Strategies for Using One Micro in a Maths ClassroomAuthor(s): Richard EnglishSource: Mathematics in School, Vol. 23, No. 2 (Mar., 1994), pp. 42-43Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30215100 .

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Strategies for using one micro in a

maths classroom

by Richard English, School of Education, University of Hull

"The increasing availability of microcomputers in schools offers considerable opportunity to teachers of mathematics both to enhance their existing practice and also to work in ways which have not hitherto been possible ... Nevertheless ... these possibilities ... are at the present time being exploited by a very small number of teachers."

You could be forgiven for thinking that this is a fairly recent comment on the use of microcomputers in math- ematics but it is in fact a quote from the Cockcroft Report (HMSO, 1982) which has already celebrated its eleventh birthday. During these eleven years there has been a massive increase in the number of microcomputers in schools but it would seem that this growth has not been matched by an increase in pupil accessibility to microcom- puters in mathematics. One source (The Mathematical Association, 1987) refers to a survey suggesting that nearly three-quarters of secondary mathematics teachers use computers in their classrooms either very rarely or never. There are many possible reasons for this but I will mention just two. Firstly, many staff are not sufficiently aware of how a microcomputer can be used effectively in mathemat- ics. Much time and money needs to be spent raising levels of awareness, confidence and competence amongst teachers. Secondly, in many secondary schools all of the microcom- puters are gathered in one room and so access is often a problem. All curriculum areas have legitimate claims on these facilities, although some tend to be more demanding than others, notably computer studies, and so use by mathematics classes is usually restricted to one or two sessions each week. This is a long way from the ideal situation of having at least one microcomputer in every maths classroom so that it is a resource that is available at all times to be used as and when necessary, rather than being a novelty item that is only used very occasionally for "special" work. A recent report by Her Majesty's Inspectorate (HMSO, 1991) says, referring to secondary schools,

"In many mathematics departments pupils did not have sufficient access to microcomputers. Schools need to review the overall number of microcomputers and their distribution in departments and central areas to ensure that they meet the requirements of the National Curriculum."

My own experiences in secondary schools are not dissimilar to those of the HMI. Very few maths classrooms that I have visited are equipped with a microcomputer or have easy access to one, but I have detected a change over the last twelve months or so. An increasing number of mathematics departments are trying to equip their class- rooms with a microcomputer or are providing a few shared, mobile machines that can be wheeled quite easily from one classroom to another. This change has come about partly because the BBC microcomputers in the computer rooms are being replaced by, for example, RM Nimbus machines, thus freeing the former for departmental use, and partly because heads of department can now put forward a much stronger case to senior management for having microcom- puters in their mathematics classrooms due to the specific references to information technology in the Mathematics National Curriculum.

So I have detected a slight improvement in the accessibility problem but what about the raising of teacher awareness, confidence and competence? I have been trying to address this during the last two years by way of inservice training for teachers and I would like to share with you some of the ideas that I have used on such occasions. For convenience I have divided the possible situations in which you might want to make use of the microcomputer into two categories.

1. A pupil or small groups of pupils at the keyboard This, by the very nature of the situation, implies that those pupils not using the microcomputer (i.e. the vast majority) need to be engaged in some other activity. I have seen this strategy widely used in primary classrooms where a flexible approach allows pupils to be enjoying a wide variety of activities often from a range of curriculum areas. While the rest of the class are busy doing art, science, geography, reading and so on, two or three pupils can be using the microcomputer for mathematics. The primary classroom lends itself to this sort of approach but there is no reason why it cannot also be used in the secondary mathematics classroom. Many mathematics departments use an "individualised" scheme of work, for example the SMP 11-16 booklets, whereby pupils progress along their own unique pathway through mathematics. In such a situation there is a wide variety of mathematical activities going on at any one time and the microcomputer can be looked upon as a resource in the same way as the fraction strips, multilink cubes, angle measurers, polydron etc., that is, it is used as and when appropriate. Particular pieces of software could be used to reinforce, consolidate and in some cases even replace the materials in such published schemes. For example the program ANGLE90 (ILECC, 1984) could be used by pupils working on the SMP 11-16 booklets "Angle 1" and "Angle 2". Some schools that I have visited have created their own booklets to add to the SMP 11-16 series. These booklets are designed specifically to make use of the microcomputer in the classroom and provide pupils with an introduction to topics such as LOGO.

