Hausa Language Academic Website

Thursday, 14 June 2018

Mathematical Heritage In Hausa Number System: (A Proposal for Teaching Mathematics 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.


 

Being a paper presented at the University Seminar Series, organized by the University Research Center, Federal University Gusau, on 17th January 2018, under the distinguished Chairmanship of Professor Magaji Garba, the Vice Chancellor, Federal University Gusau, at the ICT Twin Theatre 1, 11:00am.


 

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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 ethno-Mathematics  in Hausa cultural perspectives. The findings suggest that, teaching Mathematics in 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.

 

 

 

 

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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 meaningCultural 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 neAll 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:123456789101112
English:onetwothreefourfivesixseveneightnineteneleventwelve
French:undeuxtroisquatrecingsixsepthuitnenfdixonzedouze
German:einszweidreivierfūnfsechssiebenaçhtneuenzehneifzwolf

 

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:12345678910
Arabic:wahidisnainisalasaarba’ahamsasittasaba’atamaniyatis’aashara
 Arabic is in ‘base ten’ counting system
 
Fulfulde:go’oXixitatinayijoyijoygo’ojoyxixijoytatijoynayisappo
 Fulfulde is in ‘base five’ counting system
 
Zarma:ahoahinkaahinzaitakiiguidduiyyeahakkayaggaiwai
 Zarma is in ‘base ten’ counting system

 

 

 

Nigerian Languages































































































Numerals:12345678910
Yoruba:okan/eniejiëtaérinárunéfáéjeéjoésanewa
 Yoruba operates in ‘base ten’ counting system
           
Igbo:otuabuoátóanoiseisiiasaaasatoitoluári
 Igbo operates in the ‘base ten’ counting system
           
Nupe:innigubágutagunigutsungutwayingutwabagutwotagutwaanigúwo
 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:


 



























































Numerals12345678910
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.
Numerals12345678910
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:12345678910
 d'ayabiyuukuhud'ubiyarshidabakwaitakwastaragoma

 

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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
121314151617181920
goma sha xayagoma sha biyugoma sha ukugoma sha huxugoma sha biyargoma sha shidagoma sha bakwaigoma sha takwasgoma sha taraashirin

 

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:



























11121314151617181920
sha xayasha biyusha ukusha huxusha biyarsha shidasha bakwaisha takwassha taraashirin

 

 

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:

 






















2122232425… … …2930
ashirin

da

xaya
ashirin

da

biyu
ashirin

da

uku
ashirin

da

huxu
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:

























20212223… …29303132… …
ashirinda

xaya
da

biyu
da

uku
da

tara
talatinda

xaya
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:

 























2030405060708090
gomiyya biyugomiyya ukugomiyya huxugomiyya biyargomiyya shidagomiyya bakwaigomiyya takwasgomiyya 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:

 























2030405060708090
ashirintalatinarba’inhamsinsittinsaba’intamanintisi’in

 

Counting in 100s and 1000s


The Arabic style of counting terminates at ‘90’. Hence, ‘xari’ (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:




























101102103……200201202……100010011002……
xari

da

xaya
xari

da

biyu
xari

da

uku
xari

biyu
xari biyu

da

xaya
xari biyu

da

xaya
dubudubu xaya

da

xaya
dubu

xaya

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 countingnumeralsspecial counting
goma sha takwas18ashirin biyu babuashirin ba biyu
sha tara19ashirin xaya babuashirin ba xaya
ashirin da takwas28talatin biyu babutalatin ba biyu
da tara29talatin xaya babutalatin ba xaya
talatin da takwas38arba’in biyu babuarba’in ba biyu
da tara39arba’in xaya babuarba’in ba xaya
arba’in da takwas48hamsin biyu babuhamsin ba biyu
da tara49hamsin xaya babuhamsin ba xaya
hamsin da takwas58sittin biyu babusittin ba biyu
da tara59sittin xaya babusittin ba xaya
sittin da takwas68saba’in biyu babusaba’in ba biyu
da tara69saba’in xaya babusaba’in ba xaya
saba’in da takwas78tamanin biyu babutamanin ba biyu
da tara79tamanin xaya babutamanin ba xaya
tamanin da takwas88tisi’in biyu babutisi’in ba biyu
da tara89tisi’in xaya babutisi’in ba xaya
tisi’in da takwas98xari biyu babuxari ba biyu
da tara99xari xaya babuxari ba xaya

 

 

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 huxu babu’ or ‘talatin ba huxu’ 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:


























































NumeralsOld namesProposed names
1SilSanda
2LaujeLauje
3Kafar hanciDuwatsun murhu
4Tsayuwa bisa qafa xayaBarandami
5Babban laujeAnkwa
6Nuniyar samaQoshiya
7Kwanciyar magirbiQota
8Tukunyar dambuMari
9Nuniyar qasaQulli
10Sil da zagayeKwari da kyarmo

 

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

 

 

Symbolism (Kamantau)


Xaya – sanda ta gargaxi            One, a warning stick

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

Uku – duwatsun murhu             Three, cooking pot stones

Huxu – babban barandami        Four, a very big cutlass

Biyar – mu ce mata ankwa        Five, a police handcuff

Shida – muna da qoshiya           Six, is a wooden handle

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

Takwas – marin xaure qafa       Eight, a shackle for legs

Tara – qullin bugun maza         Nine, a clinched fist

Goma – kwari mai kyarmo       Ten, bow and arrow

 

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Number System (Qirgau)


Xaya – manunin hannu             One, the pointing finger

Biyu – idanun kallo                  Two, the looking eyes

Uku – kason jikin mutum           Three, portions of human body

Huxu – 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 method1101001000
HausaGidan XayaGidan GomaGidan XariGidan Dubu
EnglishUnitsTensHundredsThousands

 

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 xayagidan gomagidan xarigidan dubudubu dubu
unitstenshundredsthousands 
biyuashirinxari biyudubu biyudubu dubu biyu
2202002,0002,000,000
     
ukutalatinxari ukudubu ukudubu dubu uku
3303003,0003,000,000
     
huxuaraba’inxari huxudubu huxudubu dubu gida dubu
4404004,0001,000,000×1,000 = 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 huxu                        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

Xaya 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

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

 

Fraction (Qire)


The Hausa counting system recognizes fraction and it is named ‘qire’. The word ‘qire’ 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 namesrabigutsurerabin rabifatakatsitohincilaqqwacetsiritqiris
 
English nameshalfone thirdone fourthone fifthone sixthone seventhone eighthone ninthone tenth
 
Arabic namesnusifisulusirubu’ihumusisudusisubi’ithumunitusi’iushiri

 

 

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.

 

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Arithmetical Operation


The five arithmetic operations are well used in Hausa literature. These are:




























Mathematical signEnglishHausa
×Multiplication‘sau’ originated from ‘sawu’
+Addition‘tarawa’ originated from ‘haxa’ (to join or mix)
Subtraction‘xebewa’ originated from ‘xebe’(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:

  1. 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.

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

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

  4. 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.

  5. 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:

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

  2. 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.

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

  4. 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.


 

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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.

BIBLIOGRAPHY


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