The
main objective of this research is to study the relevance of indigenous
languages in teaching science education in Nigeria. The paper is very particular
to the teaching of Mathematics in Hausa language in the predominant Hausa
speaking community (northern Nigeria). In its purview, the paper specifically
concentrates on numerals and numbers in Hausa counting system. It is common
knowledge that in the field of Mathematics, numbers are among the basic
ingredients in Mathematical operations. In order to strengthen the arguments
enunciated in this paper, ten international languages were selected. The
languages are; three European languages (English, French and German), three
African languages (Arabic, Fulfulde and Zarma) and three Nigerian languages...
_______________________________
By
Aliyu
Muhammad Bunza,
Professor
of African Culture (Hausa),
Department
of Languages and Cultures,
Faculty
of Humanities and Education,
Federal
University, Gusau.
________________________________
Being
a paper presented at the University Seminar Series, organized by the University
Research Center, Federal University Gusau, on 17^{th} January 2018,
under the distinguished Chairmanship of Professor Magaji Garba, the Vice
Chancellor, Federal University Gusau, at the ICT Twin Theatre 1, 11:00am.
Abstract
The
main objective of this research is to study the relevance of indigenous
languages in teaching science education in Nigeria. The paper is very particular
to the teaching of Mathematics in Hausa language in the predominant Hausa
speaking community (northern Nigeria). In its purview, the paper specifically
concentrates on numerals and numbers in Hausa counting system. It is common
knowledge that in the field of Mathematics, numbers are among the basic
ingredients in Mathematical operations. In order to strengthen the arguments
enunciated in this paper, ten international languages were selected. The
languages are; three European languages (English, French and German), three
African languages (Arabic, Fulfulde and Zarma) and three Nigerian languages
(Yoruba, Igbo and Nupe). This is also to ensure the background of the
universality of number system in human languages. Hausa is part of the “base
10”group of languages as discovered, which makes it very suitable to
accommodate the proposal. Thus, a careful study of Hausa numbers with special
treatment in naming the numbers, Mathematical operation, the concept of odd and
even numbers, and related Hausa ethnomathematics in Hausa cultural
perspectives. The findings suggest that, teaching Mathematics in the Hausa language
is very possible and is the only antidote to the massive failure in the subject
in our schools and colleges. The paper, therefore, calls on the authorities
concerned to urgently pay attention to the need to introduce Mathematical
education in all Nigerian languages both at primary, secondary and at advanced
levels. The prayer is imperative if we seek to eradicate phobia for Mathematics
and to let our educational system address the existing realities.
Introduction
Nigerian
languages have an appreciable variety of number system (Oyebade, 2014:2) which
is observed to be under threat of extinction by Nigerian linguists. Recent
discoveries by linguists estimate that, there are about 5600 – 5700 languages
in the world today. The study further established that Africa and Asia are the
largest continents with the highest number of living indigenous languages.
Furthermore, Nigeria has the highest number of languages in Africa, and also
has the largest number of extinct and endangered languages (Nettle and Romaine,
2000: 7). To complicate issues further, in Nigeria, Hausa people are the
largest ethnic group and the Hausa language is indeed the widest spoken
language in subSaharan Africa. With this rapid language endangerment and
extinction, the most essential aspect in the treasury of human language,
numeral counting system, and Mathematical character of Hausa operation are
affected. This paper is an attempt to revisit Hausa ethnoMathematics with
special reference to ‘numerals’ as it affects Mathematical operation. The
prayer is to employ indigenous languages in teaching Mathematics at least to
reduce the number of failures in the subject in our schools and do away with
the cancer of “mathemaphobia” in the minds of our pupils.
Methodology
This
research is a proposal at a crossdisciplinary study (Mathematics and Hausa
studies). Quite a number of published and unpublished materials in Mathematics
were consulted. Research works of BA, MA and PhD specifically on the subject
under review were found very useful. The arm chair research was only to address
the introductory aspect of the paper and see to the possibility of implementing
its proposal. Oral interviews and discussions with junior and senior colleagues
in the field of Mathematics were found to be very useful. My interactions with
students of Mathematics at various levels in the tertiary institutions and
universities helped very much in addressing the desired target of the research.
Hausa scholars and researchers with the same interest contributed alot during
contacts at field work. At a personal level, I decided to try my hypothesis at
home by selecting ten of my children: 2 at nursery school, 3 at primary school,
3 at secondary school and 2 at university levels respectively. At the end of
the trial, the evaluation was successful with an excellent output.
Theory
In
the available literature on Mathematics and Hausa studies, teaching science
education in indigenous languages is not a difficult task. In a recent study,
Oyebade (2014:2), it has been observed that, our youth (most of them University
undergraduates) could not count in their indigenous languages beyond the number
10. This confirms that the counting systems of our indigenous languages are
under the threat of extinction. David K. Harrison (2008) has noted that, we
lose an important window into human cognition, problemsolving and adaptation
when our counting system disappeared. Experts confirmed the looming danger
ahead and the need to apprehend it. In the struggle to find appropriate theory
of culture to capture their prophecy and to review my research, I opt to expand
popular Hausa worldview which says: “Karen duk da ya yi cizo, da gashinsa
ake magani” (The hair of the dog that bites should be used in treating the
wound). Thus, the dog(s) represents “the imperialist and imperialism”, and the
“wound” its linguistic overloadship. Therefore, the most effective drug is to
have our indigenous languages operate in all our educational institutions
whereas, to the foreign languages we bid a farewell.
Mathematical ideas in Hausa culture
The
term Arithmetic or Mathematics is popularly known as ‘Lisafi/Qidaya’ in
Hausa. In an advanced level, it is referred to as ‘bincike’ or ‘taliyo’,
meaning research or a careful Arithmetic of an issue. To a Hausa man,
‘Mathematics’ is the best yardstick to evaluate human intelligence and his
power of reasoning. Thus, ‘lisafi’ is beyond mere calculation, it also
include the ability to arrive at the undisputable fact. Indeed, taking a wrong
decision over a sensitive issue is tantamount to condemnation of such attitude
which is literary expressed as ‘ba ya da lisafi’. A careful study of a
problem and taking a wise decision in confronting any serious issue is called “lisafi”
as in: “Bayan da na yi lisafi na yanke shawara”. Meaning: ‘After a
careful (Arithmetic) study of the problem, I then took a decision.’ In a nut
shell, ‘Arithmetic/Mathematics’ are the common terms used in describing a sound
mental capacity or intelligence of a person in Hausa cultural perspectives.
In
several Hausa games, riddles, figures of speech, and proverbs, there are traces
of Mathematics specifically dealing with numerals. The numerals captured in
these folkloric materials are far above the use of mere Mathematical operation
of the numbers involved. It represents serious intellectual discourse in Hausa
sociocultural activities. Let us consider the following examples to
demonstrate Mathematical opinion in Hausa culture:

