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SHORT COMMUNICATION
G L O B A L P E R S P E C T I V E S IN T H E M A T H E M A T I C S
C L A S S R O O M
BRIAN HUDSON
This article is partially the result of responses to a number of national and international reports and initiatives. Central amongst these is the Recom- mendation Concerning Education for International Understanding, Co- operation and Peace issued by UNESCO at its General Conference in Paris in 1976. This listed the "major problems of mankind" that all students should study as:
�9 equality of fights of people; �9 maintenance of peace; types of war; disarmament; �9 action to ensure the observance of human rights; �9 economic growth and social development; �9 conservation of natural resources; �9 preservation of the cultural heritage of mankind; �9 the role of the UN in solving such problems
I would argue that as a teacher of mathematics it is possible to meet the twin aims of developing mathematical skills, processes and understanding whilst at the same time developing an awareness of key global issues. Indeed in order to understand the complexity and interdependence of the world in the late twentieth century it is necessary to apply a great deal of mathematical skill and understanding.
During 1984/1985 I had the opportunity to work on a project with the aim of developing the curriculum in response to such issues. As a part of this it was intended to develop materials and approaches for the mathemat- ics classroom from a global perspective. Hence issues related to world development, military technology/the arms race and human fights amongst others were considered. A computer data base was developed containing data on 127 countries including life-expectancy, infant mortality rates, levels of military expenditure etc. (20 items of data on each country). An accompanying series of problems was developed for students to work on alongside the data base focusing upon particular issues such as energy, population growth, the arms trade and others. The major statistical sources for the data are listed at the end of this article.
Educational Studies in Mathematics 21: 129-136, 1990. ~) 1990 Kluwer Academic Publishers. Printed in the Netherlands.
130 B R I A N H U D S O N
The materials were developed and trialled in five schools in the UK which included a multi-ethnic inner city comprehensive school. The process of refinement has become an ongoing one in an attempt to update the statistics contained on the data base in particular.
These issues are primarily global in nature but are also very much a part of the society of the UK in which our young people are growing up. The advances in technology and in telecommunications in particular have brought the concept of the " global village" to reality and directly into the living rooms of the citizens of the UK. Hence horrifying images of war, famine and disasters are a part of the experience of most young people on a tragically frequent basis. The work of the relief agencies and other pressure groups has added to the awareness of many young people and this is reflected in the concerns that many of them have about the threat of nuclear war and for the victims of war, famine and the abuse of human rights in particular. These concerns have manifested themselves in a popular way through the groundswell of support following the "Live Aid" concert and the more recent concert organised to commemorate the birthday of Nelson Mandela and to call for his release which was organised by the Anti-Apartheid movement.
The classroom examples which follow are drawn from the package of materials which were first developed in 1984/85. The responses from teachers and pupils are drawn from the classroom trials which were carried out at that time.
It is possible to select any number of fields to be printed out from the data base and also to search through the data with parameters set on one or more particular fields. For example the tables which follow provide information on the life expectancy (LIFEXPEC) and the percentage of the population with reasonable access to safe drinking water (WATER). Figure 1 provides this information on countries with life expectancy rates of less than 50 and Figure 2 refers to those with life expectancy rates greater than 70.
The issues raised merely by the presentation of the data in this form are very far reaching and the scope for discussion of these issues wide ranging. It is not that any particular answers are suggested but that an awareness of the scale of the inequality is appreciated and that important questions are raised by young people who are the future citizens and voters in our democratic society. However it is possible to analyse these figures more systematically and to seek out possible correlations. Therefore one develop- ment in this analysis might be to plot a scatter graph of these figures and also to interrogate the data base for further information. Hence the
SHORT COMMUNICATION 131
LIFEXPEC less than 50
Country LIFEXPEC Water %
Oman 49 52 Yemen, Arab Republic 43 4 Yemen, Peoples Dem. Rep. 46 37 Afghanistan 37 10 Bangladesh 48 68 Nepal 45 11 Laos 43 48 Angola 42 17 Burundi 45 - Central African Rep. 43 18 Chad 43 26 Congo 43 26 Ethiopia 46 13 Guinea 43 10 Ivory Coast 47 14 Madagascar 48 26 Malawi 44 44 Mali 45 23 Mauritania 44 17 Mozambique 49 7 Niger 45 49 Nigeria 49 28 Rwanda 46 38 Senegal 44 35 Sierra Leone 47 9 Somalia 39 38 Sudan 47 46 Togo 48 11 Uganda 48 16 Upper Volta 44 14 Kampuchea 39 45
Matched 31 of 127
Fig. 1.
m a t h e m a t i c a l unde r s t and ing can be deve loped and con t r ibu te to the devel-
o p m e n t o f a grea ter unde r s t and ing o f some o f these issues.
