Global Leadership Training Programme in Africa 2015
Activity Report of Field Research
Research on the Influence of Mathematics Education on Children’s Understanding of
Number Concepts
1

Yuri HORIUCHI

I.
Summary< English Summary >Senegal is a country of West Africa. It gained independence from France in 1960, but continued to use theFrench curriculum of education. The official and institutional language in Senegal is French. Contrary to its ethnic
diversity, more than 80% of the population largely speak Wolof language. Thus, Wolof language serves as acommunicating tool among different ethnic groups. They do not spoken French as much as other Francophonecountries do.
The local system of counting money in Wolof language is very unique and epistemologically different from
French. Conventionally 1/5 of the value of money is largely used as a unit for counting. For example, a 25F coin is
literally “25(vingt cinq) frans” in French, but it is called “5(Jurom) derom” (derom is a monetary unit in Wolof).
This system is not applied to contexts without money. Thus, they simply call 25 boys “25(niaari fukk ak jurom) goor”
in Wolof (“goor” means boys).
For people without French education, this system is not complex because the indigenous concept of money
is not epistemologically connected with any written form of language. But the fact that mathematics is taught in
French implies that the local, spoken language is intricately linked with written French, which are rooted inculturally different systems of counting. It could be considered that this complexity is likely to affect children’s
understanding of number. To clarify this point, I decided to conduct my research.
Mathematics in and out of school, as Reed and Lave (1981) mention, “In the school-type situation, themanipulation symbols carried the burden of computation, thereby making the operations in a very real sense
divorced from reality.” Nune, Schliemann and Carraher (1993) also refer to this problem: “Realistic mathematics
education can bring children to build their knowledge of school mathematics on foundation of their already available
knowledge of street mathematics.”
What kind of mathematics education has to be done in the situation where there are big differences between
uses of numbers in and out of school? This is a fundamental question underlying my research, which is designed toseek some hints to improve mathematics education in Senegal. The objective of my field work was to clarify somefactors relating to the development of children’s attitudes towards number. First, I visited a market involving a
number of acts of counting money, in order to elucidate differences between conceptions of numbers in and out ofschool. Second, the influence of the indigenous concept of number on children’ leaning of mathematics wasanalyzed by implementing tests of word problem and numerical calculation at selected schools. Finally, I conducted
the same types of examinations and explore how numerical concepts systematically taught at school affect pupils’
understanding of numbers in and out-of-school context.

1st

1 year Master’s degree student, Graduate School for International Development and Cooperation, Hiroshima
University, Japan, Host University: Cheikh Anta Diop University, Senegal, 26 January - 24 April, 2016.
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< Japanese Summary >西アフリカに位置するセネガルは 1960 年にフランスより独立したが、教育制度やカリキュラ
ムなどはフランスの影響を色濃く残したままである。その一つに言語教育がある。公用語はフランス語であり、教授言語としてフランス語が使われている。しかし、多民族国家（ウォロフ族 43.3%、プラール族 23.8%、セレール族 14.7%など）でありながらも、実際には８０％以上の国民がウォロフ語を話し、共通語として広く使われている。そのため、日常生活における多民族間でのコミュニケーションはウォロフ語が使用されることが多く、フランス語の普及率は他の仏語圏アフリカに比べて低い。
また、お金の呼び方もフランス語と現地語では違いがある。フランス語では、硬貨に書かれた数字と呼び方は同じであるが、現地語ではその 5 分の 1 の値で呼ぶ。例えば、フランス語では 25Fcfa と書かれたコインはそのまま「25(ヴァンサンク)フランセ―ファー」と呼ぶが、ウォ
ロフ語では「５(ジュロム)デュロム」と呼ぶ(デュロムはウォロフ語でお金を言う時の単位である ) 。しかし、お金以外のものに対してはそのままの値で呼ぶ。例えば、 25 人の男の子は「 25(ニャーリ ―ジュロム )ゴール (男の子の意)」である。つまり、現地語では、お金の場合、
25Fcfa は「５」であるが、お金以外は「２５」と言うのである。
数字を読めない人やフランス語を知らない人たちにとって、これは大した問題ではない。なぜなら彼らにとって５デュロムは５でしかなく、２５であるとは思わずに生活している。しかし、学校教育を通して、フランス語を学び、数字をフランス語とだけ結びつけて学んでいく中で、数概念に影響が出てくるのではないだろうか。ここを明らかにすべく、本研究を進めるに至った。
これら、学校で学習する数学と日常生活で使われている数学について Reed&Lave(1981)は、「学校型の状況において、記号の操作は、現実世界から本当の意味において切り離されてしまっている」と述べている。また、 Nune&Schliemann&Carraher(1993) によると、「真の数学教育とは、すでに活用されうるストリートマセマティックの知識に基づいて、学校数学の知識を身に付けていくことができるものである」とも述べられている。セネガルにおいて、日常で使われている数学と、学校数学に大きな違いがあるとき、どのようにしてそれらを結びつけていくのがよいのだろうか。このことに関して、一つの手がかりにでもなるような研究ができることを期待し、本研究を進めている。
本研究の目的は、セネガルの初等教育における子どもたちの数概念の発達にかかわる要因を整理し、それらがどのように子どもたちの数概念の形成に影響しているのかをみていくことである。まず、市場での観察や日々のセネガル人とのかかわりの中で、日常生活における数のとらえ方、使い方をみていく。次に、学校教育での数のとらえ方、使い方を授業観察や、子どもたちの計算問題や文章題への回答の様子からみていく。その後、日常生活と学校教育における数のとらえ方、使い方の違いを整理したうえで、原因と思われる主要な要因をあげ、学校教育を受けている子どもたちとそうでない子どもたちの数概念の違いを追っていく。以上の過程を通して、セネガルの数学教育における問題の所 を明らかにし、 後のセネガルの数学教育のり方に対して 言を述べていきたい。

