Can videoconferencing contribute to teaching and learning? The experience of the Motivate Project
University of Cambridge, Email: firstname.lastname@example.org
University of Cambridege, Email: Marilyn.Nickson@btinternet.com
University of Cambridge, Email: email@example.com
Paper presented at the Annual Conference of the British Educational Research Association, University of Exeter, England, 12-14 September 2002
Many schools already have the facility to use videoconferencing, and as the technology develops this will increase. However the question remains: why should schools want to use videoconferencing? How can it contribute to teaching and learning? The Motivate Project uses videoconferencing to contribute to mathematics enrichment, and to give school students an idea of how practising mathematicians use mathematics in their working lives. It also gives students a real audience to whom their work is presented. The way the Project works is not specific to mathematics however: the methods used could be applied to any curriculum area. This paper also considers the difference such a project can make to the roles and practice of the teachers and students involved.
1. Theories of learning
The Motivate Project was set up with the following objectives:
This epitomises the nature of the Project and what it sets out to do. The aim is to engage young people in mathematics in such a way as to alter not only their perceptions of mathematics as a subject, but to help them to change their perceptions of themselves as individuals doing mathematics.
This approach is supported by the theoretical underpinnings of much of current research in mathematical education. In recent years there has been a shift from an essentially psychologically oriented view to a more socio-psychological interpretation of how learning takes place. This can be seen, for example, as arising from Piaget's concept of a genetic epistemology which von Glasersfeld (1991) suggests is a redefinition of the concept of knowledge. This redefinition has influenced mathematics education in particular, and has directed us toward a more pragmatic view of how knowledge comes into being. Knowledge is seen to be adaptive rather than ontological:
"This means that the results of our cognitive efforts have the purpose of helping us to cope in the world of our experience, rather than the traditional goal of furnishing an 'objective' representation of a world as it might 'exist' apart from us and our experience."
(von Glasersfeld, 1991, p xv)
Learning is not only seen as a purposeful activity, but if we want children to learn in a meaningful way, the purpose must be relevant to their adaptation to the world around them.
The other significant strand contributing to the socio-psychological view is that of Vygotsky. One of Vygotsky's main themes is that higher mental processes in the individual have their origin in social processes. In particular, his main educational tenet was that children educate themselves through interactions with the world around them, and especially with significant adults. Constructivists (such as Confrey, 1990; Richards, 1991; Steedman, 1991) believe that children need to learn from their own activities, but Vygotsky saw their discussions with those around them as primary (Gage, 2002).
"Every function in the child's cultural development appears twice: first, on the social level, and later, on the individual level; first, between people (interpsychological), and then inside the child (intrapsychological). This applies equally to voluntary attention, to logical memory, and to the formation of concepts. All the higher functions originate as actual relations between human individuals."
(Vygotsky, 1978, p57, italics in original)
Other theorists supply further reasons for the adoption of such a social approach in the teaching and learning of mathematics, eg. Skovsmose (1994), with his notion of critical mathematics education and Brousseau's (1988) didactic contract. Critical mathematics education acknowledges "the power that mathematical knowledge brings to the individual in a technological society, and how important it is for all mathematics educators to be aware of this" (Nickson, 2000, p8). The didactic contract looks at the triangular nature of the teaching relationship, which has the student, the teacher and the students' peers at the vertices of the triangle (eg. Nickson, 2000, p150f).
There has been a similar shift in philosophical issues related to mathematics education. This has involved a change in perception of the nature of mathematics from being a 'given' body of knowledge to be received or not, as the case may be, to being seen as social in its origins and its applications (Lerman, 1990; Ernest, 1991; Nickson, 1992). It has become accepted that mathematics, just as any other subject, has its origins in human activity and is a subject that grows and changes like any other as a result of problem solving, trial and error and the interpersonal exchange of ideas. The mathematical body of knowledge is not static and inert but changing and expanding. This has particular relevance for the view we have of the climate in the mathematics classroom, which is also part of the philosophy upon which the Project is founded.
Finally, there has been a dramatic increase in growth in the use of technology in the teaching and learning of mathematics which has been accompanied by an interest in research in this field. Studies of this kind have focused on matters such as the use of computers in modelling situations from which mathematics is to be derived (Yerushalmy, 1997; Nemirovsky et al, 1998), the importance of teacher intervention when using technology in teaching mathematics (Ainley and Pratt, 1995; Jones, 1997), how the technology supports learners in a technological environment (eg. Pratt and Noss, 1998) and the ways in which technology mediates students' learning (eg. Pachler, 2001).