The d e v e l o p m e n t o f p r o g r a m s which can p rov ide screen d i sp lays and
p r in t -ou t o f d a t a in g raph ica l fo rm a l low far m o r e o p p o r t u n i t y for the
analysis and in t e rp re t a t i on o f this da ta . F o r example F igure 3 is a scat ter
g raph o f the d a t a on Life Expec tancy versus the ( % ) R a t e s o f Access to
Safe D r i n k i n g Wate r . S tudents migh t be encouraged to invest igate the d a t a
base in this way, to fo rmula t e hypo theses and to test t hem out.
A n assoc ia ted issue a n d also an i l lus t ra t ion o f how such g loba l issues
are reflected wi th in the U K is tha t o f "Overseas A i d " by the Bri t ish
132 B R I A N H U D S O N
LIFEXPEC greater than 70
Country
United States Canada Argentina Cuba Jamica Panama Trinidad & Tobage Uruguay Belgium Denmark France West Germany Greece Italy Netherlands Norway Portugal United Kingdom Bulgaria Czechoslovakia East Germany Hungary Poland Romania USSR Austria Finland Spain Ireland Sweden Switzerland Yugoslavia Israel Japan Singapore Australia New Zealand Costa Rica
Matched 38 of 127
LIFEXPEC
75 75 71 73 71 71 72 71 73 75 76 73 74 74 76 76 72 74 73 72 73 71 73 71 72 73 75 74 73 77 76 71 73 77 72 74 74 73
Fig. 2.
Water
%
99 99 60 62 82 83 89 78 89 99 97 99 97 86 97 98 92 99
78 82 44 55
88 84 78 73 99 96 58 99 98
100 97 93 81
SHORT COMMUNICATION 133
1 8 8
14 Fi T E R
0
i::i::i iiil ::i :.::i :.!ii: ~i :i. iiii ~:: !il iiiil ::'/~:: ii ~:~, i~:il ? ' ::i !,il C ~' * * g * t *
* . t * *
t .
* * ***
~ k - , , , l i b
3 7 7 7 LTFEXPEC
Fig. 3.
Government. For example Figure 4 gives the contributions by the British Government to the United Nations Development Programme which exists to promote technical cooperation in developing countries.
This information could be represented in a variety of graphical forms by the students and associated calculations carried out. For instance given that inflation averaged 12% in the UK during this period the corresponding figures could be calculated in order that the amount remained the same in
YEAR AMOUNT ( s millions)
1978 25.0
1979 28.5
1980 15.0 , , . . . . . . . , , ,
1981
1982
17.5
18.5
Fig. 4.
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Lr weapons ileof 1983 red with litions used Id War II
Fig. 5.
SHORT COMMUNICATION 135
real terms as the 1978 figure. The shortfall in these figures could be calculated in percentage terms and the possible reasons for the reduction and also the probable consequences could be discussed.
The issue of the global arms race is one which has dominated the world stage. The data base provides a great deal of relevant data for further analysis and investigation. The activity outlined in Figure 5 uses data on growth of the stockpile of nuclear weapons and presents it in a form that communicates the scale of the change which has taken place since 1945 (to 1983) in a most effective way.
There will undoubtedly be resistance on the part of many mathematics teachers to the handling of controversial issues of such a wide-ranging nature. However my own experience of such an approach during classroom trials has been of very positive responses f rom both teachers and students. The following comment is f rom a teacher in an inner city multi-racial comprehensive school:
It offered an original and interesting approach to statistics and aided the pupils' personal development in their awareness of world problems. I received many comments from them regarding their astonishment at the differences between rich and poor.
Robert , a member of the class, made a comment which reflected as much on his own previous educational experiences as it did upon his response to this work:
I found the disc easy to work with, enjoyable and interesting. It tells you things you thought you would never know.
Many questions are raised in seeking to use society as a source of real problems and issues that are worth addressing. Not least amongst these is the question of how to make such an approach generally more acceptable. My own view is that there is a need for resources, courses and also for associated modes of assessment to be developed in order to encourage such an approach. There are encouraging signs that publishers in the U K are responding as evidenced by a number of projects, still at an early stage, with the aim of developing materials for the mathematics classroom based upon real contexts and real problems. The development of GCSE (General Certificate of Secondary Education) coursework is a further relevant inno- vation offering further opportunities for such an approach to be developed. In general I would hope to see the development of a view of mathematics as being to do with the "real world" and human affairs as opposed to the traditional view of the subject as being abstract and having little relation to everyday reality.
136 BRIAN H U D S O N
REFERENCES
Sivard, R. L.: 1986, World Military and Social Expenditures, World Priorities, USA. UNICEF: 1987, The State of the World's Children, Oxford University Press, UK.
Mathematics Education Centre, Sheffield City Polytechnic, 25 Broomgrove Road, Sheffield, England SIO 2NA