Literal meaning

Cultural context

Na shiga uku

“I have entered the similitude of
number three (3).”

In its cultural context, it means
“I am in trouble”. In Mathematical language, it refers to an odd situation or
a critical period of hardship. Hence three (3) is an odd number. Whatever is
odd in Hausa culture is problematic.

Mutum duka xan tara ne

All human beings are in the
category of number nine (9).

In folkloric perspectives, it
means ‘no one is perfect’, we all have shortcomings, we are all learning,
etc. In Hausa numeral, nine is the second to the last number in baseten
groups, which Hausa belongs to. It is the highest next to apex which is
humanly impossible to reach.

Ya yi mini goma na arziki

“He gave me ten of gifts/wealth.”

The beneficiary is referring to
good reception, hospitality, welltreated and so on. The number, ten (10)
here represents the highest respect and regard; hence Hausa counting system
is in ‘base ten’ groups; and ten traditionally refers to ‘goma iyakar
qirga’ (ten the last in counting). Being the highest and the last in Hausa
numerals, it always refers to the end of discussion, whatever reaches ten, is
assumed to reach its peak. In addition, ten (10) is an even number, which is
called ‘cika’ in Hausa, referring to ‘full’, as in full treatment.

An Overview of Numerals in World Languages
I
have selected only ten languages in order to undertake a comprehensive review
in terms of their numerals to build a conceptual framework of this study. In an
attempt to actualize the capability of Hausa numerals in meeting the demand of
modern Mathematics, three European languages were selected namely; English,
French and German languages. Three African languages and three Nigerian
languages were also selected for a very brief discussion of their counting base.
The random study of the numerals in world languages runs thus:
Numerals:

