to measure performance in education, tells us that 'There are many indicators of the status and health of an educational enterprise, but the most basic and important indicators ... are ... student attitudes and competencies'. Consequently this study will focus on these outcomes as indicators of the effectiveness of the program.

Attitude Outcomes
McLeod (1994: 639) in an overview of mathematics education research this century, noted that many early studies considered the relationship between attitude and achievement but without the development of a strong theoretical background rendering the results obtained questionable. He goes on to show that during the 1970s attitude was defined as enjoyment and worth and measures were developed, while in the 1980s the divisions were extended to include perception of the mathematics teacher, anxiety, self-confidence in mathematics and motivation. More recent research on problem solving in mathematics, for example Leder (1988), considers this problem of multiple perspectives on attitude and adopts an open approach to capture the complexity of the issues.

Attitudes are influenced by students' experiences, peers, home, school, community and the media (Curriculum Corporation, 1991). A positive attitude is demonstrated by a sense of purpose, confidence in the ability to succeed, pride in achievement and pleasure in the use of mathematics. However, results show (Middleton, 1995: 254) that generally teachers are not aware of what motivates students, but if they are, then their teaching is more effective and students learn better. Schiefele and Csikszentmihalyi (1995: 163) found that interest and achievement mutually influence one another so that individual differences in student backgrounds and ability will result in differing needs for motivation and reactions to motivation. The fact that achievement, interest and positive attitude are related indicates that it is useful to examine both the students' attitudes towards learning mathematics itself and towards learning using teleconferencing.

Attitudes Towards Learning Mathematics
Ainley and Fordham (1991: 114) discuss indicators of the quality of school life and correlations with other factors. In investigating teacher-student relationships, the students' sense of academic success and worth within the school and social identity, they conclude that satisfaction with school life is not necessarily associated with academic success. This is at variance with much current work being done on attitudes towards mathematics and resultant mastery. Over the past decade many mathematics educators have studied the connection between student attitudes towards mathematics and their achievement, and participation. They conclude that 'positive attitudes assist the learning and teaching of mathematics' (Department of Education, 1989b: 16). Most mathematics curriculum documents, therefore, stress the importance of a positive attitude. Consequently careful examination should be made of the satisfaction with school life and positive attitudes towards mathematics.

One view of education is that it aims to empower students so that they can interpret the world around them either globally, on the scale of Paul Davies or Stephen Hawking, or from a more defined perspective. The small section of that education being considered here is that of mathematics. The national statement on mathematics for Australian schools outlines the '... understandings, skills and processes and knowledge which should be typically be made available to students' (Curriculum Corporation, 1991: 2). That is, the students should have the opportunity to study the specified areas of mathematics but without the compulsion to do so. The British Cockcroft Report (1982) is more direct in stating that confidence is an essential part of mathematics education. A test for mathematics education is to develop in students both the attitudes and knowledge which will allow them to handle conventional tasks efficiently and also to manage novel or unfamiliar tasks. Having a positive attitude towards mathematics means generally enjoying working with mathematics and having confidence in one's own ability to do it but it does not mean that a student will display this positive attitude towards the whole area of mathematics all the time. The public perception that students dislike mathematics, together with peer pressure which makes success in mathematics socially unacceptable, are potential forces in the opposite direction (Booker et al., 1992: 16). Students see it as important to society but not to themselves (Schiefele and Csikszentmihalyi, 1995). The emphasis should be on encouraging students to achieve, take risks, see its importance in daily life and in future careers (Mathematical Sciences Education Board and National Research Council, 1989).

This highlights the view that there is more to education than the acquisition of knowledge. Motivation, attitudes, beliefs, behaviours and the desire to continue learning are also important outcomes. Holmberg (1989: 26) holds that distance education can be effective in bringing about such an attitude change. This is important in that the net effect of mathematics instruction is usually to convince school leavers that they cannot do mathematics at all.

