mathematics at work

163 Pages·2010·1.45 MB·English

by  Alger Klasson

MATHEMATICS AT WORK

A Study of Mathematical Organisations in
Rwandan Workplaces and Educational Settings

Marcel Gahamanyi

Linköping Studies in Behavioural Science No. 150
Linköping University, Department of Behavioural Sciences and
Learning
Linköping 2010
Distributed by:
Department of Behavioural Sciences and Learning
Linköping University
SE-581 83 Linköping

Marcel Gahamanyi
MATHEMATICS AT WORK
A Study of Mathematical Organisations in Rwandan Workplaces and
Educational Settings

Edition 1:1
ISBN 978-91-7393-459-6
ISSN 1654-2029

© Marcel Gahamanyi
Department of Behavioural Sciences and Learning

Printed by: LiU-Tryck 2010
ACKNOWLEDGEMENTS ...................................................................................... 7
LIST OF ABBREVIATIONS ................................................................................... 9
1 INTRODUCTION ................................................................................................ 11
1.1 BACKGROUND ................................................................................................. 12
1.2 MY EDUCATIONAL BACKGROUND ................................................................... 14
1.3 CURRENT SITUATION OF MATHEMATICS EDUCATION IN RWANDAN SCHOOLS . 14
1.3 AIM OF THE STUDY .......................................................................................... 16
1.4 STRUCTURE OF THE THESIS .............................................................................. 18
2 THEORETICAL FRAMEWORK ..................................................................... 21
2.1 ACTIVITY THEORY ........................................................................................... 21
2.1.1 Background ............................................................................................. 21
2.1.2 ENGESTRÖM’S MODEL OF HUMAN ACTIVITY SYSTEM ................................... 23
2.1.2 Expansive learning ................................................................................. 26
2.2 ANTHROPOLOGICAL THEORY OF DIDACTICS .................................................... 28
2.2.1 Didactic transposition ............................................................................. 28
2.2.2 Mathematical organisations .................................................................... 31
2.3 MATHEMATICAL TASKS ................................................................................... 35
2.3.1 The notion of mathematical task ............................................................. 35
2.3.2 Contextualised mathematical tasks ......................................................... 38
2.4 PREVIOUS RESEARCH ON IN-AND-OUT OF SCHOOL MATHEMATICS ................... 39
2.4.1 Objective social significance and subjective invisibility of mathematics 40
2.4.2 Workplace mathematics and school mathematics .................................. 40
2.4.3 Use of formal mathematics strategies ..................................................... 41
3 RESEARCH QUESTIONS AND METHODOLOGY ...................................... 43
3.1 AIMS AND RESEARCH QUESTIONS .................................................................... 43
3.2 RESEARCH METHODOLOGY ............................................................................. 43
3.2.1 The study in relation to an interpretivist research paradigm ................... 43
3.2.2 Research design ...................................................................................... 46
3.2.3 Selection of participants ......................................................................... 47
3.2.3 Instruments ............................................................................................. 48
3.2.5 Data collection ........................................................................................ 49
3.2.6 Data analysis ........................................................................................... 51
3.2.3 Ethical considerations ............................................................................. 52
4 MATHEMATICS USE AT THE WORKPLACE SETTINGS ........................ 55
4.1 AT THE DRIVERS’ WORKPLACE ........................................................................ 55
4.2 AT THE BUILDER’S WORKPLACE ...................................................................... 58
4.3 AT THE RESTAURANT OWNER’S WORKPLACE .................................................. 62
4.4 ACTIVITIES IN RUNNING SMALL SCALE ENTERPRISES ....................................... 66
5 MATHEMATICAL ACTIVITIES AT A UNIVERSITY SETTING .............. 73
5. 1 TRANSPOSING WORKPLACE MATHEMATICS FOR UNIVERSITY STUDENTS ........ 73
5.2 SOLVING CONTEXTUALISED MATHEMATICAL TASKS ....................................... 79
5.2.1 Task related to a taxi driving workplace ................................................. 80
5.2.2. Task related to the house construction workplace ................................. 92
5.2.3 Task related to the restaurant management workplace ........................... 96
5.3 TRANSPOSITION OF MATHEMATICAL TASKS FOR SECONDARY SCHOOL STUDENTS
............................................................................................................................ 101
5.3.1 Task related to the taxi driving workplace ............................................ 101
5.3.2 Task related to the house construction workplace ................................ 109
5. 3.3 Task related to the restaurant management workplace ........................ 113
5.4 STUDENT TEACHERS’ REFLECTIONS ON TASKS RELATED TO WORKPLACES .... 117
5.5 ACTIVITIES OF EXPERIENCING TO SOLVE AND TRANSPOSE MATHEMATICAL
TASKS .................................................................................................................. 118
6 MATHEMATICAL ACTIVITIES AT A SECONDARY SCHOOL SETTING
................................................................................................................................ 121
6.1 RECONSTRUCTING THE TRANSPOSED MATHEMATICAL TASKS ....................... 121
6.2 SECONDARY STUDENTS SOLVING CONTEXTUALISED TASKS .......................... 124
6.2.1 Task related to the taxi driving workplace ............................................ 124
6.2.2 Task related to the house construction workplace ................................ 130
6.2.3 Task related to the restaurant management workplace ......................... 133
6.3 SECONDARY STUDENTS’ REFLECTIONS ON THE CONTEXTUALIZED TASK ....... 135
6.4 EXPERIENCING THE ACTIVITY OF SOLVING CONTEXTUALISED TASKS ............ 136
7 DISCUSSION AND CONCLUSIONS .............................................................. 139
7.1 MATHEMATICS RELATED TO ACTIVITY SYSTEMS ........................................... 139
7.2 MATHEMATICAL ORGANISATIONS AT THE FIELDWORK SETTINGS .................. 144
7.3 DIDACTIC TRANSPOSITIONS OF CONTEXTUALISED TASKS .............................. 145
7.4 EXPANSIVE LEARNING ................................................................................... 148
7.5 CRITICAL REFLECTIONS ................................................................................. 149
7.6 PEDAGOGICAL IMPLICATIONS ........................................................................ 149
REFERENCES ...................................................................................................... 151
APPENDIX ............................................................................................................ 159

