Posted on

Zero: Much Ado About Nothing?

Zero represents nothing and as such is very important in our Hindu-Arabic base ten number system. Its job is as a placeholder in our base ten place value system. I think place value is the most important part of the primary Maths curriculum. But, many children find ‘place value’ to be a very sophisticated idea and difficult to understand, which has serious implications for their arithmetic calculations[1]. This difficulty is because the idea of place value is abstract and young children learn in a concrete way. They often see numbers as meaningless abstract symbols, so need lots of work with concrete materials such as Cuisenaire rods and/or paddle-pop sticks, before they can connect with and find meaning in such abstract concepts as numbers. Common difficulties are, for example:

Many children write five cents as .5 and fifty cents as .05. They also have difficulty when using the subtraction algorithm to find:

103-

  29

These difficulties reflect the fact that arithmetic is not a natural development of the brain[2]. Rather, it is a cognitively complicated process, which does not have a biological origin. It has to be carefully learnt by children and carefully taught by teachers.

This complexity can be viewed by taking a historical perspective.  The symbol and meaning of zero was not invented until quite late in historical terms. The Hindu-Arabic symbols that are so familiar to us, 123456789, were invented in India about the year 700 AD. Through trade and commerce these numerals gradually came into use in the Arab world. However, in Europe the system that was generally used was Roman numerals.

In the eighth century in Europe the Hindu-Arabic symbols were known mainly by academics and clerics. At the time, there was lobbying against the universal adoption of these new and revolutionary symbols by the Roman Catholic Church and vested interests.

At that time, the Roman Catholic Church regarded anybody who was not a Catholic as heretical. Furthermore, any people from the Arab world were thought to be infidels and anything they produced – the work of the devil. And so by association the numerals 123456789 were thought to be the work of the devil.

So, in Europe Roman numerals were generally in use and continue to be used today in some clocks and special circumstances. Roman numerals are not easy to use, and so before the introduction of Hindu-Arabic symbols some clerics and monks devoted their lives to Roman numeral calculations. These clerics had a vested interest in prolonging the status quo and the continued use of Roman numerals and so strongly lobbied against the use of the new, devilish Hindu-Arabic symbols.

Of course with Roman numerals there is no need for a zero, because zero is not needed as a placeholder. For example, in the Roman system, X= 10 and C=100.

Gradually people recognized that this new Hindu-Arabic number system was far simpler and easier to use when undertaking any arithmetical task. However, to indicate an empty place they used a space. This presented some difficulties because for example 1 3 could represent 13 or 103 or 1030 or 1003, depending on how big the space was. It was particularly important in financial transactions to be clear about what these new symbols represented. And so a refinement was made. Instead of leaving the space between numerals a circle was used around the space to indicate that there was a ‘missing’ entry [3]. For example, 1 o 3. Gradually the zero, with which we are so familiar was invented and the arithmetical rules of its use developed by Brahmagupta in the year 665.

Writing in the 13th century, John of Halifax explained that there is something that ”signifies nothing” but instead ” holds a place in signifies for others”. His manuscript proved popular in the universities. But it would take the invention of Gutenburg’s printing press to bring these ideas to a much wider audience. P49[4]

Tammet also comments that Shakespeare’s generation were likely to be the first generation of schoolboys to learn Arithmetic using Hindu-Arabic symbols in school (which was the King’s New School in Stratford).

This general use of the Hindu-Arabic symbols in arithmetic is very late compared with the development of reading and writing. Reading and writing were first developed in Mesopotamia, which is now Iraq. This is thought to be around the 3000 BC. In evolutionary terms this is also very recent, which again reflects the fact that reading and writing are not natural developments in the brain.

We all take for granted the three “R’s: Reading Writing and Arithmetic. We forget that they are NOT natural and easy things for children to learn, in fact teaching the three “R’s” REALLY IS rocket science.[5] It is amazing that so many of us can read, write and calculate so fluently.

 

[1] http://www.education.vic.gov.au/school/teachers/teachingresources/discipline/maths/assessment/Pages/lvl2place.aspx

[2] Dehaene, S. (1997). The Number Sense. Cambridge UK: Oxford University Press.

[3] Devlin, K. 2011, The Man of Numbers: Fibonacci’s Arithmetic Revolution, Bloomsbury.

[4] Tammet, D. 2012, Thinking in Numbers, Hodder & Stoughton

[5] Moats, L. C. (1999). Teaching reading is rocket science. Retrieved from https://www.scribd.com/doc/27456514/Teaching-Reading-is-Rocket-Science

 


 

Note – we’re actively encouraging comments on these posts! If you’ve got a response or opinion you’d like to share, let us know! You can either post this as a comment below, or contact Ann directly at awillia732@gmail.com.