Attitudes Towards Learning Using Teleconferencing
It is one of the roles of a teacher to provide a favourable learning environment leading to student learning and achievement of course and school objectives (Medley, Coker and Soar, 1984: 61). If the use of the technology is in the interests of the students (Department of Education, 1989a) it is important to determine the attitudes of the students and their teachers (who have the potential to influence the students) towards it. The teachers of the students fall into two categories as Campion (1991: 12) says technophiles and technophobes. The one group is anxious to support teaching with the technology, the other resents the efforts that have to be made to master it or alternatively ignores it. The attitudes of other groups may also influence the students - parents, administrators and the local community. The attitude of the education theorists can also affect the participants. Some theorists view the use of technologies such as teleconferencing in education with some scepticism - people such as Peters (1989) who sees technology as an element in the industrialization of education or Harris (1991: 58) who cautions that technologies are being introduced for political rather than educational reasons. Burt (1991: 100) considers the social aspects - the situation in which students find themselves, which necessitates the use of the technology, stressing that this culture underpins the technology and fashions the student attitudes towards the use of the technology. There is a need to determine how students and teachers actually feel about the technologies which form a part of the education and to determine their preferred learning styles in order to make some comparison (Barnes and Owens, 1992) between the two. Consequently this study investigates the educational environment which the technology supports, the preferred learning styles of the students and the attitudes of the participants towards the use of teleconferencing in teaching mathematics.

Learning Outcomes
Generally in judging the standard of a mathematics course, tests of various types are used to evaluate student progress. This is based on the premise that 'not only should curriculum and assessment content be aligned, but also the goals, objectives and instructional approaches should be aligned with the assessment tasks' (Chandler and Brosnan, 1995: 122).

In evaluating mathematics courses Ellerton and Clements (1990: 209) state that 'there are certain basic mathematical understandings, knowledge and skills that all students should acquire, and certain opportunities and learning experiences that they should have'. A command of mathematical terminology and verbal, symbolic, diagrammatic and graphical representations are essential aspects of numeracy. Students need to learn not only about mathematics but the techniques through which it is produced and applied. Holmberg (1989: 12) supports this broadened notion of mathematics adding that distance education with penetrating assessment procedures will ensure depth of learning with students directed away from texts towards the actual subject matter.

Gagné notes that in mathematics, rules are built up in a hierarchy, being generated from pre-requisite rules which in turn are based on previously learned discriminations. Being able to use these basic mathematical procedures automatically enables more global perspectives of a problem to be formed. These basic mathematical procedures are the tools for problem solving. From there 'once concepts have been mastered, the individual is ready to learn an amount of knowledge that is virtually without limit' (Gagné, 1970: 188). 'Students need to recognize when mathematics might be useful, choose the mathematics, do the mathematics, and evaluate its effectiveness in the circumstances' (Curriculum Corporation, 1991: 13). Therefore, in order for students to continue learning in mathematics, they must be encouraged to learn skills and then use those skills appropriately. Consequently the learning outcomes investigated comprise knowledge of mathematics, understanding of the history and derivation of that knowledge and application of that knowledge and, together with the attitudes fostered in the course, are used in the evaluation of the effectiveness of the teleconferencing in mathematics education.

Findings

The school visits clarified the context in which the particular mathematics course chosen is taught. The study focuses on a cluster of schools in which the students follow the standard New South Wales Department of School Education course and undertake the normal assessments. Teleconferencing is just one component of a course - the rest of the course (curriculum, textbook, lessons with tutors, examinations, etc.) is similar to that in classes throughout the state. Student numbers changed during the time of observation but stabilised to a core at five of the seven schools. In some schools the Diverse Use of Communication Technology (DUCT) microphone/speaker system is used in conjunction with the telephone system, in other schools integrated headphone/microphone sets are used. Facsimile contact is also available between the schools and is a significant part of the teaching equipment. All schools have a separate block for the senior students with distinct Year 11 and Year 12 rooms in which the students work at their individual study carrels. When it is time for a teleconference lesson, students go to either a special room or a separate region of the study room where the equipment is housed and operate it by themselves. To assist the students, the schools also appoint an associate teacher from among the school staff in each subject. The associate teacher, who is not necessarily a specialist in the subject, is given a time allowance for the position. In some cases the associate teacher sits with the student or students during the lesson, in other cases the students are alone with the equipment. Students meet each other once a year and the mathematics teacher visits the schools at least three times a year. Students typically each week have three 20 minute teleconferencing lessons with the teacher, four 40 minute face-to-face lessons with the associate teacher and one timetabled unsupervised lesson. However, there is variation between schools.