在

提

在

今

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II.
Research Activity
1. Introduction
When I worked as a volunteer in Senegal from 2012 to 2014, I was surprised that, although he
had never received mathematics education at school, an illiterate bus conductor was collecting
collectmoney
from passengers quickly and correctly
correctly. Meanwhile, many children struggled to deal
eal with simple
calculation, counting sticks in mathematics
ematics classes
classes.. I felt big differences between mathematics in and outof classrooms.. This experience led me to clarify these differences. Senegal is located in the West of
Africa. 95% of the population are Muslims. There are many ethnic groups; 43% of thethem
m are Wolof, 24%
are Fula, 15% are Serer, and so on. Although their medium of instruction as well as official language is
French, Wolof language is spoken by more than 80 % of the population and largely used in daily life.
Senegal gained independence from France in 1960, but continued to adopt the French system of
education. Until 2009 its mathematics curriculum ha
has not been changed over the last 30 years
yea (e.g. JICA,
2010).
While the net
et enrollment rate of primary school is 75.5% (World Bank, 2010), the completioncorate is 55.3% in Senegal (JICA, 2010)2010). The net enrollment rate of junior high school is 21.7% (JICA,
2010). Education Policy and Data C
Center (EPDC) mentions that 49% of school-age children are out ofschool in rural areas in Senegal (20112011). Approximately 50% of the younger population do not complete
primary school education, but many
any children without French-style education actually attend Koranic andArabic schools.
The system of counting money in Senegal is very unique. Even though their official language is
French, they use local languages, especially Wolof to buy and sell in a market. The local words have a
different system of counting money from French; 1/5 of the value of money is largely used as a unit for
counting.. For example, a 100F coin, which is written “100Fcfa”, they call it “20(Niaari fukki) derom”(derom is the monetary unit in Wolof). But when they use money in French, they call it the same value
with written one, that is, 100Fcfa coin is called “100(cent) frans”.
Although 1 derom (5 Fcfa) coin exists, the minimum value of a coin largely used in business
transaction is 5 derom (25Fcfa). This means that multiples of 5 are basic units for counting money andother numbers are rarely used in a market
market.
There are two distinctive features in Senegalese money context: people speak one-fifth
one
of an
actual price in Wolof; multiples of 5 (25 in French) are basically used in counting money.
money I was interested
in this unique perception of money and decided to conduct research to clarify how these featuresfeataffectchildren’’ understanding of number concept
concepts.
Table1 shows some examples of ways to count money in Senegal.