1

2

3

4

5

6

7

8

9

10

11

12

English:

one

two

three

four

five

six

seven

eight

nine

ten

eleven

twelve

French:

un

deux

trois

quatre

cing

six

sept

huit

nenf

dix

onze

douze

German:

eins

zwei

drei

vier

fÅ«nf

sechs

sieben

aÃ§ht

neuen

zehn

eif

zwolf

These
European languages operate ‘base ten’ numerals and are commonly used well in
the world of Mathematics. The majority of Hausaland happened to be in the
presentday Nigeria, though a part of it falls in the Republic of Niger. Hausa
speakers in Nigeria are using English numerals while those in Niger use French
numerals which are all in ‘base ten’. Coupled with all the linguistic
difficulties, they managed to study Mathematics and successfully scaled
through. This might not be unrelated to their ‘base ten’ numerals in their
native language which makes it easier to transadapt the English and
French numerals in their Mathematics.
African Languages
Numerals:

1

2

3

4

5

6

7

8

9

10


Arabic:

wahid

isnaini

salasa

arba’a

hamsa

sitta

saba’a

tamaniya

tis’a

ashara



Arabic is in ‘base ten’ counting
system




Fulfulde:

go’o

É—idi

tati

nayi

joyi

joygo’o

joydidi

joytati

joynayi

sappo



Fulfulde is in ‘base five’
counting system




Zarma:

aho

ahinka

ahinza

itaki

igu

iddu

iyye

ahakka

yagga

iwai



Zarma is in ‘base ten’ counting
system


Nigerian Languages
Numerals:

1

2

3

4

5

6

7

8

9

10

Yoruba:

okan/eni

eji

Ã«ta

Ã©rin

Ã¡run

Ã©fÃ¡

Ã©je

Ã©jo

Ã©san

ewa


Yoruba operates in ‘base ten’
counting system













Igbo:

otu

abuo

Ã¡tÃ³

ano

ise

isii

asaa

asato

itolu

Ã¡ri


Igbo operates in the ‘base ten’
counting system













Nupe:

inni

gubÃ¡

guta

guni

gutsun

gutwayin

gutwaba

gutwota

gutwaani

gÃºwo


Nupe operates in a ‘base five’
counting system

It
is to be noted here that, in African languages, Arabic is ‘base ten’ and
Fulfulde ‘base five’. In Nigerian languages, Yoruba and Igbo are ‘base ten’
respectively, while Nupe is ‘base five’. This is only to show that whatever
base a language may operate on, the least in base in world languages is ‘base
five’. Native speakers are able to confront all the Mathematical operations
within the limits of their numerals.
The Root of Hausa Counting System
In
human history, numerals and numbers have a common root of origin. In some
African and Asian languages, the root is from days of the week, months,
seasons, etc. The Hausa method, as per the research under review, noted it
originated from either of the following:
 Fingers and toes: Traditional Hausa people uses fingers from right to left hand (as the case may be) to count. As it uses ‘base 10’, if the counting terminates at 10, the two arms would be held together to translate ‘10’. In the case of ‘20’the hands would be clapped twice, likewise ‘30’ up to ‘100’. However, in some cases, the use of fingers stops at ‘20’, referring twenty fingers of a normal person. In this view, the sign of ‘20’ is to clap the hand one time and beat the toes at once – instantly indicating twenty. Finger pointer is also another ‘finger method’ of Hausa counting.
 Drawing/writing: In ancient Hausa culture, counting is represented by drawing lines on the ground/sand or putting dots equal to the numbers. The following were noted from the traditional counting system in Hausa markets and during family deliberations:
Numerals

1

2

3

4

5

6

7

8

9

10

Drawing

‘B

‘B’B

‘B’B’B

‘B’B’B’B

‘B’B’B’B’B

‘B’B’B’B’B’B

‘B’B’B’B’B’B’B

‘B’B’B’B’B’B’B’B

‘B’B’B’B’B’B’B’B’B

‘B’B’B’B’B’B’B’B’B’B


This is the counting method used
in Hausa facial marks as in the facial marks of Gobirawa, Kabawa, Katsinawa,
Zamfarawa, Arawa, Gubawa, etc.


Numerals

1

2

3

4

5

6

7

8

9

10

Dots

.

..

...

..
..

.
..
..

...
...

.
..
..
..

....
....

.
....
....

.....
.....