Acknowledgements
A completed PhD thesis reflects various sources and inputs which has
influenced the final product. It is against this backdrop that I wish to first and
foremost express my heartfelt gratitude to the thesis’ supervision team made
up of Ingrid Andersson and Christer Bergsten.
Since the thesis write-up process is a long and difficult journey, I needed
someone to critically look at my texts with a different pair of eyes for me to
refine my thesis and advance to the final stage. This would not have been
possible without the good will and tireless efforts of the team from Linköping
University who kindly accepted to read my thesis, and it is for this that I am
greatly indebted especially to Lars Owe Dahlgren and Sven B. Andersson. I
am also very thankful to Eva Riesbeck and Tine Wedege for being my
discussants at the important seminar discussions.
A research report like this thesis comes at the end of a long process of
studying and learning many things from many people and material sources.
When I look back I sincerely realize how I could not have made it to the final
stage without constructive knowledge and skills from and with others, and
getting their support along the way. These ‘others’ include all my teachers
and fellow PhD students from both Linköping University and the University
of Agder, Kristiansand, Department of Mathematical Sciences, Norway.
I have a special place in my heart for members of my family who
unwaveringly supported me both morally and materially throughout my study
period. This gave me a strong family base that often reinforced my
perseverance and resilience particularly at stressful periods of work.
Also I want to say that without the invaluable financial support from the
Swedish Government through the Swedish Institute and the SIDA-
SAREC/NUR-LiU Project (Sida Ref. N0 2004-000746) I would not have
been able to enrol on my PhD programme, in the first place. So, to the
success of this collaborative project I owe much for my personal success in
completing the programme.

Linköping, January 2010
Marcel Gahamanyi

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List of abbreviations
AT Activity Theory
ATD Anthropological Theory of Didactics
Frw Rwandan francs
HSFR Swedish council for scientific research in the humanities
and social sciences
ICT Information Communication and Technology
LP Level of Profit
MINEDUC Ministry of Education
MO Mathematical Organisation
NCTM National Council of Teachers of Mathematics
PC Purchasing Cost
SC Selling Cost
VAT Value Added Tax

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