Coin

Table1:: Names of Senegalese currencies in Wolof and French
Name in Wolof
Name in French
5 derom (jurom derom)
25 Fcfa (vingt cinq
nq frans cfa)

10 derom (fukki derom)

50 Fcfa (cinquante frans cfa)

20 derom (niaari fukki derom)

100 Fcfa (cent frans cfa)

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The aim of my field work was to examine how mathematic educations in French that differs fromthe indigenous understanding of numbers affect the development of children’s number concepts in
Senegal. To clarify this point, I attempted to answer three research questions below:
1. What are differences between conceptions of numbers in and out of school?
2. How do the conventional number concepts in Wolof affect children’s understanding of numbers
in classrooms?
3. How do number concepts systematically taught at school have an impact of children’s
understanding of numbers in an out-of-school context?
2. Study Area
I chose Louga city and Dara Diagne village of the State of Louga. It is located in the northwest
area of Senegal, where many Wolof races live. In the city of Louga and its adjacent villages there are a lotof Wolof races, and most of the population speak Wolof. According to Ministry of Education of Senegal,
the State of Louga has the lowest rate of gross enrolment for students in primary school in the northwest
area, where there are many Wolof races (Ministry of Education of Senegal, 2011).
3. Methodology and Findings
3-1. Observation of commercial activities and analysis of mathematics textbooks
To answer the first research question, I visited a
local market to explore how people dealt with numbers,
particularly money in language and calculation. This fieldwork included a direct observation of vendors and informal,
unstructured interviews with 7 of them. Meanwhile, somemathematics textbooks widely used in Senegal wereanalyzed, with particular interest in how numbers and waysof calculation are taught.
The results of these initial surveys are shown as
Table2. They allowed me to realize that four factors:
language, approach to solving problems, context ofsituation, numbers (multiples of 25, 5, or not) were likely to
Figure1: Woman in a market
make differences between conceptions of numbers in andout of school.
Table2: Differences of uses of numbers between in and out of school
Out of school
In school
Language
Mainly Wolof
French(But they call the simple numbers in French
ex;100Fcfa, 200Fcfa, 1000Fcfa)
Calculate
Numbers or Coins
Numbers
Money
Some vendors cannot read numbers.
Vertical operation
They tend to imagine the coins.
Numbers of theMultiple of 5 in Wolof (25 in French)
Mainly multiples of 5 incontext ofLess than 5derom is rare
FrenchMoney
Tend to use big numbers
Numbers of the
All numbers
Many counting activities
context without(But they don’t count a lot;
Money
Counting members of family and livestock istabooed)43-2. Implementation of tests
3-2-1. Tests
To answer the second question, some tests were
implemented at a primary school of Louga city, targeting 37
pupils of 5th grade. (Four basic calculations of arithmetic aremostly taught between 1st and 4th grades.) First, a calculation
test was conducted to examine pupils’ abilities of four basicarithmetic operations, particularly of dealing with multiples of25, 5, and other numbers. Then I analyzed the percentage ofcorrect answers. Second, some problems from textbooks inmathematics were modified and given to the pupils as word
problems. The modification of them was made by changing
from some numbers to multiples of 25 and 5. Then I analyzed
the percentage of correct answers and their ways of solving.
3-2-2. Interview and questionnaire survey
Following the written examinations in French,interview-style tests were implemented in French and Wolof.
While word problems of the paper test were means to explore
pupils’ conceptions of numbers in a school context, this was
expected to analyze how literally and colloquial French entail
different approaches to mathematical solution. The use of both
French and Wolof echoed my intention of demonstrating how
a language difference affects their ways of dealing withnumbers as well as operations. The interview-styleexaminations consisted of questions involving multiples of 25,
5, and other numbers.
Apart from the tests and interviews, the questionnaire
survey was conducted to explore common languages of thepupils and their uses of money in daily life.

