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New Class VI Math Textbook Highlights Indian 'Firsts' with NCERT's Focus on Ancient Scriptures

The new NCERT Class VI math book, Ganita Prakash, highlights ancient Indian mathematicians' contributions but has faced criticism for potential inaccuracies.
on Aug 26, 2024

The NCERT recently released a new Class VI mathematics textbook called Ganita Prakash. This updated edition includes new sections that detail the historical contributions of Indian mathematicians to the understanding of fractions, operations involving zero, positive and negative numbers, and a system of debit and credit accounting.

This academic year, millions of Class VI students will learn about the accomplishments of ancient Indian mathematicians. While senior mathematicians appreciate this development, they caution against the inclusion of unverified information solely for the sake of promoting nationalistic pride.

The revised Ganita Prakash book has omitted the international system of numeration, opting instead to use the Indian numbering system which refers to lakhs and crores rather than millions and billions. Furthermore, the previous edition, first introduced in 2006 and updated for this year, covered operations with eight-digit numbers, while the new version limits itself to five digits.

According to the new textbook, the Rigveda introduces the concept of a circle divided into 360 degrees, noting that the ancient text describes a wheel with 360 spokes (Verse 1.164.48). Additionally, the book mentions that many ancient calendars, including those of India, Persia, Babylonia, and Egypt, once followed a 360-day year.

Although the concept of 360 degrees in a circle originates from ancient times, it's worth noting that the mistaken belief that a year consists of 360 days is scientifically unfounded. The method of dividing a circle into 360 parts is a matter of convention, while the number of days in a year is determined through empirical observation. It's essential to clarify this distinction to prevent confusion among young learners.

The Rigveda is said to make references to fractions, with the fraction 3 by 4 being referred to as “tri-pada”. It is stated that the formal codification of general rules and procedures for working with fractions was done by Brahmagupta in a modern form. According to the book, Brahmagupta was the first to outline the zero as a number on par with positive and negative numbers and the first to establish explicit rules for conducting arithmetic operations on all types of numbers: positive, negative, and zero.

By the 9th century, these numbers had been transmitted to the Arab world, and by the 13th century, they had reached Europe, as per the book. The Arthashastra, which the book dates to 300 BCE, contains extensive writings by Kautilya on debit and credit, including recognizing the possibility of a negative account balance.

The book mentions that the way fractions are written globally today originated in India. In ancient Indian mathematical texts like the Bakshali manuscript (around 300 CE), ancient Indians wrote 1/2 as 2 underneath one without a line in between.

The old book had chapters dedicated to decimals and algebra, which the new book has omitted, likely intending them for higher classes.

Amber Habib, a professor of mathematics at Shiv Nadar University, commented that the book lacks significant claims but overlooks and lacks awareness of the development of mathematical knowledge outside India.

For instance, the book mentions Egyptians and Mesopotamians mostly dealing with unit fractions. While this holds true for Egyptians, it is not accurate for Mesopotamians, as they had a complete understanding of place value (in base 60), including ‘zero’ as an indicator of a missing place value.

Moreover, Habib noted that both of these civilizations were mathematically advanced by 2000 BC, while comparable Indian material dates back to around 800 BC at best.

Regarding the Arthashastra, the book confidently dates it to 300 BC although there is uncertainty around the date, with estimates ranging from 300 BC to AD 300.

Notably, Habib also highlighted the urban-centric concepts used for illustrations in the book. For example, the explanations of negative numbers are based on a sophisticated multi-floor building.

Hukum Singh, the former head of the Department of Education in Science and Mathematics at NCERT, emphasized that introducing children to India’s ancient knowledge is positive but stressed the importance of ensuring the accuracy and authenticity of the content.

Birendra Nayak, who previously led the mathematics department at Utkal University in Bhubaneswar, emphasized that a substantial amount of knowledge has its roots in India, as it does in other regions throughout history.

Nayak suggested that children should be motivated to learn about how knowledge has developed in India and other parts of the world. He also recommended providing information on the evolution of knowledge while advising against exaggeration.