We believe that new technologies have considerable implications for our current notion of knowledge, and the relationships between teachers and learners. We need to consider how the use of a new technology changes the basic pedagogy appropriate (Noss and Pachler, 1999). It is important that the use of videoconferencing is seen to enhance the quality of the learning experience, and to provide something not achievable in conventional teaching. One aspect of the challenge of new technology is that teachers may well no longer be the experts, but find themselves learning alongside their pupils. This change in the role of the teacher has been found to be significant in the Motivate Project. An equally important aspect is the change in the role of the learner which accompanies this: the learner is enabled to take possession of her/his learning and give an account of it to others.
2. Assumptions about the mathematics classroom
We have discussed above some of the major developments in the field of mathematics education: the move from an individual to a social basis for knowledge; the change in the perception of mathematics as given to us to an emphasis on making one's own mathematics; the impact of new technology on pedagogy. These have resulted in a change in research in mathematics education to an emphasis on studies of children's mathematical thinking in classroom or group situations rather than a study of individuals. The process of learning mathematics is seen to be one of discussion, negotiation and shared meanings. There is a concern that our pedagogy is not just effective, but is also aware of the messages it conveys about the nature of mathematics, its relevance to everyday life and its origins in social interaction. Conjecture, hypothesis, testing ideas, trial and error, all become part of the taken-for-granted aspects of the mathematics classroom.
These trends in research also include the role of teachers and the culture of the mathematics classroom that evolves as a result of the interaction between them and their pupils.
"Work with new technologies invariably involves the delegation of responsibility to learners and successful learning outcomes will depend on learners' ability to work independently and autonomously from the teacher and, increasingly, to take control of the learning process themselves."
(Noss and Pachler, 1999)
However it is certainly not true that using technology in the mathematics classroom will decrease the teacher's role. The teacher is very necessary for monitoring students' activity, assisting negotiation in groups, developing mathematical thinking and communication and generally assisting in the learning process.
3. The Motivate Project
Is it possible for videoconferencing to enrich children's learning experience and if so in what ways? This question arose in 1996 because a school had videoconferencing equipment that was not being used, and this led to the research and development initiative which later became known as the Motivate Project. The Motivate Project reflects a view of learning which is psycho-social, a view of maths which is constructivist rather than Platonic, and a view of the position of technology which is about doing new things, rather than doing old things in a new way (Noss and Pachler, 1999).
There are many different models for the use of videoconferencing, but the Motivate Project uses videoconferencing to bring people for whom mathematics is a significant part of their working lives together with school students of all ages. The school students also have the opportunity to give presentations of their work to a real audience. In this way the students' mathematical experience is enriched, they meet potential role models, their horizons are widened and they can develop communication skills needed in their future lives.
The first conference in 1996/7 set the initial pattern for the Motivate experiment. Small groups of year 10 students (aged 14-15) from five schools in London met at a Technology College in N. London which had videoconferencing equipment, and similar groups from five schools in Norfolk met at the Local Education Authority Teacher's Centre for a three-way link-up with Cambridge. This pilot phase was conducted by Toni Beardon together with the then Head of Maths from the Technology College, and two lecturers from the Mathematics Departments at Cambridge.
Since then we have involved over 60 schools from 16 different parts of the UK, from metropolitan areas including London, Birmingham, Glasgow and Newcastle, other towns and cities such as Belfast, Coventry and Fareham, and rural areas such as Somerset and Silverdale (near Carnforth in Lancashire). We try to involve schools where there is some degree of disadvantage, which could be the number of students for whom English is their second language, or some social or educational disadvantage. We have worked with 10 primary schools, including two KS1 classes (aged 6-7), one in Blackburn and, a year later, one in Bedford. During the summer term of 2002, we did a videoconference on Fractals linking primary year 6 classes with their secondary year 7 counterparts in four different areas, and a live videoconferenced Masterclass on Mathemagic at the IMECT3 conference. We have also included schools in the Cape Town area of S. Africa in the Chennai (Madras) area of India. During the forthcoming academic year (2002-03), we plan to work with schools in Singapore, India, the Johannesburg area of S. Africa, and hopefully the USA and Canada.
Our mathematicians, 17 of them so far, have come mainly from universities, particularly Cambridge, Bath, and the Open University. Our two KS1 videoconferences have been led by a Local Authority representative and a Norwich Primary teacher.
It was intended that the technical assistance given to schools, and the experience of communicating via videoconferencing, would enable schools subsequently to work with other schools in maths and in other subjects, and independently of university staff. This has been the outcome for some of the schools. We will be developing this side of our work over the next year, starting with a research project between two schools in Worthing and Fareham during the autumn term.