Figure2: Calculation test

Figure3: Boy explaining how to calculate
with imaging coins

3-2-3. Results
There was no difference in percentages of correct answers between multiples 25, 5, and othernumbers. For example, 75x4 often happens in a market, but only 72% of the surveyed pupils answered itcorrectly. This figure is lower than 96%, which is the percentage of correct answer to a problem: 72x5.
The students were not relatively good at problems of carrying and borrowing (e.g. two numbers arevertically carried for calculation of 75x4; one number is carried for 72x5). They have higher percentagesof correct answers to problems with addition than subtraction; problems with multiplication than division.
Table3 shows the relationship between language difference and ways of solving. C means that thepupils tended to use or imagine coins when they calculated. N means that pupils tended to use or imagine
numbers when they calculated.

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Table3: Relationship between language difference and ways of solving
Oral Interview
Written Word problem
Money
Not Money
Money
Not Money
Multiple of 25
C/N
N
N
N
Multiple of 5
N
N
NN
Other numbers
NN
Not implemented Not implemented
Multiple of 25
C
C/N
Multiple of 5
C
C/N
Other numbers
impossible
C/N（

French

Wolof

）

（

）

3-2-4. Discussion
With respect to percentages of correct answers, any significant difference was not seen between
problems of multiples 25, 5, and other numbers. Moreover, pupils’ ways of solving numericalcalculations verbally given in French were the same as manners in which they answered word problemsof the paper exam. Most of them utilized types of numbers, which are rarely used in an out-of-school
context. Thus, it could not be said that the indigenous conception of numbers affect children’s approaches
to mathematical solution in classrooms.
3-3. Comparison of students with different language
environments
3-3-1. Interview-style tests
Finally, I examined how pupils’ number concepts
constructed through mathematics education have an impact
on their understandings of numbers in daily life. To answer
the third research question, another type of interview-style
tests was implemented in this field work. It was designed toreveal a relationship between differences in language
environment and attitudes towards numbers, targeting 52
pupils categorized as below:•••

Figure4: Selection of children for tests
by asking their backgrounds

Group A: 20 pupils of 5th grade at urban school, where French is used for instruction
Group B: 16 pupils of 5th grade at rural school with French-speaking environment
Group C: 16 children who do not attend French school in the same rural area of Group B

All questions were five in number and read in Wolof. They represented daily communication as well as
uses of money, which involve calculations of multiples of 5 and other numbers (Table4). The pupils wereallowed to answer either in Wolof or in French, and asked to switch languages from Wolof to French, andvice versa. (e.g. If they used in Wolof at first, they were in turn requested to translate their answers to
French.) I analyzed the percentage of correct answers and ways that each group of the pupils solved thegiven problems.
Table4: Features of each question
Money
Non-Money
Multiple of 5
Q1
Q3
Non-Multiple of 5
Q2
Q4
Q1: You have 50D (250F). You buy candies which cost 15D (75F). How much money do you leave?
Q2: You have 30D (150F). You give 12D (60F) to your sister. How much money do you leave?
6Q3: In the classroom, there are 40 pupils. 25 of them are girls. How many boys are there in theclassroom?
Q4: In the garden, there are 35 eggs. You eat 18 eggs of them. How many eggs remain?
Q5: Which picture (30 beans/150 beans) shows Fanuweer (30 in Wolof) beans? (see Figure5)

A

Figure 5: Pictures for Q5
3-3-2. Findings
Table5-7 show the percentage of correct answers of each group. The numbers in brackets show
the percentage of answers which were correctly changed to another language.

(n=20)
Multiple of 5
Non-Multiple of 5

Table5: Percentages of correct answers of Group A
Money
Non-Money
40%(35%)40%(5%)
40%(5%)
25%(0%)(n=16)
Multiple of 5
Non-Multiple of 5

Table6: Percentages of correct answers of Group B
Money
Non-Money
68.8%(43.8%)
56.3%(31.3%)
56.3%(6.3%)
31.3%(0%)(n=16)
Multiple of 5
Non-Multiple of 5

Table7: Percentages of correct answer of Group C
Money
Non-Money
75.1%(18.8%)
43.8%(31.3%)
31.3%(0%)
18.8%(12.5%)

Table8-10 show that the percentages of the pupils who switched languages in answering 5 or 1/5
times of the real quantities. For example, in Q1 35D was needed to be answered 175Fcfa. But somechildren switched 35D to 35Fcfa.
Table8: Percentages of correct answers of Group A when switching languages(n=20)
Money
Non-Money
Multiple of 5
0%30%
Non-Multiple of 5
0%
0%