 Body parts/organs: In counting system, all the world languages benefitted from the very popular and visible organs of human body for their counting base. Thus, ‘base 3’ might have originated from the three parts of human body; head, chest, and legs. ‘Base 5’ might have originated from the five fingers. ‘Base 7’ might have originated from the seven major organs of the body; eyes (2), nose (2), mouth (1), ears (2), thus making ‘7’. ‘Base 10’ might have originated from the fingers of the two arms. ‘Base 20’ might have originated from the twenty fingers. The philosophy behind these base methods of counting system indicates that, number system can be best understood by pupils if it involves what they know well; what they can see and touch. Therefore, culture is the most sensitive ingredient to be comprehended by students in addressing Arithmetic and Mathematics at all levels of learning.
Hausa Numerals
Hausa,
like many European, Asian and African languages, operates in ‘base ten’, with
different style to some specific numerals, from twenty and above. The counting
reads:
Hausa:

1

2

3

4

5

6

7

8

9

10


d'aya

biyu

uku

hud'u

biyar

shida

bakwai

takwas

tara

goma

EthnoMathematics of Numerals ‘10’ and above
The
counting system from ‘11’ changes with additional ‘sha’ before the next unit.
The ‘sha’ stands for ‘swallow’. In this view, ‘10’ is to be repeated in
counting up to ‘19’ as in:
11

12

13

14

15

16

17

18

19

20

goma sha É—aya

goma sha biyu

goma sha uku

goma sha huÉ—u

goma sha biyar

goma sha shida

goma sha bakwai

goma sha takwas

goma sha tara

ashirin

In
the above counting, ‘ten’ will be swallowing units up to ‘19’. However, in
advanced counting, repeating the word ‘goma’ which represents the ‘tenth’ is
not necessary and therefore, sum it up with ‘sha’, as in:
11

12

13

14

15

16

17

18

19

20

sha É—aya

sha biyu

sha uku

sha huÉ—u

sha biyar

sha shida

sha bakwai

sha takwas

sha tara

ashirin

However,
the use of ‘sha’ terminates at ‘19’. From ‘20’ and above, ‘da’ is to substitute
‘sha’ up to trillion. In this respect, we have:
21

22

23

24

25

… … …

29

30

ashirin
da
É—aya

ashirin
da
biyu

ashirin
da
uku

ashirin
da
huÉ—u

ashirin
da
biyar

ashirin
da
tara

talatin

It
is important to note that, once ‘20’, ‘30’, ‘40’, ‘50’ … are mentioned at the
beginning, naming ‘20’, ‘30’, ‘40’, ‘50’ … ‘90’ as tenth can be dropped and the
use of ‘da’ to take over. It is Mathematically assumed by the Hausa native
speakers once ‘da’ is employed, the counting must be above ‘20’, ‘30’, ‘40’,
‘50’ …. Therefore, if the counting starts, it can take the following style:
20

21

22

23

… …

29

30

31

32

… …

ashirin

da
É—aya

da
biyu

da
uku

da
tara

talatin

da
É—aya

da
biyu

Special Case of Counting from ‘20’ and Alike
The
classical Hausa name for ‘20’ is ‘gomiyya biyu’, meaning ‘two tens’ which gives
‘20’. Thus:
20

30

40

50

60

70

80

90

gomiyya biyu

gomiyya uku

gomiyya huÉ—u

gomiyya biyar

gomiyya shida

gomiyya bakwai

gomiyya takwas

gomiyya tara

However,
with the influence of Arabic and Islam in Hausa counting system, the ‘gomiyya’
style of counting was abandoned and Arabic style was adopted in counting.
Arabic style seems to be economical in space and time:
20

30

40

50

60

70

80

90

ashirin

talatin

arba’in

hamsin

sittin

saba’in

tamanin

tisi’in

Counting in 100s and 1000s
The
Arabic style of counting terminates at ‘90’. Hence, ‘É—ari’ (100) is a
classical Hausa name for ‘hundred’. In addition, ‘dubu’ (1000) is also a
Hausa name for the value of ‘thousand’. However, in counting hundreds, the use
of ‘da’ is employed in the following respect:
101

102

103

……

200

201

202

……

1000

1001

1002

……

É—ari
da
É—aya

É—ari
da
biyu

É—ari
da
uku

É—ari
biyu

É—ari biyu
da
É—aya

É—ari biyu
da
É—aya

dubu

dubu É—aya
da
É—aya

dubu
É—aya
da biyu

The Use of ‘ba’ and ‘babu’ in Hausa Counting System
Certain
special cases in Hausa counting system employ the use of ‘ba’ and ‘babu’
specifically in respect of numbers with less than ‘1’ and ‘2’ to become
‘tenths’. For instance, in counting 18 and 19, 28 and 29, 38 and 39, 48 and 49,
58 and 59 … 98 and 99. The special counting system reads:
ordinary counting

