Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics? - Nirmala Naresh

1. 1
Bus conductors’ use of mental
computation in everyday settings
– Is it their ethnomathematics?
Nirmala Naresh
FOURTH INTERNATIONAL
CONFERENCE ON
ETHNOMATHEMATICS
(ICEM-4)
Naresh 7/29/10

2. Session Agenda
2
!!Introduction
!!Background of the study
!!Research Methods
!!Data Analysis
!!Conclusion
!!Discussion
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3. The Study
3
!! Focus on adults’ use of
mental mathematics in
everyday situations.
!! To observe, understand,
describe, and analyze the
mental mathematical
practices of the bus
conductors (in Chennai,
India) at their workplace.
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4. Ethnomathematics
4
!!Issues of social change, equity, and justice – Catalyst to
the ethnomathematics movement.
!!Forerunners of ethnomathematics
•! Otto Raum – Arithmetic in Africa (1938),
•! Dirk Struik – Sociology of mathematics (1942),
•! Gay & Cole – The new mathematics and an old
culture (1967).
!!D’ Ambrosio – Father of ethnomathematics.
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5. Four Strands of Ethnomathematics
5
!! A challenge to the traditionally told history of mathematics.
!! Analyses of mathematics associated with the traditional
cultures of indigenous people.
!! Explore the mathematics of different groups of people in
everyday settings.
!! Ethnomathematics and multicultural mathematics education.
(Vithal &Skovsmose, 1997)
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6. Everyday Mathematics
6
!! Investigation of everyday practices of groups of people.
!! Mathematical concepts that were described include mental
computation, arithmetic, proportional reasoning, and
geometry.
!! Grocery shoppers, Bankers (Lave, 1991).
!! Street vendors in Beirut (Jurdak & Shaheen,1999).
!! Candy sellers in Brazil (Carraher, Carraher, & Schliemann,
1987; Saxe, 1991).
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7. Workplace mathematics – A subset of research on
everyday mathematics
7
!! Insight into how people conceptualize the role of
mathematics in their work.
!! Is in its formative years.
!! What mathematics is used by workers? How is it used? Do
they use school-taught mathematics at work?
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8. Mental computation in everyday situations
8
!! Adults reason in problematic situations quite differently from the
way they did mathematics at school.
!! Problem solving in everyday situations is “characterized by a
pragmatic agenda and geared to solving particular
problems” (Noss, Hoyles & Pozzi, p. 17).
!! Further investigations needed to understand how people make
sense of mathematics outside school. (Carraher, 1991)
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9. Mental computation at workplaces
9
!! Work places varied mathematical demands upon workers.
(Carraher, p.195)
!! “Most of the knowledge used at the workplace remains implicit
and sometimes unconscious” (Vergnaud, 2000, p. xvii).
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10. Rationale for investigating everyday mathematics
10
!! How do people make sense of mathematics outside school ?
!! “Most of the knowledge used at the workplace remains
implicit and sometimes unconscious” (Vergnaud, 2000, p.
xvii).
!! Theoretical and empirical research base needed to develop
research methodologies and also for curriculum
development. (Millroy, 1992; Zevenbergen, 2000)
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11. Rationale for investigation in India
11
!! Desire to add to mathematics education research in
India.
!! Few contributions to the research area of everyday
mathematics from India. (e.g., Mukhopadhyay,
Resnick, & Schauble, 1990)
!! Several professions in India serve as rich sources for
investigation of mathematical practices of adults.
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12. Significance of the study
12
!! Draw out specific aspects of the bus conductors’
practice that contribute to their mental
computational activities.
!! Contribution to research field of
ethnomathematics, everyday mathematics, and
workplace mathematics by extending it to a new
social context.
!! Contribution to the line of research on mental
computation.
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13. Theoretical fields
13
Everyday
Mathematics
Mental
Ethnomathematics
computation
Adults’ use
of mental
math at
work
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14. Theoretical Model – Saxe’s model
14
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15. Theoretical model: RTC framework
15
!! Reformulation involved alteration of the numerical data
in the problem.
!! Translation strategy involved modifying the mathematical
structure of the problem.
!! Compensation technique was used to make adjustments
(to the problem) to compensate for the reformulation
and transformation techniques used.
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16. 16
Study
Setting
Bus conductors are employees of the
Metropolitan Metropolitan Transport Corporation (MTC) of
Transport Tamilnadu.
Corporation
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17. 17
Study
Setting
Metropolitan
Transport Fleet strength of 2,773 buses and 2,554
Corporation services. 486 routes 3.7 million passengers on
any single day.
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18. 18
Study Setting
Metropolitan
Transport
Corporation
The average daily collection per day is
estimated to be 10.9 million rupees.
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19. Research Purpose
19
Analyze, compare and characterize bus conductors’ use of
mental computation.
- Focus of this paper: One bus conductor’s mental
computational acts at work
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20. Overarching research methodology
20
!! Qualitative study
!! A non-experimental design
!! Case study approach
!! Instrumental case studies: Focus of this paper
"! Mr. Delta’s mental computational acts at work
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21. Research Methods: Data Sources
21
Mental computation: Work Setting
"!Archival records,
"!Official documents,
"!In situ observations.
"!Participant Responses to computational
tasks (Stimulated recall techniques)
"!Interviews – Formal, and semi structured.
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22. Research Methods: Data Analysis
22
Three levels of data analysis.
!! Level 1: Analyze data as the data are
collected.
!! Level 2: Creation of a case study database.
!! Level 3: Use Saxe’s model & RTC model to
analyze and interpret the data.
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23. Participant – Mr. Delta
23
!! Educational qualification – PUC fail (equivalent to higher
secondary school).
!! Good recommendations from superiors.
!! 27 years of service.
!! Bitter school experiences; not proficient in maths.
!! High opinion about mathematics learning.
