Mathematical Heritage In Hausa Number System: (A Proposal for TeachingMathematics using Nigerian Languages)

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By

Aliyu Muhammad Bunza,

Professor of African Culture (Hausa),

Department of Languages and Cultures,

Faculty of Humanities and Education,

Federal University, Gusau.

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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 sub-Saharan 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 ethno-Mathematics 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 “mathema-phobia” in the minds of our pupils.

Methodology

This research is a proposal at a cross-disciplinary 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, problem-solving 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 overload-ship. 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 socio-cultural 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 base-ten 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, well-treated 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

fūnf

sechs

sieben

açht

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 present-day 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 trans-adapt  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	ɗidi	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	ëta	érin	árun	éfá	éje	éjo	ésan	ewa
	Yoruba operates in ‘base ten’ counting system
Igbo:	otu	abuo	átó	ano	ise	isii	asaa	asato	itolu	ári
	Igbo operates in the ‘base ten’ counting system
Nupe:	inni	gubá	guta	guni	gutsun	gutwayin	gutwaba	gutwota	gutwaani	gúwo
	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:

1. 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.

2. 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	.	..	...	.. ..	. .. ..	... ...	. .. .. ..	.... ....	. .... ....	..... .....

1. 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

Ethno-Mathematics 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 ɗaya	goma sha biyu	goma sha uku	goma sha huɗu	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 ɗaya	sha biyu	sha uku	sha huɗu	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 ɗaya	ashirin da biyu	ashirin da uku	ashirin da huɗu	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 ɗaya	da biyu	da uku		da tara	talatin	da ɗaya	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 huɗu	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, ‘ɗari’ (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	……
ɗari da ɗaya	ɗari da biyu	ɗari da uku		ɗari biyu	ɗari biyu da ɗaya	ɗari biyu da ɗaya		dubu	dubu ɗaya da ɗaya	dubu ɗaya 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 ɗaya babu	ashirin ba ɗaya
ashirin da takwas	28	talatin biyu babu	talatin ba biyu
da tara	29	talatin ɗaya babu	talatin ba ɗaya
talatin da takwas	38	arba’in biyu babu	arba’in ba biyu
da tara	39	arba’in ɗaya babu	arba’in ba ɗaya
arba’in da takwas	48	hamsin biyu babu	hamsin ba biyu
da tara	49	hamsin ɗaya babu	hamsin ba ɗaya
hamsin da takwas	58	sittin biyu babu	sittin ba biyu
da tara	59	sittin ɗaya babu	sittin ba ɗaya
sittin da takwas	68	saba’in biyu babu	saba’in ba biyu
da tara	69	saba’in ɗaya babu	saba’in ba ɗaya
saba’in da takwas	78	tamanin biyu babu	tamanin ba biyu
da tara	79	tamanin ɗaya babu	tamanin ba ɗaya
tamanin da takwas	88	tisi’in biyu babu	tisi’in ba biyu
da tara	89	tisi’in ɗaya babu	tisi’in ba ɗaya
tisi’in da takwas	98	ɗari biyu babu	ɗari ba biyu
da tara	99	ɗari ɗaya babu	ɗari ba ɗaya

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 huɗu babu’ or ‘talatin ba huɗu’ 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 ‘1-10’ 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 ɗaya	Barandami
5	Babban lauje	Ankwa
6	Nuniyar sama	Ƙoshiya
7	Kwanciyar magirbi	Ƙota
8	Tukunyar dambu	Mari
9	Nuniyar qasa	Ƙulli
10	Sil da zagaye	Kwari da kyarmo

In view of my proposals, the numbers can be recited in the following stanzas:

Symbolism (Kamantau)

Ɗaya – sanda ta gargaɗi            One, a warning stick

Biyu – laujen yankan haki         Two, a sickle for cutting grass

Uku – duwatsun murhu             Three, cooking pot stones

Huɗu – babban barandami        Four, a very big cutlass

Biyar – mu ce mata ankwa        Five, a police handcuff

Shida – muna da ƙoshiya           Six, is a wooden handle

Bakwai – ku ce mata ƙota         Seven, a handle of implement

Takwas – marin ɗaure ƙafa       Eight, a shackle for legs

Tara – qullin bugun maza         Nine, a clinched fist

Goma – kwari mai kyarmo       Ten, bow and arrow

Number System (Qirgau)

Ɗaya – manunin hannu             One, the pointing finger

Biyu – idanun kallo                  Two, the looking eyes

Uku – kason jikin mutum           Three, portions of human body

Huɗu – 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 code-named 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 Ɗaya	Gidan Goma	Gidan Ɗari	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 5-even and 5-odd 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 ɗaya	gidan goma	gidan ɗari	gidan dubu	dubu dubu
units	tens	hundreds	thousands
biyu	ashirin	ɗari biyu	dubu biyu	dubu dubu biyu
2	20	200	2,000	2,000,000
uku	talatin	ɗari uku	dubu uku	dubu dubu uku
3	30	300	3,000	3,000,000
huɗu	araba’in	ɗari huɗu	dubu huɗu	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 ethno-Mathematics, '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 bi-da-bi                                 Follow it in twos up to the end

Biyu ka fita a ko’ina                                    Group them in twos all over

Kwatankwacin biyu da huɗu                        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

Ɗaya 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

Ɗaya ka rago a ko’ina                        One will always remain behind

Fraction (Ƙire)

The Hausa counting system recognizes fraction and it is named ‘ƙire’. The word ‘ƙire’ 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 sub-divided into ‘kashi’ unit. Hausa fraction can be divided into the following:

Fractions
Hausa names	rabi	gutsure	rabin rabi	fataka	tsito	hinci	laƙƙwace	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 ‘haɗa’ (to join or mix)
−	Subtraction	‘ɗebewa’ originated from ‘ɗebe’(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:

81. 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.

82. All odd numbers multiplied by consecutive odd terms will give odd numbers. Examples; 3×5=15, 5×7=35, 7×9=63.

83. If we add up all the odd numbers together, the result will give an odd number. Example; 1+3+5+7+9=25.

84. 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.

85. 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:

64. Any even number multiplied by itself will give an even number. Example; 2×2=4, 4×4=16, 6×6=36, 8×8=64.

65. 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.

66. If we add all the even numbers together, the result will be an even number. Example; 2+4+6+8+10=30.

67. 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 pre-colonial period. The research consequently recognizes the following important issues:

1. 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.

2. 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 (2001:97-106).

3. 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.

4. 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:

1. 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.

2. An in-house 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).

3. 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.

4. The research strongly recommends the introduction of courses in Mathematics and ethno-Mathematics 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. Mathema-phobia 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 so-called 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 snail-speed 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.

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