numerals

special counting


goma sha takwas

18

ashirin biyu babu

ashirin ba biyu

sha tara

19

ashirin É—aya babu

ashirin ba É—aya

ashirin da takwas

28

talatin biyu babu

talatin ba biyu

da tara

29

talatin É—aya babu

talatin ba É—aya

talatin da takwas

38

arba’in biyu babu

arba’in ba biyu

da tara

39

arba’in É—aya babu

arba’in ba É—aya

arba’in da takwas

48

hamsin biyu babu

hamsin ba biyu

da tara

49

hamsin É—aya babu

hamsin ba É—aya

hamsin da takwas

58

sittin biyu babu

sittin ba biyu

da tara

59

sittin É—aya babu

sittin ba É—aya

sittin da takwas

68

saba’in biyu babu

saba’in ba biyu

da tara

69

saba’in É—aya babu

saba’in ba É—aya

saba’in da takwas

78

tamanin biyu babu

tamanin ba biyu

da tara

79

tamanin É—aya babu

tamanin ba É—aya

tamanin da takwas

88

tisi’in biyu babu

tisi’in ba biyu

da tara

89

tisi’in É—aya babu

tisi’in ba É—aya

tisi’in da takwas

98

É—ari biyu babu

É—ari ba biyu

da tara

99

É—ari É—aya babu

É—ari ba É—aya

Note:
The
use of ‘babu’ and ‘ba’ stops at ‘100’. In all, only ‘1’ and ‘2’ are used and no
other number(s). Therefore, in Hausa counting system, there is nothing like
‘ashirin uku babu’ or ‘ashirin ba uku’ to represent ‘17’; or ‘talatin huÉ—u
babu’ or ‘talatin ba huÉ—u’ to represent ‘26’. The use of ‘gaira’ is very common
among elites with Arabic background. It is not very popular in Hausa counting
style.
Symbolic Features of Numbers
The
written Hausa numbers from ‘110’ are named by their features for the pupils to
recognize their physical appearance and comprehend the meaning easily. Below
are some of the proposals made earlier and my moderations to that effect:
Numerals

Old names

Proposed names

1

Sil

Sanda

2

Lauje

Lauje

3

Kafar hanci

Duwatsun murhu

4

Tsayuwa bisa qafa É—aya

Barandami

5

Babban lauje

Ankwa

6

Nuniyar sama

Æ˜oshiya

7

Kwanciyar magirbi

Æ˜ota

8

Tukunyar dambu

Mari

9

Nuniyar qasa

Æ˜ulli

10

Sil da zagaye

Kwari da kyarmo

In
view of my proposals, the numbers can be recited in the following stanzas:
Symbolism (Kamantau)
ÆŠaya
– sanda ta gargaÉ—i
One, a warning stick
Biyu
– laujen yankan haki Two, a
sickle for cutting grass
Uku
– duwatsun murhu
Three, cooking pot
stones
HuÉ—u
– babban barandami Four, a very big
cutlass
Biyar
– mu ce mata ankwa Five, a police
handcuff
Shida
– muna da Æ™oshiya Six,
is a wooden handle
Bakwai
– ku ce mata Æ™ota Seven, a
handle of implement
Takwas
– marin É—aure Æ™afa Eight, a shackle for
legs
Tara
– qullin bugun maza Nine, a
clinched fist
Goma
– kwari mai kyarmo Ten, bow and arrow
Number System (Qirgau)
ÆŠaya
– manunin hannu
One, the pointing finger
Biyu
– idanun
kallo
Two, the looking eyes
Uku
– kason jikin mutum
Three, portions of human body
HuÉ—u
– qafafun
dabba
Four, the animal legs
Biyar
– na yatsun hannu
Five, the five fingers
Shida
– na yatsun
cindo Six,
for the extra finger
Bakwai
– na ramunan jiki Seven, for
the seven holes in the body
Takwas
– gavovin fuska
Eight, the major organs on the face
Tara
– gurabun
gashi
Nine, locations of hair
Goma
– jimillar
yatsu
Ten, the total of hands’ fingers
In
the counting system of many world languages, the numbers are mostly derived
from fingers and sensitive visible organs of the human body. In addition,
numbers reduced into writing are named after very common materials close to
children in the house, specifically in the kitchen or bedroom. In this respect,
the symbolic features may be named kamantau (symbolism) and the number
counting of human parts can be codenamed as qirgau. With this
development, pupils would develop an intelligent view of Hausa numbers and at
least a child is provided with basic principles to memorize them carefully and
recognize its physical appearance, which would assist them in reducing each
number into writing without much difficulty.
Numbers in Hausa Mathematical Operation
Having
gone through the Hausa counting in brief, it is clear that Hausa uses ‘base 10’
counting system. In operating the numbers, traditional method of counting
bundles of grain or herd of sheep are employed. In Hausa Bukin Dubu da
Tambarci “the farming ceremony for counting bundles of millet/corn/late
millet or herd of sheep”. The counting method is divided into four, namely:
Counting method

