I continue to be amazed at the lack of basic understanding of mathematics, and its principles, in young people leaving educational establishments – regardless of which country or system.
As a pilot/engineer, I am constantly using numbers - large numbers and small numbers. Knowing how to express a number is essential in passing on understanding.
In aviation there are ‘rules’ for how we say numbers, even down to the pronunciation of each number! The aviator pronounces each number with a specific emphasis, in order to avoid confusion: 1 – one, 2 – two, 3 – tree, 4 - fo-wer, 5 – fife, 6 – six, 7 – seven, 8 – eight (although it may sound more like aaayte), 9 – niner , 0 –zero, 1,000 – tousand. These subtle pronunciation methods provide clearer radio transmissions. Such precision and detail is part and parcel of safety. Getting the number wrong, or misunderstanding what was meant, can lead to an accident or mistake, and we don’t like those!
Interestingly, aviation has other rules on numbers. We like to speak each number out. For example ‘change frequency to one – tree – zero – decimal – niner’ means select 130.900 Mhz on the radio. Runway numbers are given as digits (‘runway one niner’ for runway 19). Altitudes (below 10,000 feet) are spoken differently. For example 3,400 feet is said ‘tree tousand fo-wer hundred feet’. Once we get above ten thousand feet it should be said with digits, but many pilots will compile both together, for example 14,000feet may be said as ‘one, fo-wer – fourteen tousand feet’, making sure that everybody understood.
Perhaps a simple way to put this together is to read an ATIS (Automated Traffic Information Service) broadcast, this example being from Schiphol in the Netherlands, the words said on the radio broadcast are on the left, and what they mean on the right:
|This is Schiphol arrival information Kilo||Identification that you are listening to the Schiphol airport arrival broadcast. Kilo meaning that it is the 11th broadcast of the day (K being the 11th letter of the alphabet)|
|Main landing runway one eight Right||The runway with 18R painted at the threshold should be used. There are two runways parallel to each other running from 180degrees magnetic (hence the 18), the R means the one on the right!|
|Transition level fife zero||When you descend below five thousand feet change your altimeter setting from 1013.25 to the QNH setting we will give you later.|
|Two zero zero degrees, one one knots||Wind direction 200 degrees (from the south west direction) at 11kts.|
|Visibility one zero kilometers||Clear visibility for at least ten kilometres|
|Few one thousand tree hundred feet||There are a few clouds at 1,300feet|
|Temperature one fife, dewpoint one tree||Temperature in the shade on the ground is 15C, and water would condense (precipitation begin) at 13C.|
|QNH niner niner fife hectopascal||The altimeter setting once you get below five thousand feet is 995mb or hectopascals (the same units with different names – hectopascals being the more correct modern term). This makes the altimeter give height above sea level (based on the pressure at the time of the recording)|
|End of information Kilo||End of the thirteenth transmission recording of the day.|
What is really important is that everybody understands the numbers being said, and we go to great lengths to get it right! Yes, we work hard to make sure that there are no misunderstandings – and we do not use ‘oh’ to mean zero either!
I do not expect ‘Joe Public’ nor ‘Kwame Public’ or even ‘Abena Public’ to be so precise as we expect in aviation, but I do not like confusion.
I asked some school leavers to read out this number: 1,356,105.125, for which the correct answer should be ‘one million, three hundred and fifty six thousand, one hundred and five, decimal (or point) one hundred and twenty five thousandths’, although it may be easier to read ‘…. decimal one two five’. The answers I got were bizzare! Some started with ‘one billion’. Others had a ‘one oh five’ embedded in their answer (oh (O) is a letter, not a number). Some ended with ‘decimal one hundred and twenty five’. Out of the ten youngsters I asked, not a single one was able to express the number in a way that avoided confusion.
In an attempt to clarify the situation, I asked them all to explain ‘place value’ to me. The question was lost. It seems that the UNDERSTANDING of the value of a number by its PLACE to the left or right of a decimal point is not being taught – or if it is, not being understood.
Those who went through the ‘old school’ system would have learned about ‘hundreds – tens and units’. Those who learned the ‘base’ system would understand the use of indices, where number positions are valued according to the power of the base, relative to the position in relation to the decimal place,for example 103, 102, 101, 100 . 10-1, 10-2, 10-3 meaning 1000, 100, 10, 1, 1/10, 1/100, 1/1000
Not knowing that the third position after the decimal point means ‘one thousandth’ is a problem. I teach youngsters how to program robotic production tools – and we work to 0.001mm. That is one thousandth of a millimeter – also called a micron. It is not just necessary to get the big numbers right, but the small ones too, and yet it seems that schools are not managing in getting the BASICS understood – and retianed.
There is no point in trying to teach calculus or simultaneous equations to students unless we first get the basics of our number system into their heads. Frankly, I would rather see FEWER mathematics topics taught in schools, but that they be taught better and that students left school with better understanding – an able to apply maths in their everyday lives.
I still seem to struggle to find students who can calculate 10% in their heads or multiply two single digit numbers together, without using a piece of paper – or more atrociously, using a calculator.
Parents, you are to blame too. You need to drill your offspring in simple math’s – tables, addition,10% and reading out numbers so that others can understand. The lack of mathematics across the board is a barrier to sustainable development. As an employer, I spend way too much of my time ‘fixing’ the heads of those who have graduated from education without the ability to carry out the necessary daily tasks that make industry function.
Capt. Yaw is Chief Flying Instructor and Chief Engineer at WAASPS, and lead Pilot with Medicine on the Move, Humanitarian Aviation Logistics (www.waasps.com www.medicineonthemove.org e-mail email@example.com )