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This article was downloaded by: [Otto-von-Guericke-Universitaet Magdeburg]On: 22 October 2014, At: 04:52Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

International Journal ofMathematical Education in Scienceand TechnologyPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/tmes20

Interactive video for mathematicsteachingDavid Burghes a & Dudley Kennett aa Centre for Innovation in Mathematics Teaching ,University of Exeter , St Luke's, Exeter, EnglandPublished online: 09 Jul 2006.

To cite this article: David Burghes & Dudley Kennett (1988) Interactive video formathematics teaching, International Journal of Mathematical Education in Science andTechnology, 19:5, 705-710, DOI: 10.1080/0020739880190507

To link to this article: http://dx.doi.org/10.1080/0020739880190507

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IN'T. J. MATH. F.DUC. SCI. TRCHNOL., 1988 , VOL. 19, NO. 5, 7 0 5 - 7 1 0

Interactive video for mathematics teaching

by DAVID BURGHES and DUDLEY KENNETT

Centre for Innovation in Mathematics Teaching, University of Exeter,St Luke's, Exeter, England

(Received 20 November 1986)

In this article, we outline the design of an interactive video (IV) disc currentlybeing produced for mathematics teaching. It is centred on the simulation ofrunning a school disco, and involves decision making with economical andfinancial implications. The paper also explores further possible uses for IV inmathematics teaching.

1. Introduction to interactive videoIt is with some trepidation that we put forward another new technology as the

possible solution to many of the problems faced by mathematics teachers and theirpupils today. The history of new technological advances in education is notaltogether a happy one; over the past few decades we have had:

RadioSlidesTeaching MachinesOverhead ProjectorsLanguage LaboratoriesVideoComputer Software.

In a typical maths lesson, how much use is made of these resources? Even computersoftware, of which there is now much available, is not widely used for mathematicsteaching. So it is with some doubts, but with great enthusiasm, that we outline thedevelopment of what we think is the first British interactive video (IV) disc formathematics teaching in schools.

First, let us just indicate the potential of an IV system. Such systems link togethera microcomputer (with a disc operation) with a video disc player, as illustratedbelow.

MicroDisc Drive

Video DiscPlayer

The learning is controlled by computer software, but the advantage of thissystem over conventional computer software is that material on the video disc can beassessed easily. Indeed, video discs (as opposed to conventional videotape players)give precise and rapid access to any frame on the disc, with the added advantage that

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706 D. Burghes and D. Kennett

the still-frame is clear with no interference. The frames can be played at varyingspeeds and, in short, the IV system takes what is best from both computing andvideo, linking them together. Although the material on the video disc cannot bechanged, different computer software can be used to motivate students of varyingability and age. The video also has two sound tracks so that real spoken language canbe used which is at present a distinct disadvantage of computer software.

On the negative side, we have the high cost of producing just one video disc andassociated software (about 100 000), and also the expected cost of an IV system forschools (about 1500). Will schools be able to buy the equipment, and if they do,how many systems will they buy? We suspect that if there is a sufficient number ofhigh-quality educational discs available, that might provide the motivation needed,but the situation is very much that of 'chicken and egg'.

2. Software and videosAs we have mentioned earlier, there is much good software now available for

teaching mathematics (see, for example, Bajpai [1]). So why is it so little used in theclassroom? It has many advantages, for example, instant and individual feedback,infinite patience and perseverance and attractive graphics; but some disadvantages,for example, need for sufficient workstations to be readily available, cost of dedicatedsystem for a maths room, and lack of spoken word.

The early potential that school-based computer power promised has yet to befulfilled. Although, if used effectively by keen teachers, they do provide anotheruseful resource, they have not as yet changed dramatically either the way we teachmathematics, or indeed what we teach in the mathematics curriculum.

The new hand-held graphics display calculators will probably have more effecton what we teach. Unless they are banned from examinations, examiners will not beable to set the traditional curve sketching problems! It should also be noted thathand-held computers which manipulate algebraic expressions, differentiate andintegrate etc., will soon be available. Again these are bound to have some effect ontraditional mathematics curricula.

