Australian Historian (Re)Introduces Ancient Mathematics Teaching Method

AUSTRALIA. Melbourne. An Australian mathematics teacher is determined to correct the mathematics pedagogy around the globe. For 37 years, John Crabtree has been researching the mistakes in methods of teaching “zero” and “negative numbers.” He came to the conclusion that ancient teaching of Bramhagupta is more effective, and he has evidence to prove his point.

When he was 7 years old, he asked a question about negative numbers. The teacher taught him the concept of negative numbers as debt. His teacher told him that you have a debt of $7, you can call it -7. But on a number line -7 is less than -4. John’s tender mind could not grasp the negative number concept. He asked,” If negative numbers are like debt then how can debt of $7 can be less than $4?” It was not reconciling with John’s mind at all.

A near-fatal accident

While studying economics at the University of Melbourne he met with an accident. A heavy lorry hit him from behind and broke his spinal cord. He was told that he probably wouldn’t recover and would never have a normal life. What was needed was a miracle. Crabtree told Transcontinental Times, “I promised to God – If I ever live a normal life, I am going to fix mathematics and will resurrect the old Hindu teaching.”

The rigorous search for errors

To understand the flaw, he had to search for many mathematical books. He studied Vedic math of the sixteenth century, Trachtenberg mathematics, Shakuntala Devi and many more. But no mathematics books could explain how mathematics fit together. So, he shifted his focus on ancient texts. For this, he had to learn Greek, Arabic, Hebrew, German, Italian, Dutch, Russian, Czech, Spanish, Mandarin. “I discovered the gold at the end of the rainbow six years before,” he said. “When I came to know Brahmaputra’s mathematics in Sanskrit, I began to analyze the work of Aryabhatta, Brahmagupta, and Bhaskara and tried to make sense of math so that children could completely and intuitively understand mathematics which teachers are unable to explain.”

Confusion traced to mistranslation

When Arabs took Hindu numerals and spread them to the European world, they made grave mistakes. Al-Khwarizmi was the mathematician who translated Brahmagupta’s book Brahma Sphuta Siddhanta (BSS) into the Persian Language. Brahmagupta was a mathematician and an astronomer, whereas Al-Khwarizmi was an accountant. Mathematics took a wrong turn because of these misinterpretations.

According to Crabtree, “Brahmagupta’s zero concept was based on the addition of two equal and opposite numbers. It makes sense in modern physics. It is similar to the addition of a negative electron and a positive positron (with the same mass as an electron) and results in zero. His concept of zero is consistent with the laws of physics.”

In the 9th century Arabic translation, the eighteenth chapter of BSS seems to have been missed, which gave the rules of algebra of negative, positive and zero. So, Arabs were not at all concerned with negative numbers and zero. When this concept traveled to Europe, first by Fibonacci, the “zero” was only a place holder and nothing more. So, 107 is 17 without “0”. Zero is like a number subtracted from itself, but this conception was against Brahmagupta’s understanding of zero. He pointed out the mistake in “multiplication is repeated addition”. It works for positive numbers like 2 x 3 = 2 x (0+1+1+1) = 0+2+2+2 = 6. But what happens when we try to multiply 2 x (-3)=2x(0-1-1-1)=-2-2-2=-6. Repeated subtraction! Similarly, 2³ = 8, but 2⁰ = 1, why ? Now when this contradiction occurs we force children to remember the law – minus into plus is minus[(-) x (+) =-)] and anything raised to zero is 1. These absurdities often create a complete dislike of mathematics for children.

New teaching method

Crabtree has developed a method purely based on the 1400 year old mathematics teaching of Brahmagupta. He calls it podometic. He said, “This is the simplest way mathematics can be taught. We study 5-2 in standard 2 (second grade) and then 2-5 in standard 7 (seventh grade). We can make children understand negative numbers in standard 2 only.” The present ranking of Indian students mathematics skill is ranking second from last among 74 nations.

“What happens in India?” He asked, ”Why the country who had given basic and even [advance mathematics] to the world is presently struggling with mathematics teaching?” He answered,” Because of rejection of their own traditional teaching method and mugging up British teaching method”. He is ready to teach children by his podometic method. ”I want to teach Indian students free of cost. I don’t want money or fame, I have an obligation to teach”.

He has delivered lectures in various parts of the world, including India (www.podometic.in). He has sent letters to the Human Resource Ministry of India, the Prime Minister of India, and the head of the RSS. But the present pandemic has negated his efforts. It is hoped he will have an opportunity to see his teaching methods implemented as he just been diagnosed with skin cancer.