bus conductors’ use of mental computation in everyday settings – is it their ethnomathematics?
DESCRIPTION
Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics? - Nirmala NareshTRANSCRIPT
![Page 1: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/1.jpg)
1
7/29/10 Naresh
Bus conductors’ use of mental
computation in everyday settings
– Is it their ethnomathematics?
Nirmala Naresh
FOURTH INTERNATIONAL
CONFERENCE ON
ETHNOMATHEMATICS
(ICEM-4)
![Page 2: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/2.jpg)
Session Agenda
!!Introduction
!!Background of the study
!!Research Methods
!!Data Analysis
!!Conclusion
!!Discussion
7/29/10
2
Naresh
![Page 3: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/3.jpg)
The Study
7/29/10 Naresh
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.
![Page 4: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/4.jpg)
Ethnomathematics
7/29/10 Naresh
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.
![Page 5: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/5.jpg)
Four Strands of Ethnomathematics
!! 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)
7/29/10
5
Naresh
![Page 6: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/6.jpg)
Everyday Mathematics
!! 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).
7/29/10
6
Naresh
![Page 7: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/7.jpg)
Workplace mathematics – A subset of research on
everyday mathematics
!! 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?
7/29/10
7
Naresh
![Page 8: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/8.jpg)
Mental computation in everyday situations
!! 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)
7/29/10
8
Naresh
![Page 9: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/9.jpg)
Mental computation at workplaces
!! 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).
7/29/10
9
Naresh
![Page 10: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/10.jpg)
Rationale for investigating everyday mathematics
!! 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)
7/29/10
10
Naresh
![Page 11: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/11.jpg)
Rationale for investigation in India
!!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.
7/29/10
11
Naresh
![Page 12: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/12.jpg)
Significance of the study
!! 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.
7/29/10
12
Naresh
![Page 13: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/13.jpg)
Theoretical fields
Adults’ use of mental math at
work
Ethnomathematics
Everyday Mathematics
Mental computation
7/29/10
13
Naresh
![Page 14: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/14.jpg)
Theoretical Model – Saxe’s model
7/29/10 Naresh
14
![Page 15: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/15.jpg)
!!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.
Theoretical model: RTC framework
7/29/10
15
Naresh
![Page 16: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/16.jpg)
Bus conductors are employees of the
Metropolitan Transport Corporation (MTC) of
Tamilnadu.
Study
Setting
Metropolitan
Transport
Corporation
7/29/10
16
Naresh
![Page 17: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/17.jpg)
Fleet strength of 2,773 buses and 2,554
services. 486 routes 3.7 million passengers on
any single day.
Study
Setting
Metropolitan
Transport
Corporation
7/29/10
17
Naresh
![Page 18: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/18.jpg)
The average daily collection per day is
estimated to be 10.9 million rupees.
Study Setting
Metropolitan
Transport
Corporation
7/29/10
18
Naresh
![Page 19: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/19.jpg)
Research Purpose
Analyze, compare and characterize bus conductors’ use of
mental computation.
- Focus of this paper: One bus conductor’s mental
computational acts at work
7/29/10
19
Naresh
![Page 20: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/20.jpg)
Overarching research methodology
!! Qualitative study
!! A non-experimental design
!! Case study approach
!! Instrumental case studies: Focus of this paper
"! Mr. Delta’s mental computational acts at work
7/29/10
20
Naresh
![Page 21: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/21.jpg)
Research Methods: Data Sources
Mental computation: Work Setting
"!Archival records,
"!Official documents,
"!In situ observations.
"!Participant Responses to computational
tasks (Stimulated recall techniques)
"!Interviews – Formal, and semi structured.
7/29/10
21
Naresh
![Page 22: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/22.jpg)
Research Methods: Data Analysis
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.
7/29/10
22
Naresh
![Page 23: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/23.jpg)
Participant – Mr. Delta
!!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.
7/29/10
23
Naresh
![Page 24: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/24.jpg)
List of Terminologies
!!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.
7/29/10
24
Naresh
![Page 25: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/25.jpg)
25
TICKET
Receipt for passenger paid fare
7/29/10 Naresh
![Page 26: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/26.jpg)
Traffic Return
An official
document used to record ticket sales
7/29/10
26
Naresh
![Page 27: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/27.jpg)
Waybill
Official
document used
to record total
ticket sales,
collection
amount.
7/29/10
27
Naresh
![Page 28: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/28.jpg)
Analysis: What are Mr. Delta’s duties at work?
!! 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.
7/29/10
28
Naresh
![Page 29: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/29.jpg)
Analysis: Three-phase structure of Mr.Delta’s work
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
7/29/10
29
Naresh
![Page 30: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/30.jpg)
Analysis: Evidence of mental computation at work
Sign on time
•!Little evidence of mental computational acts
Spread over time
•!Execution of ticket transactions
•!Completion of official records
Sign off time
•!Calculation of daily batta
•!Calculation of overall trip earnings
7/29/10
30
Naresh
![Page 31: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/31.jpg)
Ticket transaction scenario: More terminology
7/29/10 Naresh
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
![Page 32: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/32.jpg)
Possible ticket transaction scenarios
7/29/10
32
Naresh
![Page 33: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/33.jpg)
A snippet from workplace activity
!!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.
7/29/10
33
Naresh
![Page 34: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/34.jpg)
Concomitant perceptions of goals associated with
the activity
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)
7/29/10
34
Naresh
![Page 35: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/35.jpg)
Overall work-related goals
!! 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.
7/29/10
35
Naresh
![Page 36: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/36.jpg)
Emergent goals
!! 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
7/29/10
36
Naresh
![Page 37: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/37.jpg)
Activity structures
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
7/29/10
37
Naresh
![Page 38: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/38.jpg)
Prior understandings
!! 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.
7/29/10
38
Naresh
![Page 39: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/39.jpg)
Conventions and artifacts
!! 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.
7/29/10
39
Naresh
![Page 40: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/40.jpg)
Social Interactions
!! 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.
7/29/10
40
Naresh
![Page 41: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/41.jpg)
Evidence of mental computation: Mr. Delta’s method of
completing a waybill
7/29/10
41
Naresh
![Page 42: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/42.jpg)
Evidence of Mental calculation: Completion of a waybill
Waybill contents
7/29/10
42
Naresh
![Page 43: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/43.jpg)
Evidence of Mental calculation: Mr.Delta’s method of
calculating batta
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.
7/29/10
43
Naresh
![Page 44: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/44.jpg)
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!
![Page 45: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/45.jpg)
Discussion
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.”
7/29/10
45
Naresh
![Page 46: Bus conductors’ use of mental computation in everyday settings – Is it their ethnomathematics?](https://reader035.vdocuments.us/reader035/viewer/2022062220/5587999dd8b42af3408b471d/html5/thumbnails/46.jpg)
Thank You!
Questions?
7/29/10
46
Naresh