Structural and Curricular Practices of teaching and learning Mathematical at Tinnai Schools in Tamil Nadu (South India)

I. Introduction

The Tinnai schools were the local elementary schools or pathshalas in the state of Tamil Nadu in South India during pre-colonial and colonial times. In Southeast India, verandahs were called tinnai (tin.n.ai) or pial (Tamil: payal, from Portuguese poial, “stone bench at the entrance of a house”), hence the name tinnaippallikutam (tin.n.aippal.l.ikuˉ – t.am) or pial school.₃

Antiquity of the tinnai schools in Tamil Nadu, South India is not known. No inscription available in Tamil seems to mention the tinnai schools. Some European travel accounts in the seventeenth century have accounts of such institutions. ₆ The existence of the tinnai schools first time showed up in the Minutes on Native Education, a survey report on indigenous schools that was ordered by the British East India Company under the Governorship of Thomas Munro in 1822.

A survey conducted by Thomas Munro shows that there were 12,498 schools and 188,000 students in a population of 12,850,941 — roughly 1 school per 1000 persons and 1 student per 67 persons in the year 1823-25. Commenting on the status of education Munro said, ‘The state of education here, low as it is compared with that of our own country, is higher than it was in most European countries at a not very distant period’ _5.

(Figure 1: A Tamil Veranda School in Pondicherry in the 1930s – Credit: French Institute of Pondicherry)

II. Tinnai Schools

● About

The Tinnai schools were local elementary schools in Tamil Nadu, South India. The schools were held in front verandahs of houses that usually belonged to prominent notables or school teachers. The schools were usually run by a single teacher (typically male).

Every village or a group of villages had one tinnai school, where the children would be within walking distance of seven to eight miles.₂₁

● Core Values

The primary ethos of the tinnai schools was to get the children ready for adulthood. The fundamental aim was to enable the children to become competent/skilled participants in the transactions of letters and numbers within the local society and its networks in the region. ₁₇

● Admission

Local boys at the age of 5 from upper and middle caste groups were eligible for admission in the tinnai Schools. The children from the lower, manual labouring caste groups had, however, no access to these institutions _17. In the rare circumstances in which the children from lower caste were allowed into the schools, they were made to sit separately and taught different things. ₃

The period of instruction would vary between seven to eight years. This is not an accurate figure, for variations in different areas of South India could be seen in the British surveys of tinnai schools. ₈

● Fees

There was no rigid fee structure. Fees varied from school to school and village to village.

Families of the children paid straight to the teacher, in cash and in kind, on a periodic basis. The teacher was paid on specific occasions of religious significance and during particular stages of progress made in the curriculum. ₃ Free labour on the agricultural land of the teacher is also noted as a kind of payment.₂₁

● Faculty

In the past, tinnai teachers included pānchāngis (Brahmans who knew the almanac and determined the auspicious times to commence rituals and events), pantārams (non-Brahman priests), the ubiquitous kanakkan, and purānic reciters (usually textual reciters of long epic poems). By the first quarter of the nineteenth century, tinnai teachers included scribes and accountants who could not get clerical jobs in Company offices, as well as converts educated by Protestant missionaries. ₃

● School Council

There was no formal governing body that was responsible for the day-to-day functioning of the schools. However, the community actively participated or gave input to what was taught depending on the societal needs at the local level.

● Class Structure

A unique feature of the classes was that children were grouped according to their level of understanding of language and mathematics and not age. Classes did not have a minimum or maximum number of students.

The teacher would appoint a brighter senior student from the class as a monitor. The senior student, called the cattampillai, would receive direct instruction from the teacher, and instruct batches of other children in the daily routine, occasionally supervised by the teacher himself.₁₇

● Curriculum

The curriculum adopted by the tinnai schools was not standardized. The teacher and the community customized the content for societal needs and for personalized learning within the broader framework.

The curriculum blended language and number learning together using pedagogic strategies rooted in memory as a modality of learning. ₁₇

The usual curriculum was Tamil alphabets and elementary language lessons, Tamil numerals and tables, elementary Tamil grammar, Tamil calendar, Tamil dictionaries, ballads, moral lessons, forms of letter writing, and elementary bookkeeping related to agricultural and commercial accounts. ₂₂

• Daily Routine

Extract from a Tamil book written by Tamil Thatha, Dr. U. V. Saminathayyar named, “Yen Charithiram.”