We have also seen work on providing suitable tape video sequencies for school(see Berry and Huntley [2]). Although this gives a welcome chance to bring the realworld into the mathematics classroom, and it can be interrupted, it is not trulyinteractive in the sense of being able to branch in different directions according tostudents' responses. Indeed, videos alone cannot produce individual feedback ormonitor progress. Their use in school is also hampered, like computer software, bythe difficulties associated with access to the hardware. The school video will need tobe booked in advance, and it will need to be moved (or the class will have to move),and it is these rather mundane problems which are a real damper for using newtechnology in mathematics teaching.

But will IV fair any better? It does have advantages over software and videoindeed, in many ways, it takes what is best from both of these systems, namely,instant feedback, infinite patience, and spoken word, and adds to these the extraqualities, such as, branching in many different directions, clarity of pictures, andspeed of access of material.

There remain, though, two serious problems, namely: (a) the access to thehardwarewill schools even have one IV system (costing about 2000) in thefuture?; and (b) the cost of production of IV discsestimated at about 100 000 for

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Interactive video for mathematics teaching 707

one disc. Although these are severe problems, we contend that they are notinsurmountable. Sponsorship or subsidy of development and production costs couldbe one way of obtaining a high quality of IV mathematics discs, which really couldprovide a new resource for teaching mathematicsand if the discs are really good,we suspect that they will provide the necessary incentive to finding money fordedicated hardware.

3. Mathematics through interactive videoIn the autumn of 1985, we were successful in obtaining a grant from the

Department of Trade and Industry, Industry Education Unit, to produce amathematics IV disc. Our first thoughts were to exploit the potential of the system bybringing the real world into the classroom. We suggested, for example, using BobBeamon's Mexico Olympics World Long Jump record, motorbike stunts by EddieKidd, and the Tacoma Bridge collapse, but all these examples, and other similarones, involve fairly high level mathematics. They all suffer from the defect of being'linear', that is, although they certainly do bring reality into the maths lesson, theyare not suitable vehicles for computer-aided learning which will branch according tostudents' responses and progress through a package.

Our principal aim for the IV maths package was to provide a significant resourcewhich would really help students (ages 14-16) to overcome mathematical difficultiesand blockages which result in lack of progression for many students. For example,such topics as percentages, elementary probability, using letters for numbers, andratio, all give rise to difficulties for many students. To exploit the potential of IV tothe full, we felt that we must provide a resource which helped students with at leastsome of these recurring difficulties.

After much discussion and argument, and with help from Bill Plummer, theoverall director of all the Industry Education Unit IV discsf and the commercialcompany with whom we are working, we eventually chose the idea of running aSCHOOL DISCO as the theme for the disc.

There will be several ways of using the IV discpupils will be able to play thesimulation straight through, making decisions where needed, and eventually eitherlosing or making money. Alternatively, pupils will be able to explore individualdecisions modules in depth, returning some time later to continue the completesimulation.

4. School discoThe aim of our IV disc is to run a school disco, the pupils taking decisions where

necessary, and seeing the outcome of these decisions. They will start with a smallfloat, and will either be aiming to break even, or make a profit, at the end of the event.

The principal decisions (as illustrated in figure 1) to be taken relate to:

(1) Locationwhere should the disco be held?(2) Musicwhat sort of music (live/tapes)?(3) Refreshmentswhat food and drink to buy?(4) Pricehow much should the tickets cost?(5) Publicityhow much should be spent and in what way?

f Eight IV discs in various disciplines are being funded; full details from: NIVC, 24-32Stephenson Way, Euston, London NW1 2HD, U.K.

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DATE

INFORMATION

I Summary[Decision-making

CASH ACCOUNT

SCHEDULE

1 DECISIONS

SUPPORT

CONCLUSION

h

Use arrow keys to change position

Press RETURN to continue

ODO

toS

ia.