!! Sincere and dedicated – did not hold his job in high
esteem.
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24. List of Terminologies
24
!! Fare – Depends on entry and exit point, type of
bus.
!! Batta (allowance) – Allowance conductors get
everyday based on total collection amount, type
of bus operated.
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25. 25
TICKET
Receipt for
passenger paid
fare
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26. 26
Traffic
Return
An official
document
used to
record
ticket sales
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27. 27
Waybill
Official
document used
to record total
ticket sales,
collection
amount.
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28. Analysis: What are Mr. Delta’s duties at work?
28
!! Commute several times from point A to point B & pick up
and drop off passengers en route.
!! Issue ticket to a commuter based on his entry and exit point.
!! Tender exact change back if the commuter gives more
money than the required amount.
!! Keep a record of the number of tickets issued from stage to
stage.
!! Calculate the daily allowance based on the day’s collection.
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29. Analysis: Three-phase structure of Mr.Delta’s work
29
Sign on time (Before bus trips)
Collect imprest amount (Rs. 30.00), locate
bus route, bus #, bus driver.
Spread over time (During bus
trips)
Issue tickets to passengers, update travel
records
Sign off time (End of bus trips)
Calculate daily batta, submit trip earnings
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30. Analysis: Evidence of mental computation at work
30
Spread over
Sign on time Sign off time
time
•!Little evidence •!Execution of •!Calculation of
of mental ticket daily batta
computational transactions •!Calculation of
acts •!Completion of overall trip
official records earnings
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31. Ticket transaction scenario: More terminology
31
!! PPF: Passenger Paid Fare
"! Fare a passenger hands over to the conductor
!! ATF: Actual Ticket Fare
"! Fare pre determined to travel from point A to point B
!! BA: Balance Amount
"! If the PPF > ATF, the balance amount the conductor hands
over to the passenger
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32. Possible ticket transaction scenarios
32
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33. A snippet from workplace activity
33
!! A passenger boarded the bus at point P along with four
members of his family. Mr. Delta approached the
passenger. The passenger handed out a 50-rupee note
and requested the conductor for five tickets to point Q.
Mr. Delta requested the passenger to give him an extra
50 paise coin and the passenger obliged. He then gave
the passenger five tickets and handed 33 rupees back to
the passenger.
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34. Concomitant perceptions of goals associated with
the activity
34
Conductor’s perception
Carry out a ticket transaction - Issue 5 tickets to
passengers travelling from P to Q.
Researcher's perception
Complete a mental computational problem
Solve 50 – (3.50 * 5)
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35. Overall work-related goals
35
!! Have an incident free day,
!! Serve passengers to the best of his ability to avoid
confrontations with the commuters
!! Authenticate every person’s travel in the bus;
!! Earn maximum collection and daily allowance.
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36. Emergent goals
36
!! Associated with work-related goal-directed
mathematical activities.
!! Emerge and fade with each activity.
!! Little “I need to do ….” things associated with work-
related activities.
!! Concomitant perceptions of goals
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37. Activity structures
37
Tasks in activity cycle (conductor’s interpretation)
!! Approach passenger
!! Gather information
!! Issue tickets
Tasks in activity cycle (researcher’s interpretation)
!! Determine actual ticket fare
!! Evaluate passenger paid fare
!! Compare passenger paid fare with the actual ticket fare;
!! Determine the balance amount
!! Match currency with the balance amount
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38. Prior understandings
38
!! Knowledge about the bus routes;
!! Names and number of bus stops and fare stages along
their bus routes;
!! Stage fares and ticket denominations for different
types of buses; and
!! School-learnt mathematical strategies.
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39. Conventions and artifacts
39
!! Routine activities – Approach passenger, gather
travel information, negotiate in reformulating the
problem.
!! Use of currency – helps do quick computation,
serves to cross check calculation.
!! Printed tickets help keep track of the figures
involved in the transaction.
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40. Social Interactions
40
!! Interacted with the passenger to initial ticket transaction
!! Crucial to completion of tasks set in activity structures.
!! Sought passenger’s cooperation in reformulation the
original problem.
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41. Evidence of mental computation: Mr. Delta’s method of
completing a waybill
41
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42. Evidence of Mental calculation: Completion of a waybill
42
Waybill contents
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43. Evidence of Mental calculation: Mr.Delta’s method of
calculating batta
43
Note: Total ticket collection amount for the day 7100.
"! Variable allowance: Rs. 2.00 (for every Rs. 100 collected)
"! For Rs. 1000, the allowance is Rs. 20.00.
"! For Rs. 7000 it is 140.
!! I added 7 thousands to get 7000. So I added 20 seven times to get
140. I added another two to this amount to account for the extra
100. The total variable allowance is 142.00.
!! The fixed allowance is Rs. 45. Penalty for lost trips: Rs. 10.
!! Actual allowance claimed: 142 + 35 = 177.
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44. Characterization of Conductors’ Mathematics
Three components of conductors’ mathematics:
"! Use of prior knowledge.
"! Use of work-specific knowledge.
"! Use of monetary units.
Acquire, appropriate, and specialize the above three
forms, that I term
“Bus conductors’ mathematics”.
Their ethnomathematics indeed!

45. Discussion
45
Mr. Delta’s reaction:
“You may be right.
However, when I work, I don’t think about what mathematics I
am using.
I see money, I hear words, my hands deal with tickets and
money and I calculate in my heart.
There is little time to think about anything else.
I don’t gloat about the mathematics that I do everyday.
I cannot afford to make mistakes in my calculations because I
may end up losing government money.
So I only concentrate on doing my job quickly and correctly.”
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46. Thank You!
46
Questions?
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