My Young Days in School
In those days, the village school was called “Thinnai Pallikoodam “. The system of learning was entirely different. All the boys have to arrive at the school at 5 A.M. itself with their palm leaf (Panai Olai) chuvadis”. All the chuvadis are connected to a wooden piece of same size attached by means of a string and tied. This is called “chuvadi thooku”. As soon as the boys arrive at the school, they have to hang their chuvadi thooku in the walls and they have to recite the lessons taught on the previous day loudly, taking turns. The teacher would be inside the house (the school) and would be listening to their recitations.
After 6 A.M., all the boys go out to finish their morning duties, bathe in the river or canal, wear their religious symbols on their forehead and chant the necessary mantras/ slokas sitting on the riverbank. Then they will carry in their clothes, sufficient quantity of clean sand and come to the school. They will remove the sand already spread on the floor on the previous day and spread the new sand in its place for writing purposes. Some will write and some will read.
At 9 A.M., they will eat the rice which they have brought along. This rice is called “Pazhayadhu”. Before eating, the teacher will give each boy a blow with his cane in his palm. This is probably to remind them that they are in school and not in their house.
The teacher will appoint one boy as “monitor”. He is normally a well-built boy who has to control the other boys. It is his duty not only to control but also listen to the recitations and note the mistakes. Some boys try to earn his good-will by giving something to eat from their homes.
After noon, the boys will go to their homes for lunch and come back at 3 P.M. The classes may extend up to 7 P.M. even.
Everyday evening, the teacher will tell each boy the name of either a flower or a bird, or an animal or a village and he has to remember the name and tell the teacher correctly the next day. This exercise is to improve the memory power of the boy.

(Figure 2: Snapshot of a typical day)

III. Curriculum framework for mathematics

For the purpose of this study the author is focused on examining the mathematics curriculum and pedagogy only.

Content

1. Ponnilākkam – Elementary number series

a. 1st Layer – Perilākkām: Series of ordinal numbers

b. 2nd Layer – Kilvāiilakkām: Series of fractions in units of 1/320

c. 3rd Layer – Cirren: Series of fractions consisting of 1/320 parts of 1/320

2. Nellilakām – Primer that dealt with volumetric or cubic measures.

3. Encuvāti – Compilation of multiplication tables

a. Multiplication tables of one, two…up to ten

b. Tables with multiplication of whole numbers with each standard fraction from the Kilvāiilakkām series

c. Tables of fractions multiplied with fractions from Kilvāiilakkām

d. Grain measures from Nellilakām multiplied by whole numbers.

e. Grain measures from Nellilakām multiplied by fractions from Kilvāiilakkām.

4. Kulimāttu – Table of Squares

5. Additional Learning

a. Varucāppirāppu

b. Kanitanul

c. Kannakkatikaram

1. Ponnilākkam – Elementary number series

Ponnilakkam, pon = gold; ilakkam = number place, in the literal sense.

The mathematics lessons in tinnai schools always started with the learning of Tamil numerals from the elementary number series called Ponnilākkam.

Steps for learning:

1. First the class monitor would pronounce the number names.
2. Students would follow him and recite the number names aloud.
3. Monitor would then introduce the graphic symbol of the number in the Tamil notation.
4. The students had to remember the association of the number names and the graphic symbols as they tried to write by themselves in sand.
5. At times, the monitor would hold their hand to help them with the writing.
6. This practice of oral repetition and writing in sand would continue till the students mastered writing each number with the name and symbol.
7. Once proficient, they would then be asked to write it on palm leaves.
8. These copies became the pages of the students’ own books.

