Author: Gerry Foley & Sandy Schuck

University of Technology, Sydney

Keywords: primary teacher education, priamry teaching, mathematics, World Wide Web, Web-Based Conferencing Tool, Web-Mediated intervention, virtual learning, user-friendly environment, supportive environment, teaching and learning.

Article style and source: Peer reviewed. Original ultiBASE publication. Paper initially prepared for "Initial Teacher Education Forum: Showcasing excellence in initial teacher education and schooling" RMIT University, Melbourne 17-19 February 1999.

Contents

• Abstract
• Introduction
• Using the Web-Based Conferencing Tool
  • Setting up and conducting the conference
  • Examples from the conference site
  • The Question and Answer facility
• The Value of Web-Mediated Interventions
• Discussion
• References

Introduction

In 1997, the authors were successful in gaining funding to develop a flexible learning package for a first year subject, Mathematics Education 1, in the Bachelor of Education (Primary) at their university, where academics are being encouraged to constantly assess how best to "read" their students’ needs, and "match" these to suitable learning contexts (Scott, 1997).

One of the concerns we wished to address in the development of this subject was that prospective primary school teachers often view mathematics in very restricted terms. Mathematics is seen by many of them as being highly rule based and best learned by rote; as being principally about numbers, algorisms and procedures, and not about problem solving or creative endeavour. Prospective teachers often fail to see connections between mathematical ideas and applications. Negative attitudes to mathematics are often also displayed by students who hold such views. (These phenomena have been widely commented upon in the mathematics education literature – see, for example, Mayers, 1994; Burton, 1996; Crawford and Deer, 1993.) The authors considered that an important purpose of the mathematics education subject would be to challenge the beliefs held by their students about mathematics, and to attempt to improve students’ attitude to mathematics.

A recent development in the university’s information technology resources was seen by the authors as presenting an avenue by which students’ beliefs could be challenged and attitudes to mathematics improved. This was a Web based conferencing tool, which could be accessed by students both from within the university, and remotely. The authors were encouraged by some studies, including those by Carty, Stark, van der Zwan and Whitsed (1996), Eklund and Eklund (1997) and Blumenfeld, Marx, Soloway and Krajcik (1996) which suggest Web based conferencing can be effective in developing a learning community in which participants support each other’s learning. Moreover, the system appeared to present the potential to support our own shared socio-cultural view of learning, whereby discussion and debate could be held amongst the students without the lecturers being construed as the "experts" handing down pre-ordained knowledge.

In their teacher education courses, prospective primary school teachers are often encouraged to take a constructivist perspective in their approach to teaching and learning. This approach encourages shared interactions and collaboration by children in the construction of meaning (see, for example, Groundwater-Smith, Cusworth and Dobbins, 1998). However, as pointed out by Hoban (1999) it is often the case that such a perspective is not integral to the way these tertiary students learn in their courses on campus. The Web based conferencing tool appeared to us to hold out the promise of our being able to model with our own students a style of learning which we would like them to apply in their own teaching.

The Web based conferencing tool, TopClass, can be accessed from computer laboratories on campus, or from any other place where a computer can be connected to the World Wide Web. Remote options include access from home, the local library, even from overseas. TopClass includes an e-mail facility, which allows students to communicate with each other and with university staff. top

Using the Web-Based Conferencing Tool

The Web based conferencing tool was used for two aspects of the mathematics education subject:

1. a discussion designed to challenge students’ beliefs about mathematics, and
2. a Question and Answer facility where students could post questions and answers about the use of technology, or any issues or concerns relevant to the mathematics education subject. top

The Web mediated conference

Setting up and conducting the conference

In 1997, we proceeded to set up a Web mediated conference as a component of Mathematics Education 1, taken by students in the Spring Semester (the other component of this subject comprised a series of workshops on the topic of measurement).

Two focus statements discussion on the cultural context and nature of mathematics were provided on the Web site as a basis for discussion:

The cultural context of mathematics

"Mathematics is universal, objective and unchanging. It is independent of social, cultural and political values."

