Educational Technology: The Use of Tape / Slide Packs in In-Service TrainingAuthor(s): John ClarkeSource: Mathematics in School, Vol. 2, No. 1 (Jan., 1973), pp. 22-24Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30210921 .

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Educational Technology

The use of tape/slide packs in

in-service training

by John Clarke

The article in Volume 1, Number 4 of Mathematics in School outlined briefly the development of. an approach to the learning of mathematics in the Primary School which, whilst structural in presentation, nevertheless allowed the children wide scope in individual application and interpretation. Such an approach requires of the teachers a good background knowledge of the mathematical content, an awareness of the overall aims of such a course and a level of skill in classroom management which will make the implementation of the scheme effective.

The experiment began in Dundee four years ago and a teacher from each of fourteen schools attended an in-service course for two hours each fortnight to study the approach, to learn as much as possible of the background mathematics, to prepare materials for use by children and to discuss among themselves and with College lecturers the difficulties likely to be encountered in the initiation of the work in the classroom.

During the second and third years of the development the number of schools involved almost trebled and more than one hundred local teachers attended various in-service courses run in school time and in the evenings. As the courses evolved the teachers became much more actively involved in the learning process, the presentation changing from an instructional approach of both mathematical content and method of classroom organisation to a process which simulated that to be experienced by the children. Regular discussion was an essential element of each session to make evident the reason for each activity, its mathematical relevance and its place in the overall scheme (a flow chart of a part of the scheme was reproduced in the issue quoted above).

In October, 1970, an experiment intended to assess the value of the use of concrete materials in the learning of mathematics in the Primary School was initiated in seven Dundee schools. It had the support of the Scottish Education Department and was also devised to assess whether or not such a radical new approach (i.e. new to the schools concerned) to an area within the overall curriculum could be introduced by teachers, inexperienced in subject content and method of imple- mentation, supported only by some form of self-instructional aids. The criteria by which schools chosen to participate in the research were selected were that neither the schools nor the teachers had at any previous period taken part in in-service training relevant to the experimental approach.

The aids for the teachers had clearly defined characteristics. 1. The course content had to be (a) comprehensive in terms of the philosophy behind the new approach, the mathematics to be included in the children's work, the psychological justification for the change, and classroom practice and management. (b) readily assimilated and expressed in language understood by teachers with little if any knowledge of the psychological background to and the content of a modern approach to the learning of mathematics. 22

2. As 2, 3 or 4 teachers were to be involved in each school, it would be advisable for group interaction to be possible in the use of the study packs. 3. Bearing the second consideration (above) in mind, it would also be advantageous if the material could be in a form readily accessible to teachers who rarely, if ever, had "free" periods. 4. Any technical equipment used, particularly if automatic in operation, had to be reliable and easily set up.

These requirements were met as follows: 1. It was decided that the main aids should be in two forms; the first, coloured film, both still and cine, linked to an audio commentary; the second, booklets outlining in sufficient detail the aspects listed in section 1 (a) above. 2. The need for group interaction seemed best to be met by synchronised tape/slide packs which could be viewed in the staffroom whenever time could be made available to the group as a whole. 3. Film strips, containing the same material as the slide packs accompanied by printed commentaries, were prepared so that teachers could take home projectors and study at their leisure. Consolidation was to be assisted by the reading of the booklets alongside the use of the visual material. 4. Kodak Carousel projectors linked to Philips 1011 tape recorders (now replaced by Philips 2209) were used. The synchronising device, both for record and for replay, is built in to these tape recorders and, as they use compact cassettes, no problems arise in the lacing of the tape.

Opinions expressed by the teachers involved in the research programme were generally favourable to the use of the packs. For some they provided a readily digestible course which could be sampled as required. For others, although the diet was agreeable, the substance was rather heavy and had to be consumed slowly in small doses. The nature of the tape/slide packs enabled the teachers speedily to review quite large areas of the curriculum, a process adding much to their confidence in introducing and supervising the children's mathematical work which as stated before was often unfamiliar to them in both content and method.

On the other hand, reports received indicated that the timing of viewing was important. When a need was felt for information contained in a particular pack it was important that that pack was available to be seen at the earliest opportunity. Anticipating this need, the material on the slides was also made available in film strips with commentaries to the schools involved in the earlier reserach, this form of aid having the added virtue that it could very easily be studied at home.

Each booklet, intended to be used together with the tape/slide packs, contains three sections: 1. The main body of the booklet containing the psychological background to and the basic content of the mathematics. 2. A sequential layout of the relevant activities related to the

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stage in the Primary School at which each would be introduced, its aim and the related notation. 3. Appendices: summarising the activities; detailing the aids to be used and their methods of construction; listing the names

and addresses of firms from whom structural aids and materials for their preparation can be obtained; lists of information such as metric measures.

The set of illustrations above shows samples of these aids.

23

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The second set are specimen pages from the publications. The first of these, Figure 3, is taken from a section dealing with the concept of "cardinal number"; the second, Figure 4, from the book which includes suggestions for the use of MAB material; the third, Figure 5, from a section dealing with weight; the fourth, Figure 6, from that section of the book which introduces the ideas of "Relations" and, hence, much notation likely to be unfamiliar to most teachers in the Primary School; th9 fifth, Figure 7, from the summary of activities in the booklet, "Number Base and Place Value".