The course in this study is the centrally developed 2 Unit Mathematics course of the New South Wales Board of Secondary School Studies. Content is presented in the usual order, consistent with the accepted textbook being used. Students have tests at the end of each major topic, mandatory assessment tasks and prepare for the Higher School Certificate examination at the end of Year 12. There is regular feedback on progress to students orally, through worksheets and tests, and to parents through regular school reports and interviews.

Attitudes

- Attendance
Attendance has been used as one of the indicators of student attitudes towards the learning environment. The class commenced with fifteen students. One student joined the group in June and seven had moved to a lower level of mathematics by September leaving a base number of nine students. The average attendance is shown in Table 2.

Table 2: Attendance at Lessons Examined

The teacher was asked the approximate percentage attendance in February and September. The estimate is above that achieved during the sessions examined. Absences were due to illness, school visits, sporting events, line failure and external deterrents such as floods.

- Retention
Retention rate of the teleconferencing project can also be used as an indicator of the students' attitudes towards study. Tables 3 and 4 show the student enrolment at of the five schools. A more detailed summary for 1990 is given by Squires and Sinclair (1993: 70).

Table 3: School Enrolment in 1993

* includes 2 part-time students

 

Table 4: School Enrolment Since Program Commencement

* includes 2 part-time students

- Attitude Towards Mathematics
The students have a wide range of backgrounds and attitudes in mathematics. These attitudes are mostly positive with some students liking mathematics for the sheer joy and challenge of engaging with the discipline, however, there is a big range from 1 to 10 on a 10 point scale with 10 indicating liking mathematics very much. The overall average is 7.4. Students like mathematics generally for its logic, accuracy and especially the practical nature of the subject. They like using formulae and the fact that the validity or otherwise of their answers can be easily determined. They enjoy building up their mathematical knowledge and using mathematics that they have learned previously. They like it best when they understand where they are going and appreciate the teacher explaining how to do a problem, talking with them, then guiding them through similar problems. They like being able to ask for help as they work problems through.

Some students do not like mathematics at all. They find it hard and dislike making mistakes, especially publicly. They do not like having to remember formulae, and feel embarrassed that the teacher has to spend so much time from the lesson with them to ensure their understanding. They feel that the teacher does not have that time available in a twenty minute lesson.

- Attitude Towards Learning Using Teleconferencing
Students generally appreciate that without the teleconferencing they would not be able to remain at their own school or in some cases continue their education. All students interviewed have a positive attitude towards studying with teleconferencing and at the time planned to continue in Year 12 and the majority of students planned to continue study after Year 12.

Some typical responses of the teacher and students regarding the use of the technology are given in Table 5.

Table 5: Some Attitudes Expressed by the Teacher and Students.

The concentrated effort needed by students during the teleconference and the accent on verbal skills and de-emphasis on blackboard work is seen by the students as both positive and negative aspects of teleconferencing.

Most students appreciate having a bigger class with the flexibility of not joining in, if it is not necessary. They appreciate the opportunity to talk and ask questions of the teacher as well as the associate teacher. One student noted that it is not necessary to look at the teacher during the lesson enabling concentration to write down notes during the lesson. Surprisingly, a number are pleased that the teacher and class cannot see them, especially when they make mistakes.