The nature of mathematics

"I'd describe maths as the calculation of certain things to do with numbers, and the use of certain formulas and methods, simplifying, counting and subtracting and things like that." (Maria, first year prospective primary schoolteacher)

A third focus question was included when the subject was run in 1998, to provide more choice:

On the teaching of mathematics

"The best way to teach maths is by giving clear explanations followed by extensive drill and practice." (George, classroom teacher)

The students were introduced to the conferencing tool in the campus computing laboratories by the authors. They also gained further familiarity with the system in an information technology subject being undertaken in the same semester. Students were required to form groups of five or six, and formulate a response to one of the above statements. Extra reading material was made available providing a wide range of views on the focus statements. It fell into three categories:

• Relevant material from Web sites around the world, via links provided by the subject developers.
• Responses to the focus statements placed on the discussion site from respected mathematics educators who had been invited to make a contribution by the subject developers. These mathematics educators were from a number of countries, including Australia, Fiji, New Zealand and the United Kingdom. A brief C.V. and, where possible, a digitised image of the contributor were also placed on the discussion site.
• Selected journal articles, placed in the library’s special reserve.

On the basis of reading from the material provided, and group discussion (possibly taking advantage of the e-mail facility), a response of about 500 words was formulated by each group and posted on the discussion site of TopClass. After each group had posted its response, students were required to read all other groups’ responses to their chosen focus statement and, in the same groups as before, formulate and post a second response taking into account the views expressed by other groups. The mathematics educators who initially responded to the focus statements also had the opportunity to contribute to the continuing discussion on the Web. We read both postings by each group and graded them as part of the subject assessment. Grades with comments were sent to each group via the TopClass e-mail facility.

In the 1997 intervention, students found some difficulty in arranging collaboration in-groups of six. Also, the delay of about 6 weeks before they posted their first response meant that the authors were unaware of the difficulties that some of the students were experiencing with the software until halfway through the semester. Further, many students only experienced these difficulties when trying to post the assignment in the last few days before the submission date – often a critical time for experiencing frustration. If more students had chosen to use the e-mail option in their interactions they might well have been under less pressure at this point.

Consequently, when we ran the subject in 1998, we changed the system of grouping. This time, teams of three posted to other teams of three on a fortnightly basis. If a team did not post their response by the required date, the subject coordinator would be aware of it, and could offer more timely assistance. After six weeks of two teams posting responses to each other in alternate weeks, those two teams combined to collate their previous responses into a combined statement. top

Examples from the conference site

The reading material and links to various Web sites provided a wealth of information and diverse views on the issues under discussion. Ideas and perspectives which were quite unfamiliar to many of the students were made available. For example, one URL presented an article about the traditional use of mathematical patterns by females in Madras.

This article is most attractive in its presentation, as it contains some very striking graphics of the kolum patterns. It illustrates the Web’s ability to deliver material which engages the students’ attention very effectively. The writer goes on to reflect on the possible significance of these activities for the performance of girls in mathematics:

In the section ‘What the experts say’, Steve Lerman’s (1997) contribution introduced the notion that mathematics might not be value free. This notion, and the idea that mathematics might have a political dimension, came as a revelation to many of the students.

As students had read some of Steve Lerman’s work in recommended texts, it was exciting for them to receive a prepared response to their group in this way.

A very interesting contribution to the discussion site was made by Sala Bakalevu (1997a), who is a vice-principal at a secondary school in Fiji, but who was in New Zealand at the time of the computer mediated conference. She was able to bring her own very personal perspective as a Fijian to both the discussion on the cultural context of mathematics and the discussion on the nature of mathematics. The following excerpt gives an indication of Sala’s thinking on the issues:

Some of our students were surprised and gratified when Sala posted a further response, this time to clarify some points for one of the student teams who had posted their initial contribution on TopClass.

