After my suggestions last week for 'essential outcomes of education', I was asked about some particular 'expectations'. I had proposed that all students should be 'indelibly stained with knowledge and the ability to apply it in the world of work', giving examples of certain understandings and skills sets, that for me at least, are essential in all aspects of living and working.

Let us consider in more depth some headlines that have raised a little controversy!

**Understanding of ratios**

These are essential skills - whether in the workplace, kitchen or on a building site. Correct understanding and execution of ratios is required everywhere. The most common one that gets 'guessed at' is the mixing of concrete - a product we all rely on. A standard 'general purpose' mix would be a 1:2:4 or 1:2:5 mix. That is one volume of cement, with two identical volumes of sand (head-pans, wheel barrows or even buckets, the basic volume of measure does not matter - the ratio of them does!) and then four or five identical volumes of stones. If you have a car engine, it will be working on roughly a 15:1 mixture of air to fuel in the combustion chamber (cylinder). Then there is the ratio of herbicide concentrate to water and the dispersal per acre or hectare... or the mixture for a two stroke engine (chainsaw, outboard motor, some small gensets, etc)... I could go on with examples, but the point is that so many people are unable to identify, work reliably with, or adjust accordingly - and safely - when it comes to ratios!

**Cartesian co-ordinates (2 and 3 dimensional)**

It really does perturb me that so many people are not at ease with Cartesian coordinates - you know, X, Y and Z axis - and plotting thereon. X is generally referred to as the horizontal axis (also called Y=0), Y is generally called the vertical axis (also known as X=0) and Z is the axis that comes out of the page at you! Z adds '3-dimesnionality' and the ability to locate a point in 3D (real world) space.

Unless you understand the basics of co-ordinates you cannot produce any parts on a lathe, mill, press, cutter, etc. - manually or under computer control (CNC).

Without an excellent understanding of co-ordinates you cannot use a Computer Aided Design (CAD) programme to produce a drawing... or Computer Aided Manufacturing (CAM) systems, you cannot do so many things that are considered essential in today's world of information.

Take a look at your mobile phone. The mould for your phone was produced on a CNC mill. Yes, it was. That mill was controlled in X, Y and Z by a simple computer programme, called a G-Code part programme. A sample of the sort of code it would contain (along with an explanation in brackets) would be as follows:

G90 (use absolute co-ordinates, ie work from the axis datum)

G00 X10 Y30 Z0 (position the tip of the tool at X10, Y30 and usually Z0 refers to the top of the work piece, at maximum speed)

G01 Z-0.25 S2500 F100 (plunge the tool into the material with a spindle speed of two thousand five hundred revolutions per minute and a feed rate of 100mm per minute)

G01 X102.52 Y50.35 (move in a straight line to these coordinates which would cut away the top .25mm of material along that line)

G91 (use relative co-ordinates)

G01 X25.6 Y0 (move in a straight line, with the same tool, spindle and feed-rates, at the same depth, since we have not changed Z)

etc...

Well, I could go on (and often do), but it really is very simple - and we all have tens of thousands of items and parts around us that are produced using simple systems like this. I have taught G-Code programming to many young people, often as young as seven years old - but it only works when they have the solid basics of co-ordinates. It is not difficult, but it is essential - and it is sadly missing in too many students, teachers and those who should be better equipped.

**Able to rearrange a formula to find an unknown variable - correctly.**

Well, we have to do this all the time, if we want to be efficient. Just last week I had to rearrange the voltage divider formula V1=V2(R2/(R2+R1)). Without it I could have destroyed a very expensive piece of equipment. Understanding simple re-arrangement of formulae is key to working. Failure to understand can lead to expensive mistakes. Perhaps the most simple, everyday formula that we use is that for another 'hot topic':

**Work seamlessly, accurately and quickly in problems related to distance, speed and time.**

Distance = Speed x Time. Which is the same as Speed = Distance / Time. Which is the same as Time = Distance / Speed.

The same formula, rearranged to give us the 'missing value'. Of course, you must use consistent units (don't start me on the misunderstandings of unit of measure), so that distance should be in, say, kilometres, time in hours and therefore speed in kilometres per hour. Failure to ensure that the 'appropriate units of measure for the problem are in place', would invalidate the whole thing.

For instance, I know that is approximately 90km from Kpong Airfield to the Accra Mall. I know that it takes me, on average, 90minutes to get there. 90minutes is 1.5hours. So, my average speed is (90/1.5) - or 60km/hr or 1km/min. That was easy, but the principle works for all distances, speeds and times. Yes, we need to know time, speed and distances and be 'mentally conversant with them' to ensure that we are optimised in our travel and timely in our arrival! For pilots this is essential learning since we recalculate our distance, ground speed, and estimated time to arrival on a regular basis!

**Be aware of the how light, magnetism and electricity behave and how they can be used in practical applications.**

It amazes me how few people are conversant with aspects related to how light travels - and the speed at which it travels. Understanding how shadows are formed; the fact that the image of what you see is 'upside down' on the retina of your eye and that your brain rotates it to make it look 'normal'; how rainbows are formed; why a day is perceived as misty, foggy, hazy, etc. Light travels at 299,792,458 metres per second. It is very fast. Sound only travels at 340.29 metres per second. That explains why, when you see lightning, the sound of thunder comes much later. The sound of the collapsing air hitting together in the vacuum caused by the plasma, called thunder, takes about 3 seconds to travel one kilometre, whilst the light from the lightning (a stream of plasma created by interaction between charged particles in clouds) can cover one kilometre in roughly one three hundred thousandths of a second - what we call, wrongly, 'instantly'.

Magnetism can seem almost like magic, and once was considered as such! The way magnets attract and repel each other is fascinating - but it is more than that. Magnets and magnetic fields are present in so many things around you. Lady's handbags often use magnetic catches, closures on some cell phone cases, the motor that creates vibrations on your phone, the heading determined by a compass in the ship or plane that you travel on, the generators at Akosombo dam, the alternator in the motor vehicle you travel on, and so much more... But what about the magnetic field that surrounds our planet. Earth is a BIG (VERY VERY BIG) magnet. Our planets iron core emits a magnetic field that protects us from cosmic radiation, it provides the field with which we navigate - and is essential to so many animals that use the earths magnetic field in migration patterns.

Magnetism is even more exciting when we see it along side electricity... but I surely do not need to identify the plethora of items that we all use every day that rely on electricity! Understanding it is essential.

Therefore, knowing the basics of physics and nature, and how to use mathematics to calculate effects, creating new and exciting products should be, without any doubt in my mind, made a priority for every student - and if you are an adult and don't understand it, you should take the time to grasp it, it will open up your world and enable you to do so much more.

Capt. Yaw is Chief Flying Instructor and Chief Engineer at WAASPS, and Pilot/Engineer with Medicine on the Move, Humanitarian Aviation Logistics (www.waasps.com www.medicineonthemove.org e-mail capt.yaw@waasps.com)

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