Some students find the technology limits their preferred classroom behaviour. They are not able to just butt in when they want to as has been the norm in their face-to-face classes. Generally students are happy with the teacher's approach but several remote students commented that it is more onerous, but not impossible, to contact the teacher if they are experiencing difficulties. Most students commented on the limitations of the lack of visual contact and the ensuing difficulty with diagrams and in developing proofs through the limited contact with the facsimile machine or verbal explanations. They yearn to see the faces of their peers but not necessarily for their peers to see them. They find it hard to get all their work done on time for the short structured lessons and when the class was larger they found it hard to correct any misunderstandings. The students are unanimous in their condemnation of the quality of the technology and find the time lost in setting up and in resolving technical breakdowns very disturbing during their short lessons. Other administrative breakdowns they find they can cope with, although some are annoyed by the lack of preparation on the part of their some of their peers.

The learning preference scales of the students determined by the standardized ACER test (Barnes and Owens, 1992) have been broken into three sub-categories as listed in Table 6.

Table 6: Learning preference scores. Jennifer Barnes, Lee Owens, ACER, 1992

Learning Outcomes
The class undertook a skills survey to assess their understanding of the Sine Rule, and a traditional 2 Unit Mathematics class in a city school undertook the same survey. The graph in Figure 1 illustrates the results of the two groups when classified according to the outcome statements categorized in A national statement on mathematics for Australian schools. The possible total score for each outcome is also shown.

Figure 1: Student Scores Achieved Grouped According to Outcome Statements

These data can alternatively be shown as a percentage of the possible total score. It should be noted that the small number of students involved makes in-depth statistical analysis unreliable.

Figure 2: Student Scores as a Percentage of Possible Scores According to Outcome Statements

Comparison with Program Goals
In the original project set up in 1989 and implemented in 1990 there was no attempt to incorporate a 'self-reflection in a critical community model' (Carr and Kemmis, 1986) into the program on a permanent basis. However, in this study, the ideas of Nunan (1990) and Candy, Harri-Augstein and Thomas (1985) on reflection on a educational program have been used. The use of diaries, interviews and discussion facilitated reflection on the course. Table 7 shows some student reflections on the learning process categorized in a format which illustrates students' evaluation of the course and their own learning experience and competence.

Table 7: Some reflections of the students.

Discussion of Findings

Results indicate that there is a network of support for both the students and the teachers within the teleconferencing project. Both Squires and Sinclair (1993) and Long (1994) stress the vital role of such support with special reference to the distant and off-campus students. The students have access to, and use, help from their peers, the associate teacher and the teacher. The associate teachers and teacher have access to peer support, the school teleconferencing co-ordinator, technical assistant and the cluster Distance Education Co-ordinator. This study found that support has been evident at all levels of the teleconferencing project.

Attitudes

- Attendance
Attendance records reveal the students who persisted with the course as well as those who dropped to a lower level. Further investigation of the reasons for students leaving the class could reveal factors other than those of enjoyment and career prospects that influenced the students who continued. Attendance at class is below the level that the teacher estimated but it is noted that the disturbances to a normal school schedule such as sports days or excursions, are multiplied five fold when five schools are involved. The actual organization of the timetable would seem to be indicative of the wisdom of trading some individual freedom for the schools, for the efficiency of the centralized system. This could also be considered in regard to individual school events which impact on the joint lessons with other schools. The many reasons for absence from the mathematics lessons, illustrate the disruption caused to the lessons by such events. The centralized timetable eliminated many difficulties and a centralized calendar could do likewise. Attendance was also affected by technical difficulties on several occasions when the bridge malfunctioned. On the whole the students seem concerned not to miss classes thus indicating their positive attitude to schooling by teleconferencing.

- Retention Rate
The total retention rate between Years 10 and 11 is just under 50% and between Years 11 and 12 just above 80%, but there is much variability between schools. Although the retention to Year 12 is well below the 70.6% for the state (Australian College of Education, 1994: 11) it should be noted that one of the goals in setting up this teleconferencing program is to increase the low retention rate of students in rural areas. Although some students would have continued their senior secondary education without the teleconferencing program, others would not have done so. Table 4 demonstrates that this enrolment pattern has been steady since the inception of the program in 1990. It would be expected that entry into the program would rise in line with the Australia wide trend, but there are other circumstances such as declining numbers in rural areas, which would put a downwards pressure on numbers. Therefore, continued monitoring of the enrolment patterns and demography of the catchment area has the potential to clarify further the ability of the program to increase retention rates.