1

10

100

1000

Hausa

Gidan ÆŠaya

Gidan Goma

Gidan ÆŠari

Gidan Dubu

English

Units

Tens

Hundreds

Thousands

In
the Arithmetic of these numbers, as it used to be in ‘tarken goro’
(kolanut counting) and ‘bukin dubu’ ceremony, ‘units’ are the ‘kulkin
bugu’ (operational figure/number). As usual, ‘units’ are the combination of
even and odd numbers, as we noted 5even and 5odd numbers. The numbers in
‘units’, ‘tens’, ‘hundreds’ and ‘thousands’ are all even numbers. In Hausa
Mathematical operation, ‘units’ are the base ‘turke’ hence; Hausa
counting terminates at one thousand. Let us have a look at the following
examples:
gidan É—aya

gidan goma

gidan É—ari

gidan dubu

dubu dubu

units

tens

hundreds

thousands


biyu

ashirin

É—ari biyu

dubu biyu

dubu dubu biyu

2

20

200

2,000

2,000,000






uku

talatin

É—ari uku

dubu uku

dubu dubu uku

3

30

300

3,000

3,000,000






huÉ—u

araba’in

É—ari huÉ—u

dubu huÉ—u

dubu dubu gida dubu

4

40

400

4,000

1,000,000×1,000 = 1,000,000,000

If
Hausa counting reaches million ‘dubu dubu’ (1,000×1,000=1,000,000) it continues
to ‘dubu dubu dubu’ (1,000,000×1,000,000=1,000,000,000,000) that is trillion,
which I assumed is what is called ‘dubu malaliyar qasa’ (not very much popular)
but it reflects the Hausa proverb which says: ‘Sani ya fi qasa yawa’
(Knowledge is as broad as sand).
Hausa Perception of 'even' and 'odd' Numbers
In
Hausa ethnoMathematics, 'even' numbers are named 'cika' while 'odd' numbers
are 'mara'. 'Cika' in Hausa indicates that, the said number is
complete. What makes it complete is that, if it is divided into two (2) the
result would give a complete two numbers. In contrast, 'odd' numbers are always
odd in counting and hence known as 'mara' incomplete. Any number that
cannot be divided by two (2) completely is assumed to be 'odd' and hence called
'mara' (incomplete). In this argument, Hausa numbers are divided into
two broad categories:
Even
numbers (cika): 2 4 6 8 10
Odd
numbers (mara): 1 3 5 7 9
If
this is properly addressed into the minds of pupils, it can be further
developed into the following poem:
Even
Numbers (cika)
Abin
da ke zama
cika
What is called even
A
tabbatar da ya
cika
Make sure it is complete
Babu
ragowa ga
guda
Nothing should remain behind
A
lisafa shi
bibbiyu
Count all in twos
Har
qarshensa bidabi
Follow it in twos up to the end
Biyu
ka fita a
ko’ina
Group them in twos all over
Kwatankwacin
biyu da huÉ—u
Example is numbers two and four
Walau
a ce shida da takwas
It can be six and eight
Da
goma an gama
magana
Ten is the largest in decimal
Odd
Numbers (mara)
A
lura zancen
mara
Look at the issue of odd numbers
Biyu
ka shiga ta yi
saura
Two will divide it and leave a remainder
Idan
ka ware
bibbiyu
If you group them in twos
ÆŠaya ka rago cikin
biyu
One will always remain behind two
Ka
xauki uku ko biyar
Take example of three or five
Gidan
bakwai, gidan tara
In the affairs of unit seven and nine
Da
ka kasa su
bibbiyu
If you divide them into twos
ÆŠaya ka rago a
ko’ina
One will always remain behind
Fraction (Æ˜ire)
The
Hausa counting system recognizes fraction and it is named ‘Æ™ire’. The
word ‘Æ™ire’ refers to a very small part of a whole number. In Hausa
counting system, the technical meaning of fraction is ‘kashi’ and any
number can be subdivided into ‘kashi’ unit. Hausa fraction can be
divided into the following:
Fractions