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Table9: Percentages of correct answers of Group B when switching languages(n=16)
Money
Non-Money
Multiple of 50%
12.5%
Non-Multiple of 50%0%Table10: Percentages of correct answers of Group C when switching languages(n=16)
Multiple of 5
Non-Multiple of 5

Money
25%
0%

Non-Money0%
0%

Table11 shows the percentages of various answers to Q5. “Small” and “large” represent Picture A
and B. It was considered that Fanuweer was answered in two ways: 30 or 150 beans. For example, “Small
150” was one of pupils’ answers, indicating that some of them correctly associated Fanuweer with Picture
A, but mistakenly answered 150 beans in number. The correct answer to this question was actually “Small
30.”

Group AGroup B
Group C

Small 30
15%
43.8%
56.3%

Table11: Percentages of various answers
Small 150
Large 30
40%
5%
43.8%
6.3%
6.3%
25%

Large 150
30%
6.3%
0%

Generally, all groups were not good at Q1 (Not Money; Not Multiple of 5). They were also goodat Q4 (Money; Multiple of 5), but Group C was not good at switching Wolof to French numbers. 25% ofGroup C answered 35derom and 35Fcfa to Q1 (Money; Multiple of 5) in Wolof and French. This error
was not seen in other groups. Some pupils of Groups A and B replied 5 times of the correct answers to Q3(Non Money; Multiple of 5) (e.g. 15 boys in Wolof to 75 boys in French). No students in Group C did
this conversion. In terms of Q5, 30% of Group A thought that 30 in Wolof is the same amount as 150.
More than 40% of Group A and B regarded 30 beans as 150 in French. 25% of Group C was unlikely tohave a good sense of 30.
3-3-3. Discussion
It was found that all groups were better at calculation with multiples of 5 than other numbers. The
surveyed children were better at questions involving money context than non-money context. In a nonmoney context, some pupils attending school, especially in urban areas, replied 5 times of the realquantities when they were requested to switch language from Wolof to French. Moreover, some children
without schooling did not change figures of their answers to questions involving money when theyswitched language from Wolof to French. The fact that children attending urban school do not commonly
use Wolof numbers except in a money context is likely to be one of the reason why they tend to think that
Wolof numbers uniformly mean 5 times of French numbers.
Meanwhile, children who do not go to school tend to think that a Wolof number has the samevalue as one in French even in the context of money. 5derom and 5Fcfa has the same value. One reason ofthis misconception is that children who do not attend French school do not know written forms of number.

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Although it is written “25” on the coin of 25Fcfa, they are unable to read it. They just think it 5Fcfa
because they call it 5derom in Wolof.
It could be considered that some children without French-style education do not connect two
distinctive concepts of amount and number. By contract, children who attend school can connect themthrough a lot of activities of counting in classrooms.
4. Conclusions
I have currently been involved in a qualitative analysis to identify children’s misconception of
number, exploring responses of surveyed children to my questionnaires. This research was originallydesigned to clarify how the differences of using numbers between in and out of school influence on thechildren’s developing the number concepts. However, this field work revealed that the indigenous
attitudes towards numbers do not necessarily influence their number concepts which are systematicallydeveloped at school. It could be said that children do not develop the concept of number just within an
everyday context; rather it is likely to be acquired through schooling.
This result of the initial study led me to examine how a mathematic understanding of number
which children learn at school have an impact on their concepts of number in daily life. I found thatmathematics education results in perception gaps between conceptualizations of amount in Wolof andFrench. Some children connect Wolof and French systems of numbering in a wrong way because written
numbers are thought at school in French. They seem to link these two systems by imagining money, andthis way of understanding number is mistakenly applied even in non-money contexts. This is problematic
because an increasing number of pupils who use Wolof numbers in everyday life have been leaning
mathematics in French in schoolrooms.
Mathematic education is not necessarily
characterized by its negative impact. In fact, it enables
children to connect the concept of quantity with written
numbers. However, it is unlikely to be significant in Senegal.
There is a cultural taboo which prohibits people fromcounting the member of family and livestock, and they putemphasis on sharing rather than accuracy in number. In
order to share all forms of properties with others, they preferto have bigger amount of things than they really need. For
them, accuracy in number is not so important value. It could
Figure6: Traditional emphasis on
be thought that an action of counting does not frequently
sharingrather than accuracy in number
occur in their lives.
The knowledge acquired in French is becoming more and more important for Senegalese tosurvive in a globalized society. However, if mathematic education continues to ignore the indigenous,
constructed concept of number, it would lead to the loss of their cultural identity. Their identity as such
could not be examined, but at least my research reveals that the French-only principle in mathematics
classes makes children get confused. This implies that the education system ought to be developed
according to unique cultural aspects as well as locality. I believe that this is the only way that Senegalese
could achieve their genuine development of country.
• Acknowledgement
First, I am grateful for the help I received from Dr. Osamu Saito, Dr. Natsuko Imai, Ms. Reiko
Sato, Ms. Yuki Nakano and other staffs in United Nations University. Thanks to your big efforts, I wasable to conduct field work in Senegal.
Second, I would like to thank Dr. Mangary KA and his colleagues of mathematics department of
FASTEF of Cheikh Anta Diop University for their support. Although I stayed in Louga city which is9located 200km from Dakar, Mr. Ka contacted me many times about caring out my research and aboutliving in Senegal.
Third, thanks to the teachers who accepted my proposal to conduct my research and to thechildren who came to school on weekends for the interviews.
Last, thanks to my friends who helped me with and those who supported me during my stay in
Senegal.
• References
André, P. & Demonsant, J.L., 2009, Koranic Schools in Senegal: A real barrier to formal education,
Agence Francaise de Developpement (AFD).

