VSO Course for Trained Maths &Science TeachersAuthor(s): Mary CraneSource: Mathematics in School, Vol. 14, No. 3 (May, 1985), pp. 30-31Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30214004 .

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VSO

VSO Course for Trained Maths & Science Teachers by Mary Crane, VSO Education Desk

The aim of the course is to introduce trained teachers to some of the differences and difficulties they may encounter when teaching in a secondary school in a developing country as opposed to teaching in a British school, parti- cularly in the fields of Maths, and Science teaching.

We concentrate mainly on three areas - language, lack of equipment and cultural context.

Language Mathematics is supposedly an international language in itself. If travelling abroad, you would expect to understand the mathematics if nothing else. However, most volunteers find that this is not quite the case.

The majority of volunteers will be teaching pupils whose second or even third language is English, although English will be the medium of instruction in the school. In an attempt to put the volunteers in their pupils' place, volun- teers are given a lesson completely in French and asked to analyse their own thoughts and feelings.

This is followed up by looking at examples of pupils' work from various countries, not only from a second language learner's point of view but also looking for possi- ble cultural differences. In many countries in which volun- teers are working, the way of expressing a mathematical concept in a pupils' mother tongue may be quite different to the way it is expressed in English, often causing confusion with vocabulary and terminology. In some cases the con- cept may be entirely foreign to the child's culture and there is no concise way of explaining in the child's own language. For example, in the Baruya language of Papua New Guinea, there is no standard unit of measurement, other than, for distance, "a day's walk", or, for time, "the day". The child is therefore learning a new concept and new vocabulary at the same time.

Sessions are held to make the volunteers aware of the complexity of their own language and that found in many texts developed particularly for use in the Third-World. Practice is given in simplifying both spoken and written language, partly through peer group teaching, and in making certain mathematical topics as practical and visual as possible.

Many maths teachers will be aware of a pictorial way of explaining "taking x from both sides". e.g. How much does the hedgehog weigh?

Balance

And taking this a stage further, how much does one cat weigh? (Assuming, of course, that the cats are all identical weights).

Balance

Surprisingly, a lot of newly-trained maths teachers and physics teachers who also teach maths have never seen the above before.

Picture algebra is a useful tactic most volunteers find themselves adopting in an attempt to overcome the lan- guage barrier.

Lack of Equipment Relates more to science teachers than mathematicians, therefore possibly not relevant. We have sessions on impro- vising apparatus.

Cultural Context Mainly through discussion papers, talking to ex-volunteers, etc. Concepts presented in science lessons in particular may be foreign and in conflict with the child's traditional world view. Many concepts and vocabularly introduced in school will not be used outside school - parents are unable to help the child and there is often little or no reinforcement at home. Some concepts presented by the teacher assume prior knowledge and experiences that a child does not have while ignoring the different set of knowledge and ex- periences the child does have. Volunteers are encouraged to look at the syllabus they will be asked to teach (often based on traditional British 'O' and 'A' levels) in the light of the above. In this way it is hoped the volunteer will become aware of some of the problems and may be able to make adaptations where possible.

An interesting example of one common problem has been given by Professor N. O. Anim, former Director-General of the Ghana Education Service in his paper "Language and Maths in Ghana":

"In the last days of the pound weight as a weighing unit in Ghana I was personally growing very worried. It used to be that the market woman from whom we bought our rice conceived the pound as a calabashful* of rice (*a dried gourd). Then, for utilitarian reasons, this calabash became a quaker oat-tinful of rice, with obvious implica- tions to my pocket. The woman refused to believe that the Calabash could scoop more rice than the tin. Then, due to import restrictions, this tin was changed to two cigarette tinfuls of rice, again with an obvious reduction in rice. Continued pressures on the economy quickly removed the cigarette tin till we were left with 21 milk tinfuls to represent 1 lb. Our adamant seller continued to believe that one pound weight was what she was giving us. A child brought up by this market woman must obviously be living in two different "pound weight worlds", the "School pound weight", and the "practical operational market woman's pound weight." An attempt to "bring in" the local environment to maths

teaching has been made in various ways. Here are two examples presented to volunteers, who are left to form their own opinions.