Hausa names

rabi

gutsure

rabin rabi

fataka

tsito

hinci

laÆ™Æ™wace

tsirit

qiris



English names

half

one third

one fourth

one fifth

one sixth

one seventh

one eighth

one ninth

one tenth



Arabic names

nusifi

sulusi

rubu’i

humusi

sudusi

subi’i

thumuni

tusi’i

ushiri

I
proposed the adoption of traditional fraction system to add more weight to the
cultural impact in the Arithmetic. It should be noted that, numbers from
to
have been proposed by this research using intuition.
Arithmetical Operation
The
five arithmetic operations are well used in Hausa literature. These are:
Mathematical sign

English

Hausa

×

Multiplication

‘sau’ originated from ‘sawu’

+

Addition

‘tarawa’ originated from ‘haÉ—a’
(to join or mix)

−

Subtraction

‘É—ebewa’ originated from ‘É—ebe’(remove)

Division

‘rabawa’ originated from ‘raba’
(grouping)

Arithmetic Significance of ‘Cika’ and ‘Mara’
in Hausa
In
Hausa Arithmetical ideas, understanding the concept of ‘even’ and ‘odd’ numbers
(cika and mara) is more advanced in Mathematics for those who
wish to know more about counting system. In the study of ‘cika’ and ‘mara’,
unit number ‘2’ is the yardstick in the operation. Thus, unit number ‘2’ is
named ‘kulkin bugu’ (operational figure). This opinion is viewed in
three stages:
Stage One: Identification (Lura)
Odd
(mara) all the five units in ‘mara’ that is 1, 3, 5, 7, and 9
with exception of ‘1’, if divided by ‘2’, ‘mara’ of ‘1’ unit number will
remain. That is why unit ‘1’is the opening and closing in the numerals of ‘mara’.
Even
(cika) the five figures of ‘cika’, 2, 4, 6, 8 and 10, unit number
‘2’ will enter into any of the ‘cika’ numbers without any remainder.
Stage Two: Analysis
Characteristics
of Odd Numbers (Xabi’un Mara)
As
for odd numbers (mara), there are six observations in their analysis:
 Each unit multiplied by itself will give a product of odd number, i.e. 1×1=1, 3×3=9, 5×5=25, 7×7=49, 9×9=81.
 All odd numbers multiplied by consecutive odd terms will give odd numbers. Examples; 3×5=15, 5×7=35, 7×9=63.
 If we add up all the odd numbers together, the result will give an odd number. Example; 1+3+5+7+9=25.
 If an odd number is multiplied by 25, (the grand total of all odd unit numbers) the result will give an odd number. Example; 1×25=25, 3×25=75, 5×25=125, 7×25=175, 9×25=225.
 Any odd number added to an even number will give an odd number. Example; 1+2=3, 3+2=5, 5+4=9, 7+6=13.
Characteristics
of Even Numbers (Xabi’un Cika)
In
the case of even numbers (cika), it is observed that:
 Any even number multiplied by itself will give an even number. Example; 2×2=4, 4×4=16, 6×6=36, 8×8=64.
 Any even number multiplied by its consecutive even number will give an even number. Example; 2×4=8, 4×6=24, 6×8=48, 8×10=80.
 If we add all the even numbers together, the result will be an even number. Example; 2+4+6+8+10=30.
 Any of the even numbers multiplied by 30 (the grand total of all even numbers between 2 to 10) will give even number. Example; 2×30=60, 4×30=120, 6×30=180, 8×30=240, 10×30=300.
These
two stages of Mathematical analysis of odd and even numbers is what is known as
laluben ‘canjaras’ or ‘tangam’ in Hausa counting. This is the
reason behind Hausa figure of speech that says: “Lisafi ba ya ci”
(counting always gives accurate result).
The Origin of Zero
The
use of ‘sifili’ to represent zero in Hausa counting system is an
adaptation from Arabic language, ‘sifir’. The nearest Hausa word to that
is ‘babu/banza/fanko’. In Hausa counting, there is no
place for the zero. However, in writing numbers and numbers for Mathematical
operations, zero is an important segment. In Hausa games of ‘Aboki na bakin
kogi’ and ‘Allah kai ni gidan akwai’, zero is named ‘banza’
or ‘gidan babu’. It is okay to retain name ‘zero’ as English adaptation,
but it is more appropriate to adapt ‘babu’ the classical Hausa name in
place.
Research Findings
This
is a tentative look at the possibility of using our indigenous languages in
teaching sciences with particular emphasis on Mathematics, the ‘mother’ of
scientific development. The paper is more of a review of our previous
Mathematical knowledge in the precolonial period. The research consequently
recognizes the following important issues:
 Hausa counting system is in ‘base 10’ which is very popular across languages of the world. There is nothing difficult in Hausanizing Mathematics at all levels of learning. The most popular developed languages in the world; English, French, German, Arabic, Japanese Russian, etc. are all in ‘base 10’ counting system. Mathematics is being taught in these languages successfully. Equally, Hausa has all the Mathematical operations to handle the teaching of Mathematical units efficiently.