Although students are led by an expert user of mathematics, they do not merely listen to a lecture. They come to the first videoconference having completed a preliminary task to give them a flavour of what is to come. During the first videoconference, they take part in activities, discuss questions amongst themselves, hypothesise about possible answers, and listen to the ideas of the other schools involved. Between the first and second videoconferences, students work on projects which lead them further into an area of maths which will probably be unfamiliar and for which there may be no definitive right answers. They make hypotheses, try things out, move forwards and backwards and learn to treat wrong answers as a useful step along the way, rather than an undesirable end. Students learn what it is to be fully engaged in mathematical activity, making their own discoveries (sometimes original in the case of older students): they become working mathematicians.
Up to the end of the 2001-02 academic year, this process has generally lasted for about a month with schools using perhaps one or two lessons a week or using maths clubs for the project work. The pressure of the curriculum in most school years is now making this less and less possible for many, particularly older, students and we are looking at other models. These include the Masterclass model, with videoconferences and periods of activity spread over a day. We are also considering periods of 24 hours off timetable to work just on the project work, or a week of intense activity in all maths lessons between two videoconferences.
All of this contributes to the enrichment of the maths lesson and the students' experience. Their horizons are broadened, they become aware of how maths can be used in daily life, and how the skills they have learnt can be used to solve a problem. This can make a difference to a whole school. One school, which took part in a year 8 conference about "Mazes" in the summer of 2002, made a maze in their grounds, and invited the mathematician involved to open it. He commented: "Wow - what a difference the videoconference has made. They have a huge maze and a massive display of all the activities that they were involved with for the conference. Just about the whole school turned up for the grand opening of the maze, and they all walked round it. Lots of photos were taken and a video ... They can't wait to do another videoconf[erence] next year."
This type of project work enables students to work collaboratively, discussing strategies, negotiating what to do, sharing meanings, and being truly one of a team. In this context, mathematical communication has a real purpose, and can therefore be developed in a meaningful way. Having to formulate their own ideas verbally helps students to clarify what it is they think; discussion helps them to refine their arguments. They are talking both for themselves and for others (Pimm, 1987). In so doing they are finding out what it is to communicate mathematically, and what it is to think mathematically.
The Motivate Project runs a bulletin board intended for students to communicate with each other between the videoconferences. However, it is clear that some students do not yet have sufficient access to the internet for there to be real communication between schools between conferences, despite the numbers of computers with internet access now present in schools. There are still problems about booking the computer room or the speed of connection when a whole class is trying to use e-mail at the same time. This prevents relationships between students in different schools forming, so their presentations tend to be addressed to the mathematician, rather than to all the students present at the second videoconference. Some teachers have been disappointed by this lack of real interaction between students. However on other occasions the bulletin board has really taken off, and the students have exchanged messages about their work and about social interests. This is an example of one such message from year 5 London primary students to Belfast students, about paper helicopters, weighted with paperclips, which were used to model real helicopters used to drop relief supplies to refugees:
[They started by telling the Belfast students what they had discovered over the past week, then continued as follows]:
What we think would be another useful investigation is, that you can see how fast the helicopter drops because it might be a very dangorous [sic] place where they need to bring the supplies, so they need to get down very quickly. We would like you to investigate how long it takes the helicopter to reach the floor. Please give us your results as soon as posible [sic].
We hope you are enjoying the investigation and we hope to hear from you soon.
Rashel, Joseph, Amritha, Patrick and Thomas."
Very little of what has been said above is specific to the maths classroom; indeed much could be applied to other subjects. Among our speakers we have had three engineers, two physicists, a cosmologist, a mathematical biologist ... These are all mathematically based, but there is no reason why this approach should not be used throughout the curriculum.
Much of what has been said is also not specific to videoconferencing: a class could be involved in similar activity without any need for a videoconference. The differences a videoconference makes are to allow interaction with people outside one's own classroom and to provide a real audience. During the first videoconference the students interact with the presenter and the students from other schools, talking about their own work, giving answers, listening to others' ideas and answers. During the second videoconference, each school gives a presentation of what they have discovered during the project period. It is rare for school students to present their own work to others, and even rarer for them to have an audience outside their own class, let alone their own school.
One of the problems faced by students making such a presentation is making themselves clear to others who have not been present while the work was on going. Explanations have to be more explicit when "You know what I mean!" will not do. I believe that if students have the opportunity to use videoconferencing between classes over a longer period, with the videoconferences taking part regularly, that this will enable them to develop how they explain themselves, and thus to develop their mathematical communication. We will be testing this next term when two schools work together over a term, with fortnightly videoconferences, to see how the students' powers of explanation and communication develop.