Production of these aids continues in the belief that many

teachers, trying to come to terms with changing aspects of the curriculum, will find them useful. So far they have fulfilled a clear need. Our aim is to improve their effectiveness and also thereby to develop and exploit such aids for, undoubtedly, they have a great potential in the field of in-service training.

ACKNOWLEDGEMENTS Figures 1 & 2 - taken from tape/slide programmes available from Dundee College of Education.

Figures 3-7 - taken from Mathematics in the Primary School by John Clarke, published by Longman for Dundee College of Education.

Before a child can recognise that the sets have some property in common ('fourness'), he must first become aware that sets can.be compared by attempting to match their members each to each.

No one-to-one correspondence

(i.e. no 'exact match')

One-to-one correspondenc

(i.e. 'exact match')

Once able to establish a one-to-one correspon- dence between two sets (a concept by no means easily grasped by young children), the child will come to recognise that sets can be classi- fied (i.e. sets of sets formed) according to whether or not the member sets are in one-to-one correspondence with each other

0 C a

5.

He is now recognising a common property in these sets. This common property is called the Cardinal Number Property or 'the number of mem- bers in the set'.

Finally, we have to associate a word with the Cardinal Number Property Just as we associate words 'red', 'blue', 'green' with colour propep ties. This is done by matching each member of the chosen set in turn with the words 'one', 'two', 'three', and so on until a one-to-one correspondence has been set up.

one - two

-three - four 17L

Quite simply the last word matched in the set of words is used as the word to describe the Cardinal Property of all the sets which can be matched with the one containing the words 'one' 'two', 'three', 'four'.

This is a concept which is only gained by some children after a lot of practical experience for, to appreciate its real significance, they must ignore all the other properties of the objects within the sets. For instance, many children consider a set of elephants to be much greater in number than a set of the same number of mice. The reason for this is that eTep"nts are much larger than mice and so the

Ordinal Number' - page 13) can be demonstrated by re-combining the two subsets to restore the original set (stage four).

stage one (base 4)

amount to be

part tiosed a13\ ~F12~X Ist subset

stage two

LB B F L U 2nd subset w

Ist subset

a

i

stage three

LB B F LI

subset l \2nd subset (brought down to answer space)

stage four

LB B F L,

U

original amount restored

When the children can manipulate the operation successfully, the amount to be taken away can be composed of more units, longs and flats than the amount from which it is to be taken and the principle of DECOMIPOSITION will then be DIS- COVERED by the children. They should not be told how to remove (possibly) 3 units from 2 units but should, if necessary, be led by ques- tioning to the principle that more units can be obtained by changing a long from the same

elastic

large car

50

60

90

The scale can be calibrated by placing a given number of stan- dard units re- peatedly in the can and markinE the extension on a piece of paper placed on the wall at the back of the can.

--cale (Wooden cubes were used to calibr te this scale)

Records of activities can be similar to those above.

parcel

A B C D

I estimate It weighed

cubes

50

60 20 70

about 38 about 55

about 15

about 60

Or, exercises in comparison could be recorded as follows:

wehs less tpDncubeC

parcel C

weighs about 40 cubes

parcel A

weighs nore than O cubes

parcel D

parcel D

CHAPTER 10 TFI USE OF METRIC UNITS

As already stated, the basic metric unit for weight is the kilogramme which is equivalent to about 24 pounds. Few, if any, single items of

equipment in the average classroom weigh this amount or more and so it would seem that there are four aspects we should consider. First, activities should be devised which will allow comparisons to be made of a variety of articles with a kilogramme weight. Tables can then be made up as shown.

weighs less

than 1 kg book box parcel B

weighs about 1 kg

parcel A (filled with

soil)

weighs more than 1 kg

brickh

parcel C

parcel E (filled with sand, salt,

etc.)

is the ******* of

Tom

Bob Bill James ne

ala Ila Which word is missing? (brother) How many families?

add multiply or ubtrvide

(adivide

( 12 , 3 )

( 12 , 4 )

( 12 , 6 )

- 36

- 48

- 72

12.

This last diagram illustrates a particular type of relation which we call a MAPPING or a FUNCTION. An understanding of this mathe- matical idea is not vital at this stage and reference will be made to it, and further de- tail of relations given, in the booklet en- titled 'Muitiplication and Division'.

CHAPTER 5 NOTATION FOR RELATIONS

Children will regularly meet ideas of ordering and other relationships. Different forms of notation, therefore, are now noted, all of which can be used throughout the later stages of the Primary School. However, for young children it is advisable to use only forms 1 - 3 and, possibly, 4.

Suppose the ages of these children are to be compared:

Tom a ry e Bob

Figure 3 Figure 4

Figure 5 Figure 6

Figure 7

46.

Stage and age group

8.

P3/4 onwards

9.

P /4 onwards

Aim of activity

to give understanding of the extension of the notation to include fractions.

(Compare with 'Relations and Measurement'. - summary of notation: stages 10 and 11)

(see game on page 12)

to develop an ability to extend the manipulation of the number system to include decimal fractions. (Compare with 'Relations and Measurement' - summary of notation: stages 13 and 14)

(for techniques for multipli- cation and division see 'Hulti- plication and Division')

Record

John green blue grey (ones) (quarters) (sixteenths)

1st game 1 3 3 2nd game 1i 2 2

total score 3 2

develop into John

orange squares

1st score 1 3 3 2nd score 1 2 2

total score 3 a 2 1

John's total scorewas w orange squnres.

25"67

+37 54

63.21

37.54

-25 67 11 087

24

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