 The Mathematical ideas in Hausa culture and folklore are the basic Mathematical methods to be employed in teaching Hausa pupils and advanced learners Mathematics in the Hausa language. These methods have been tested and found to be very effective, Abbas (2001:97106).
 This paper is only a review of the previous efforts of Hausa scholars dealing with the subject of Mathematics in which terminologies and techniques were mostly translated into Hausa by early Hausa scholars and teachers Jinju (1990). Therefore, the proposal of going back to the drawing board in handling science courses in our native languages as a viable project is long overdue for implementation. It is high time to respect the proposal considering the massive failure in Mathematics examination at all levels of learning in our schools and colleges.
 Mathematics is not a difficult subject at all; the method and the language applied in teaching the subject and dispensing the knowledge in the subject are the problems. The methods are far from the cultural background of the learners; and the language is strange and difficult to comprehend the meaning by the learners. Consequently, the learners are always at the receiving end, faced with three obstacles; learning the Mathematical culture, learning the foreign language and the subject in question at the same time. What a hell of learning burden indeed!
Recommendations
To
understand the question is some way into finding the answer, the research
findings recognize ‘language’ as the main obstacle in teaching Mathematics. In
this respect, the following solutions are recommended:
 There is need for an emergency workshop to address Mathematical formulas and theories in Hausa language to enable teachers of Mathematics to employ the appropriate methods. The workshop can be divided into two: Hausa teachers to know or to have an idea of Mathematical problems, formulas, operations etc. The second workshop should concentrate on developing in teachers of Mathematics the technical knowledge of Hausa Mathematical terminologies.
 An inhouse arrangement or joint effort between the teachers of Mathematics and Hausa to translate a good book of basic Mathematics into Hausa, preferably one published by Mathematical Association of Nigeria (MAN).
 To have demonstration classes at primary, secondary and tertiary levels of education in which Mathematics would be taught in Hausa purely. I suggest the project should begin with students preparing for the 2018 SSCE (NECO and WAEC). If possible, the teaching should be conducted bilingually (English and Hausa) for a start.
 The research strongly recommends the introduction of courses in Mathematics and ethnoMathematics in all Departments of Nigerian Languages in Universities and Colleges of Education. This must be done with minimum delay.
Conclusion
The
most serious side effect of colonial education in Africa and beyond is the
linguistic imperialism, which is the ‘mother’ of language endangerment and
extinction. Denying our children the rights to be educated in our indigenous
languages is equally denying them the right to the education they deserved to
have. Mathemaphobia thrown into the minds of our children and students at
advanced levels is artificial; it was intentionally done to deprive our
children access to the basic science instruments in science education. Rapid
development and the achievement of science and technology in India, China,
Japan, Egypt, Iran, Saudi Arabia, Qatar, Poland, Russia, and in the socalled
western powers is not a magic, but a linguistic revolution in the advancement
of education. It is very sad to note that, for more than a century of colonial
education in colonial language in our country ‘Nigeria’, our only achievement
is that, we are able to produce pencil in the year 2017. Factor behind the
snailspeed in our development is ‘language’. This was the observation of UN,
AU, UNESCO and ISESSCO in assessing African development. It was based on this
observation that UN introduced RANA programme in the West and East Africa,
which Nigeria happens to be among the beneficiaries. With RANA programme, Hausa
language has all the opportunities to dismiss English language from the
teaching of Mathematics and related science subjects in our school curriculum.
My prayer is, the Federal University, Gusau should be the first amongst the
Nigerian Universities to initiate this credible, though daunting task, with all
the resources at its disposal.
BIBLIOGRAPHY
Allah yaja zamanin Prof
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