Computer Page: Microprocessors, What Shall We Do with Them?Author(s): Maurice HartSource: Mathematics in School, Vol. 8, No. 2 (Mar., 1979), pp. 10-11Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30213440 .

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The article and letters on microcomputers in the September

1978 issue of Mathematics in School provoked a good deal of interest from

our readers. The following two articles were written for publication in MUSE letter (the

newsletter of Minicomputer Users in Secondary Education). They look at work done in the

classroom using programming as an aid to help pupils understand mathematical concepts and as a

CSE topic.

Microprocessors What shall we do with them?

by Maurice Hart, Trent Polytechnic

The aim of this article is to discuss some aspects of what to do with micros in schools. One doesn't need a 1 28K crystal ball in order to be able to foretell that in a few years' time every school could have several micros connected to cassettes and TVs with at least one equipped with a disc and printer. In contrast, at the moment it is likely that microprocessors are available to only a small fraction of 1 per cent of the secondary school population. If the use of calculators gives us any guide, then the signs are poor as they are still banned in many maths classrooms. Will the same happen to micros?

What surely needs to be done is to try methods in which micros can be used to enhance teaching in ways that are evident and which will motivate teachers to make the effort to cope with the hardware. Two overall points emerge as being necessary to make this happen.

(i) the use of the computer will have to enable pupils to understand more easily material which is in syllabuses already, with hopefully the additional bonus of giving a motivating factor

(ii) computer use should make life easier for the teacher.

For the first, the children, besides seeing demonstrations, should use the computer themselves so the questions are how and in what context, and the second seems almost impossible because at the moment involvement means a lot more work for the teacher not less! Perhaps one answer to the second may lie in the use of text editors. Many schools are turning to workcard systems and are experiencing the difficulties in upkeep, including expense, that they can cause. If, however, the complete set of "cards" was stored on disc or cassette, then copies could be run off as needed and the editor could be used to modify or adapt individual cards for particular purposes. It is also not beyond the bounds of possibility to put some of the material in programmed learning form, perhaps using graphics.

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Thinking of really useful ways in which pupils could use computers during lessons in geography, science, maths, etc, is even more difficult. So far computer use in these subjects has been at best peripheral instead of being seen really to help with fundamentals. Of course such use in general does have to be in the form of pupils using packages but how about programming because that is, and will be, easily available. The only subject that programming could possibly enhance is mathematics and the questions are in what ways and how much. Would it be worthwhile every secondary school pupil in the country learning how to program during maths lessons with all the teacher education that would involve? Does using the computer through programming help pupils understand any fundamental mathematical concepts better than they would have done without such use? This particular idea has been concerning several people inspired largely by David Johnson of the University of Minnesota who was co- author of the CAMP series.1 Last year I wrote an article in Mathematics Teaching2 and since then a group of teachers in the Nottingham area have done further work with children. The main target group for the work has been mixed ability first year maths classes and the fundamental concept that we hoped that programming would reinforce was that of a variable, perhaps one of the poorest understood of any at secondary level. In fact the evidence was that programming did help, indeed it was rather comic that the pupils couldn't see any difficulty at all. As a result of this work it is certainly my belief that all pupils should learn how to program in secondary maths classes, especially as there are all sorts of other spin-offs including learning something of what computer usage is all about.

How does programming help and how can it be approached so that virtually the whole range of ability can cope? I suppose the main answer to the second question is "very carefully". In fact the work was based on class teaching but two very important

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principles were incorporated: firstly the children had relevant and fairly easy tasks to carry out every 10 minutes or so during the lesson, second the programs they ran on the computer were different from everybody elses as far as possible. The totality of the work is described in a 25 page booklet together with examples of children's work.3 However, in order to make the point about variables I will describe the way the use of them within programming was approached. On a worksheet the children were asked to enter their day and month of birth in boxes as shown.