4. Motivate from the teacher's viewpoint
The following analysis of teachers' views on the Motivate Project is based on over 50 evaluation forms returned by secondary and primary teachers at the end of their projects over the last two academic years. It is also based on face-to-face interviews with thirteen teachers completed during this time, and e-mailed comments from other teachers.
On the whole, teachers see involvement in Motivate as a positive experience for their students and for themselves. In particular they pick out the challenge such an experience gives their students both in their mathematical thinking, and in the need to think about communicating their findings to other people. Teachers value the opportunity for students to begin to learn to work independently and collaboratively as they work on problems beyond the normal curriculum. "Within the usual lesson students do not often have the opportunity to discover mathematics, as they should. The teacher delivers the particulars of the topic and the students are expected to work on questions that require and are closely related to the content of the lesson. Teachers could use VC to introduce a task or sets of problems and then allow students to discuss and research to gain an insight or improve their perception of the problem at hand. In this instance, teachers need not be available in the room acting as "learning crutches" but are instead facilitators of learning, merely steering the activity at strategic points. Students will have the opportunity of gaining ownership and taking responsibility for their own learning. " (teacher from London).
They see the opportunity the students have to present their findings to a real audience as a very positive one: "But I think for the kids to be able to get up and make a presentation like that. As I said before, I never had the opportunity to do that, and I wish I had, because I think I would have been a much more confident person if I had had the opportunity..." (a Belfast teacher). They also highlight the motivating effect the students experience in using technology effectively: "Videoconferencing was definitely a positive experience for the children. It (the ICT element) definitely inspired participation in the maths 'side' of the project." (a London teacher).
The majority of teachers find their own involvement with Motivate a positive experience: 26% agreed strongly with this statement, 43% agreed, while 25% were neutral about it, and 5% strongly disagreed. Most would like to be involved again after their first time, and feel that they could make better use of the opportunity a second time. However a lot of teacher input is needed if the students' experience is to be a good one. Some see this as a challenge, some as a bit of a nuisance. Those who view it as a challenge gain personally: "I personally enjoyed the challenge, something new. My colleagues at ... also rose to the challenge ... One of them was last seen walking off into the distance muttering 'big bang or evolution?'" (a Newcastle teacher).
A former London Head of Department (who is now an Assistant Principal) saw this kind of activity as a type of staff development. "I think you need to do something more than teach, mark, prepare ... You need to enrich the pupils' lives and also yourself ... You're giving them [teachers] a chance of excellence themselves ... It's staff development because they're taking on board maths which is not part of their normal run-of-the-mill things."
Another London teacher emphasised that the enthusiasm of the teacher is crucial. We would agree with this. Teachers who are enthusiastic have classes who are enthusiastic about what they are doing, and this can then have a knock-on effect in the school. The same London teacher said that the project had started in her year 8 class, but had spread through the whole of their year 8 in a lunchtime club. Students saw it as a special privilege to be involved in something like this.
It is clear also that teachers value the opportunity to widen their students' appreciation of what constitutes mathematical activity and how techniques learnt in class can be used in problem solving. One year 12 teacher from London commented: "I think some of them were surprised that this was mathematics! Their perception of maths was very number/algebra orientated, and it was a revelation that it could also be so purely geometric. They found this refreshing." 77% of the teachers felt that the experience their students had during the videoconferencing and while working on the projects had made maths more accessible to their students. A teacher from Somerset felt it was a useful mathematical experience for the whole class: "... they were able to use their algebra in a 'real' situation, and were able to manipulate algebraic expressions reasonably confidently ..." (year 9 students).
Teachers also commented on the value of open-ended questions which can be worked on collaboratively. The Newcastle teacher quoted above wrote that "I feel you achieved your aim 'to provide students with the opportunity to do real maths, to be creative, to get away from single right answer problems and to enjoy working together'". A London teacher commented that they had "... seen the value of questioning and of not knowing an answer ..." Another said that the students enjoyed the practical activity and found the group work very motivating, and this was confirmed by one of her students.
There was a general feeling amongst the teachers that "... [m]odern technology [is] there to be used" (Somerset teacher). They saw the value of their students learning to use different types of new technology. It was clear on some occasions that the students' use of technology was ahead of that of their teachers, and this is a factor which may put some teachers off being involved in a project like this. Other teachers used the technology confidently and were able to introduce their students to new uses of eg. spreadsheets, PowerPoint, electronic whiteboards.
