Local AND Global – navigating the dimensions of learning.

Now the new academic year is well under way, the termly/annual cycle of quality assurance activities is underway, from parent/teacher evenings and forward facing Open Day events to work scrutiny, lesson observations and work scrutiny. I chose Boys Year 10 Maths lessons to visit earlier this week, and found ‘SURDS’ being taught with top set. To save you quickly reaching for Google to find out what a surd is, the definition is “A surd is an expression that includes a square root, cube root or other root symbol.” There, that’s put you right hasn’t it!

Here’s Wilding’s brief explanation, involving a bit of history. Whatever you do as an engineer, you need to have accurate numbers, and if the number isn’t actually capable of resolving into a finite number, such as Pi (π) – back in Babylonian time, 1700 or so years before Archimedes (c. 287 – c. 212 BC) they made use of Pi and geometry to sort their land sales and estate boundaries. The Babylonian tablet below (ca. 1900–1680 BC) indicates a value of 3.125, good for even these days.

Trouble is of course that plenty of numbers like Pi actually don’t resolve as a decimal, going on for ever. You may remember Pi=22/7; please carry out the maths and you’ll see what I mean. Numbers that complete are called REAL numbers, and those that don’t are called IRRATIONAL numbers. π is an irrational number, which has no end however many decimal points you get to.

For a huge number of engineering operations, you don’t not just need π, but you also need to know what the Square Root of a number is, for calculations to find the radius of a circle when you know its area and circumference, r = √(A / π). Early in the days of learning about √, we find out that /4=2. √9 is 3, √16 is 4 and so forth. But for example, when you try to work out what is the /7 is, i.e. what number multiplied by itself = 7, then you fin that you get an answer that never comes to an end or to a predictable repeating pattern. For engineers then, rather then know that they are dealing with 2.64575131106…, it’s so much easier for them to know they have /7 as the value – then if they are taking about mm, the above accuracy to 2 decimal places would be enough, whereas if they were talking about 7km, they might need to use many more places to ensure the accuracy didn’t rob someone of land that was theirs, or dare a say leave some engineering miracle like the Forth Bridge a few metres adrift of the accuracy needed (and metal to span!). Numbers as √2, √3. √5. √7 and √11 all have irrational numbers as answers – this kind of √ answers is known as a SURD (remember by thinking that’s abSURD). There are six different types of surds, namely: Simple surds, Pure Surds, Similar Surds, Mixed Surds, Compound Surds, and Binomial Surd. To conclude, take something incredibly complex, irrational and never ending or deal with /number, and I know why engineers need surds – elegantly expressing what the answer is – under the square root sign √.

The SURDS above are just one example of many types of learning that have spanned the globe and the centuries, and we all know to the present day that there remains so much more about the world that we don’t know than we will ever begin to learn. It’s incredibly important then that learning in schools carries this GLOBAL dimension, and not just to span the tangible, such as Maths, but also the theoretical such as religious beliefs and customs and of course the evidence and experience that comes from Geography and History, such as the effects of Global Warming (definitely a thing, Mr Trump!) and ‘never appease a dictator’.

The trouble with Globalism, even dare I say Nationalism, is that is that it chooses by its very approach to ignore the local, with all the dangers that then ensue, that all that is local becomes devalued and ignored. We’ve seen it in the modern political failure of national governments not to ensure all parts of a country are invested in, and in the race for cost and convenience over the rights and wrongs of employment and environment. Schools such as mine that have taken the trouble to work locally on their engagement with the locality in which they are seated find incredible, unbelievable items on their doorstep. You only have to see the utter fascination of an A level group undertaking observation work around a pond (thanks Woolley Firs field centre) to see the miracle of real learning happening.

And therein has lain the problem of overweening, nanny statesmen, who might fear for example that specialist English teachers might be ignoring their favourite male victorian authors, but in reality as a consequence have forced an inappropriate and insufficiently diverse set of authors on children, in turn perhaps stunted truly their emotional development and a love of literature. Whilst our sector can choose to be different, it is perhaps no surprise now to note that for the country as a whole, English A level has dropped out of the top 10 subjects list. How could you reverse the trend? Why not start with a bit of John O’Farrell’s ‘Things can only get worse’ to cheer the mood!

What getting onto the localism agenda means of course is finding every possible reason to study what’s local, in part because perhaps it has not been sanitised. As a school, we’ve a fabulous relationship with the Stanley Spencer gallery in Cookham, and the opportunity to see his paintings as well as visit the ‘set’ where he painted so many of his works (and of course where he is buried) gives real presence to learning of his work. I’ve written plenty of times about the work we have created with the National Trust at Cliveden, and as we embrace more the language, literature, history and culture of immediate surrounds, the tangible growth in knowledge actually permits the learners (children and adults) to become even more creative about the comparisons they can then draw with the other evidence arising from across the globe.

And of course, for fear of being branded nany statesmen, Mrs Truss and her new government seems to be avoiding lecturing to us about the cost of energy and how to reduce it. The one thing politicians can be sure of is they could mobilise the eco-army they need to keep energy consumption down this winter. To every family home each day we send home a climate warrior wishing to make a difference. They absolutely get the need to change attitudes about global warming and climate change, and really they should be mobilised to turn the heating down a notch or 5. You’ve only got to look at the fun boys and girls are able to have at school each day, refusing to wear anything warmer than their minum school uniform to know they can ‘do’ colder climes. There might still be a bit of a way to go with getting 10 set 1 to navigate the heinz variety of surds they see in the classroom, but at a fell swoop they’d certainly help get UK’s gas bill down a couple of notches – and that requires local action in every home!

About jameswilding

Academic Principal Claires Court Schools Long term member & advocate of the Independent Schools Association
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