- Attitude Towards Mathematics
Most students like their mathematics and enjoy their mathematics classes. The chance to learn mathematics with the larger group is seen as a chance to work on mathematics as a team and the teacher facilitates this view of mathematics education during lessons. Investigation of the attitudes of the students who left the course could give a different perspective on this. It could be that only those students with a positive attitude towards mathematics survive when it is taught in this mode. Alternatively a student's attitude towards mathematics may have no bearing on the decision to drop to a lower level and out of the class.

- Attitude Towards Learning Using Teleconferencing
Teleconferencing in itself does not appear to affect students' attitudes towards mathematics, but is seen by the students rather as a tool to give them access to mathematics education. To this end it is worth noting the concern of weaker students that they take up a disproportionate amount of time during the lessons and ensuring that they have easy access to help through learning materials, the associate teacher or the subject teacher. The dispersed nature of the preferred learning environment of the students is noteworthy. Although they are small in number, scattered singly or in pairs over more than 30,000 square kilometres, their preferences covered the whole range of co-operative, competitive and independent learning styles. This highlights the fact that even a small class is made up of students each with their own preferred learning style. To fully cater for this situation, just as in a traditional class, teachers will need to use a multiplicity of teaching strategies if education is to be geared to the needs of the individual student. The teleconferencing situation would seem to facilitate independent learning although this is not the most favoured style. A conscious effort has to be made in this situation by the teacher, to encourage co-operative and competitive learning by the students.

The students stress that learning by teleconferencing means that they have to prepare and pay attention more than they do in a traditional classroom. This they accept as part of the different teaching methods involved with teleconferencing. However, they do not accept the technical breakdowns and become very annoyed when they happen. Most students are even less accepting of breakdowns as the year progresses. Technical difficulties due to equipment and administrative difficulties still account for 20% of the short lessons. This would seem to be a prime area to address in improving the efficiency of the system.

Learning Outcomes
Desirable learning outcomes in this case, will be those associated with the Year 11, 2 Unit Mathematics course. Although the number of students involved in the skills survey is too small for detailed statistical analysis, and factors such as teacher competence or the mathematical background of the students are not strictly controlled, the similarity of the results of the skills test is notable. The students from the city school show marginally more familiarity with spatial concepts while the rural students' number skills are marginally better. However, the most noticeable result is the evenness of the two groups. Even considering the rural school results alone, it can be seen that they have achieved the majority of the learning outcomes specified in A national statement on mathematics for Australian schools for the Sine Rule in trigonometry. It is interesting that of the five major areas considered - working mathematically, space, number, measurement and algebra, that space is the weakest area of knowledge of the students. Although the trigonometry skills test is deliberately focused on this section, it may have been more appropriate to use a test that looks at more general learning areas of mathematics. Results such as those obtained, support the hypothesis of Granholm (1973) and Childs (1965) that the quality of learning is not diminished when students study by distance education, but the small number of students involved in this case, prevents these results being used as evidence in their own right.

Comparison with Program Goals
In comparing the outcomes of the teleconferencing program with the original goals of the program, the results of the skills survey indicate that intellectual development is being achieved. The students themselves almost universally see their growing familiarity with technology helping them in the technological world they are entering, although not all the students plan careers in technology or in areas that require higher education. At the present time a basic set of subjects is available but now that the system is in place, extension of the choices is a matter for negotiation between the schools, the Department of School Education and the cluster Distance Education Co-ordinator. Students universally stated that the opportunity to study locally beyond Year 10 is worthwhile. Although just under 50% of the students are continuing on from Year 10 to Year 11 at the schools, the majority of the students stated that they would not have continued their school education except for the availability of this program. As such, the program is fulfilling its objectives of increasing access to education for rural students and encouraging increased retention rates in Years 11 and 12.

