Tiṇṇai : Making of a Measuring Public

What are Tiṇṇai Schools?

Tiṇṇai schools were the main form of education across the precolonial Tamilakam (present Tamil Nadu, Kerala, Andhra Pradesh, Puducherry, Lakshadweep, Karnataka). Each of them consisted of ten to thirty children gathering on a tiṇṇai (veranda) to be taught by one teacher, all day long. There used to be one tiṇṇai school per group of three or four villages, i.e. a distance of 7 or 8 miles to walk at most. These schools were meant to enable any child to take up any occupation, and relate competently in any local transaction or discussion. Students were mainly taught Tamil literature and Tamil mathematics.

The tiṇṇai school is central in the development of Tamil mathematics for several reasons. First, it is a must for any practitioner engaged with mathematical practices to graduate from a tiṇṇai school; therefore, every transaction, wage or tax computation is dictated by 'tiṇṇai mathematics'. Conversely, as tiṇṇai schools were meant for future professional practice, the practitioner’s techniques and concerns were for many parts of the curriculum.
The students attending tiṇṇai schools were from the upper and middle caste (artisans, traders, accountants, musicians, etc), whose families could afford them not working, alongside with the teaching fee. Only boys from 5 years old onwards were possibly admitted, following a procession and a ritual after that, called vittiyāppiyācam or vityārampam. Girls and children from lower castes were not given admission.

The Tiṇṇai Teacher

The tiṇṇai teacher is a man whose pedagogical skills are acknowledged, without consideration of age. Although he is the target of public evaluation, and thus sometimes of certain satire works, the tiṇṇai teacher remains a very respected figure in the village. His reputation also largely depended on his network – whose tutelage he sought and his familiarity with instructors for further (specialized) studies.

A typical wage for a tiṇṇai teacher was four rupees and eight annas per month. The students’ monthly fee was often paid through goods like fruits, oil, fuelwood, paddy or rice, and even some exceptional payments such as free land work. On special occasions and holidays, some accounts note that the teacher was paid a quarter of a rupee as vāvukkācu. The tiṇṇai teacher was free to teach however he thinks it is best. Usually, children were organized by level, regardless of age. The best student takes some teaching responsibilities as cattampillai (monitor). Harsh punishments were inflicted as deemed fit by the teacher or the cattampillai, ranging from being caned to being hung upside down.

The Learning of Mathematics

Tiṇṇai teaching was fully focused on practice – children were trained to solve concrete problems that they might encounter in their future jobs. Moreover, memory was central, as children were asked to recite tables out loud, and memorize their lessons for the next day. For this, the textbooks were written using verses and prosody, a word play that stimulates memory, alongside with the musicality of the recitals of tables.

Numbers were grouped into three: large numbers (one and above), middle numbers (from 1/320 to 1) and small numbers (from1/320 × 1/320 to 1/320). Some numbers are also measure units, such as muntiri (1/320), kani (1/80 ) and ma (1/20), which also denote the corresponding fraction of the veļi (basic area unit).

The next step involved learning to compute multiplications, by reciting and memorizing the tables of the Eṇcuvaṭi (literally 'multiplication book'). A text called Varucappirappu that contained general knowledge of cities, days, stars, directions, gods, etc was the next destination for the tiṇṇai student. Finally, the student had to memorize the tables of squares using the Kuḻimāttu.

The main feature of tiṇṇai education was the focus on problem solving, as it kept the learning process meaningful. They were usually meant to be solved mentally and then recited orally in front of the teacher. The details of computation were to be explicated, as prudence was considered more valuable than speed when it came to computation, given the social significance of the result (wage, tax, price, etc).

Transformations during the colonial rule

At the start of colonial time, in order for the British to efficiently take full control over private property and measurement of land using a central administration, they needed to impose a standard way of measuring land, computing taxes, wages, the price of gold, etc. In position of power, they were able to progressively introduce western mathematics into Tamil Nadu.

However, colonial heuristics were deeply incompatible with tiṇṇai mathematics, as for example numbers were abstract entities, different from Tamil numbers, theory was first and applications second. The indigenous thus found themselves extremely disadvantaged regarding the new curriculums, and therefore on the quick-evolving job market, resulting in them descending the social ladder.

Tiṇṇai schools tried by multiple ways to get closer to western mathematics during the period 1800-1840. For instance, the Vilakkam was a trial to re-write the Eṇcuvaṭi with the rule-first paradigm, but has never been published. The Kanitadeepikai was the first textbook in Tamil printed by the British, revising the whole Tamil terminology and adding the concept of 0 (zero). It was used in the schools imagined by Thomas Munro (British colonial administrator), but neither these schools nor the Kanitadeepikai ended up becoming widespread.

In the 1840's and 1850's, the British managed to standardize weights, measures and Arabic numerals, with new books and sets of tables. This was operated by a growing centralized educational bureaucracy able to provide certification of schools, and increasingly many elite schools. Although tiṇṇai schools suffered from being rarely certified by this new administration, they managed to survive out of negotiation with School Inspectors. The latter would (poorly) remunerate the tiṇṇai teachers for each student able to pass English examinations, without interfering with the teacher's curriculum. Disappointed by the non-tiṇṇai generation, the British decided to integrate tiṇṇai curriculum into the western one from the 1880's onwards. This new way of doing mathematics, in between Tamil and English mathematics, was called bazaar mathematics. The new mathematical blend only prescribed learning the conversions of weights and measures to the British standard. The once unique tiṇṇai mathematics was slowly assimilated in modern mathematics, thus resulting in the disappearance of tiṇṇai schools.

What this story shows however, is the autonomy of Tamil mathematics from the Sanskrit tradition in precolonial times, which have strikingly been forgotten by historians of Indian mathematics. It also shows that efficient ways of practicing mathematics in stark contrast to how modern mathematics have been in operation. The Tamil branch of the history of Indian mathematics should thus be subject to further study.