30 Mathematics in School, May 1985

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From Zimbabwe comes this example, printed in Teachers' Forum (Zimbabwe) April 1984: "The Mathema- tics in Traditional Buildings" by Jesta Fungisai.

Construction of a roof Builders inserted a straight long pole at the centre of the building, which acted as a common centre. At the top end were tied nhungo using string from tree fibre. Two beams were placed across the top of the wall in such a way that they crossed each other at the centre. The nhungo were left overlapping the top of the wall to form a verandah.

Thatching grass is then applied on top to prevent rain from soaking into the building.

The mathematics in the roof The roof of a hut forms a right circular cone of the same radius R as the outer wall of the hut, and of height H. The area of the curve surface is given by nRRI where / is the slanting height (nhungo). From Pythagoras' theorem, we get /2 = H2 + R2

/= JH-R2 The total surface area of the whole building would

be the sum of the wall area and that of the roof i.e. 2RH+ nRI

The other example comes from a form 4 mathematics examination set by the National Examinations Council of Tanzania some years ago.

Another problem maths teachers in particular may find is that pupils have difficulty with understanding depth per- ception in diagrams and drawings. Conventions associated with the representation of three dimensional objects such as

drawings on a two dimensional page are rarely known before a child reaches school age, books and pictures being in short supply. A child in such a position may acquire mathematical concepts two or three years later than his counterpart brought up in a more mathematically orientated society.

A freedom fighter fires a bullet at an enemy group consisting of 12 soldiers and 3 civilians all equally exposed to the bullet. Assume one person is hit by a bullet, find the probability that the person hit is (a) a soldier (b) a civilian.

Another aspect of the course is that of "Maths Clubs" and games. Many volunteers wil find themselves teaching in boarding schools and running a Club is definitely expected. At least one session is devoted to the playing of maths games and discussing their relevance to maths teaching. People Games, such as those used on the ATM children's work- shop weekends always prove popular, as do those from Gardner's Mathematical Puzzles and Diversions. Volunteers are encouraged to find out about local games. Most are intrigued with the "African Network Patterns" from Zaslavsky's Africa Counts, (Lawrence Hill & Co, Westport 1973). For those unfamiliar with these patterns, some are reproduced below. Shongo children of the Congo area draw these patterns in a continuous line without lifting the finger. (It is easier if you use "spotty" paper!)

The course last year ended with a session on standard "Teaching English as a Second Language" techniques. The maths teaching volunteers generally find they have to be almost as much of an English teacher as a maths teacher, and all this in an unfamiliar cultural context. The course lasted for only four days!

Draw some bigger ones. What is the next size? Look at numbers and arrangement of squares and finishing points.

Preparing to teach Mathematics with VSO

by Graeme Keslake,

Voluntary Service Overseas (VSO) was an organisation I had first encountered on the completion of my Econometrics degree at Manchester University, through a friend who turned out to be a returned volunteer. From then the idea of working overseas in a professional capacity which might assist in the development of a Third-World country seemed attractive to me. Initial contacts, at that time, with VSO made me realise that my contribution to any developing country would only be of real value if I had some specific skill to offer. Three years later, after comple- ting a PGCE course in Mathematics at the University of London Institute of Education, and having taught maths for a year at a middle-school comprehensive in Richmond, I felt ready to make a serious application to VSO. The response from the Education office of VSO was both friendly and informative. VSO usually receives a large number of requests for teachers from many countries, so I was told that there would be a good chance of finding me a suitable post as a mathematics teacher, subject to interview, etc.

A month later I was interviewed by a VSO selection board. The interview was both a professional and a personal one designed to test my suitability for life as a volunteer overseas and as such was fair, but gruelling. Subsequently I

Mathematics in School, May 1985 31

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