Street Mathematics and School Mathematics

Front Cover
Cambridge University Press, Apr 30, 1993 - Education - 170 pages
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People who learn to solve problems 'on the job' often have to do it differently from people who learn in theory. Practical knowledge and theoretical knowledge is different in some ways but similar in other ways - or else one would end up with wrong solutions to the problems. Mathematics is also like this. People who learn to calculate, for example, because they are involved in commerce frequently have a more practical way of doing mathematics than the way we are taught at school. This book is about the differences between what we call practical knowledge of mathematics - that is street mathematics - and mathematics learned in school, which is not learned in practice. The authors look at the differences between these two ways of solving mathematical problems and discuss their advantages and disadvantages. They also discuss ways of trying to put theory and practice together in mathematics teaching.
 

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Contents

What is street mathematics?
1
II The significance of street mathematics
6
1 Social factors in the emergence of street mathematics
7
III Plan of the book
11
Arithmetic in the streets and in schools
13
II The cultural context
15
III The empirical study
17
2 Procedure
18
II A psychological analysis of the concept of proportions
78
Social and learning contrasts
84
IV Solving problems about proportions
87
V Conclusions
101
Reversibility and transfer in the schema of proportionality
103
I Proportionality in fishermens everyday life
104
2 Seafood and other foods
106
3 Hypothetical models for fishermens knowledge of proportions
107

3 Results and discussion
20
IV Further questions
26
Written and oral arithmetic
28
II The empirical study
30
2 Subjects
33
4 Results and discussion
34
III Conclusions and further questions
47
Situational representation in oral and written mathematics
49
II Different views of schooling and cognitive development
50
Farmers and students
56
Arithmetic for the shop and for school
62
V Conclusions
74
Situational and mathematical relations A study on understanding proportions
77
II Reversibility and transfer of fishermens knowledge of proportions
108
2 Preservation of meaning in outofschool strategies to solve proportions problems
114
3 A contrast between solving problems about fishing and about agriculture
117
III Strategies in solving proportions problems in and out of school
121
IV Conclusions
126
Reflections on street mathematics in hindsight
127
2 Psychological processes in mathematizing situations
132
II Lessons for education
147
2 Street mathematics school mathematics and critical thinking
151
III Final comments
153
References
155
Index
161
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