Birth Day Month

8 3

With the use of a wooden "pigeon-hole" model the way that

10 LET X=8

labelled and filled a store was demonstrated. They had already seen a piece of "old-fashioned" core store. Allied with this the pupils themselves entered these details on "stores paper" which looks like this:

Store label X

Contents 8

Subsequently they entered the results of

20 LET Y=3 and 30 LET Z =X+Y etc.

equally easily on to stores paper. None of this is original but I think one shouldn't underestimate what a breakthrough it could be in terms of understanding. The children gain a concrete image of X as a label of a store whose contents can change and they go on to use this principle in programming, so reinforcing it. The difference that a concrete realisation could make to a child at this stage must be considerable and there is no other easily accessible way of making this particular concept concrete. Other spin-offs that occur are real use of flow diagrams, use of notation (it is arguable that 2 * X is better than 2X for first years!), ideas about conditional looping and in our case, as we used marked cards, ideas about coding. Further major developments would be in the concepts of equations in algebra and programming of algorithms. The other slightly surprising aspect was the children's attitude. They were not at all frightened about using a computer, indeed they seemed to think it entirely natural and proper for their generation and surely they are right?

References

1. L. Hatfield and D. Johnson Computer Assisted Mathematics Program. Scott, Foresman and Co.

2. Maurice Hart "Using Computers to Understand Mathematics" Mathematics Teaching No. 80.

3. Booklet available from M. L. Hart, Trent Polytechnic, Clifton (send A4 sae).

Programming in the classroom by Bob Elliott, Toothill Comprehensive School, Bingham

We went "mixed ability" at this school about four years ago. Like many others in the same situation we decided that we would write our own material. After reaching the third year and coping with many problems we decided to embark upon a CSE syllabus which involved coursework. One of the topics now covered is programming.

The material used is based on work done with a first year group and was developed with Maurice Hart of Trent Polytechnic. A slightly different approach is taken because (a) it is going to be used with fourth years instead of firsts and (b) it will be a continuous piece of work rather than a "one off" per week. In all the units, which is what we call the topics of work, we aim to ring the changes in teaching techniques, i.e. some class teaching, individual work, group work and investigations. We are relying heavily upon a speedy turn round time, about 24 hours, for our success with this venture because rapid feedback is even more important at this level than at higher levels. A micro in the classroom would, of course, greatly enhance the unit and provide immediate feedback.

The limitations at the moment are hard copy and only one pupil being hands on. There are, I know, moves afoot to remedy these limitations and once they have been remedied the sky is the limit. Imagine being able to demonstrate "on line" in the classroom and being able to edit with the child as she or he punches in the program. Calculators are used in the classroom when laborious or monotonous calculations are to be carried out, e.g. means from grouped frequency tables, and the children never seem to tire of their use. What would a micro do in terms of enrichment and motivation in other topics?

For those who would feel apprehension at programming at this level, I can offer encouragement. The approach taken in the unit has worked well with first years in a mixed ability situation. Even with some ESN children in the group all but one managed the mark sense cards and the one who could not manage had trouble remembering his date and month of birth. I feel confident that the fourth years will all produce programmes of some sort. Some will be copied from the sheets but others will be original. Some won't finish the unit but others will go beyond it. I am also confident that they will "appreciate" the computer if the reactions of the first years are anything to go by. There was no awe nor a "big brother" concept formed and there was a real awareness of the limitations of the computer when it came to reading error messages.

There is a lot of effort required in setting up a unit like this but after the initial effort it is very much reduced. The effort is worthwhile though in terms of a very real return in interest, effort and awareness on the part of the children. With a micro in the classroom the efforts would be less on the teachers part and the rewards for both pupil and teacher a lot higher.

We are, as you will have gathered, without a micro and as a consequence have tried to reinforce the idea of how a computer works by using three complementary techniques. These are the flow diagram, the programme, and paper stores. It is hoped that by doing this the computer is seen for what it is; a logical, accurate and speedy device which needs to be told, with precision, what to do.

I look forward to using the unit and feel confident about it, but I am not unaware of the unexpected events that can, and do, turn up in the classroom.

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