This exchange illustrates well the potential of the Web to build international electronic learning communities. Here was a mathematics educator in New Zealand able to link into the discussion on the Web and make pertinent comments related to her own experience and culture, all within a few days of the original posting by the students.

That the views of many students about mathematics had been challenged by their exposure to the Web-supported and other readings, was illustrated in many of the collaborative postings from students on the discussion site. For example:

Another example:

The Question and Answer facility

When the subject was offered in 1998, a Q&A facility on the Web based conferencing tool was set up to present students with an opportunity to participate in a community of learners, where they could share their ideas and generate knowledge for themselves with minimal contribution from their lecturers. The following examples of student conversations using Q&A illustrate how the students were able to support one another in several areas: the use of computer technology, understanding aspects of measurement (the topic being addressed in their workshops), clarification of some pedagogical issues concerning the development of mathematical concepts in children, and issues arising directly from the students’ field based experiences.

The subject of the first exchange is a printing problem encountered by Melinda (pseudonyms are used in all cases). Several students offer assistance.

Tumboon appears to be quite proud of his knowledge of how to print on the network, and very happy to share it with another student.

The next message starts with a question of fact, then broaches an important issue about the teaching of measurement. One reply develops the discussion about teaching, while the other gives a very succinct answer to the question.

The next message initiates a conversation about group activity and discussion in class on campus, and its relevance to children’s learning of mathematics.

Three further messages develop this conversation, but are not reported here as they are rather lengthy.

The final example given below illustrates how useful a Q&A facility can be in generating fruitful discussion about the students’ experiences in their field-based experience. A concern is raised by Sarah about difficulties met in using workstations furnished with learning activities for young children. This leads to an exchange of helpful ideas as other students draw on their own practicum experiences, reflect on some of the difficulties they themselves met and the steps they took to overcome them. The students write with enthusiasm about these early teaching episodes and they appear to be eager to support one another in the suggestions they have offered.

There was one more rather long response to Sarah, offering encouragement and outlining in detail some strategies which the student had found particularly useful in the practicum. Again, this sharing of experiences on the Web allowed students who might have been reticent to speak out at a mass lecture for 200 students, to communicate with the whole cohort. top

The Value of Web-Mediated Interventions

We carried out very detailed evaluations of both the 1997 and 1998 interventions. Data was gathered from various sources: pre-and post intervention surveys assessing the students’ beliefs about mathematics and computer-mediated learning, reflective journals maintained by students during the semester, and, for the 1998 intervention, a mid-semester evaluation. Detailed descriptions of these interventions may be found in Schuck and Foley,1998; Foley and Schuck, 1998; Schuck and Foley 1999.

• the opportunity for the sharing of opinions and ideas in collaborative groups;
• access to very up-to-date material with a range of alternative viewpoints on the conferencing site;
• the immediacy and relevance of the contributions of the mathematics educators from around the world written especially for the discussion (a student commented that "it makes the world a great deal smaller when experts are able to comment on your ideas on the Internet");
• the opportunity to develop computing skills which would be important for them in their teaching careers;
• the public nature of their postings, which tended to motivate them to do their best work;
• the convenience of remote access to the conferencing site;
• the opportunity to share their ideas on the Q&A section (in the 1998 intervention).
• Negative findings were that some students had difficulty:
• in arranging their collaboration when the group size was too big (ie. about six);
• in following some of the instructions for the use of the conferencing software;
• with the occasional unreliability of access to the conferencing site, both on and off campus.

We found that students generally did not have difficulty with the content of the Web mediated conference, and that overall, the discussions posted by the groups were satisfactory. Evidence was provided in the reflective journals and the surveys that students’ views about mathematics had been successfully challenged.

However, contrary to our expectations, in the 1997 intervention we found that many students became disenchanted with the technology as the semester progressed. Whereas many had approached the Web based tasks optimistically, by the end of the semester they had become frustrated and negative about the use of technology. In fact, the component of the pre- and post intervention surveys dealing with the affective/valuing aspects of the use of computer mediated learning showed an overall shift in the negative direction during the course of the semester. We also found that some students had not become very familiar with the conferencing tool, because they had left to others to do the postings.