Baba,T., Iwasaki,H., 2001, The Development of Mathematics Education Based on
Ethnomathematics (2): Analysis of Universal Activities in terms of Verbs, International
Journal of Curriculum Development and Practice 3(1), pp.65-75.
Battestini, S., 2006; De l’écrit africain à l’oral. Le phénomène graphique africain, Paris,

L’Harmattan.
Berry, J.W., 1985, Learning Mathematics in a Second Language: Some Cross-Cultural Issues, For
the Learning of Mathematics, 5 (2).
Bishop, A., 1988, Mathematics Enculturation, New York, Kluwer Academic Publishers.
Daniel, J., 2003, The Mother-Tongue Dilemma, Education TODAY No 6, The Newsletter of
UNESCO’s Education Sector, July-September 2003, www.unesco.org/education
Diagne, M., 2005, Critique de la raison orale, Paris : KarthalaGay, J. & Cole, M., 1967, The new mathematics and an old culture, New York, Holt, Rinehart andWinston, Inc.
Kuenzi, M., 2011, Education and democracy in Senegal, New York, Palgrave Macmilan.
Nunes, T., Schliemann, A. D. & Carraher, D.W., 1993, Street mathematics and Schoolmathematics, New York, Cambridge University Press.
Reed, H. J., & Lave, J., 1979, Arithmetic as a tool for investigating relations between culture andcognition, New York, American Ethnologist.
Yanagihara, Y., 2008, A Study of Cognition in the Language of Instruction for Science andMathematics Education in the Pilippines: Based on Learning How to Prove Two Triangles
Congruent- The Keiai Journal of International Studies, No21, pp.133-158.
Zaslavsky,C., 1973; Africa Counts: Number and Pattern in African Culture, New York, Lawrence
Hill Books.

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Reflection to the GLTP in Africa
As I was a volunteer in Senegal, I spent a lot of time with villagers who complained about
poverty and teachers who complained about low salary. They do not feel valued by people in authority.
Naturally, I tended to think like them when I was a volunteer. But I found that the professors and theircolleagues love Senegal a lot and think a lot about the future of Senegal. They always work hard for it.
Especially Mr. KA and the researchers around him understand the importance of education in Wolof.
They have already tried a lot to promote this. By exchanging ideas, I got confidence in my research andrethink about my research.
Mr. KA and his colleague taught me a lot not only about my research, but also their spirit, loving
one’s country and trying to act in his best interest. International collaboration allows us to learn together
and learn from each other, and exchanging ideas and experiences help us to respect each other. I have notyet decided my next stage, but I want to hold this attitude whatever I will do.
III.

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