Another strategy is to allow pupils to use the microcom- puter on a rota basis. For example, when doing work on data handling, I allow each pupil to enter his or her own information onto the database in turn while the rest of the

Mathematics in School, March 1994 42

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A graph-plotting package provides an effective way of demonstrating transformation geometry.

class is engaged in another activity. The usual data to use in such situations is personal data (heights, weights, armspans etc.) but a useful alternative is to use data generated by an estimating activity. I usually provide the class with several measures for which they have to make estimates. For example, I will draw an angle on the blackboard, pass an unknown weight around the classroom, hold up a bag containing multilink cubes, ask for an estimate of the distance diagonally across the room, and so on. The pupils make a note of their estimates and then in turn enter them onto the computer. When this is done I gather the whole class around and use the data as the basis of a valuable discussion, often initiated with a question such as "How can we use this information to get an overall class estimate for each measure?" This starting point leads on to important aspects of data handling such as graphs, averages, ranges, quartiles, measures of variation, and so on. If the activity is repeated with the same pupils at a later date it is useful to look at ways of comparing the two sets of results and ask questions such as "Have we got any better at estimating angles, weights, etc?".

2. The teacher at the keyboard These situations will usually involve the teacher working in front of the whole class, although it is possible that he or she may work with a smaller group of pupils. I have identified three situations in this second category.

(a) The microcomputer being used as an electronic blackboard to provide a more effective way of giving demonstrations, examples and solutions. For speed, accu- racy, colour and for the fact that it is dynamic, the microcomputer beats the blackboard (or whiteboard) hands down but there is of course the problem of the relatively small display provided by a standard monitor. It is not impossible for thirty pupils to get a satisfactory view of the screen all at the same time (I have done this on many occasions) but this does require very careful classroom management and some movement of desks and chairs. Alternatively a larger monitor could be used but cost is a prohibiting factor here, especially if we want all classrooms to be equipped in this way.

(b) The microcomputer being used to promote class discussion. This plays a vital role in the learning of mathematics and so a whole lesson sat around a computer discussing, questioning and answering is not a wasted one. Some teachers still need to move away from the notion that work is being done and learning is taking place only when pupils are producing something on paper. Discussion also provides a valuable means of assessing pupil progress.

One excellent example of software that can be used in

this sort of situation is COUNTER which appears in the package "Some More Lessons in Mathematics with a Micro" (ATM 1985). I have used this program with whole classes of pupils in Infant, Junior and Secondary schools and so it is a very versatile program in terms of age suitability and also in terms of the mathematics that can be done with it. The book that accompanies the package contains many ideas that have been used successfully in the classroom and you can also find suggestions for activities in other published articles (English, 1992a).

(c) The computer being used to provide a starting point for a wide range of practical, investigative and open-ended activities away from the microcomputer. One of my favourite pieces of software that can be used in this way is MONTY which is part of the same package as COUNTER mentioned above. I usually use MONTY with the whole class gathered around the computer for about the first fifteen minutes of a session. This initial use of the microcomputer captures the interest and imagination of the pupils and provides a suitable introduction for the series of activities that follow. A more detailed description of MONTY and suggested follow-up activities can be found in other published articles (English, 1992b).

Monty Screendump. Monty provides an interesting starting point for open-ended activities

away from the computer.

Summary The effective use of information technology lies at the heart of the education of pupils today. Teachers can no longer ignore the vast potential that the microcomputer offers in the teaching and learning of mathematics but if this potential it to be realised then it is vital that the problems of access and teacher confidence are addressed. In those schools where progress has been made to overcome such problems and where the microcomputer is used effectively in a wide variety of ways, the benefit to the pupils has been immense. F-

Notes and References English, R. (1992a) Using Counter in the Classroom, Micromath, Spring. English, R. (1992b) Working Around Monty, Micromath, Autumn. HMSO (1982) Mathematics Counts. HMSO (1991) Mathematics, Key Stages 1 and 3. ILECC (1984) Microsmile - the first 30 programs. ATM (1985) Slimwam 2. The Mathematical Association (1987) Will Mathematics Count?

Computers in Mathematical Education.

Mathematics in School, March 1994 43

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