Conclusion

In determining the effectiveness of teleconferencing in mathematics education at the upper secondary level, this study has focused on the form of the learning environment and the outcomes of its use. The education system, schools and individuals involved in teaching mathematics using teleconferencing in this case generally go to great lengths to 'make the system work' by providing the equipment, personnel and support. Students are generally appreciative of the opportunity afforded to them by the project and are co-operative in their attitude.

The positive attitude of students, staff and administration towards the use of teleconferencing is to be applauded and may be the key to the success of the teleconferencing project in retaining students at school. If this is the case then it is important to monitor these attitudes as the project continues and to determine which aspects contribute to the high morale of the participants. The wide range of preferred learning styles among the students reflect the traditional teaching situation. Consequently, teaching strategies that cater for varied learning styles should be highlighted in any professional development course. The data indicate that the audio links provide a vehicle for student learning and confidence building of both the students and the teacher, however, the quality of the sound and the number of breaks in the line cause frustration among the students. In spite of this, most students prefer the substandard audio communication to no communication at all. Teachers and students see the advantage of an audio-graphic link in adding an extra dimension to the learning in mathematics and other subjects and this perceived need for visual contact was addressed concurrently with this study. Again as circumstances change there is value in determining which aspects of teaching with teleconferencing are transferable to the visual or other modes of instruction. It is important that the technology does not interfere with the learning, so to this end, while it is to be expected that pilot programs will have some technical difficulties, it is vital that the technology used is reliable, robust, maintained and adequate for the task,. This is even more important as the schools serviced by this technology are distant from technical assistance. The majority of students see their future in rural New South Wales. With access to continuing education in rural areas being mainly through distance education or open learning, this experience, of supported independent learning and access to assistance through technology, has the potential to be the foundation for lifetime learning.

The similarity of the learning outcomes of this small number of rural students and the results of the city school, raises many questions. These, together with previous like findings of Granholm (1973), Childs (1965) and Kaeley (1988), should lead us to determine which aspects of the teaching process, common to distance education and conventional education, are the important ones in learning - to resolve which aspects are needed to cater for the variety of students in a class, and ascertain those that have just lingered on from Seventeenth Century classrooms seemingly without value. Is the use of technology to mimic a traditional classroom exposing the strengths and weaknesses of our current model of education? Is the traditional classroom the appropriate one to model? Answers to these questions should underpin the implementation of all new distance education programs, and in fact, education programs generally.

It has been demonstrated that it is essential that the learning outcomes of the different forms of education be constantly monitored to ensure appropriate parity of results in line with principles of equity. This research could form the basis for subsequent longitudinal studies in addition to providing both formative and summative evaluation data for the development of future courses and technologies. Future projects should capitalize on the strengths of both traditional and innovative projects in the teaching of mathematics. It is also worthwhile to consider how the technology might be used to provide new opportunities for teaching and learning mathematics with the potential to improve not only distance education but education in its widest possible sense.

In this particular study it has been demonstrated that the teleconferencing environment is supportive and can cater for a variety of learning styles. The results from the study indicate that the attitudes towards the subject and towards the learning environment provided are positive and that the learning outcomes are comparable to those of students studying in a traditional classroom. They support the hypothesis that using teleconferencing in teaching mathematics by distance education gives the students access to education that, although different from that available in a traditional classroom, forms an effective learning environment.

Acknowledgments

This study was undertaken as one section of a Masters thesis for Deakin University. I wish to acknowledge the support I have received from two distinct groups in undertaking this research. Firstly the students, staff and administrators of the schools from which the information is drawn. Their helpfulness and tolerance is much appreciated. Secondly, the staff of Deakin University, for enabling me to view this investigation critically and Peter Routcliffe and Robert Fitzgerald of Australian Catholic University in the initial stages of the investigation.

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Author

Joan Robson is a former teacher and presently a lecturer in the Faculty of Education.