SCHOOL DISCO - Ha in map

Figure 1.Dow

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Interactive video for mathematics teaching 709

There are many possibilities for all these decisions, and so you can run the gamemany times without repeating a particular simulation. For example, for the decision'Location' there are three possibilities, namely:

(a) St George's Halllarge, with stage, but expensive;(b) School Halllarge, cheap, but not very attractive;(c) Buddie Lane Hallsmall, but intimate atmosphere.

The IV disc provides three different plans of each location. Having chosen thelocation, and looked at the plans, the maximum number of tickets to be sold must bedecided. As well as consideration of crowding on the dance floor, verbal and writteninformation about fire regulations have to be interpreted.

For students who are not playing the simulation straight through, but lookingmore closely at each decision stage, there will be 'help' material and extensionsthroughout. The 'help' material refers to the mathematical techniques needed, andgives further practice in the basic skills needed; for example, topics such as, personalfinance, VAT, length, area and capacity, scale plans and probability, will all have'help' material available. This material will either be paper-based or computersoftware.

The extension material relates more to the underlying mathematical modelsused. For example, the economic theory behind price and demand is explored insome detail. A typical price/demand curve is shown in figure 2.

Clearly, as the price rises, demand falls, but sales revenue will continue toincrease up to a certain limit. Note, though, that sales revenue is just one part of thefinancial aspect of the scenario. For example, we must also remember that increasednumbers coming to the disco will mean increased food and drink sales, which shouldincrease profits.

Although the problem is a simple one to understand, i.e., how to make a discopay, and although the mathematics used is not complex, the decision making processis highly inter-related, and students will find that they have to pay for their decisions.

It is expected that this disc, along with others financed in a similar way, will betested in schools in 1987, and the discs should be generally available in 1988. Itshould be noted that one of the difficulties in the development of IV packages is thatonce the video disc has been made, it cannot be changed. We can, of course, changethe controlling software, and so the decision for the developers concerning what goes

Price

Figure 2.

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710 Interactive video for mathematics teaching

on the video disc and what is left for the software is difficult. For this first maths disc,we are also hoping to include a number of important footages of tape on the IV discillustrating such events as the Tacoma Bridge collapse, rocket flights, and stunts.Suitable software could be developed for these situations at a later stage.

5. Future discsWe regard the development of this IV mathematics disc very much as a pilot.

Although we have spent much time agonizing over the theme of our disc, we are stillnot convinced that we are exploiting the technology to its fullest extent. Just ascomputer software for mathematics teaching has significantly developed over thepast five years, and today's packages are very sophisticated compared with earliersoftware, we suspect that there will be similar developments in the sophistication ofIV material. We are hopeful, though, that this disc will be of sufficient interest toindicate what can be achieved.

The theme of our disc is essential to the running of a small business, and weexpect the combination of

Business Studies

Mathematics! Information Technology

to provide the scenario for future discs. For example, another disc could concentrateon cash flow and stock control in a small enterprise, bringing out both the importantfacets of small business trading, as well as the basic mathematics required for suchsituations. Another area that is suitable for exploitation is that of travel, and as anexample, an IV disc could be produced in which the student has effectively to run aportion of British Railthe major decisions required relating to the development ofa suitable timetable and deployment of stock and personnel. As with the 'SchoolDisco', students will see the consequences of their decisions as the simulation is run.Yet another area that could be exploited for IV is that of mechanics, and in particularthe use of mathematics in determining optimal decisions, e.g. throwing events, or inexplaining actual events, e.g. Bob Beamon's Mexico City long jump.

We hope that the development of our IV Mathematics Disc will at least providethe stimulation for the development of further discs. Although the needs ofeducation are not the same as those of training, and we must be careful not to becarried away by the hype of the new technology, we are convinced that interactivevideo, if fully exploited, could be a significant factor in helping students to reachtheir mathematical potential.

References[1] BAJPAI, A. C, et al., 1984, Int. J. Math. Educ. Sci. Technol., 15, 781.[2] BERRY, J. S., and HUNTLEY, I., 1986, Int. J. Math. Educ. Sci. Technol., 17, 403.

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