The detailed evaluation of the first intervention led us to re-assess some aspects of the organisation of the Web mediated component of Mathematics Education 1. The changes relating to the extra focus question, the smaller discussion teams and the Q&A site have already been discussed. In addition, in 1998, all students were required to do at least one posting to ensure that they became familiar with the conferencing tool, and tutorial sessions were booked in computer laboratories with academics in attendance to provide advice and support for those students who were experiencing difficulty with the technology.

The TopClass system proved itself to be more reliable in 1998, as many of the teething problems of the previous year appeared to have been resolved. However, there were still occasional problems, such as computers crashing on occasions of heavy student usage.

Our evaluation of the 1998 intervention showed even stronger evidence that the beliefs of students about mathematics had been successfully challenged, when compared with the 1997 findings. However, in regard to the affective/valuing side of computer mediated learning, although the pre- and post-intervention surveys did not show an overall shift in the negative direction, seven out of ten individual items showed a statistically significant shift in the negative direction. This shift appeared to occur at the time of presentation of the large group response, which was to be graded. Previous team interactions did not seem to attract the same level of feeling. Some students also reported difficulty in maintaining worthwhile discussion over the course of six responses. top

Discussion

Having implemented the computer mediated discussion in consecutive years, and carried out quite extensive evaluation on both occasions, it appears to us that the computer based conferencing tool has much merit in the provision of opportunities to promote collaborative learning amongst prospective primary school students. The way in which the students and mathematics educators participated in the discussion, posting their responses to the focus questions then continuing the discussion with further postings, broadened the collaboration to that of a world wide community of learners. Our analysis of the results of the evaluations showed a trend towards a more liberating view of mathematics on the part of the students. The Q&A section proved to be very successful in allowing students to take responsibility for their own learning, and to learn by interactions with their peers, with minimal contribution from academics.

Yet we continued to find that some students were dissatisfied with the use of the technology, even in the second intervention, when the equipment was performing more reliably and greater support was being provided by the academics. The period of greatest frustration often coincided with the time of posting for assessment, when the greater pressure seemed to magnify difficulties. The number of students in a team seemed to be critical, as well. In the first intervention, when the teams were of size five or six, and in the second intervention, at the point when two teams of three combined to plan their final posting, students complained of the difficulties they met in organising their collaboration.

Despite these difficulties, we believe that it important to expose our students to Web based technology, as it will play a significant part in their teaching careers. Perhaps the way forward is to remove the assessment aspect from the students’ early interactions with this technology – although a difficulty with this approach could be that students often view an unassessable item as one that is not important. It would essential for students to be convinced of the value of the Web based activity. The question of the team size will also need to be carefully addressed in future Web mediated conferences. It appears that it is important to keep the number in the team quite small – about three seems to be an effective number. We anticipate, however, that as more of our students obtain remote access to the Web, and gain more flexibility in the time and location of their use of e-mail and conferencing tools, some of the difficulties in collaboration will be overcome.

To sum up, briefly, even though computer mediated conferencing promises new and powerful ways of supporting the learning of prospective primary teachers, we found that it is necessary to continually ground the approach to its implementation in practical realities. top

References

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Bakalevu, S. (1997a). Contribution by Sala Bakalevu. Mathematics Education 1 TopClass Site, What the experts say, University of Technology, Sydney.

Bakalevu, S. (1997b). Reply to Amanda Clare’s Group. Mathematics Education 1 TopClass Site, What the experts say, University of Technology, Sydney.

Burton, L. (1996). Mathematics, and its learning, as narrative - A literacy for the twenty-first century. In D. Baker, J. Clay, & C. Fox (Eds), Challenging ways of knowing English, Mathematics and Science pp. pp. 29-40. London: Falmer Press.

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