(Figure 3: A palm leaf from Ponnilakkam showing tables in Tamil Numerical notation)

This number series had the following three layers.

a. 1^st Layer – Perilakkam: Series of Ordinal numbers

The series of all the numbers from one to ten million. Numbers 1 to 10, 100 and 1000 were represented by 12 letters, which were then used to denote all the numbers in the series.

b. 2nd Layer – Kilvāiilakkām: Series of fractions from 1/320 to one

The basic units of this series are Munitiri (1/320), kāni (1/80), and mā (1/20). Munitiri and kāni are the units of land measures, while mā is the unit of land and gold measures.

The fraction series of Muntiriāllākām starts with muntiri (1/320). The subsequent fractions in the series are obtained by adding 1/320 at each step.

After this the series continued as follows:

• onnekäl = Onru + käl (1 + ¼)
• onoāräi = Onru + arāi (1 + ½)
• onnemukkäl = Onru + mukkāl (1 + ¾)
• Onru + Onru (1+ 1 = 2)

After 2 the students continued with the Périlakkam series of whole numbers.

Other two sub-series in this series:

• käni series beginning with käni with successive additions of 1/80 till one is reached.
• mä series beginning with mä with successive additions of 1/20 till one is reached.

Standard fractions occurred in these series, which would again be represented as combinations of the fractions in addition. The idea of fractions as parts of whole — or parts of parts in a whole can be well established in this form of representation. ₁₆

To establish this aspect, there was another table, which had to be recited in a rhyming fashion:

In one, mukkäl (3/4) is three parts in four.

In one, käl (1/4) is one part in four.

In one, arai (1/2) is one part in two.

—-

—-

In one, mäkäni (1/20 + 1/80) is one part in sixteen.

—-

—-

In one, muntiri (1/320) is one part in three hundred and twenty.

—-

—-

In one, kil araikkäl (1/320 x 1/8), is one part in two thousand five hundred and sixty.

—-

—-

In one, kil muntiri (1/320 x 1/320) is one part in one lakh and two thousand four hundred.

 c. 3rd Layer – Cirren: Series of fractions from 1/320 × 1/320 to 1/320

This series also starts with Munitiri (1/320), but here the subsequent fractions in the series are obtained by multiplying with 1/320 at each step.

2. Nellilakām – Series of standard units of grain measures

nellilakkam (nel = paddy; ilakkam = number place)

This series starts with the basic unit of grain measure, the cevitu. The subsequent numbers in the series are obtained by adding cevitu at each step till the highest unit the kalam is reached.

The standard units of the grain measure, that occur on the way from cevitu to kalam are cevitu, äläkku, ulakku, uri, näli, kuruni, patakku, tüni and kalam.

3. Encuvāti: Compilation of multiplication tables

Encuvāti were so central to the life of the tinnai school rhythm that they prompted an early observer to call them “multiplication schools”₁₇

a. Multiplication Table Book 1

Multiplication tables of whole numbers from one to ten. Each table ended with a line of verse that was equal to the sum of all the products and helped as a mnemonic.

b. Multiplication Table Book 2

Multiplication tables of each standard fraction in the second series of Ponnilākkām (Kilvāiilakkām) multiplied with whole numbers from the first series of Ponnilākkām (Perilākkām)

Example: Table of muntiri

c. Multiplication Table Book 3

Multiplication tables of each standard fraction of the second series of Ponnilākkam (Kilvāiilakkām) multiplied with each other.

Example: Table for mukkāl

d. Multiplication Table Book 4

Multiplication tables of grain measures from nellilākām series multiplied with whole numbers from the first series of Ponnilākkām (Perilākkām)

Example: Table for cevitu

e. Multiplication Table Book 5

Multiplication tables of grain measures from nellilākām series multiplied with fractions from second series of Ponnilākkām (Kilvāiilakkām)

Example: Table for nali

4. Kulimāttu – Table of Squares

Kuli – a square unit for the measure of land.

There were two types of tables: large measures and small measures.

1. Perunkuli (Large measures): Table beginning with 1 and ending with the square of 32.

Students would be expected to learn the squares from 1 to 10.

• 1 x 1 = 1
• 2 x 2 = 4
• 3 x 3 = 9
• 4 x 4 = 16
• 5 x 5 = 25
• 6 x 6 = 36
• 7 x 7 = 49
• 8 x 8 = 64
• 9 x 9 = 81
• 10 x 10 =100

Typical steps were followed to find the square of whole numbers from 11 to 32.

