What is zero? A number or nothing at all? Before the lecture about place value, I had never considered the significance of zero or how anything interesting can be gleaned from it. Essentially, it was another number that was just there along with its friends 1,2,3 and so on. Though after some research, it becomes more apparent that zero has a lot more to say than I initially thought.
All numbers have a history – that had to begin somewhere and follow a path to become the number we use throughout maths. Zero is no different, slowly being developed by various civilisations. Its tale begins with the Babylonians, who helped developed the concept of place value using a variety of different symbols to represent their numbers (Haylock and Manning, 2014). Around 400BC it can be seen on clay slabs that the Babylonians began to include two wedge shaped marks between numbers where in modern times we would place a zero (Lamb, 2014). This was since a blank area to indicate a lack of value confused many, so the marks were used to avoid this (Bellos, 2010). Thus, begins the journey of zero.
Move forwards in time to the seventh century India where the Indians took the two wedge marks and developed it further, turning it into a real number. Indian mathematicians, like Brahmagupta, highlighted how zero effected other numbers and gave it the name ‘shunya’ (Bellos, 2010). Travelling to the Middle East, it was given an Arabic symbol – 0. Though it took longer for some countries to adopt the Indians method of using zero and the Arabic symbols for a variety of reasons – lack of trust of the Middle East or that many thought this new symbol could be easily manipulated to another number (Bellos, 2010). Eventually, everyone became more accustomed to the idea of zero and accepted this new number – obviously as we use it today during our own maths learning.
What is the importance of learning the history of zero? It covers a variety of civilisations around the globe which can be intriguing to pupils. Learning the history means incorporating another curricular area into maths, helping children to engage with the subject. Also, it shows how people used numbers before zero and provides an alternative way to using the place value system – linking into Ma’s fundamental principle of “multiple perspectives” as the way we use the place value system is not the only method. The place value connects with the children’s knowledge of numbers and working out which ones are larger than others. Take the number 109, the zero here represents the fact that there is no value in the tens column as well as highlight the fact that this number is ‘one hundred and nine’. Without the zero where it is, then it would be difficult to tell the difference between 109, 19, 190, 109 000 000 or 1090 apart (Haylock and Manning, 2014).
There is a quote from Alex Bellos’s book ‘Alex’s Adventures in Numberland ’ that made me stop to think about the number zero. “The present mathematical system considers zero as a non-existent entity’ (Bellos, 2010, p.138), from experience and initial outlook of zero I feel that this is a common misconception of zero. Many do not think zero is a significant number, I remember overhearing a child during a placement telling their friend that zero ‘was not a real number’. It is a real number and provides important functions in the maths universe. Take the example of positive and negative integers to emphasise the importance of zero. A positive integer is any number above zero and a negative integer are numbers lower than zero (Haylock and Manning, 2014). This idea would not be feasible if zero was not around – no zero means no numbers could come before. Linking this to the real world in terms of temperature, 0˚C can be felt be felt and when temperature sinks into the negatives this can be felt (memories of ‘Beast from the East’ anyone?) – and we need the idea of negative integers so this temperature can be measured. Additionally, there is a connection to another aspect of maths when it comes to counting numbers that are lesser than zero – cardinal (sets of things) and ordinal (the order things come in) numbers. We cannot count negative numbers in the cardinal way as it is impossible to have a negative quantity of numbers. So we count as ordinal numbers as this makes more sense (Haylock and Manning, 2014). This creates a “unified body of knowledge” (Ma, 1999, p.122) for the pupils.
Zero is a more interesting than I had anticipated – it has a colourful history spanning a variety of countries, had become deeply engrained into the maths we do and is nearly impossible to do mathematical concepts without. Zero is unique and links into a lot of Liping Ma’s fundamental principles.
Bellos, A. (2010) Alex’s Adventures in Numberland London: Bloomsbury
Haylock, D. and Manning, R. (2014) Mathematics Explained for Primary Teachers. 5th edn. London: SAGE
Ma, L. (1999) Knowing and Teaching Elementary Mathematics – Teachers’ Understanding of Fundamental Mathematics in China and The United States. London: Routledge