5. Motivate from the student's viewpoint
Figures in this section are based on some 250 evaluation questionnaires received during the academic year 2001-02. Generally students indicate that they have enjoyed and appreciated the opportunity: "I like the project because it is fun and I have learnt a lot." (year 5 primary student, London); "I enjoyed researching and presenting my results. Working with a group which included MY BEST FRIEND made it a lot more fun. I would like to participate in a similar event again." (year 8 secondary student, London, original capitals). Some are aware of their attitudes to maths being changed by the experience: "This project was very enjoyable and interesting... I think about maths a bit more differently than usual." (year 7 London secondary student). Others find the discipline necessary while the mathematician or other students are presenting their work difficult: "Doing this conference was good even though it was tiring to sit there for ages (2nd one). 1st was fun. I'd like to do this again." (year 9 Wednesfield secondary student, referring to the second videoconference at which students make their presentations).
Students feel that opportunities such as this boost their confidence in their abilities. One student commented: "I feel that this is a valuable experience and I have improved both my mathematical and presentational skills." (year 12 Newcastle student). Another said: "I really liked communicating with other people on a TV" (year 3 Silverdale student). However a minority, particularly of primary students, expressed reservations, commenting on their shyness in front of other schools. One secondary student commented: "A bit nervous at first but got over it immediately" in answer to a question about how s/he felt about the conference (year 9 London student). However several primary students made comments like: "I did not like it when I had to stand up and speak" (year 3 Silverdale student) in answer to a question about what they had liked least about the conferences.
It is difficult to be sure if the students' self-esteem has been changed as a result of their experiences in the videoconferences. A majority of secondary students (60%) said they felt more confident about their ability to do maths as a result of the Project, however 21% were ambivalent, and 19% said they felt less confident.
60% of secondary students felt that taking part in this Project had encouraged them to think of studying maths at higher education level. One of the aims of the Project is to increase the number of students considering maths at a higher level, so this is a pleasing result. 18% were ambivalent, and 21% disagreed that they would want to study maths further as a result of the Project. This is an indication that giving students experiences of this type does encourage them to want to take maths further. 69% said that the experience had improved their ability to see the relevance of maths to the real world, again supporting the view that projects of this type enable students to see the relevance of studying maths.
Most students felt that being able to discuss problems in maths helps them to understand better (92%), with only 3% disagreeing, and 5% ambivalent. This is the strongest view indicated in the student evaluation questionnaires. Further, 61% agreed that talking about maths problems with classmates is enjoyable, although 30% are ambivalent here, and 9% disagreed. Compared to the usual classroom style of students working individually, group work encourages students to develop mathematical communication and gives them support for their ideas.
6. The future
We feel that we are succeeding in meeting our objectives on the evidence of both teachers and students given in evaluation questionnaires. However there are concerns about the impact a project of this nature has on an individual teacher, and the difficulty of finding time for the project work, now that so many school years have public exams.
If a teacher is working on a project of this nature in isolation, it can result in a lot of extra work, and a feeling of being unsupported in dealing with new ways of working, with new mathematical ideas and with new technology. One teacher commented: "Appreciated technical support. Had a lot of 'flying by the pants' experiences." Although the majority of teachers are positive about the experience, the views of those who were ambivalent, or did not enjoy the experience, are also significant.
Time is becoming a more and more important consideration. A year 12 teacher (London) said: " They were reluctant/unable to commit much time to the project; understandably as they have external exams." To enable post-16 students to take part, we are starting one-day videoconferences this year for this age group, using the model of a Masterclass. These will involve group sessions, where all the students and the mathematician meet via the videoconference, with periods where the students work in their own groups with their own teachers. If this proves successful, we may extend it to other school years. This may also be a way to tackle some of the problems for teachers, as a one-day videoconference, with individual group work between general videoconferenced sessions, could be less demanding in terms of teacher time and input, and mean they feel more supported.
We believe that videoconferencing can give students a unique opportunity to develop their skills of mathematical communication, and are running a research project over the next 6 months to consider this further. Two schools, who were both successfully involved in our projects last term, will choose a year 8 class to work with the other school. The schools will follow a common curriculum for a 10 week period, with videoconferences every 2 weeks. Tasks will be chosen for these which enable the students to work together over the videoconference. Evidence will be gathered to establish if the students' skills at mathematical communication, both written and oral have improved over this period.
We started by asking the question why should schools want to use videoconferencing. The Motivate Project shows that it can be used to great advantage by schools wanting to increase the degree to which their students use ICT, by those wanting to increase the communication skills of their students, and by those wanting to give their students worthwhile opportunities to present their own work to an audience outside their immediate peers. The Project shows how videoconferencing can be used to enrich mathematics lessons, giving students a wider vision of what maths is, and how it is used by practising mathematicians and others.
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