Example: Find square of 11

Identify the number into two easily recognizable parts. Here 10 and 1

Multiplication then proceeded as a series of additions.

During the actual process of memorizing, the operation would be recited out loud, step by step.

Image for the calculation of finding the square of 17.

2. Cirukuli (Small Measures)

Table beginning with the square of

• makani (1/20 + 1/80)
• araikkal (1/8 + 1/8)
• kal (1/4)
• arai (1/2)
• mukkal (3/4)
• onnekal (1 + 1/4)
• onnarai (1 + 1/2)
• onne mukkal (1 + 3/4)
• irantekal (2 + 1/4)
• …up to ten

Example: Steps for finding square of munre mukkal,

 5. Additional Learning

a. Varucāppirāppu [Birth of a year]

In addition to memorizing all the tables discussed before, students were also required to learn the names in the list given here.

Senthil Babu in his book Mathematics and Society: Numbers and Measures in Early Modern India (p.161) puts forth a rationale behind the memorizing of this list:

“The meticulous way in which these lists appear to have been constructed, involving names, however, should not mislead us to conclude that the students were compelled to memorize more. There was a distinct possibility that each of these lists would have been an occasion for the teacher to actually teach the children about worldly affairs, spending long hours on these lists, narrating stories, interpreting the lore associated with these names.”

b. Kanita Nul

 Treatise in mathematics presented in the form of verses, using different forms of Tamil prosody.

Example 1. The following verse from Kanita Nul informs us how to find the length of the yardstick if the area is given.

(Samuel, 2005a, p. 136)

Translation:

When measured by a 12- yard stick, the area is 100 kuli (unit for area).

When the same area is measured by another stick of unknown length, the area becomes 25 kuli.

Find the length of the yard stick.

 

 

Example 2. The following verse from Kanita Nul informs us how to find the sum of squares.

1² + 2² + 3² + 4² + 5² + 6² + 7² + 8² + 9² + 10²

Translation:

1. Multiplying 10² (which is 100) by 10 we get 1000.
2. By subtracting 10 from 1000, we get 990.
3. Dividing 990 by 3, we get 330.
4. Adding the sum of numerals from 1 to 10 (which is 55) to 330, we get 385, which is the answer for the problem.

c. Kannakkatikaram

Kaṇakkatikāram denotes a genre of texts of the same kind. [Mathematics and Its images in Public]

A typical kaṇakkatikāram text had six distinct sections, classified according to the objects of computation rather than the type of operations or techniques. There were sixty types or ‘inam‘ in verses dealing with land (23), gold (20), paddy or grain (6), rice (2), solid stones (3), volume measures (1) and general problems (5) _20.

• Land: Various ways to measure areas of land of different dimensions involving magnitudes of whole and fractions, and techniques to calculate total produce from an estimated area, assessment of profit from the produce, ways of sharing the produce and so on.
• Gold: Various computational techniques related to estimation of quality of gold, its price and computations related to various combinations in the making of per unit of gold. Gold was also a unit of money, and this section would also have various types of computations related to transactions in money in goods and labor.
• Grains, paddy, and rice: Different techniques to compute volumes of grain using different units, conversion techniques, profit, and loss etc.
• Solid stones: Various problems related to measures of slicing solid bodies like rocks into pillars and of similar kind.
• Water: Distribution of irrigation water for agriculture from tanks and canals.
• General Problems: In the last section there would usually be various problems that use different rules and of various situations that were both practical and immediate as well as the fantastic and the recreational.

IV. Tinnai Pedagogy

The core of the tinnai pedagogy was attention to practical learning and problem-solving that focused on the students’ particular, localized environments and daily living.

Key pedagogical aspects were:

• Memorization using Learning by listening, Visualization, Oral repetition, and Recall.
• Differentiated instruction.
• Localized curriculum
• Mental Mathematics
• Problem Solving

Memorization

The 5-step process was followed to memorize every number in the ponilakkam and nelilakkam series. Listening to the sound of the number, visual recognition of the symbol, oral repetition, writing in sand and testing (recall) by the monitor and teacher at each level.

There were separate sessions in the tinnai routine, where children would stand up and recite the entire series in unison, loudly in front of the teacher, one series after the other, repeatedly, day after day till the logic of addition as the basis of number organization is cognitively internalized along with the process of building memory registers for the numbers in a particular order.₁₄

Differentiated Instruction

Differentiated instruction is the process of tailoring lessons to meet each student’s individual interests, needs, and strengths.

The report of D. Campbell, one of the colonial officials from Bellary Campbell, 1834) shows that the curriculum in the tinnai schools was clearly tailored to the needs and interests of the students. The report mentions that what was taught to each student depended upon his caste and social standing. For example, the ‘manufacturing castes’ studied books that were ‘peculiar to their own religious tenets’ while those who worship ‘lingam’ studied texts that ‘all considered sacred’.

Also, the fact that in the classroom the children were grouped according to their level of understanding of language and mathematics and not age, points to the fact that the curriculum was grounded on the strength or understanding of the students.

Localized curriculum

Senthil Babu in his paper “Memory and Mathematics in the Tamil Tinnai Schools of South India in the Eighteenth and Nineteenth Centuries” affirms that “There was no standardized curriculum of the tinnai schools cutting across regions. The orientation of the curriculum was local, and it seems the idea was not to produce scholars but to enable pupils to become scholars, if interested. The fundamental aim was to enable the children to become competent/skilled participants in the transactions of letters and numbers within the local society and its networks in the region.” This indicates that the curriculum in the tinnai schools was localized, ensuring that the learning resources, activities, and teaching processes were relevant to the students.

Problem solving

Janet Stramel, Professor at Fort Hays State University in “Chapter 5 – Teaching Mathematics Through Problem Solving” of her book “Mathematics Methods for Early Childhood” (2021) states that “Problem solving in mathematics is one of the most important topics to teach; learning to problem solve helps students develop a sense of solving real-life problems and apply mathematics to real world situations. It is also used for a deeper understanding of mathematical concepts. Learning “math facts” is not enough; students must also learn how to use these facts to develop their thinking skills.”

The 18^th century tinnai schools unquestionably followed these learning principles.

In the case of mathematics, problem solving was the mode by which the entire exercise of memorizing tables was given meaning, and skills of retrieval and associative memory were called upon in an algorithmic context. Problems were posed as word problems, as in the modern sense. Problems usually involved operations of addition, subtraction, multiplication and division, and reduction of measures involving the rule of three even though there were no separate tables for addition or subtraction. ₁₂

Mental Mathematics

Mental mathematics is a skill to do math “in head” without using pencil and paper or a calculator. Mental mathematics is useful in school and in everyday life and can help to understand mathematical concepts better and get to the answer faster.

In the tinnai schools, “The word problems, posed orally, were meant to be computed mentally, though initially the process of solving was proceeded by each student reciting each step aloud, to be heard by the whole class, monitored by the teacher. This was popularly known in Tamil as manakkanakku, (Caminata Iyer, 1990, p. 56) meaning mental computation._12.” This demonstrates that the teachers in the tinnai schools distinctly understood the importance of doing mathematics in their head and trained the students to develop these everyday needed skills.

V. Conclusion

Most of the primary source materials for the tinnai are untranslated from Tamil and the information available in English regarding these schools is limited to the extensive research of Senthil Babu D., a researcher at the French Institute of Pondicherry, India.

Using the research of Senthil Babu D. as a primary source and based on the study of other researchers, this paper attempted to draw out the structural and curricular practices of the tinnai schools, specifically focusing on the teaching and learning of mathematics.

After the study, the structural and curricular practices in mathematics that unraveled are an exemplar of a highly sophisticated framework that characterized powerful learning environments in clear and actionable ways with a focus on the needs of the local community.

The author hopes to continue her exploration to capture similar pre-colonial and colonial indigenous methodologies to imagine a path towards decolonizing India’s current system of education.

VI. References and Study

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23. Boys-School-Vepery-Chennai-Madras-Tamil-Nadu -India-1862-Rare-Old-Vintage-Photos.jpg
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